# LightMySky: the full library

> 1,690 topics ordered by prerequisites. LightMySky tracks what a learner knows and brings a topic back before it is forgotten.

Every topic below, in teaching order: nothing appears before what it depends on.
"Needs first" lists the prerequisites. Each link opens the lesson, video and practice.

## Science

1274 topics, ages 5 to 24. https://lightmysky.com/learn/science

### Insects & Minibeasts

https://lightmysky.com/learn/science/areas/insects-and-minibeasts

#### What is a minibeast? (ages 5-7)

What is a minibeast? Small creatures without backbones, found in gardens, parks, and woodland. Bug hunts — searching under logs, stones, and leaves using magnifying glasses to observe minibeasts up close.

Ready when they can: Explain that minibeasts are small animals without a backbone found in gardens and parks; Find at least three different minibeasts during a garden bug hunt under logs, stones, or leaves; Use a magnifying glass to observe and describe one minibeast's appearance in detail.

https://lightmysky.com/learn/science/what-is-a-minibeast-mt_BI6oGIO-xM

#### Caterpillar to butterfly (ages 5-7)

Caterpillar to butterfly: the life cycle of a butterfly as an observable transformation. Egg → caterpillar → chrysalis → butterfly. The idea that one creature can change its whole form. Classroom butterfly kits, The Very Hungry Caterpillar.

Ready when they can: Describe the four stages of a butterfly's life in order: egg, caterpillar, chrysalis, butterfly; Explain that the caterpillar and the butterfly are the same creature at different stages of life; Retell or draw the transformation from caterpillar to butterfly after reading a story or watching it happen.

Needs first: What is a minibeast?.

https://lightmysky.com/learn/science/caterpillar-to-butterfly-mt_Wr6DDgr_kH

#### Common minibeasts: naming and recognising (ages 5-7)

Recognising and naming common minibeasts: ladybird, ant, bee, butterfly, spider, snail, worm, woodlouse, caterpillar, beetle. Building positive attitudes toward all minibeasts, not just the 'pretty' ones.

Ready when they can: Name and identify at least six common minibeasts from pictures or real encounters; Describe one visible feature that helps tell a ladybird from a beetle or a spider from an ant; Show interest or curiosity toward less popular minibeasts like woodlice, worms, or spiders rather than only butterflies.

Needs first: What is a minibeast?.

https://lightmysky.com/learn/science/common-minibeasts-naming-and-recognising-mt_yR1moI5kX1

#### How minibeasts move (ages 5-7)

How minibeasts move: crawling (ants, beetles), flying (butterflies, bees), slithering (worms, slugs), jumping (grasshoppers, fleas), burrowing (earthworms). Counting legs as a first step toward grouping creatures.

Ready when they can: Describe at least three different ways minibeasts move such as crawling, flying, and slithering; Match a minibeast to its way of moving, for example grasshoppers jump and worms slither; Count legs on a minibeast and notice that ants have six while spiders have eight.

Needs first: Common minibeasts: naming and recognising.

https://lightmysky.com/learn/science/how-minibeasts-move-mt__7hXSTbu9s

#### Minibeast Habitats (ages 5-7)

Where minibeasts live: micro-habitats. Different minibeasts prefer different conditions — under logs (damp, dark), in soil (underground), on leaves (sunny), in pond water (wet). The idea that you find different creatures in different places.

Ready when they can: Name at least two micro-habitats where minibeasts live such as under logs, in soil, or on leaves; Predict what type of minibeast might be found in a damp dark place versus a sunny leaf; Explain that different minibeasts prefer different conditions like wet, dry, dark, or light.

Needs first: Common minibeasts: naming and recognising.

https://lightmysky.com/learn/science/minibeast-habitats-mt_zir5yyAzUB

#### Minibeasts in the food chain (ages 5-7)

Minibeasts in the food chain: simple garden food chains. A caterpillar eats a leaf, a bird eats the caterpillar. The idea that minibeasts are food for other animals, and that minibeasts eat things too.

Ready when they can: Describe a simple food chain such as leaf → caterpillar → bird; Explain that minibeasts eat plants or other tiny creatures and are eaten by bigger animals; Give an example of what a specific minibeast eats, such as caterpillars eating leaves or ladybirds eating aphids.

Needs first: Common minibeasts: naming and recognising.

https://lightmysky.com/learn/science/minibeasts-in-the-food-chain-mt_QH-Fs97twT

#### Caring for minibeasts (ages 5-7)

Caring for minibeasts: observing minibeasts gently, handling them carefully, putting them back where you found them. Why minibeasts matter — they help gardens grow, break down dead leaves, and feed other animals.

Ready when they can: Demonstrate careful handling of a minibeast such as letting a woodlouse walk onto a hand rather than grabbing it; Explain one reason why minibeasts are important, such as bees helping flowers grow or worms helping soil; State that minibeasts should be returned to where they were found after observing them.

Needs first: What is a minibeast?, Minibeasts in the food chain.

https://lightmysky.com/learn/science/caring-for-minibeasts-mt_LTb0ZReMR2

#### Insect life cycles: complete metamorphosis (ages 7-9)

Insect life cycles — complete metamorphosis in detail. Egg → larva → pupa → adult. The larva (caterpillar, grub, maggot) looks completely different from the adult. Inside the pupa the body is rebuilt. Butterflies, beetles, flies, and ladybirds all undergo complete metamorphosis.

Ready when they can: Name the four stages of complete metamorphosis using the correct terms: egg, larva, pupa, adult; Explain that the larva stage is when the insect eats and grows, and the pupa stage is when its body transforms; Give at least two examples of insects that undergo complete metamorphosis such as butterflies and beetles.

Needs first: Caterpillar to butterfly.

https://lightmysky.com/learn/science/insect-life-cycles-complete-metamorphosis-mt_hsN-YvCNQY

#### The insect body plan (ages 7-9)

The insect body plan: all insects share three body parts (head, thorax, abdomen), six legs attached to the thorax, and antennae on the head. Most have wings. They have an exoskeleton — a hard outer shell — instead of bones inside.

Ready when they can: Label the three body parts of an insect — head, thorax, and abdomen — on a diagram or real specimen; State that all insects have exactly six legs and that the legs attach to the thorax; Explain that insects have an exoskeleton, a hard outer covering, instead of bones inside their body.

Needs first: How minibeasts move, Common minibeasts: naming and recognising.

https://lightmysky.com/learn/science/the-insect-body-plan-mt_oNWXXAn3cn

#### Camouflage, warning colours, and mimicry (ages 7-9)

Camouflage, warning colours, and mimicry: how insects survive by hiding or sending visual signals. Stick insects look like twigs, leaf insects look like leaves. Wasps have warning stripes; hoverflies mimic wasps but are harmless. The 'can you spot it?' challenge.

Ready when they can: Give at least two examples of insect camouflage such as stick insects resembling twigs or leaf insects resembling leaves; Explain why bright warning colours like a wasp's yellow and black stripes help the insect survive; Describe mimicry by explaining that a harmless insect like a hoverfly copies a dangerous one like a wasp to trick predators.

Needs first: The insect body plan.

https://lightmysky.com/learn/science/camouflage-warning-colours-and-mimicry-mt_07Geg7LITa

#### Incredible insects: record-breakers (ages 7-9)

Incredible insects — record-breakers and superpowers. Dung beetles are the strongest animals relative to body weight. Dragonflies are among the fastest flying insects. Fleas can jump over 150 times their own body length. Bombardier beetles spray boiling chemicals. The 'wow factor' of the insect world.

Ready when they can: Name at least three insect record-breakers and their extreme abilities such as dung beetle strength or flea jumping; Compare an insect's ability to a human scale, for example a flea's jump would be like a person leaping over a skyscraper; Explain why being very small helps insects achieve extreme feats of strength or speed relative to their size.

Needs first: The insect body plan.

https://lightmysky.com/learn/science/incredible-insects-record-breakers-mt_M7YrfAZk8u

#### Not all minibeasts are insects (ages 7-9)

Not all minibeasts are insects: distinguishing insects from other minibeasts. Spiders have 8 legs and 2 body parts (arachnids), woodlice have 14 legs (crustaceans), worms have no legs, snails have a shell and one foot. The 'Is it an insect?' sorting game.

Ready when they can: Sort a set of minibeasts into 'insect' and 'not insect' groups using the six-legs rule; Explain why a spider is not an insect by noting it has eight legs and two body parts; Name at least one difference between insects and another minibeast group such as worms having no legs or woodlice having fourteen.

Needs first: The insect body plan.

https://lightmysky.com/learn/science/not-all-minibeasts-are-insects-mt_4vHa3I5bNj

#### Social insects: ants and bees (ages 7-9)

Social insects: how ants and bees live and work together in colonies. Queens, workers, and drones. Division of labour — some gather food, some build, some guard. Ant tunnels and bee hives as organised homes. Parallels to human teamwork.

Ready when they can: Describe at least two different roles within an ant colony or bee hive such as queen, worker, or guard; Explain that social insects live together in large groups and divide up the jobs needed to survive; Compare an ant colony or bee hive to a human team, describing how different members do different tasks.

Needs first: The insect body plan.

https://lightmysky.com/learn/science/social-insects-ants-and-bees-mt_guaaD6Dn2M

#### Bees and pollination (ages 7-9)

Bees and pollination: how flowers and insects depend on each other. Bees visit flowers for nectar, pollen sticks to their bodies and transfers to the next flower. Without pollination many plants cannot make seeds or fruit. Why bees matter for the food we eat.

Ready when they can: Describe how pollen moves from one flower to another when a bee visits to collect nectar; Explain that many fruits and vegetables depend on bees or other insects for pollination; State what would happen to a garden or farm if there were no pollinating insects.

Needs first: Social insects: ants and bees, Minibeasts in the food chain.

https://lightmysky.com/learn/science/bees-and-pollination-mt_SZJ1mN7Vfk

#### Sorting and Identifying Minibeasts (ages 7-9)

Using classification keys to identify minibeasts. Branching yes/no questions: 'Does it have legs?' → 'How many legs?' → 'Does it have wings?' Dichotomous keys as a systematic tool for sorting and identifying creatures.

Ready when they can: Follow a simple branching key to correctly identify at least four different minibeasts; Create a yes/no question that separates insects from spiders, such as 'Does it have six legs?'; Explain why asking questions in a set order helps identify a creature you have never seen before.

Needs first: Not all minibeasts are insects.

https://lightmysky.com/learn/science/sorting-and-identifying-minibeasts-mt__bhJX2SuFJ

#### Insect anatomy in depth (ages 9-11)

Insect anatomy in depth: compound eyes made of thousands of tiny lenses, spiracles (breathing holes along the body), diverse mouthparts (chewing mandibles in beetles, sucking proboscis in butterflies, sponging pad in flies), and moulting the exoskeleton to grow. Biomimicry — how engineers copy insect designs.

Ready when they can: Describe at least two specialised insect structures such as compound eyes or spiracles and explain their function; Compare the mouthparts of a beetle (chewing) and a butterfly (sucking) and explain how each is suited to its food; Give one example of biomimicry where human technology is inspired by an insect structure or ability.

Needs first: Camouflage, warning colours, and mimicry, The insect body plan.

https://lightmysky.com/learn/science/insect-anatomy-in-depth-mt_Oz8yNPNtub

#### Insect communication and behaviour (ages 9-11)

Insect communication and behaviour: bees perform a waggle dance to tell hive-mates where flowers are. Ants lay pheromone trails for others to follow. Fireflies flash light patterns to find mates. Crickets chirp by rubbing their wings. Monarch butterflies migrate thousands of miles across continents. How insects 'talk' without words.

Ready when they can: Describe at least three ways insects communicate such as the bee waggle dance, ant pheromone trails, and firefly light signals; Explain what information a bee conveys through its waggle dance, including direction and distance to flowers; Describe the monarch butterfly migration and explain why it is remarkable in terms of distance and navigation.

Needs first: Social insects: ants and bees, Incredible insects: record-breakers.

https://lightmysky.com/learn/science/insect-communication-and-behaviour-mt_a9VnPBhoYs

#### Types of Metamorphosis (ages 9-11)

Complete vs incomplete metamorphosis. Complete: egg → larva → pupa → adult (butterflies, beetles, flies). Incomplete: egg → nymph → adult — the nymph looks like a small version of the adult and moults as it grows (grasshoppers, dragonflies, crickets). Why do some insects transform completely while others grow gradually?

Ready when they can: Compare complete and incomplete metamorphosis by describing the stages of each on a diagram; Classify at least three insects into the correct metamorphosis type such as butterfly (complete) and grasshopper (incomplete); Explain that nymphs resemble adults while larvae look completely different from their adult form.

Needs first: Insect life cycles: complete metamorphosis.

https://lightmysky.com/learn/science/types-of-metamorphosis-mt_ShAptVcQR3

#### Insect Adaptations (ages 9-11)

Adaptation and evolution in insects: peppered moths as a famous example of natural selection (dark moths survived better on soot-covered trees during the Industrial Revolution). Stick insects evolved to look like twigs. Ant-mimicking spiders evolved to fool predators. How small changes over many generations lead to remarkable disguises.

Ready when they can: Retell the peppered moth story and explain how the environment changed which colour moth survived best; Describe how a stick insect's body shape is an adaptation that helps it avoid being eaten; Explain that adaptations develop over many generations through natural selection, not during one insect's lifetime.

Needs first: Camouflage, warning colours, and mimicry, Types of Metamorphosis.

https://lightmysky.com/learn/science/insect-adaptations-mt_7_XXh9NCp0

#### Insects in ecosystems (ages 9-11)

Insects in ecosystems: the many roles insects play. Pollinators (bees, butterflies, hoverflies), decomposers (dung beetles, fly larvae), food source for birds, bats, fish, and frogs, and pest controllers (ladybirds eating aphids). The thought experiment: what would happen if all insects disappeared?

Ready when they can: Name at least three different ecological roles that insects play such as pollinator, decomposer, and food source; Explain how the removal of one insect group like bees would affect plants, other animals, and humans; Describe a specific example of insects as pest controllers such as ladybirds controlling aphid populations.

Needs first: Food Chains & Energy Transfer, Minibeasts in the food chain, Bees and pollination.

https://lightmysky.com/learn/science/insects-in-ecosystems-mt_r6oKXpN0er

#### The most successful animals on Earth (ages 9-11)

The most successful animals on Earth: there are roughly one million described insect species, and scientists estimate 5–10 million may exist. More insect species than all other animal groups combined. Why so many? Small body size means less food needed, fast reproduction with many offspring, flight allows reaching new habitats, and the exoskeleton is incredibly versatile.

Ready when they can: State that insects are the most species-rich group of animals with about one million known species; Give at least two reasons why insects are so successful such as small size, fast reproduction, or flight; Compare insect diversity to another animal group, explaining that there are far more insect species than mammals or birds.

Needs first: Not all minibeasts are insects, Insects in ecosystems.

https://lightmysky.com/learn/science/the-most-successful-animals-on-earth-mt_5_Zr9xXDNH

#### Threats to insects and conservation (ages 9-11)

Threats to insects and conservation: insect populations are declining worldwide. Causes include habitat loss, pesticide use, light pollution disrupting nocturnal insects, and climate change. Pollinator decline threatens food production. What children can do: plant pollinator-friendly gardens, reduce pesticide use, participate in citizen science like the Big Butterfly Count.

Ready when they can: Name at least three threats to insect populations such as habitat loss, pesticides, and light pollution; Explain why declining bee populations are a problem for humans and the food we eat; Suggest at least two actions that children or families can take to help insects such as planting wildflowers or joining a butterfly count.

Needs first: Caring for minibeasts, Insects in ecosystems.

https://lightmysky.com/learn/science/threats-to-insects-and-conservation-mt__EL7DHjf5R

### Space Exploration

https://lightmysky.com/learn/science/areas/space-exploration

#### Sun, Moon & Stars (ages 5-7)

Identify the Sun, Moon, and stars as objects in the sky and describe basic differences: the Sun gives light and heat during the day, stars are tiny points of light at night, and the Moon can appear in both the day and night sky

Ready when they can: Name the Sun, Moon, and stars as objects in the sky; State that the Sun appears during the day and gives us light and heat; State that stars appear at night and the Moon can sometimes be seen during the day too.

Needs first: Why seasons change.

https://lightmysky.com/learn/science/sun-moon-and-stars-mt_PiWZA8Z0ZJ

#### Moon Phases (ages 5-7)

Observe and describe the Moon's changing shape over about a month, recognising that it goes through a repeating cycle of phases from new moon (invisible) to full moon (complete circle) and back again

Ready when they can: Describe that the Moon appears to change shape over about a month; Name or draw at least three phases: new moon (dark), half moon, and full moon; State that the pattern repeats — the Moon goes through the same shapes again and again.

Needs first: Sun, Moon & Stars.

https://lightmysky.com/learn/science/moon-phases-mt_ByXgbTld6R

#### Our Solar System (ages 5-7)

Know that there are other planets besides Earth and that our group of planets orbiting the Sun is called the solar system — and that space is the vast area beyond Earth's sky

Ready when they can: State that Earth is a planet and there are other planets too; Use the term 'solar system' to describe the Sun and the planets that orbit it; Explain that space is the area beyond the Earth's sky, where the planets and stars are.

Needs first: Sun, Moon & Stars.

https://lightmysky.com/learn/science/our-solar-system-mt_XlyF294bPR

#### Spotting Constellations (ages 5-7)

Recognise a few star patterns (constellations) in the night sky, starting with the Big Dipper (the Plough), and understand that the North Star (Polaris) can be found using the Big Dipper

Ready when they can: Identify or draw the Big Dipper (the Plough) as a pattern of seven stars; Explain that the two end stars of the Big Dipper's bowl point towards the North Star; State that constellations are patterns of stars that people have named.

Needs first: Sun, Moon & Stars.

https://lightmysky.com/learn/science/spotting-constellations-mt_BVpB5wyijZ

#### What Astronauts Do (ages 5-7)

Know that astronauts are people who travel to space in rockets, that humans have walked on the Moon (Apollo missions), and that astronauts today live and work on the International Space Station

Ready when they can: Define an astronaut as a person who travels to space; State that humans landed on the Moon during the Apollo missions; Describe the International Space Station as a place where astronauts live and work in orbit around Earth.

Needs first: Our Solar System.

https://lightmysky.com/learn/science/what-astronauts-do-mt_oiqsIP97V3

#### The Sun is a star (ages 7-9)

Know that the Sun is a star — the closest star to Earth — and that it is at the centre of our solar system, with all eight planets orbiting around it

Ready when they can: State that the Sun is a star, not a unique type of object; Explain that the Sun appears bigger and brighter than other stars because it is much closer; Describe the solar system as the Sun at the centre with planets orbiting around it.

Needs first: Our Solar System.

https://lightmysky.com/learn/science/the-sun-is-a-star-mt_u3Y3Tb-G_n

#### Earth's Spin & Orbit (ages 7-9)

Understand that Earth moves in two ways: it rotates (spins) on its axis once every 24 hours causing day and night, and it orbits (travels around) the Sun once every 365 days, which is one year

Ready when they can: Demonstrate with a globe or ball that Earth's rotation causes day on the Sun-facing side and night on the opposite side; State that one full rotation takes about 24 hours (one day); State that one full orbit around the Sun takes about 365 days (one year).

Needs first: Seasons & Weather Patterns, The Sun is a star.

https://lightmysky.com/learn/science/earths-spin-and-orbit-mt_w2xiMNkyyX

#### How Telescopes Work (ages 7-9)

Know that telescopes are instruments that help us see distant objects in space, and that space telescopes like Hubble and James Webb orbit above Earth’s atmosphere to get clearer views of the universe

Ready when they can: Explain that a telescope magnifies distant objects so we can see them in more detail; State that Earth's atmosphere blurs the view, so space telescopes get clearer pictures; Name at least one space telescope (Hubble or James Webb) and describe what it does.

Needs first: The Sun is a star.

https://lightmysky.com/learn/science/how-telescopes-work-mt_-SZU6cVB_-

#### The Eight Planets (ages 7-9)

Name the eight planets in order from the Sun (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune), know that Pluto is a dwarf planet, and distinguish rocky inner planets from gas giant outer planets

Ready when they can: List all eight planets in order from the Sun; State that Pluto was reclassified as a dwarf planet in 2006; Explain that the four inner planets are small and rocky while the four outer planets are large gas giants.

Needs first: The Sun is a star.

https://lightmysky.com/learn/science/the-eight-planets-mt_AVk2EmSULC

#### Asteroids, Comets & Dwarf Planets (ages 7-9)

Identify other objects in the solar system beyond planets: asteroids (rocky bodies mostly between Mars and Jupiter), comets (icy bodies with tails when near the Sun), and meteoroids/meteors/meteorites (space rocks that enter Earth’s atmosphere)

Ready when they can: Describe asteroids as rocky bodies mostly found in the belt between Mars and Jupiter; Describe comets as icy bodies that develop a glowing tail when they approach the Sun; Explain the difference between a meteoroid (in space), meteor (streak of light in atmosphere), and meteorite (lands on Earth).

Needs first: The Eight Planets.

https://lightmysky.com/learn/science/asteroids-comets-and-dwarf-planets-mt_uoTBeyMhGm

#### Planet Features (ages 7-9)

Describe a key feature of each planet: Mercury is smallest and closest, Venus is the hottest, Mars is red with rust, Jupiter is the largest with a Great Red Spot, Saturn has rings, Uranus tilts on its side, Neptune is the farthest and very cold

Ready when they can: State one distinctive feature for at least six of the eight planets; Compare at least two planets (e.g. Jupiter is much bigger than Earth, Venus is hotter than Mercury); Explain why Mars appears red (iron oxide/rust in its rocks).

Needs first: The Eight Planets.

https://lightmysky.com/learn/science/planet-features-mt_W8Eq3CqWJf

#### Space Robots & Rovers (ages 7-9)

Describe how robots and rovers have explored places humans cannot easily go — Mars rovers like Curiosity and Perseverance drive across Mars taking photos, collecting rock samples, and searching for signs of past water

Ready when they can: Name at least one Mars rover (Curiosity or Perseverance) and state it drives on Mars's surface; Explain that rovers take photos, analyse rocks, and look for evidence of water; State why we send robots instead of people: Mars is very far away and has no breathable air.

Needs first: What Astronauts Do, Planet Features.

https://lightmysky.com/learn/science/space-robots-and-rovers-mt_7GwWplh-48

#### The Moon's Orbit (ages 7-9)

Know that the Moon orbits Earth approximately once a month, that it does not make its own light but reflects sunlight, and that its changing appearance (phases) is caused by how much of the sunlit side we can see from Earth

Ready when they can: State that the Moon orbits Earth roughly once every 28-30 days; Explain that the Moon reflects sunlight rather than producing its own light; Describe how Moon phases happen: we see different amounts of the lit-up side as the Moon orbits Earth.

Needs first: Moon Phases, Earth's Spin & Orbit.

https://lightmysky.com/learn/science/the-moons-orbit-mt_15FduGRf5c

#### Changing Ideas About Space (ages 9-11)

Understand that ideas about the solar system changed over time: ancient people believed Earth was at the centre (geocentric model, Ptolemy), until Copernicus proposed the Sun was at the centre (heliocentric model), later confirmed by Galileo’s telescope observations

Ready when they can: Describe the geocentric model (Earth at the centre) and name Ptolemy as its main proponent; Describe the heliocentric model (Sun at the centre) and name Copernicus as the person who proposed it; Explain that Galileo used a telescope to find evidence supporting the heliocentric model (e.g. moons orbiting Jupiter).

Needs first: Earth's Spin & Orbit.

https://lightmysky.com/learn/science/changing-ideas-about-space-mt_KiRn5lnRgj

#### Seasonal Constellations (ages 9-11)

Recognise named constellations visible in different seasons and understand why we see different constellations at different times of year — because Earth’s orbit around the Sun changes which part of the sky we face at night

Ready when they can: Name at least three constellations (e.g. Orion, Ursa Major/Big Dipper, Leo, Cassiopeia); State that different constellations are visible in different seasons; Explain that this happens because Earth's orbit means we face different directions in space at different times of year.

Needs first: Spotting Constellations, Earth's Spin & Orbit.

https://lightmysky.com/learn/science/seasonal-constellations-mt_9VZem2vUqk

#### Space Exploration Milestones (ages 9-11)

Describe key milestones in human space exploration: the Space Race (Sputnik, Yuri Gagarin, Apollo 11 Moon landing), the Space Shuttle era, the International Space Station, and current missions (Artemis programme, Mars exploration plans, commercial spaceflight)

Ready when they can: Name Sputnik as the first satellite (1957) and Yuri Gagarin as the first person in space (1961); Describe the Apollo 11 Moon landing (1969) with Neil Armstrong and Buzz Aldrin; Name at least one current space programme (Artemis, SpaceX, ISS) and describe its goal.

Needs first: Space Robots & Rovers, What Astronauts Do.

https://lightmysky.com/learn/science/space-exploration-milestones-mt_H9RAGGiHBL

#### The Vast Scale of Space (ages 9-11)

Describe the scale of the universe in nested layers: Earth is one planet in our solar system, the Sun is one star among billions in the Milky Way galaxy, and the Milky Way is one galaxy among billions in the universe

Ready when they can: State that the Milky Way is our galaxy and it contains billions of stars; Explain the hierarchy: planet → solar system → galaxy → universe; Use a comparison to convey cosmic scale (e.g. if the Sun were a football, Earth would be a peppercorn 26 metres away).

Needs first: The Eight Planets, The Sun is a star.

https://lightmysky.com/learn/science/the-vast-scale-of-space-mt_aulwq39aj8

#### Scale of the Solar System (ages 9-11)

Use scale models, diagrams, or calculations to represent the relative sizes and distances of objects in the solar system, understanding that the distances between planets are enormously larger than the planets themselves

Ready when they can: Explain that if the Sun were the size of a beach ball, Earth would be a pea about 26 metres away; State that the distances between planets are much greater than the sizes of the planets themselves; Create or interpret a scale model showing both relative sizes and distances.

Needs first: The Vast Scale of Space, The Eight Planets.

https://lightmysky.com/learn/science/scale-of-the-solar-system-mt_TlGhXAqC4p

#### Why the Sun Looks Brightest (ages 9-11)

Explain why the Sun appears much brighter than other stars: it is the nearest star to Earth, not the biggest or brightest star in the universe — understanding the difference between apparent brightness (how bright something looks) and actual brightness

Ready when they can: State that the Sun is a medium-sized star that appears brightest because it is the closest star to Earth; Explain the difference between apparent brightness (how bright it looks) and actual brightness (how much light it gives off); Give an example: a torch held close looks brighter than a distant floodlight, even though the floodlight is more powerful.

Needs first: The Sun is a star.

https://lightmysky.com/learn/science/why-the-sun-looks-brightest-mt_ae-cHHFR76

#### Life Cycle of Stars (ages 9-11)

Understand the basics of a star’s life cycle: stars are born in clouds of gas and dust (nebulae), shine for millions or billions of years by fusing hydrogen, and eventually die — massive stars explode as supernovae while smaller stars fade into white dwarfs

Ready when they can: Describe that stars form from clouds of gas and dust called nebulae; State that stars produce energy by fusing hydrogen into helium in their cores; Explain that massive stars end in a supernova explosion while smaller stars shrink to become white dwarfs.

Needs first: Why the Sun Looks Brightest, The Sun is a star.

https://lightmysky.com/learn/science/life-cycle-of-stars-mt_iTjrKEdAOj

#### Observing with Light Waves (ages 11-13)

Explain how the electromagnetic spectrum is the primary tool of modern astronomy — different wavelengths (radio, infrared, visible, ultraviolet, X-ray, gamma-ray) reveal different phenomena, why some telescopes must be in space, and what specific discoveries each wavelength range has enabled (e.g. CMB in microwave, black hole jets in X-ray, cold gas clouds in radio)

Ready when they can: Lists at least four regions of the EM spectrum and gives a specific astronomical object or phenomenon observed in each; Explains why some telescopes must be placed in space (Earth's atmosphere blocks X-ray, gamma-ray, and much infrared radiation); Describes the James Webb Space Telescope or Hubble and explains which part of the spectrum each primarily observes and why that was chosen.

Needs first: Why the Sun Looks Brightest.

https://lightmysky.com/learn/science/observing-with-light-waves-mt_rbY77m8_s1

#### Gravity Pulls Things Down (ages 9-11)

Understand gravity as a force that pulls objects towards the centre of the Earth, that 'down' means towards Earth’s centre regardless of where you stand on the sphere, and that gravity keeps the Moon orbiting Earth and planets orbiting the Sun

Ready when they can: Define gravity as a pulling force that attracts objects towards the centre of the Earth; Explain that 'down' points towards Earth's centre, so people on opposite sides of the globe both feel pulled 'down'; State that gravity keeps the Moon orbiting Earth and planets orbiting the Sun.

Needs first: The solar system, Earth's Spin & Orbit.

https://lightmysky.com/learn/science/gravity-pulls-things-down-mt_Y2WcY2lOTK

#### Finding Exoplanets (ages 11-13)

Describe how astronomers detect planets around other stars using transit photometry (dip in starlight as a planet crosses) and radial velocity (Doppler wobble of the star), explain the habitable zone concept, and discuss what atmospheric biosignatures — such as oxygen, methane, and water vapour detected together — would suggest about a planet

Ready when they can: Explains transit photometry: the small, periodic dip in a star's brightness when a planet passes in front of it; Explains the habitable zone as the range of distances from a star where liquid water could exist on a planet's surface; Describes two or more atmospheric biosignatures and explains why their co-presence is significant (e.g. oxygen + methane together suggests active life replenishing both).

Needs first: The solar system (age 11+), The Vast Scale of Space.

https://lightmysky.com/learn/science/finding-exoplanets-mt_UjuriPLVgT

#### Orbital Mechanics (ages 12-13)

Apply Newton's laws to explain orbital motion: why orbit is continuously falling sideways rather than floating; how a gravity assist (slingshot manoeuvre) transfers momentum from a planet to a spacecraft; and why rockets need to reach a specific speed to enter orbit — with a conceptual (not algebraic) treatment of the Tsiolkovsky rocket equation

Ready when they can: Explains that orbit is a state of continuous freefall — the spacecraft is falling towards Earth but moving so fast horizontally that it keeps missing; Describes how a gravity assist works: a spacecraft flying past a planet gains speed by 'borrowing' from the planet's orbital momentum; Explains the key insight of the rocket equation: the ratio of fuel to final spacecraft mass grows exponentially with required Δv, explaining why large rockets are mostly fuel.

Needs first: Universal Gravitation, Gravity Pulls Things Down.

https://lightmysky.com/learn/science/orbital-mechanics-mt_1nl396BaVa

#### Journey to Mars (ages 13-14)

Evaluate the engineering and human challenges of long-duration spaceflight to Mars — radiation exposure, muscle and bone loss, psychological isolation, communication delays — and assess the current state of the SETI programme: what methods are used, what has been detected so far, and what the Fermi Paradox is

Ready when they can: Identifies and explains at least three major challenges of a Mars mission: radiation (no magnetosphere), bone/muscle loss from low gravity, psychological isolation, and delayed communications; Describes how SETI searches for intelligent life (radio signals, laser pulses, technosignatures) and explains why the lack of detection so far is not proof of absence; States the Fermi Paradox ('Where is everybody?') and discusses two contrasting proposed resolutions.

Needs first: Space Exploration Milestones, Galaxies and the universe.

https://lightmysky.com/learn/science/journey-to-mars-mt_EIbltgXRWR

#### Where Elements Come From (ages 12-14)

Explain stellar nucleosynthesis: the Big Bang produced mainly hydrogen and helium; main-sequence fusion builds elements up to iron; and supernovae produce elements heavier than iron and scatter them into space — meaning the atoms in our bodies were forged in ancient stars

Ready when they can: States that the Big Bang produced primarily hydrogen and helium, and that all heavier elements were made later in stars; Explains that nuclear fusion in main-sequence stars converts hydrogen to helium and can continue building heavier elements up to iron; Explains why elements heavier than iron require supernova explosions to form, and describes how supernovae distribute these elements into interstellar space where they become the raw material for new stars, planets, and life.

Needs first: Life Cycle of Stars, Atoms, Elements & Compounds.

https://lightmysky.com/learn/science/where-elements-come-from-mt_KYx0m4OyZv

### Animals of the World

https://lightmysky.com/learn/science/areas/animals-of-the-world

#### Animals Everywhere (ages 5-7)

Know that animals live all over the world — on land, in water, and in the air — and that every continent, even icy Antarctica, is home to animals, each suited to the conditions where they live

Ready when they can: Names at least 3 animals from different environments (e.g., forest, ocean, desert); States that animals live on land, in water, and some can fly; Recognises that animals live on every continent.

https://lightmysky.com/learn/science/animals-everywhere-mt_v3Vz_Pgjjv

#### Animal Homes (ages 5-7)

Know that animals make or find many different kinds of homes — birds build nests, rabbits dig burrows, bees live in hives, hermit crabs use empty shells, spiders spin webs — and that these shelters protect them and their young

Ready when they can: Names at least 4 different types of animal homes (nest, burrow, hive, web, shell, den, lodge); Explains that animals need homes for shelter and to keep their babies safe; Matches common animals to their homes.

Needs first: Animals Everywhere.

https://lightmysky.com/learn/science/animal-homes-mt_oLHXfLujmh

#### Animal Record-Holders (ages 5-7)

Know some of the world's animal record-holders — the blue whale is the largest animal ever, the cheetah is the fastest land animal, the bee hummingbird is the smallest bird, the giraffe is the tallest — and compare their sizes to familiar objects

Ready when they can: Names at least 4 animal record-holders with their record (fastest, biggest, tallest, smallest, etc.); Compares an animal's size or ability to a familiar reference; Shows enthusiasm for superlative animal facts.

Needs first: Animals Everywhere.

https://lightmysky.com/learn/science/animal-record-holders-mt_goZW_hQUa4

#### How Animals Have Babies (ages 5-7)

Know that different animals have their babies in different ways — some lay eggs (birds, reptiles, fish, insects), some give birth to live young (most mammals) — and that babies may look like miniature adults or look very different from their parents

Ready when they can: Gives examples of animals that lay eggs and animals that give birth to live young; Describes at least one example of a baby that looks different from its parent (e.g., tadpole/frog, caterpillar/butterfly); Shows curiosity about how different animals have their babies.

Needs first: Animals Everywhere.

https://lightmysky.com/learn/science/how-animals-have-babies-mt_-vsLvsxp0L

#### Nocturnal Animals (ages 5-7)

Know that some animals are nocturnal — active at night and sleeping during the day — and that nocturnal animals often have special features like big eyes (owls, tarsiers), large ears (bats, fennec foxes), or sensitive whiskers to help them find food in the dark

Ready when they can: Explains what 'nocturnal' means; Names at least 3 nocturnal animals (e.g., owl, bat, fox, hedgehog, moth); Describes one feature that helps a nocturnal animal (e.g., big eyes, echolocation, whiskers).

Needs first: Animal Homes, Animals Everywhere.

https://lightmysky.com/learn/science/nocturnal-animals-mt_V_wIdRZLsG

#### Animal Camouflage (ages 5-7)

Know that many animals use camouflage — colours and patterns that help them blend into their surroundings — to hide from predators or to sneak up on prey, like a leaf insect that looks like a leaf or an Arctic hare that turns white in winter

Ready when they can: Explains that camouflage means blending in with surroundings; Gives at least 3 examples of camouflaged animals; Explains that camouflage helps animals hide from predators or sneak up on food.

Needs first: Animals Everywhere, Nocturnal Animals.

https://lightmysky.com/learn/science/animal-camouflage-mt_pwo81ls_J-

#### Desert Animals (ages 7-9)

Explore animals of the desert — camels, fennec foxes, scorpions, rattlesnakes, meerkats — and understand how desert animals survive extreme heat and lack of water through being active at night, storing water or fat, burrowing underground during the day, and having large ears to lose heat

Ready when they can: Names at least 4 desert animals; Explains at least two desert survival adaptations (nocturnal behaviour, water storage, burrowing, large ears for cooling); Knows deserts can be hot or cold but are always dry.

Needs first: Nocturnal Animals.

https://lightmysky.com/learn/science/desert-animals-mt_0zqOTjjW2k

#### Rainforest Animals (ages 7-9)

Explore animals of the tropical rainforest — the most species-rich habitat on Earth — learning that the forest has layers (canopy, understory, forest floor) with different animals at each level: toucans and monkeys in the canopy, jaguars and frogs on the floor, and that rainforests are found near the equator

Ready when they can: Names at least 4 rainforest animals from different layers; Describes the rainforest as having layers (canopy, understory, forest floor); Explains that rainforests are near the equator and are hot and wet; Recognises that rainforests have more species than almost any other habitat.

Needs first: Rainforest Layers, Animal Homes, Animals Everywhere, Iconic Rainforest Animals.

https://lightmysky.com/learn/science/rainforest-animals-mt_DCelLx_H1A

#### Wild, Farm & Pet Animals (ages 5-7)

Understand the difference between wild animals, farm animals, and pets — wild animals find their own food and shelter in nature; farm animals are kept by people for food, wool, or eggs; pets are animals people keep for companionship — and know that wild animals should be observed from a distance

Ready when they can: Sorts animals into wild, farm, and pet categories with examples; Explains one key difference between each category; Understands that wild animals should be observed, not approached.

Needs first: Animals Everywhere, Naming Common Animals.

https://lightmysky.com/learn/science/wild-farm-and-pet-animals-mt_muxjw0fxxN

#### Savanna & Grassland Animals (ages 7-9)

Explore animals of the grasslands and savanna — lions, zebras, wildebeest, elephants, cheetahs in African savanna; bison and prairie dogs in American grasslands — understanding why large herds form on open grasslands and how predators and prey interact in these wide-open spaces

Ready when they can: Names at least 5 grassland/savanna animals; Explains that herding provides safety in numbers against predators; Describes the predator-prey relationship (e.g., lions hunt zebras); Knows grasslands/savannas are wide-open habitats with few trees.

Needs first: Wild, Farm & Pet Animals, Animals Everywhere.

https://lightmysky.com/learn/science/savanna-and-grassland-animals-mt_YynJoQcm_M

#### The World of Minibeasts (ages 7-9)

Know that insects and other minibeasts (spiders, worms, snails, centipedes) are the most numerous and diverse group of animals on Earth — there are more species of beetle than any other animal — and that they play vital roles as pollinators (bees, butterflies), decomposers (woodlice, worms), and food for other animals

Ready when they can: Knows that insects/minibeasts are the most numerous animal group; Names at least 3 roles minibeasts play: pollinators, decomposers, food source; Distinguishes insects (6 legs) from spiders (8 legs) from other minibeasts; Shows appreciation for the importance of invertebrates.

Needs first: Animal Body Groups, Animal Homes, Animals Everywhere.

https://lightmysky.com/learn/science/the-world-of-minibeasts-mt_R7LEuZjTmx

#### Animal Communication (ages 7-9)

Understand that animals communicate in many different ways — birds sing to attract mates and defend territory, whales call across vast ocean distances, bees dance to show other bees where food is, wolves howl to keep the pack together, and fireflies flash light signals — and that communication is essential for survival

Ready when they can: Describes at least 4 different methods of animal communication (sound, dance, light, scent, body language); Gives a specific animal example for each method; Explains that animals communicate to find mates, warn of danger, or share food locations.

Needs first: The World of Minibeasts, Animals Everywhere.

https://lightmysky.com/learn/science/animal-communication-mt_wHN14Unk7h

#### Predator Hunting Strategies (ages 7-9)

Understand that predators have evolved hunting strategies — wolves hunt in packs, chameleons use their long tongues, spiders build webs, crocodiles ambush at water's edge — and prey animals have evolved defences — porcupine spines, skunk spray, poison dart frog toxins, zebra stripes confusing predators, playing dead

Ready when they can: Describes at least 3 predator hunting strategies with examples; Describes at least 3 prey defence mechanisms with examples; Understands the concept of an 'arms race' between predators and prey.

Needs first: Herbivores, Carnivores & Omnivores, Animal Camouflage, Nocturnal Animals, Savanna & Grassland Animals.

https://lightmysky.com/learn/science/predator-hunting-strategies-mt_Bztatrv-_v

#### Animal Intelligence (ages 9-11)

Explore animal intelligence and complex behaviour — chimpanzees and crows use tools, dolphins recognise themselves in mirrors, octopuses solve puzzles and escape enclosures, elephants mourn their dead, meerkats teach their young to handle scorpions — understanding that many animals think, learn, and have social lives more complex than once believed

Ready when they can: Gives at least 4 examples of animal intelligence or complex behaviour; Explains what 'tool use' means and names at least 2 tool-using animals; Discusses how scientists test animal intelligence (mirror test, puzzle boxes, observation); Shows understanding that intelligence takes different forms in different species.

Needs first: Predator Hunting Strategies, Senses, Brain & Responses, Animal Communication.

https://lightmysky.com/learn/science/animal-intelligence-mt_fpPLWFIRVo

#### Animal Migration (ages 7-9)

Know that many animals make incredible journeys called migrations — Arctic terns fly from pole to pole, monarch butterflies travel thousands of miles across North America, wildebeest cross the Serengeti following rain, and humpback whales swim between polar feeding grounds and tropical breeding waters — and that these journeys are linked to food, breeding, and seasons

Ready when they can: Defines migration as a regular long journey animals make; Names at least 3 migratory animals with their routes or destinations; Explains that migration is driven by food availability, breeding, or seasonal changes.

Needs first: More Polar Animals, Animals Everywhere, Savanna & Grassland Animals.

https://lightmysky.com/learn/science/animal-migration-mt_bK84sPehyP

#### Polar Animals (ages 7-9)

Explore animals of the Arctic and Antarctic — polar bears, Arctic foxes, and walruses in the north; penguins, seals, and albatrosses in the south — and understand how polar animals survive extreme cold through thick fur or blubber, huddling behaviour, and seasonal changes like white winter coats

Ready when they can: Names at least 3 animals each from the Arctic and Antarctic; Explains at least two adaptations for surviving cold (blubber, thick fur, huddling, white camouflage); Knows polar bears live only in the Arctic and penguins only in the Antarctic/Southern Hemisphere.

Needs first: Desert Animals, More Polar Animals, Ocean Animal Adaptations, Arctic vs Antarctic, Animal Camouflage, Animals Everywhere.

https://lightmysky.com/learn/science/polar-animals-mt_D4lyx0iYyB

#### Structural Adaptations (ages 9-11)

Understand that animals have structural adaptations (body features like the giraffe's long neck, eagle's talons, dolphin's streamlined shape), behavioural adaptations (migration, hibernation, tool use), and physiological adaptations (antifreeze in Arctic fish blood, echolocation in bats) — and that these developed over many generations through natural selection

Ready when they can: Defines adaptation as a feature or behaviour that helps an animal survive in its environment; Gives examples of structural, behavioural, and physiological adaptations; Explains that adaptations develop over many generations, not during one animal's lifetime; Connects adaptations to the concept of natural selection at a basic level.

Needs first: Desert Animals, Animal Migration, Predator Hunting Strategies, Polar Animals, How animals adapt to environments, Animal Camouflage.

https://lightmysky.com/learn/science/structural-adaptations-mt_EaWjCyn8W2

#### Endangered & Extinct Species (ages 9-11)

Understand why some animal species become endangered or go extinct — habitat destruction, hunting/poaching, pollution, climate change, and invasive species — and know examples like the giant panda, mountain gorilla, Amur leopard, and the now-extinct dodo and thylacine, using the IUCN Red List as the system scientists use to track threatened species

Ready when they can: Defines endangered as a species at risk of extinction; Names at least 3 causes of species becoming endangered; Gives at least 3 examples of endangered or extinct animals; Knows the IUCN Red List exists as a tracking system.

Needs first: Climate Change Basics, Rainforest Animals, Structural Adaptations, Animals Everywhere, Changing Environments.

https://lightmysky.com/learn/science/endangered-and-extinct-species-mt_5S4byWDX6n

#### Invasive Species (ages 9-11)

Understand that invasive species are animals (or plants) that have been introduced to a place where they don't naturally belong — like grey squirrels outcompeting red squirrels in the UK, cane toads poisoning native predators in Australia, or rabbits devastating ecosystems in Australia — and that they can cause serious harm to native wildlife by competing for food, spreading disease, or having no natural predators

Ready when they can: Defines invasive species as non-native animals introduced to a new environment; Names at least 2 examples of invasive species and their impacts; Explains at least 2 reasons invasive species are harmful (no predators, outcompete natives, spread disease); Understands the difference between a species naturally expanding its range and being introduced by humans.

Needs first: Endangered & Extinct Species, Structural Adaptations, Animals Everywhere.

https://lightmysky.com/learn/science/invasive-species-mt_CBxOcjh69x

#### Symbiosis (ages 9-11)

Understand symbiosis — close relationships between different species — including mutualism (both benefit, like clownfish and anemones), commensalism (one benefits without harming the other, like remora fish riding sharks), and parasitism (one benefits at the other's expense, like ticks on deer) — and recognise these relationships in nature

Ready when they can: Defines symbiosis as a close relationship between different species; Distinguishes mutualism, commensalism, and parasitism with an example of each; Identifies symbiotic relationships when presented with new scenarios.

Needs first: Rainforest Animals, Structural Adaptations, The World of Minibeasts, Animal Groups & Survival.

https://lightmysky.com/learn/science/symbiosis-mt_H8OgKZbgGe

#### Biodiversity (ages 9-11)

Understand that biodiversity — the variety of different species in an ecosystem — is essential for healthy ecosystems, and that keystone species (like wolves in Yellowstone, sea otters in kelp forests, or bees as pollinators) have an outsized impact on their ecosystem, so that losing one key species can cause a cascade of changes affecting many others

Ready when they can: Defines biodiversity as the variety of species in an ecosystem; Explains why biodiversity matters (stability, resilience, ecosystem services); Defines keystone species and gives at least 2 examples; Describes a trophic cascade or chain reaction from removing/adding a species.

Needs first: Endangered & Extinct Species, Predator Hunting Strategies, Structural Adaptations, Symbiosis, The World of Minibeasts.

https://lightmysky.com/learn/science/biodiversity-mt_NDZYiLvApW

#### Protecting Endangered Animals (ages 9-11)

Know how people work to protect endangered animals — through national parks and marine reserves, captive breeding programmes (like those that saved the California condor and Arabian oryx), anti-poaching patrols, wildlife corridors connecting habitats, and laws banning trade in endangered species — and understand that children can contribute through habitat-friendly choices

Ready when they can: Describes at least 3 conservation strategies with specific examples; Names an animal saved from near-extinction by conservation efforts; Suggests at least one action children or families can take to help wildlife; Understands that conservation requires both protecting habitats and helping individual species.

Needs first: Protecting the Ocean, Endangered & Extinct Species, Invasive Species, Biodiversity.

https://lightmysky.com/learn/science/protecting-endangered-animals-mt_pWwV_8OgXD

#### The Red Queen Hypothesis (ages 11-12)

Introduce the Red Queen hypothesis — species must keep evolving just to maintain fitness relative to co-evolving partners; describe predator-prey arms races (cheetah speed vs gazelle speed, bat echolocation vs moth hearing jamming) and parasite-host co-evolution (myxomatosis in rabbits); explain Darwin's hawk moth and orchid as a classic example of mutualistic co-evolution predicting an unknown species; understand that co-evolution is a major driver of biological diversification

Needs first: Predator Hunting Strategies, Structural Adaptations.

https://lightmysky.com/learn/science/the-red-queen-hypothesis-mt_mKNmXqz_Oo

#### Deep-Sea Survival (ages 12-13)

Explain how deep-sea animals cope with crushing pressure (no gas-filled spaces, flexible proteins, pressure-adapted enzymes); describe thermoregulation extremes — antifreeze glycoproteins in Antarctic fish, supercooling in wood frogs; introduce tardigrades and cryptobiosis (surviving desiccation, extreme temperatures, radiation, vacuum); survey other extremophiles (thermophiles at hydrothermal vents, halophiles in salt flats); consider what these organisms tell us about the limits of life

Needs first: Polar Animals, Symbiosis.

https://lightmysky.com/learn/science/deep-sea-survival-mt_ot9rcUwBtK

#### Sexual Selection (ages 12-13)

Explain sexual selection as a form of natural selection: runaway selection for peacock tails, bird of paradise displays, and frog calls; explain kin selection and altruistic behaviour — why worker bees die to protect the hive, why meerkats stand guard at personal risk (Hamilton's rule, inclusive fitness); introduce game theory in animal behaviour using the hawk-dove model; define cognitive ethology and survey evidence for animal emotions, play, and culture

Needs first: Animal Intelligence, The Red Queen Hypothesis.

https://lightmysky.com/learn/science/sexual-selection-mt_YNrrNE23dZ

#### The Biodiversity Crisis (ages 12-14)

Quantify the current biodiversity crisis: extinction rates 100-1000x the background rate; explain methods for measuring biodiversity loss (species-area relationship, population viability analysis, IUCN Red List categories); evaluate rewilding case studies — Yellowstone wolf reintroduction triggering a trophic cascade that changed river courses; Iberian lynx recovery; describe minimum viable population theory and conservation triage; examine ethical debates in deciding which species to prioritise

Needs first: Endangered & Extinct Species, Biodiversity, Protecting Endangered Animals.

https://lightmysky.com/learn/science/the-biodiversity-crisis-mt_44HkROUnzE

#### Grouping Species Using DNA (ages 13-14)

Explain cladistics: organisms are grouped by shared derived characters, not just similarity; how phylogenetic trees are built using molecular data (DNA sequence alignment) and the molecular clock; explain why birds are technically a group within dinosaurs (crown Avemetatarsalia); distinguish convergent evolution (unrelated species evolving similar traits) from parallel evolution; introduce horizontal gene transfer and why the tree of life is more accurately a web; explain why classification systems keep changing as new data emerge

Needs first: The Biodiversity Crisis, Chromosomes, Genes & DNA, Invasive Species, Evidence-Based Classification.

https://lightmysky.com/learn/science/grouping-species-using-dna-mt_fqAkSv3cUE

### Dinosaurs & Paleontology

https://lightmysky.com/learn/science/areas/dinosaurs-and-paleontology

#### Dinosaurs Were Real (ages 5-7)

Understand that dinosaurs were real animals that lived on Earth a very long time ago and are now extinct — none are alive today

Ready when they can: State that dinosaurs were real animals, not made up; Explain that 'extinct' means no living ones are left anywhere; Distinguish between 'a long time ago' and recent events like last year.

https://lightmysky.com/learn/science/dinosaurs-were-real-mt_dpM1l5IOk6

#### Famous Dinosaur Species (ages 5-7)

Recognise and name common well-known dinosaur species: Tyrannosaurus rex, Triceratops, Stegosaurus, and Brachiosaurus/Diplodocus, describing a basic feature of each

Ready when they can: Name at least four common dinosaur species from pictures or models; Describe one visible feature of each (e.g. T. rex has tiny arms, Triceratops has three horns); Match a dinosaur name to a picture or model without help.

Needs first: Dinosaurs Were Real.

https://lightmysky.com/learn/science/famous-dinosaur-species-mt_BnabTHkNIp

#### Dinosaur Sizes (ages 5-7)

Compare dinosaur sizes to familiar things — some dinosaurs were as tall as a house, others were as small as a chicken — and understand that dinosaurs came in a huge range of sizes

Ready when they can: Compare the size of a large dinosaur to a familiar object like a bus or house; Name a very large dinosaur (e.g. Brachiosaurus) and a small one (e.g. Compsognathus); Use words like 'taller than', 'longer than', 'heavier than' when comparing.

Needs first: Famous Dinosaur Species.

https://lightmysky.com/learn/science/dinosaur-sizes-mt_u0TeRwRII_

#### Fossils & Palaeontologists (ages 5-7)

Understand that fossils are the remains of ancient living things preserved in rock, and that scientists called palaeontologists study fossils to learn about dinosaurs

Ready when they can: Describe a fossil as the remains of a living thing preserved in rock; Name the job of a palaeontologist as someone who studies fossils; Identify examples of fossils: bones, teeth, footprints in rock.

Needs first: Dinosaurs Were Real.

https://lightmysky.com/learn/science/fossils-and-palaeontologists-mt_bKlnc7dyVK

#### Real Dinosaurs vs Fiction (ages 5-7)

Distinguish real dinosaurs from fictional or commonly confused creatures — pterosaurs (flying reptiles) and plesiosaurs (marine reptiles) were not dinosaurs, and movie dinosaurs are not always accurate

Ready when they can: State that pterosaurs could fly but were not dinosaurs; State that plesiosaurs lived in the sea but were not dinosaurs; Identify at least one way a movie or cartoon dinosaur differs from the real animal.

Needs first: Famous Dinosaur Species.

https://lightmysky.com/learn/science/real-dinosaurs-vs-fiction-mt_JednrdYqpt

#### Fossils Reveal Ancient Environments (ages 7-9)

Understand that fossils tell us not only about ancient animals but also about ancient environments — for example, marine fossils found on a mountaintop show that area was once underwater

Ready when they can: Give an example of a fossil that reveals a past environment different from today's; Explain that finding marine fossils inland means that area was once covered by sea; State that plant fossils can show whether an area was once a forest, desert, or swamp.

Needs first: Fossils & Palaeontologists.

https://lightmysky.com/learn/science/fossils-reveal-ancient-environments-mt_fKwgN61ttR

#### Mary Anning, Fossil Hunter (ages 7-9)

Know who Mary Anning was — a pioneering fossil hunter from Lyme Regis, England, who discovered ichthyosaur and plesiosaur skeletons in the early 1800s and contributed to our understanding of prehistoric life

Ready when they can: State that Mary Anning lived in England in the early 1800s and hunted for fossils along the coast; Name at least one of her major discoveries (ichthyosaur or plesiosaur); Explain why her work was important — she helped scientists understand that extinct creatures once lived on Earth.

Needs first: Fossils & Palaeontologists.

https://lightmysky.com/learn/science/mary-anning-fossil-hunter-mt_excSPNHJWZ

#### The Mesozoic Era (ages 7-9)

Place the three periods of the Mesozoic Era — Triassic, Jurassic, and Cretaceous — in order and understand that different dinosaurs lived in different periods, not all at the same time

Ready when they can: List Triassic, Jurassic, and Cretaceous in the correct chronological order; Assign at least one well-known dinosaur to the correct period; Explain that millions of years separated these periods and different species lived in each.

Needs first: Famous Dinosaur Species, Dinosaurs Were Real, Dinosaur Sizes.

https://lightmysky.com/learn/science/the-mesozoic-era-mt_uQljqc0J5j

#### Dinosaurs Around the World (ages 7-9)

Understand that different dinosaurs lived on different continents and that fossil discoveries around the world show dinosaurs were a global phenomenon, with some species found only in certain regions

Ready when they can: State that dinosaur fossils have been found on every continent including Antarctica; Name at least one dinosaur discovery location (e.g. T. rex in North America, Velociraptor in Mongolia); Suggest a reason why the same type of dinosaur is sometimes found on continents now far apart.

Needs first: Dinosaurs Were Real, The Mesozoic Era.

https://lightmysky.com/learn/science/dinosaurs-around-the-world-mt_oH1XC8aQYn

#### The K-Pg Extinction Event (ages 9-11)

Describe the Cretaceous–Palaeogene (K-Pg) extinction event approximately 66 million years ago, including the asteroid impact theory and its evidence (iridium layer, Chicxulub crater), and understand that this ended the reign of non-avian dinosaurs

Ready when they can: State that the K-Pg extinction happened about 66 million years ago and wiped out non-avian dinosaurs; Describe the asteroid impact hypothesis and name the Chicxulub crater in Mexico; Explain one piece of evidence: the iridium-rich layer found worldwide in rocks from that time.

Needs first: Dinosaurs Were Real, The Mesozoic Era.

https://lightmysky.com/learn/science/the-k-pg-extinction-event-mt_QHKqckBdAk

#### Fossilisation: Why Sediment, Minerals and Luck All Matter (ages 7-9)

Explain in simple terms how fossils form: an organism dies and is quickly buried in sediment; over millions of years minerals replace the remains and the sediment turns to rock, preserving the shape

Ready when they can: Describe the basic sequence: organism dies, buried in sediment, minerals replace remains over time; Explain why fossilisation is rare — most organisms decompose before being buried; Use the words 'sediment', 'minerals', and 'rock' correctly when explaining.

Needs first: Fossils & Palaeontologists, Real Dinosaurs vs Fiction, How fossils form.

https://lightmysky.com/learn/science/fossilisation-why-sediment-minerals-and-luck-all-matter-mt_iycQEai3dK

#### Types of Fossils (ages 7-9)

Distinguish body fossils (preserved bones, teeth, shells) from trace fossils (footprints, trackways, eggs, burrows, coprolites) and explain what each type can tell scientists

Ready when they can: Sort examples into body fossils (bones, teeth, shells) and trace fossils (footprints, eggs, dung); Explain that body fossils show what an animal looked like physically; Explain that trace fossils show how an animal behaved — how it moved, what it ate, where it nested.

Needs first: Fossils & Palaeontologists, Fossilisation: Why Sediment, Minerals and Luck All Matter.

https://lightmysky.com/learn/science/types-of-fossils-mt_1VSFoM44JU

#### Reading Dinosaur Trackways (ages 7-9)

Use dinosaur trackways (fossilised footprints) to make inferences about a dinosaur's size, speed, and behaviour — widely spaced prints suggest running, closely spaced suggest walking

Ready when they can: Explain that larger footprints generally mean a larger dinosaur; Compare spacing between prints to infer walking versus running; Suggest what a set of parallel trackways might mean (e.g. dinosaurs travelling in a group).

Needs first: Types of Fossils.

https://lightmysky.com/learn/science/reading-dinosaur-trackways-mt_Wpvuz3mvBq

#### Rock Layers & Relative Dating (ages 9-11)

Understand that rock layers (strata) form in sequence with the oldest at the bottom and the youngest at the top, and that fossils found in deeper layers are older — this is the principle of relative dating

Ready when they can: Explain that sedimentary rock forms in layers with the oldest at the bottom; Use a diagram of rock strata to determine which fossil is older based on its position; Define relative dating as working out the age of something by comparing its position in rock layers.

Needs first: Fossilisation: Why Sediment, Minerals and Luck All Matter, Types of Rock, Properties of materials, The Mesozoic Era.

https://lightmysky.com/learn/science/rock-layers-and-relative-dating-mt_EGIlsfHxb6

#### Radiometric Dating (ages 11-13)

Explain how radiometric dating works — radioactive isotopes decay at a known rate (half-life), so measuring the ratio of parent to daughter isotope in a rock or fossil gives an absolute age; distinguish between carbon-14 (useful up to ~50,000 years) and uranium-lead (useful for millions to billions of years)

Ready when they can: Defines half-life as the time for half the radioactive parent isotope to decay to the daughter isotope; Explains that the parent:daughter ratio in a sample gives an estimate of absolute age; Distinguishes carbon-14 (for recent organic material) from uranium-lead or potassium-argon (for deep geological time), explaining why carbon-14 cannot be used for dinosaur bones.

Needs first: Rock Layers & Relative Dating, Atoms, Elements & Compounds.

https://lightmysky.com/learn/science/radiometric-dating-mt_bHbpLW1HUg

#### Plant-Eaters vs Meat-Eaters (ages 5-7)

Sort dinosaurs into plant-eaters (herbivores) and meat-eaters (carnivores) by looking at clues like tooth shape — flat teeth for plants, sharp teeth for meat

Ready when they can: Sort a set of dinosaur pictures or models into herbivore and carnivore groups; Explain that sharp pointed teeth are for tearing meat and flat teeth are for grinding plants; Give an example of one herbivore and one carnivore dinosaur.

Needs first: Herbivores, Carnivores & Omnivores, Famous Dinosaur Species, Dinosaurs Were Real.

https://lightmysky.com/learn/science/plant-eaters-vs-meat-eaters-mt_DJh2JPwTf6

#### Fossilised Dinosaur Dung (ages 7-9)

Describe what coprolites are (fossilised dinosaur dung) and how palaeontologists analyse them to discover what dinosaurs ate, including plant fragments, bones, and seeds

Ready when they can: Define a coprolite as fossilised dung (animal droppings preserved as rock); Explain that scientists cut coprolites open to find plant seeds, bone fragments, or fish scales inside; State one example of what coprolite contents reveal about a dinosaur's diet.

Needs first: Types of Fossils, Plant-Eaters vs Meat-Eaters.

https://lightmysky.com/learn/science/fossilised-dinosaur-dung-mt_1dXhJp6qLJ

#### Dinosaur Hip Groups (ages 9-11)

Classify dinosaurs into the two major groups based on hip structure: Saurischia (lizard-hipped, including theropods and sauropods) and Ornithischia (bird-hipped, including Triceratops and Stegosaurus)

Ready when they can: Name the two major dinosaur groups: Saurischia and Ornithischia; Explain the difference is based on hip bone structure (lizard-hipped vs bird-hipped); Correctly classify at least two dinosaurs into each group (e.g. T. rex = Saurischia, Triceratops = Ornithischia).

Needs first: Famous Dinosaur Species, Plant-Eaters vs Meat-Eaters.

https://lightmysky.com/learn/science/dinosaur-hip-groups-mt_yrSdVrXrsF

#### How Palaeontologists Work (ages 9-11)

Describe how palaeontologists work in the field and lab: prospecting for exposed fossils, careful excavation with hand tools, plaster jacketing for transport, preparation in the lab, and scientific description and publication

Ready when they can: List the main stages: prospecting, excavation, jacketing, transport, preparation, study, display; Explain why careful excavation with small tools is necessary to avoid damaging the fossil; Describe plaster jacketing as wrapping fossils in plaster for safe transport to a lab.

Needs first: Fossilised Dinosaur Dung, Types of Fossils, Fossilisation: Why Sediment, Minerals and Luck All Matter, Reading Dinosaur Trackways.

https://lightmysky.com/learn/science/how-palaeontologists-work-mt_JBWMqZVO7S

#### Fossils as Evidence (ages 8-11)

Analyse and interpret data from fossils to provide evidence of organisms and environments that existed long ago

Ready when they can: Explain that fossils are preserved remains or traces of organisms that lived long ago; Use fossil evidence to make inferences about past organisms and their environments; Describe how comparing fossils with living organisms helps us understand how life has changed.

Needs first: Fossils Reveal Ancient Environments, Evolution vocabulary, How fossils form, Scaled picture graphs and bar graphs, Living, Dead & Never Alive.

https://lightmysky.com/learn/science/fossils-as-evidence-mt_6Z42wJaKYG

#### Life Changed Over Time (ages 10-11)

Recognise that living things have changed over time and that fossils provide information about organisms that inhabited the Earth millions of years ago

Ready when they can: State that living things have changed (evolved) over millions of years; Describe how fossils form and what information they provide about the past; Compare a fossil organism with a modern relative, noting similarities and differences.

Needs first: Life Cycles of Organisms, Fossils as Evidence, Evolution vocabulary.

https://lightmysky.com/learn/science/life-changed-over-time-mt_gTDqxYkLs9

#### Birds Evolved from Dinosaurs (ages 9-11)

Understand that modern birds evolved from a group of small feathered theropod dinosaurs, using evidence such as the fossil Archaeopteryx, feathered dinosaur fossils from China, and shared skeletal features

Ready when they can: State that birds evolved from small theropod dinosaurs; Name Archaeopteryx or Chinese feathered dinosaurs as key fossil evidence; List at least two features birds share with theropods (e.g. hollow bones, wishbone, three-toed feet).

Needs first: How animals adapt to environments, Dinosaur Hip Groups.

https://lightmysky.com/learn/science/birds-evolved-from-dinosaurs-mt_T8JGTJ-oNI

#### Palaeoart & Speculation (ages 9-11)

Understand that palaeoart — scientific illustrations and models of dinosaurs — is based on fossil evidence but involves informed speculation about skin colour, feathers, and soft tissues that don't usually fossilise

Ready when they can: Explain that bones and teeth are known from fossils but skin colour and soft tissues usually are not; State that recent discoveries of preserved skin impressions and feather fossils have improved reconstructions; Give an example of how our picture of a dinosaur has changed over time (e.g. feathered vs scaly Velociraptor).

Needs first: Fossils & Palaeontologists, Birds Evolved from Dinosaurs.

https://lightmysky.com/learn/science/palaeoart-and-speculation-mt_M8UQTURODF

#### Dinosaur-to-Bird Transition (ages 11-13)

Trace the evidence for the dinosaur-to-bird transition in depth: feathered theropods from the Liaoning Formation (China), the mix of dinosaur and bird features in Archaeopteryx, and the competing ground-up versus trees-down hypotheses for the origin of flight

Ready when they can: Describes at least three specific feathered theropod fossils (e.g. Microraptor, Anchiornis, Sinosauropteryx) and what each tells us; Describes Archaeopteryx as showing a mix of bird features (feathers, wishbone) and dinosaur features (teeth, clawed wings, long bony tail); Outlines the ground-up (running and leaping) and trees-down (gliding from trees) hypotheses for flight origin and the evidence supporting each.

Needs first: Birds Evolved from Dinosaurs.

https://lightmysky.com/learn/science/dinosaur-to-bird-transition-mt_mqQ-DtH5m-

#### Mass Extinctions in Earth History (ages 12-14)

Compare the five major mass extinction events in Earth history (End-Ordovician, Late Devonian, End-Permian, End-Triassic, K-Pg), describe proposed kill mechanisms for each (glaciation, oceanic anoxia, volcanic mega-eruptions, asteroid impact), and explain why mass extinctions, while catastrophic, also open ecological space for subsequent evolutionary radiations

Ready when they can: Names all five major mass extinctions in chronological order with approximate dates; Describes the End-Permian extinction as the most severe and links it to the Siberian Traps volcanic eruption and its atmospheric consequences; Explains how each mass extinction was followed by an adaptive radiation — e.g. the K-Pg extinction removing non-avian dinosaurs allowed mammals to diversify and eventually produce humans.

Needs first: The K-Pg Extinction Event, Extinction & Rapid Change.

https://lightmysky.com/learn/science/mass-extinctions-in-earth-history-mt_IP0PTVfTXp

#### Megafauna Extinction & De-Extinction (ages 13-14)

Evaluate the debate over what drove Pleistocene megafauna to extinction — human overkill, climate change, or a combination — using evidence from fossil records, ancient DNA, and archaeological sites; connect to the present-day sixth mass extinction and consider the ethics and feasibility of de-extinction using ancient DNA

Ready when they can: Summarises the overkill hypothesis (human hunting pressure) and the climate hypothesis (rapid warming) for Pleistocene megafauna extinction, citing specific evidence for each; Explains how ancient DNA sequencing from permafrost-preserved specimens provides information about genetics, diet, and relatedness of extinct species; Evaluates the de-extinction concept — describing what it would take technically and raising at least two substantive scientific or ecological arguments for and against.

Needs first: Chromosomes, Genes & DNA, Mass Extinctions in Earth History.

https://lightmysky.com/learn/science/megafauna-extinction-and-de-extinction-mt_tGZ2sMzMGz

#### Reading Cladograms (ages 9-11)

Read and create simple cladograms (branching diagrams) that show how groups of dinosaurs are related based on shared features, understanding that species sharing more features are more closely related

Ready when they can: Explain that a cladogram shows evolutionary relationships based on shared features; Read a simple cladogram to identify which two dinosaurs share the most recent common ancestor; Add a new species to a partially completed cladogram based on its listed features.

Needs first: Using evidence to answer questions, Dinosaur Hip Groups.

https://lightmysky.com/learn/science/reading-cladograms-mt_cSPtyLF3q1

#### Changing Scientific Knowledge (ages 9-11)

Evaluate competing scientific explanations about dinosaurs by weighing fossil evidence — understanding that scientific knowledge changes as new fossils are discovered and new methods of analysis are developed

Ready when they can: Give an example of a scientific idea about dinosaurs that changed when new evidence was found; Explain that different scientists may interpret the same fossil evidence differently; State that the best scientific explanation is the one supported by the most evidence from multiple sources.

Needs first: Evidence Supporting Ideas, How Palaeontologists Work, Palaeoart & Speculation, Dinosaurs Around the World, The K-Pg Extinction Event, Birds Evolved from Dinosaurs.

https://lightmysky.com/learn/science/changing-scientific-knowledge-mt_0T0Zf0YG6k

#### Reconstructing Ancient Ecosystems (ages 12-14)

Reconstruct an ancient ecosystem using multiple independent lines of evidence: isotope analysis of teeth to infer diet and migration, bone histology (growth rings) to estimate age and growth rate, coprolite chemistry for diet, and palaeobotany for habitat — understanding that palaeontology is an evidence-synthesis discipline

Ready when they can: Explains how stable oxygen isotope ratios in teeth shift with geographic location, allowing detection of seasonal migration; Explains how annual growth rings in bone cross-sections reveal growth rate and approximate age at death; Describes how combining evidence from teeth isotopes, coprolites, and fossil plant assemblages builds a richer picture of ancient ecology than any single source alone.

Needs first: Drawing conclusions from evidence (age 12+), Radiometric Dating, Reading Cladograms.

https://lightmysky.com/learn/science/reconstructing-ancient-ecosystems-mt_8_BxtNDrLZ

### Earth's Systems

https://lightmysky.com/learn/science/areas/earths-systems

#### Seasonal changes (ages 5-6)

Observe changes across the four seasons and describe weather associated with each season, including how day length varies

Ready when they can: Name the four seasons and describe typical weather for each; Describe how day length changes through the year (longer in summer, shorter in winter); Give examples of changes in the natural world associated with each season (e.g. leaves, flowers, animal behaviour).

Needs first: Days, Weeks, Months & Years.

https://lightmysky.com/learn/science/seasonal-changes-mt_go5i87u2b9

#### Local weather patterns (ages 5-6)

Use and share observations of local weather conditions to describe patterns over time, recording temperature, rainfall, and other conditions

Ready when they can: Observe and record daily weather conditions (temperature, cloud cover, precipitation, wind); Identify patterns in weather data over days or weeks; Use observations to make simple predictions about upcoming weather.

Needs first: Days, Weeks, Months & Years, Seasonal changes.

https://lightmysky.com/learn/science/local-weather-patterns-mt_HZvTriQWTh

#### Evaporation and condensation (ages 7-9)

Name and use vocabulary for the water cycle — evaporation, condensation, precipitation, collection, transpiration, water vapour, runoff, groundwater — and describe each stage of the cycle using these terms in the correct sequence

Ready when they can: Describe the complete water cycle using at least four correct technical terms in the right order; Distinguish 'evaporation' from 'condensation' and explain where each occurs in the water cycle; Use 'water vapour' and 'precipitation' correctly in descriptions of weather and the water cycle.

https://lightmysky.com/learn/science/evaporation-and-condensation-mt_zCGwH1OQZa

#### Shapes of land and water (ages 7-8)

Develop a model to represent the shapes and kinds of land (mountains, valleys, plains) and bodies of water (rivers, lakes, oceans) in an area

Ready when they can: Name and describe at least four types of landforms (mountain, valley, plain, hill, cliff); Name and describe at least three types of water bodies (river, lake, ocean, pond); Create or interpret a simple model or map showing land and water features of an area.

Needs first: Seasonal changes.

https://lightmysky.com/learn/science/shapes-of-land-and-water-mt_KsKLVW_ssY

#### Preventing Erosion (ages 7-8)

Compare multiple solutions designed to slow or prevent wind or water from changing the shape of the land

Ready when they can: Describe how wind and water can change the shape of land (erosion); Compare at least two design solutions for reducing erosion (e.g. retaining walls, plants, windbreaks); Evaluate which solution works best based on evidence from tests or observations.

Needs first: Shapes of land and water.

https://lightmysky.com/learn/science/preventing-erosion-mt_m6UaSmrQVG

#### Graphing seasonal weather data (ages 8-9)

Represent data in tables and graphical displays to describe typical weather conditions expected during a particular season

Ready when they can: Collect and organise weather data in a table (temperature, precipitation, cloud cover); Create a graphical display (bar chart, pictogram) showing weather patterns for a season; Use the data to describe typical weather conditions for that season and compare with other seasons.

Needs first: Bar graphs, Local weather patterns, Scaled picture graphs and bar graphs, Evaporation and condensation.

https://lightmysky.com/learn/science/graphing-seasonal-weather-data-mt_NYsz6QgaaE

#### Types of rocks (ages 9-11)

Use vocabulary for Earth's geological processes and rock types — igneous, sedimentary, metamorphic, erosion, weathering, deposition, fossil, sediment, strata, permeable, impermeable — and apply these when explaining how rocks form and how landscapes change over time

Ready when they can: Correctly classify igneous, sedimentary, and metamorphic rocks and explain in one sentence how each type forms; Use 'erosion', 'weathering', and 'deposition' correctly as three distinct stages in a sequence; Explain how fossils form using 'sediment' and 'sedimentary rock' correctly.

https://lightmysky.com/learn/science/types-of-rocks-mt_bqL8DD1SbV

#### Rock layers and Earth's history (ages 10-11)

Interpret cross-section diagrams of the Earth's interior, geological strata, and rock cycle; read and label layers (crust, mantle, outer core, inner core); understand that deeper layers in sedimentary sequences are older

Ready when they can: Label the four layers of the Earth on a cross-section diagram using the correct terms; Interpret a diagram of sedimentary rock layers and identify which layer was deposited first; Read a rock cycle diagram and trace the pathway of a rock from igneous to sedimentary to metamorphic.

Needs first: 3-D shapes (age 9+), Types of rocks.

https://lightmysky.com/learn/science/rock-layers-and-earths-history-mt_0_K-GrKQpd

#### Climates around the world (ages 8-9)

Obtain and combine information to describe climates in different regions of the world, distinguishing between weather and climate

Ready when they can: Define weather as day-to-day conditions and climate as the long-term pattern of weather in an area; Describe at least three different climate types (tropical, temperate, polar, desert) with examples; Explain that climate varies by region due to factors like distance from the equator.

Needs first: Weather vs Climate, Graphing seasonal weather data, Evaporation and condensation.

https://lightmysky.com/learn/science/climates-around-the-world-mt_Gm12BzcCfX

#### Properties of materials (ages 7-8)

Compare and group different kinds of rocks based on their appearance and simple physical properties such as hardness, texture, and colour

Ready when they can: Describe at least three observable properties of rocks: hardness, texture, colour, grain size; Sort a collection of rocks into groups based on chosen properties; Compare two rocks and describe how their properties differ.

Needs first: Grouping Materials.

https://lightmysky.com/learn/science/properties-of-materials-mt_R6YoRXkRxS

#### Rocks and soil (ages 7-8)

Recognise that soils are made from rocks and organic matter, and that different soils have different properties

Ready when they can: State that soil is a mixture of broken-down rock particles and decomposed organic matter (humus); Compare at least two types of soil (sandy, clay, loam) and describe their different properties; Explain that soil formation takes a very long time as rocks gradually break down.

Needs first: Properties of materials.

https://lightmysky.com/learn/science/rocks-and-soil-mt_yhhprm7dZK

#### Erosion and weathering (ages 9-10)

Make observations and measurements to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation

Ready when they can: Define weathering (breaking down of rock in place) and erosion (movement of broken rock/soil); Describe the effects of at least three agents of weathering/erosion: water, ice, wind, vegetation; Provide evidence from observations showing how weathering or erosion has changed a landscape.

Needs first: Types of rocks, Preventing Erosion, Properties of materials.

https://lightmysky.com/learn/science/erosion-and-weathering-mt_vAP_A986IQ

#### Finding patterns in data (ages 9-10)

Analyse and interpret data from maps to describe patterns of Earth's features, recognising that many features result from processes that occur over long periods

Ready when they can: Use a map to identify patterns in the location of mountains, rivers, lakes, and other features; Describe patterns observed (e.g. mountains in chains, rivers flow from high to low ground); Explain that Earth's features result from processes like erosion, volcanic activity, and plate movement over long periods.

Needs first: Rock layers and Earth's history, Types of rocks, Shapes of land and water, Erosion and weathering.

https://lightmysky.com/learn/science/finding-patterns-in-data-mt_-G6erQvLig

#### Plate Tectonics: the Evidence and the Engine (ages 14-15)

The idea that continents move was resisted for fifty years because nobody could say what pushed them, and it was accepted when the sea floor turned out to be spreading and recording magnetic reversals as it went. Density differences driving slow flow in the mantle are what make the plates move, and every boundary type follows from the direction of that motion.

Ready when they can: List the independent lines of evidence for plate motion and say what each one alone could not show; Explain sea-floor spreading and the magnetic stripe pattern that confirmed it; Predict the landforms, earthquakes and volcanism expected at each type of plate boundary.

https://lightmysky.com/learn/science/plate-tectonics-the-evidence-and-the-engine-mt_K4hJlyOZ7p

#### Where water is found on Earth (ages 7-8)

Identify where water is found on Earth and understand that water can exist as solid (ice) or liquid, recognising water in oceans, rivers, glaciers, and underground

Ready when they can: List where water is found on Earth: oceans, rivers, lakes, glaciers, underground, atmosphere; Explain that water exists as liquid (rivers, oceans) and solid (ice, glaciers, snow); Recognise that most of Earth's water is in the oceans.

Needs first: Shapes of land and water, Heating & Cooling Changes.

https://lightmysky.com/learn/science/where-water-is-found-on-earth-mt_nRF_VRntrW

#### Minerals and the Three Rock Families (ages 14-15)

A rock is an assemblage of minerals, and which minerals are present plus how they are arranged says how the rock formed. Grain size in an igneous rock records cooling rate, sorting in a sedimentary one records transport, and banding in a metamorphic one records directed pressure.

Ready when they can: Identify a hand specimen as igneous, sedimentary or metamorphic from texture rather than colour; Explain what crystal size in an igneous rock tells you about where it cooled; Relate the sorting and rounding of sediment grains to how far they travelled.

https://lightmysky.com/learn/science/minerals-and-the-three-rock-families-mt_S0edEKh084

#### Weathering, Erosion and How Soil Forms (ages 14-15)

Rock at the surface is attacked chemically and physically before anything moves it, and the two processes help each other because breaking rock up gives the chemistry more surface. Soil is what remains where that breakdown mixes with the products of life, which is why soil depth and fertility vary with climate.

Ready when they can: Distinguish chemical from physical weathering and explain how each accelerates the other; Explain why the same rock weathers at different rates in different climates; Describe a soil profile and say what produced each horizon.

https://lightmysky.com/learn/science/weathering-erosion-and-how-soil-forms-mt_nQOPOt1VTH

#### Sediment on the Move: Rivers, Coasts and Where It Settles (ages 15-16)

Moving water carries grains until it slows, and the size it can carry falls sharply as it does, which is why deposits are sorted. Following a grain from a hillside to a delta explains most river and coastal landforms without needing a separate rule for each one.

Ready when they can: Explain why a slowing current deposits coarse grains before fine ones; Account for a named river or coastal landform as erosion and deposition in one system; Predict what happens downstream when sediment supply is cut off by a dam or a sea wall.

https://lightmysky.com/learn/science/sediment-on-the-move-rivers-coasts-and-where-it-settles-mt_d1vVJBG6K7

#### How fossils form (ages 7-8)

Describe in simple terms how fossils are formed when things that have lived are trapped within rock over millions of years

Ready when they can: Describe the basic process: organism dies, gets buried in mud/sand, layers build up, material turns to rock over millions of years; Explain that the organism's shape is preserved as a fossil within the rock; Give examples of common fossils (shells, bones, leaf imprints, footprints).

Needs first: Properties of materials, Living, Dead & Never Alive.

https://lightmysky.com/learn/science/how-fossils-form-mt_mwirOvigWD

#### How Organisms Shape Habitats (ages 5-6)

Construct an argument supported by evidence for how plants and animals can change the environment to meet their needs

Ready when they can: Give at least three examples of organisms changing their environment (beaver dams, bird nests, plant roots breaking rock); Explain why organisms change their environment (to meet needs for shelter, food, water); Construct an argument with evidence showing how a specific organism changes its environment.

Needs first: What Living Things Need.

https://lightmysky.com/learn/science/how-organisms-shape-habitats-mt_qixeaiswFP

#### Reading a Rock Sequence: Superposition, Fossils and Correlation (ages 15-16)

A cliff face is a sequence of events in order, and a few simple rules put them in that order without any dates at all. Fossils then let sequences in different places be matched, which is how a regional history is assembled from scattered outcrops.

Ready when they can: Apply superposition, cross-cutting relationships and inclusions to order the events in a drawn section; Explain what an unconformity represents and why it is easy to miss; Use index fossils to correlate two sections and say what makes a fossil suitable for the job.

https://lightmysky.com/learn/science/reading-a-rock-sequence-superposition-fossils-and-correlation-mt_gIwqGoQsag

#### Earth's atmosphere (ages 10-11)

Develop a model to describe ways the geosphere, biosphere, hydrosphere, and atmosphere interact as connected Earth systems

Ready when they can: Name the four Earth systems: geosphere (rock/land), hydrosphere (water), atmosphere (air), biosphere (living things); Describe at least two interactions between different Earth systems with examples; Create or interpret a model showing how a change in one system affects others.

Needs first: Rock layers and Earth's history, Types of rocks, The Atmosphere, Climates around the world, Oceans & Climate, Where water is found on Earth, Evaporation & the Water Cycle, Famous Eruptions & Pangaea, Evaporation and condensation.

https://lightmysky.com/learn/science/earths-atmosphere-mt_LKagN9GJPX

#### Salt Water vs Fresh Water (ages 10-11)

Describe and graph the amounts of salt water and fresh water in various reservoirs to provide evidence about the distribution of water on Earth

Ready when they can: State that about 97% of Earth's water is salt water in the oceans; Describe where fresh water is found: glaciers/ice caps, groundwater, rivers, lakes; Create or interpret a graph showing the relative amounts of salt water vs fresh water.

Needs first: Oceans & Climate, Where water is found on Earth, Scaled picture graphs and bar graphs.

https://lightmysky.com/learn/science/salt-water-vs-fresh-water-mt_LsY4-T2fU7

#### Deep Time: Radiometric Dating and the Geological Column (ages 15-16)

Radioactive decay gives a clock that started when a mineral crystallised, and choosing the right isotope pair for the age being measured is most of the skill. Hanging numbers on the relative sequence is what turned the geological column into a timescale with an age for the Earth.

Ready when they can: Calculate an age from a parent-to-daughter ratio and a half-life; Explain why one isotope pair suits young material and another suits ancient rock; State what a radiometric date is actually dating, and give a case where that is not the event of interest.

https://lightmysky.com/learn/science/deep-time-radiometric-dating-and-the-geological-column-mt_w5DL8yRghy

#### The Layered Atmosphere and Why Temperature Reverses With Height (ages 16-17)

Air thins smoothly with height but temperature does not, and each reversal marks a different thing absorbing radiation. Those temperature layers decide where air can rise, which is why nearly all weather is trapped in the bottom one.

Ready when they can: Read a temperature profile of the atmosphere and name what heats each layer; Explain why a layer that warms with height suppresses vertical mixing; Relate the ozone layer's altitude to where the relevant radiation is absorbed.

https://lightmysky.com/learn/science/the-layered-atmosphere-and-why-temperature-reverses-with-height-mt_2icQ747JhN

#### Earth's Energy Balance and the Greenhouse Effect, Quantified (ages 16-17)

A planet settles at the temperature where it radiates away as much as it absorbs, and that calculation gives an Earth well below freezing. The gap between that figure and the real surface temperature is the greenhouse effect, measured rather than asserted.

Ready when they can: Compute an equilibrium temperature from solar input and albedo, and compare it with the measured surface temperature; Explain which gases absorb outgoing radiation and why the main constituents of air do not; Read an energy budget diagram and check that the incoming and outgoing terms balance.

https://lightmysky.com/learn/science/earths-energy-balance-and-the-greenhouse-effect-quantified-mt_dDV2fr06nO

#### Forcing, Feedback and Climate Sensitivity (ages 17-18)

A change to the energy balance is a forcing, and the system's response depends on feedbacks that amplify or damp it. Sensitivity is the number that summarises all of them, and it is uncertain mainly because clouds can feed back either way.

Ready when they can: Distinguish a forcing from a feedback using a worked example of each; Explain the water vapour and ice-albedo feedbacks and say which direction each pushes; State what climate sensitivity means and why its uncertainty range is dominated by clouds.

https://lightmysky.com/learn/science/forcing-feedback-and-climate-sensitivity-mt_os28W6fEkW

#### Palaeoclimate: Ice Cores, Isotopes and the Record of Past Change (ages 17-18)

Past climate is reconstructed from proxies, each of which records something related to temperature rather than temperature itself. Ice cores are the strongest case because they trap the air of the time alongside an isotope thermometer, letting greenhouse gas and temperature be compared directly.

Ready when they can: Explain what an oxygen isotope ratio in ice or in a shell records, and what assumption the reading rests on; Say why trapped air bubbles make an ice core a stronger record than most proxies; Read a palaeoclimate series and distinguish an orbital pacing from an amplifying response.

https://lightmysky.com/learn/science/palaeoclimate-ice-cores-isotopes-and-the-record-of-past-change-mt_JabMZ5ZeaL

#### Global Circulation: Cells, Jets and Why Deserts Sit Where They Do (ages 16-17)

The tropics receive more energy than they radiate and the poles less, and the atmosphere moves the difference in a pattern of overturning cells bent by the Earth's rotation. Where air sinks it dries, which is why the great deserts lie in two bands rather than at random.

Ready when they can: Explain the three-cell pattern as a consequence of unequal heating plus rotation; Predict the latitude bands of high rainfall and of desert from where air rises and sinks; Say what a jet stream is and why it sits at the boundary between cells.

https://lightmysky.com/learn/science/global-circulation-cells-jets-and-why-deserts-sit-where-they-do-mt_nHAXncXpaS

#### The Ocean in Motion: Wind-Driven Gyres and the Deep Overturning (ages 17-18)

Surface currents are driven by the wind and steered by rotation into basin-scale gyres, while a much slower circulation is driven by density differences from temperature and salt. The deep branch carries heat and carbon on a timescale of centuries, which is why its state matters for climate.

Ready when they can: Explain why surface currents form closed gyres rather than following the wind directly; Describe where deep water forms and what makes it dense enough to sink; Estimate the timescale of the deep circulation and say what that implies for climate response.

https://lightmysky.com/learn/science/the-ocean-in-motion-wind-driven-gyres-and-the-deep-overturning-mt_ZaWclUQ-fh

#### Seawater Chemistry: Salinity, the Carbonate System and pH (ages 17-18)

Seawater is a buffered solution whose pH is held by a set of coupled carbonate equilibria, and adding carbon dioxide shifts them all. The same equilibria decide the depth below which carbonate shells dissolve, which links ocean chemistry directly to what can live where.

Ready when they can: Write the carbonate equilibria and explain which species dominates at seawater pH; Predict the effect of dissolving more carbon dioxide on pH and on carbonate ion concentration; Explain why a shell-forming organism is affected by a pH change that sounds small.

https://lightmysky.com/learn/science/seawater-chemistry-salinity-the-carbonate-system-and-ph-mt_BrdrNZmBzE

#### The Carbon Cycle on Two Timescales (ages 17-18)

Carbon moves fast between air, ocean and life, and slowly between rock and everything else through weathering and volcanism. Burning fossil carbon moves an amount that belongs to the slow cycle into the fast one, which is why the surplus takes so long to clear.

Ready when they can: Separate the fast and slow carbon cycles by reservoir and turnover time; Explain how silicate weathering acts as a thermostat over geological time; Estimate how long an added pulse of carbon dioxide stays in the atmosphere, and say what removes it.

https://lightmysky.com/learn/science/the-carbon-cycle-on-two-timescales-mt_OXBubQOPk7

### Ecosystems & Habitats

https://lightmysky.com/learn/science/areas/ecosystems-and-habitats

#### Habitat Vocabulary (ages 6-8)

Name and use vocabulary for where living things are found — habitat, environment, microhabitat, conditions, woodland, ocean, desert, rainforest, pond — and use terms to describe what animals need to survive: food, water, shelter, space, and suitable conditions

Ready when they can: Match animals to their habitats and explain the match using 'adapted to', 'conditions', or 'shelter'; Correctly use 'habitat' and 'microhabitat' to describe different scales of environment with examples; Name at least three contrasting habitats and describe what makes each distinctive.

https://lightmysky.com/learn/science/habitat-vocabulary-mt_Fw0bbM1e_g

#### Ecology Vocabulary (ages 8-10)

Use vocabulary for feeding relationships and ecological roles — producer, consumer, predator, prey, herbivore, carnivore, omnivore, decomposer, food chain, food web, nutrient cycle — and describe how energy and matter flow through ecosystems using these terms

Ready when they can: Construct a food chain correctly using producer, consumer, predator, and prey in the right positions; Distinguish between herbivore, carnivore, and omnivore with correct examples from a given ecosystem; Explain what a decomposer does and why it matters, using the correct vocabulary.

https://lightmysky.com/learn/science/ecology-vocabulary-mt_M7XhBBzYof

#### Human impact on environments (ages 8-11)

Use vocabulary for human impact on the environment — pollution, habitat destruction, deforestation, biodiversity, conservation, renewable energy, non-renewable energy, fossil fuel, carbon footprint, sustainability, endangered, extinct — and apply these when discussing environmental issues and human choices

Ready when they can: Distinguish between renewable and non-renewable energy sources using the correct terms and give examples of each; Use 'biodiversity' and 'conservation' correctly in discussing why protecting habitats matters; Apply 'carbon footprint' and 'sustainability' correctly in a discussion about everyday human choices.

https://lightmysky.com/learn/science/human-impact-on-environments-mt_YB0qF5KX9C

#### Reading Food Web Diagrams (ages 8-9)

Read and interpret food web diagrams — identify producers, primary and secondary consumers, and decomposers; trace energy flow along food chains within the web; predict the effect of removing or adding a species

Ready when they can: Identify the producer, herbivore, and carnivore in a food web from a diagram; Trace two food chains through the same food web and identify shared species; Predict what would happen to fox numbers if rabbits were removed from a food web diagram.

Needs first: Reading and drawing circuit diagrams.

https://lightmysky.com/learn/science/reading-food-web-diagrams-mt_uVaS12lN1i

#### The Water Cycle in Detail (ages 11-12)

Describe the water cycle, tracing water through evaporation, condensation, precipitation, surface runoff, and transpiration in plants, explaining how the sun drives the cycle

Ready when they can: Labels a water cycle diagram correctly; Explains what drives each stage of the water cycle (e.g. solar energy drives evaporation); Explains the role of transpiration (plants releasing water vapour) in the water cycle; Discusses how human activities (deforestation, paving) affect the water cycle.

Needs first: The Water Cycle, Evaporation & the Water Cycle.

https://lightmysky.com/learn/science/the-water-cycle-in-detail-mt_V2lNzEex_a

#### Living, Dead & Never Alive (ages 6-7)

Explore and compare the differences between things that are living, dead, and things that have never been alive

Ready when they can: Sort a collection of objects into three groups: living, dead (was once alive), never alive; Give reasons for each sorting decision (e.g. 'the leaf was on a tree so it was alive once'); List characteristics of living things such as growing, breathing, reproducing, and moving.

Needs first: Common Plants & Trees, Living Things Vocabulary, Naming Common Animals.

https://lightmysky.com/learn/science/living-dead-and-never-alive-mt_Sa48W7KXB5

#### Plants and animals in their habitats (ages 5-6)

Use a model to represent the relationship between the needs of different plants and animals and the places they live, connecting organism needs to habitat features

Ready when they can: Use a simple model (drawing, diagram) to show how a habitat provides what an organism needs; Match at least three organisms to their habitats and explain why each needs that specific place; Describe what would happen if an organism were placed in a habitat that doesn't meet its needs.

Needs first: What Living Things Need.

https://lightmysky.com/learn/science/plants-and-animals-in-their-habitats-mt_e6PP4ip39V

#### Reducing Human Impact (ages 5-6)

Communicate solutions that will reduce the impact of humans on the land, water, air, and other living things in the local environment

Ready when they can: Identify at least three ways humans negatively impact the local environment (litter, pollution, habitat destruction); Propose at least three solutions to reduce human impact (recycling, reducing waste, conserving water, planting trees); Explain how each solution helps protect land, water, air, or living things.

Needs first: Plants and animals in their habitats.

https://lightmysky.com/learn/science/reducing-human-impact-mt_deexfCHU9m

#### Chromosomes, Genes & DNA (ages 12-13)

Describe the relationship between chromosomes, genes, and DNA in heredity, including the double helix structure of DNA and the historical roles of Watson, Crick, Franklin, and Wilkins

Ready when they can: Explains the hierarchy: DNA → gene → chromosome → nucleus → cell; Describes what a gene is and what it codes for; States that human body cells contain 46 chromosomes in 23 pairs; Describes the contributions of Watson, Crick, Franklin, and Wilkins to the discovery of DNA structure.

Needs first: Cells Under the Microscope.

https://lightmysky.com/learn/science/chromosomes-genes-and-dna-mt_6aJUzBYGNs

#### Genetic Mutation (ages 12-14)

Explain genetic mutation as a random change in DNA sequence, describe causes of mutation (e.g. radiation, chemicals, copying errors), and explain that most mutations are neutral, some harmful, and a few beneficial

Ready when they can: Defines mutation as a change to DNA sequence; Names at least two things that can cause mutations (mutagens); Explains that mutations are the original source of all genetic variation; Explains that beneficial mutations can be selected for by natural selection.

Needs first: Chromosomes, Genes & DNA.

https://lightmysky.com/learn/science/genetic-mutation-mt_rOqo-8GeKt

#### Habitats & Basic Needs (ages 6-8)

Identify that most living things live in habitats to which they are suited and describe how habitats provide for basic needs and how organisms depend on each other

Ready when they can: Define a habitat as a place where an organism lives that provides what it needs; Give examples of how specific habitats meet organisms' needs (e.g. pond provides water and food for frogs); Describe at least one way organisms in a habitat depend on each other (e.g. bees pollinate flowers, flowers feed bees).

Needs first: Where Are the Poles?, Habitat Vocabulary, What Is a Rainforest?, What Living Things Need, What Ocean Animals Need, Animal Homes, Living, Dead & Never Alive, Minibeast Habitats.

https://lightmysky.com/learn/science/habitats-and-basic-needs-mt_cM8YS6NXqi

#### Local Plants & Animals (ages 6-8)

Identify and name a variety of plants and animals in their habitats, including microhabitats such as under a log or in a pond

Ready when they can: Name at least three animals and plants found in a specific local habitat; Explain what a microhabitat is (a very small habitat within a larger one); Describe conditions in a microhabitat (e.g. 'under a stone is damp and dark, woodlice like that').

Needs first: Habitats & Basic Needs, Habitat Vocabulary, Rock Pool Habitats, Iconic Rainforest Animals, Minibeast Habitats.

https://lightmysky.com/learn/science/local-plants-and-animals-mt_ppENoD8vf1

#### Simple Food Chains (ages 6-7)

Describe how animals obtain their food from plants and other animals, using the idea of a simple food chain, and identify different sources of food

Ready when they can: Draw a simple food chain with at least three organisms using arrows to show energy flow; Explain that food chains always start with a plant (producer) that makes its own food; Use the terms 'producer' and 'consumer' correctly when describing a food chain.

Needs first: Herbivores, Carnivores & Omnivores, Habitats & Basic Needs, Ocean Food Chains, Minibeasts in the food chain, Iconic Rainforest Animals.

https://lightmysky.com/learn/science/simple-food-chains-mt_EygMHKs8Ed

#### Animal Groups & Survival (ages 8-9)

Construct an argument that some animals form groups that help members survive, such as herds, packs, or colonies

Ready when they can: Give at least two examples of animals that live in groups (e.g. wolves, ants, fish schools); Explain how group living provides survival advantages (protection, finding food, raising young); Construct a simple argument with evidence for why a specific animal benefits from group behaviour.

Needs first: Habitats & Basic Needs, Animal Body Groups, Social insects: ants and bees, Savanna & Grassland Animals.

https://lightmysky.com/learn/science/animal-groups-and-survival-mt_i4bDqjyglj

#### Changing Environments (ages 8-9)

Recognise that environments can change and that this can sometimes pose dangers and challenges to living things

Ready when they can: Give at least two examples of environmental changes (natural and human-caused); Describe how a specific change affects the organisms in that environment; Explain why some organisms may not survive if their environment changes too quickly.

Needs first: Habitats & Basic Needs, Simple Food Chains, Habitat Vocabulary.

https://lightmysky.com/learn/science/changing-environments-mt_Wyd-l-6H7G

#### Food Chains & Energy Transfer (ages 8-9)

Construct and interpret food chains identifying producers, predators, and prey, and understand energy transfer between trophic levels

Ready when they can: Construct a food chain with at least four organisms, labelling producer, primary consumer, predator; Define producer, predator, and prey with examples; Interpret a given food chain to predict what happens if one organism is removed.

Needs first: Rainforest Food Webs, Animal Nutrition, Simple Food Chains, Ecology Vocabulary, Ocean Food Webs.

https://lightmysky.com/learn/science/food-chains-and-energy-transfer-mt_oB-L8EVdIP

#### Grouping Living Things (ages 8-9)

Recognise that living things can be grouped in a variety of ways based on observable features

Ready when they can: Group a set of organisms using at least two different criteria (e.g. by habitat, by body covering, by diet); Explain the reasoning behind each grouping choice; Recognise that the same organism can belong to different groups depending on the criteria used.

Needs first: Animal Classification Vocabulary, Not all minibeasts are insects, Classifying Ocean Animals, Classifying Rainforest Organisms, Local Plants & Animals, Naming Common Animals.

https://lightmysky.com/learn/science/grouping-living-things-mt_AylKwhbDWM

#### Classification Keys (ages 8-9)

Explore and use classification keys to identify, group, and name living things in local and wider environments

Ready when they can: Follow a branching classification key to identify an unknown organism; Create a simple yes/no classification key for a set of 6-8 organisms; Use a key to identify organisms in the local environment during a field activity.

Needs first: Grouping Living Things, Sorting and Identifying Minibeasts.

https://lightmysky.com/learn/science/classification-keys-mt_brgde1Vx0P

#### Animal Life Cycles (ages 9-10)

Describe differences in the life cycles of mammals, amphibians, insects, and birds, comparing metamorphosis with direct development

Ready when they can: Describe the life cycle of a mammal, amphibian, insect, and bird with key stages for each; Compare metamorphosis (complete change of form) with direct development (gradual growth); Identify which groups undergo metamorphosis and which do not.

Needs first: Life Cycles of Organisms, Grouping Living Things, Types of Metamorphosis.

https://lightmysky.com/learn/science/animal-life-cycles-mt_A1Xfu5p5KT

#### Plant & Animal Reproduction (ages 9-10)

Describe the life process of reproduction in some plants and animals, including sexual and asexual reproduction in plants

Ready when they can: Describe sexual reproduction in plants: pollination, fertilisation, seed production; Give examples of asexual reproduction in plants: runners (strawberries), bulbs, cuttings; Compare reproduction in egg-laying animals (birds, frogs) vs live-bearing mammals.

Needs first: Animal Life Cycles, Pollination & Seed Dispersal.

https://lightmysky.com/learn/science/plant-and-animal-reproduction-mt_yNWt3GQBNp

#### Classifying Organisms (ages 10-11)

Describe how living things are classified into broad groups (micro-organisms, plants, animals) according to common observable characteristics, similarities, and differences

Ready when they can: Name the broad classification groups: micro-organisms, plants, animals (and fungi if known); Describe observable characteristics used for classification (e.g. plants make own food, animals move and eat); Give examples of organisms in each group, including micro-organisms like bacteria.

Needs first: Classification Keys.

https://lightmysky.com/learn/science/classifying-organisms-mt_IY3KwGLZgk

#### Food Webs & Interdependence (ages 11-12)

Construct and interpret food webs showing the interdependence of organisms in an ecosystem, explaining how a change in one population affects others

Ready when they can: Draws a food web from given data with arrows showing energy flow direction; Predicts how the population of one species would change if another species increased or decreased; Distinguishes a food web from a food chain and explains why webs are more realistic; Identifies producers, primary consumers, secondary consumers, and apex predators.

Needs first: Food Chains & Energy Transfer, Reading Food Web Diagrams.

https://lightmysky.com/learn/science/food-webs-and-interdependence-mt_URTJbS3hhs

#### Energy Loss Between Levels (ages 11-12)

Explain how energy is transferred between trophic levels in a food chain, why energy is lost at each stage, and use pyramids of biomass/numbers to represent this

Ready when they can: Explains that only about 10% of energy passes from one trophic level to the next; Constructs a pyramid of biomass from data and explains its shape; Identifies where energy is lost at each trophic level (heat, movement, waste); Explains why food chains rarely have more than five trophic levels.

Needs first: Food Webs & Interdependence.

https://lightmysky.com/learn/science/energy-loss-between-levels-mt_BOG5zRYtQz

#### Pollination & Pollinator Decline (ages 11-12)

Explain the importance of insect pollination for plant reproduction and human food security, and discuss the consequences of pollinator decline

Ready when they can: Explains why many food crops depend on insect pollination to produce fruit and seeds; Names examples of crops that require insect pollination (e.g. apples, almonds, oilseed rape); Discusses the potential impact of bee population decline on food production; Connects to plant reproduction — flowers are adapted to attract specific pollinators.

Needs first: Food Webs & Interdependence, Pollination & Seed Dispersal, Threats to insects and conservation.

https://lightmysky.com/learn/science/pollination-and-pollinator-decline-mt_wWpa5fFDZP

#### Species Distribution & Change (ages 12-13)

Explain how environmental change (climate change, habitat loss, pollution) affects the distribution of species, including range shifts, local extinction, and invasive species

Ready when they can: Describes at least two ways environmental change can affect species distribution; Gives a real example of a species whose range has shifted due to climate change; Explains what an invasive species is and how environmental change can enable invasions; Discusses why some species are more vulnerable to environmental change than others.

Needs first: Food Webs & Interdependence, Changing Environments.

https://lightmysky.com/learn/science/species-distribution-and-change-mt_JSUGQ5Repv

#### Toxins Building Up in Food Chains (ages 12-13)

Explain how organisms affect and are affected by their environment, including the bioaccumulation of toxic materials (e.g. pesticides, heavy metals) through food chains

Ready when they can: Defines bioaccumulation and explains why toxins increase in concentration higher up the food chain; Gives a real example of bioaccumulation (e.g. DDT in peregrine falcons, mercury in tuna); Explains how organisms can change their habitat (e.g. earthworms aerating soil, beavers creating wetlands); Discusses why top predators are most at risk from bioaccumulation.

Needs first: Food Webs & Interdependence.

https://lightmysky.com/learn/science/toxins-building-up-in-food-chains-mt_YvCgDM0Scg

#### Variation in Species (ages 12-13)

Explain variation within and between species, distinguishing between continuous variation (e.g. height) and discontinuous variation (e.g. blood group), and between genetic and environmental causes

Ready when they can: Gives examples of continuous and discontinuous variation in humans; Distinguishes between genetic causes of variation (inherited differences) and environmental causes (diet, sunlight, etc.); Explains why sexual reproduction produces greater variation than asexual reproduction; Draws or interprets a frequency graph showing continuous variation.

Needs first: Chromosomes, Genes & DNA, Grouping Living Things, Traits: inherited and environmental.

https://lightmysky.com/learn/science/variation-in-species-mt_k1HXbEwG8f

#### Communities Protecting Resources (ages 10-11)

Obtain and combine information about ways individual communities use science ideas to protect the Earth's resources and environment

Ready when they can: Describe at least three real-world examples of communities protecting resources or the environment; Explain the science ideas behind each example (e.g. solar panels convert sunlight to electricity, reducing fossil fuel use); Discuss how individual actions and community efforts combine to make a difference.

Needs first: Reducing Human Impact, Natural resources, Human impact on environments.

https://lightmysky.com/learn/science/communities-protecting-resources-mt_7e-lG7YOWa

#### Biodiversity & Resilience (ages 12-14)

Explain what biodiversity means, why high biodiversity makes ecosystems more resilient, and describe the ways human activity threatens biodiversity (habitat destruction, pollution, invasive species, climate change)

Ready when they can: Defines biodiversity at the species, genetic, and ecosystem levels; Explains why high biodiversity makes an ecosystem more stable and resilient to disruption; Identifies at least three human activities that reduce biodiversity; Discusses why biodiversity loss matters for humans as well as wildlife.

Needs first: Species Distribution & Change, Food Webs & Interdependence, Communities Protecting Resources, Toxins Building Up in Food Chains.

https://lightmysky.com/learn/science/biodiversity-and-resilience-mt_xSs0xAd6i1

#### Matter Cycling in Ecosystems (ages 10-11)

Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment in an ecosystem

Ready when they can: Describe the role of decomposers (fungi, bacteria, worms) in breaking down dead matter; Trace the movement of matter: plant grows using soil nutrients → animal eats plant → animal dies → decomposers return nutrients to soil; Create or interpret a simple diagram showing matter cycling through an ecosystem.

Needs first: Biodiversity, Food Chains & Energy Transfer, Energy from Food & the Sun, Ocean Ecosystems.

https://lightmysky.com/learn/science/matter-cycling-in-ecosystems-mt_0ajzcoKAKw

#### How Natural Selection Works (ages 12-14)

Explain natural selection as the mechanism of evolution: heritable variation + competition for resources + differential survival and reproduction = change in allele frequency over generations

Ready when they can: Describes the four conditions required for natural selection to operate (variation, heritability, competition, selection); Applies the concept to a specific example (e.g. antibiotic resistance in bacteria, peppered moth); Explains why individuals with advantageous traits leave more offspring; Distinguishes natural selection from evolution (selection is the mechanism; evolution is the result over many generations).

Needs first: Classifying Organisms, Variation in Species, The Red Queen Hypothesis, Dinosaur-to-Bird Transition, Genetic Mutation, Sexual Selection.

https://lightmysky.com/learn/science/how-natural-selection-works-mt_FuVEZ1Ac9s

#### Evidence for Evolution (ages 12-14)

Describe the main types of evidence for evolution: the fossil record (change over time), comparative anatomy (homologous structures), and the geographic distribution of related species

Ready when they can: Explains how fossils form and what they can tell us about past life; Uses the fossil record as evidence that species have changed over time; Describes homologous structures (e.g. pentadactyl limb) as evidence for common ancestry; Explains why island species provide evidence for evolution (e.g. Darwin's finches, Galapagos).

Needs first: How Natural Selection Works.

https://lightmysky.com/learn/science/evidence-for-evolution-mt_ohUnzoI_nx

#### Extinction & Rapid Change (ages 12-14)

Explain how environmental change can outpace a species' ability to adapt through natural selection, leading to extinction, using historical and contemporary examples

Ready when they can: Explains why extinction occurs when environmental change is faster than the rate of adaptation; Gives a historical example (e.g. woolly mammoth, dodo) and a contemporary example of threatened extinction; Distinguishes between background extinction rates and mass extinctions; Explains how human activity (habitat loss, hunting, climate change) is driving current species loss.

Needs first: The Biodiversity Crisis, How Natural Selection Works, Species Distribution & Change.

https://lightmysky.com/learn/science/extinction-and-rapid-change-mt_-r3B4FQyX3

#### The Carbon Cycle (ages 12-13)

Describe the carbon cycle, tracing carbon through photosynthesis, respiration, feeding, decomposition, and combustion, and explain the role of each process

Ready when they can: Draws or labels a diagram of the carbon cycle showing the main processes; Explains how photosynthesis removes carbon dioxide from the atmosphere; Explains how respiration, combustion, and decomposition return carbon dioxide to the atmosphere; Discusses how human activities (burning fossil fuels, deforestation) disrupt the carbon cycle.

Needs first: Matter Cycling in Ecosystems, Aerobic Respiration, Food Webs & Interdependence, Photosynthesis, Nutrient Cycling in Thin Soil.

https://lightmysky.com/learn/science/the-carbon-cycle-mt_Be1A88GUpu

#### Evidence-Based Classification (ages 10-11)

Give reasons for classifying plants and animals based on specific characteristics, using evidence to justify classification decisions

Ready when they can: Classify an unfamiliar organism using specific observable characteristics with reasoning; Compare two similar organisms and explain which characteristics distinguish their classification; Justify a classification decision using at least two pieces of evidence from observation.

Needs first: Structures for Survival, Classifying Organisms.

https://lightmysky.com/learn/science/evidence-based-classification-mt_B8lX8OCzGu

#### Predicting Inherited Traits (ages 13-14)

Explain how alleles are inherited in sexual reproduction and use Punnett squares to predict the probability of offspring inheriting a characteristic, including dominant and recessive alleles

Ready when they can: Defines allele, dominant, and recessive in the context of inheritance; Constructs a Punnett square for a monohybrid cross and calculates probability ratios; Explains the difference between genotype and phenotype; Gives an example of a human characteristic controlled by dominant/recessive alleles.

Needs first: DNA & Genes, Chromosomes, Genes & DNA.

https://lightmysky.com/learn/science/predicting-inherited-traits-mt_o7FJPDsHiW

### Energy

https://lightmysky.com/learn/science/areas/energy

#### Sunlight warms things up (ages 5-6)

Make observations to determine the effect of sunlight on Earth's surface, noticing that sunlight warms the ground, water, and objects

Ready when they can: Observe that surfaces in sunlight feel warmer than those in shade; Describe that sunlight provides warmth (heat energy) to Earth's surface; Compare temperatures of surfaces in sun vs shade using touch or a thermometer.

Needs first: Seasonal changes.

https://lightmysky.com/learn/science/sunlight-warms-things-up-mt_iGSfQg3g5c

#### Naming types of energy (ages 7-9)

Name and use vocabulary for types of energy and energy transfer — kinetic energy, potential energy, heat energy, light energy, sound energy, electrical energy, chemical energy, stored energy, energy transfer, energy transformation — and describe energy changes in familiar situations using these terms

Ready when they can: Name the type of energy stored in a battery, a stretched spring, and a moving ball; Use 'energy transfer' or 'energy transformation' to describe what happens in a simple device such as a torch or a toaster; Distinguish between 'stored energy' and 'transferred energy' with a correct example of each.

https://lightmysky.com/learn/science/naming-types-of-energy-mt_akBotspaf2

#### What uses electricity at home (ages 8-9)

Identify common appliances that run on electricity and understand that electricity is a form of energy that powers devices in everyday life

Ready when they can: Name at least ten common appliances that run on electricity; Distinguish between mains-powered and battery-powered appliances; Explain that electricity provides the energy that makes these devices work.

https://lightmysky.com/learn/science/what-uses-electricity-at-home-mt_9nxyFoYD_b

#### Building a simple circuit (ages 8-9)

Construct a simple series electrical circuit, identifying and naming its basic parts: cells, wires, bulbs, switches, and buzzers

Ready when they can: Build a complete series circuit that lights a bulb or sounds a buzzer; Name each component: cell (battery), wire, bulb, switch, buzzer; Explain the role of each component in making the circuit work.

Needs first: What uses electricity at home.

https://lightmysky.com/learn/science/building-a-simple-circuit-mt_DA7-JYRvtP

#### Conductors and insulators (ages 8-9)

Recognise some common conductors and insulators, and associate metals with being good conductors of electricity

Ready when they can: Define conductors (allow electricity to flow through) and insulators (block electricity); Test at least six materials and correctly classify them as conductors or insulators; State that metals are generally good conductors and explain why wires are made of metal with plastic coating.

Needs first: Building a simple circuit.

https://lightmysky.com/learn/science/conductors-and-insulators-mt_d-EKO-pKkP

#### Will the bulb light up? (ages 8-9)

Identify whether or not a lamp will light in a simple series circuit, based on whether the lamp is part of a complete loop with a battery

Ready when they can: Predict whether a lamp will light by tracing the circuit for a complete loop; Explain that a gap anywhere in the circuit breaks the loop and the bulb won't light; Identify the fault in a non-working circuit (e.g. loose wire, missing connection).

Needs first: Building a simple circuit.

https://lightmysky.com/learn/science/will-the-bulb-light-up-mt_NNNbPccwB4

#### How switches work (ages 8-9)

Recognise that a switch opens and closes a circuit, controlling whether a lamp lights or a buzzer sounds

Ready when they can: Explain that a closed switch completes the circuit (current flows) and an open switch breaks it (current stops); Demonstrate adding a switch to a circuit and using it to control a bulb or buzzer; Relate the switch concept to everyday switches in the home.

Needs first: Will the bulb light up?.

https://lightmysky.com/learn/science/how-switches-work-mt_Hah24nbToi

#### Circuit vocabulary (ages 9-11)

Use technical vocabulary for electrical circuits — circuit, component, cell, battery, current, voltage, resistance, conductor, insulator, switch, series circuit, parallel circuit — and apply these when describing, drawing, and designing working circuits

Ready when they can: Use 'series' and 'parallel' correctly to describe two different circuit configurations and explain the key difference; Apply 'current', 'voltage', and 'resistance' correctly in a written description of how a circuit works; Name at least six standard circuit components and describe what each one does.

Needs first: Building a simple circuit.

https://lightmysky.com/learn/science/circuit-vocabulary-mt_NzCNuABT3E

#### Reading and drawing circuit diagrams (ages 9-10)

Draw and read simple circuit diagrams using standard symbols for cells, bulbs, switches, buzzers, and wires; identify whether a circuit is complete or broken from a diagram; match circuit diagrams to physical circuits

Ready when they can: Draw a circuit diagram for a cell, switch, and bulb using standard symbols; Identify from a diagram whether a switch is open or closed and predict whether the bulb lights; Match a photograph of a physical circuit to the correct circuit diagram from a set of options.

Needs first: Building a simple circuit.

https://lightmysky.com/learn/science/reading-and-drawing-circuit-diagrams-mt_loYPGHJ8lm

#### How energy travels around (ages 9-10)

Observe and provide evidence that energy can be transferred from place to place by sound, light, heat, and electric currents

Ready when they can: Give at least one example of energy transfer by each: sound, light, heat, electric current; Explain that energy moves from a source to a destination through these means; Describe how electric currents transfer energy from a battery to a bulb through wires.

Needs first: Light & Seeing in the Dark, Naming types of energy, Building a simple circuit, Vibrations & Sound.

https://lightmysky.com/learn/science/how-energy-travels-around-mt_X_aDUBh-HF

#### Building an energy-converting device (ages 9-10)

Apply scientific ideas to design, test, and refine a device that converts energy from one form to another

Ready when they can: Design a device that converts one form of energy to another (e.g. electrical to light, kinetic to sound); Build, test, and identify what works well and what needs improvement; Explain the energy conversion taking place in the device.

Needs first: How energy travels around.

https://lightmysky.com/learn/science/building-an-energy-converting-device-mt_K1-HopEJAB

#### More batteries, brighter bulb (ages 10-11)

Associate the brightness of a lamp or volume of a buzzer with the number and voltage of cells used in a series circuit

Ready when they can: Describe the pattern: more cells (or higher voltage) = brighter bulb / louder buzzer; Explain that more cells provide more energy to the circuit; Predict the effect of changing the number of cells on a component's behaviour.

Needs first: How switches work, Circuit vocabulary, How energy travels around.

https://lightmysky.com/learn/science/more-batteries-brighter-bulb-mt_vFT_GbkP9m

#### Why circuit components behave differently (ages 10-11)

Compare and give reasons for variations in how circuit components function, including brightness of bulbs, loudness of buzzers, and switch positions

Ready when they can: Explain why adding more components in series reduces brightness/loudness (energy shared); Compare circuits with different configurations and predict component behaviour; Give reasoned explanations for observed variations in component function.

Needs first: Circuit vocabulary, More batteries, brighter bulb.

https://lightmysky.com/learn/science/why-circuit-components-behave-differently-mt_-QY08-88rw

#### Drawing circuits with proper symbols (ages 10-11)

Use recognised symbols when representing a simple circuit in a diagram, including cell, wire, bulb, switch, buzzer, and motor

Ready when they can: Draw a circuit diagram using standard symbols for at least five components; Interpret a circuit diagram drawn by someone else and describe what the circuit does; Convert between a physical circuit and its diagram representation.

Needs first: Why circuit components behave differently, More batteries, brighter bulb, Reading and drawing circuit diagrams.

https://lightmysky.com/learn/science/drawing-circuits-with-proper-symbols-mt_NzNLYDb9CZ

#### Current, voltage, and what they measure (ages 11-12)

Understand that electric current is the rate of flow of charge (measured in amperes using an ammeter), and that potential difference (voltage) is the energy transferred per unit charge (measured in volts using a voltmeter)

Ready when they can: States that current is measured in amperes (A) and is the rate at which charge flows around a circuit; States that potential difference (voltage) is measured in volts (V) and represents energy transferred per unit charge; Correctly connects an ammeter in series and a voltmeter in parallel when building or interpreting a circuit.

Needs first: Circuit vocabulary, Drawing circuits with proper symbols, More batteries, brighter bulb.

https://lightmysky.com/learn/science/current-voltage-and-what-they-measure-mt_2bnXrfS4Iq

#### Static electricity and sparks (ages 11-12)

Explain static electricity as the build-up of electric charge through friction, describe how charged objects attract or repel each other, and relate static discharge to everyday phenomena such as lightning

Ready when they can: Explains that rubbing transfers electrons from one material to another, creating opposite charges; States that like charges repel and unlike charges attract; Links the concept of static discharge to the formation of lightning as a large-scale electric spark.

Needs first: Current, voltage, and what they measure, Conductors and insulators.

https://lightmysky.com/learn/science/static-electricity-and-sparks-mt_2_YoprauaJ

#### Ohm's Law: voltage, current, resistance (ages 12-13)

Apply Ohm's Law (V = IR) to calculate current, voltage, or resistance in a simple circuit, and explain that resistance opposes the flow of current

Ready when they can: States Ohm's Law as V = IR and identifies the units for each quantity; Rearranges V = IR to find the unknown value given the other two; Explains that resistance opposes current flow and identifies factors that affect resistance (material, length, thickness).

Needs first: Current, voltage, and what they measure.

https://lightmysky.com/learn/science/ohms-law-voltage-current-resistance-mt_H3ZDK0EYNV

#### Series vs parallel circuits (ages 12-13)

Describe and apply the rules for current, voltage, and resistance in series and parallel circuits, and explain the practical uses of each circuit type

Ready when they can: States the rules for current and voltage in series circuits (current same everywhere; voltages add up); States the rules for current and voltage in parallel circuits (voltages same across each branch; currents add up); Explains why household wiring uses parallel circuits and identifies the advantage of each type.

Needs first: Ohm's Law: voltage, current, resistance, Circuit vocabulary, Why circuit components behave differently.

https://lightmysky.com/learn/science/series-vs-parallel-circuits-mt_loEMaQ8kFA

#### Current-Voltage Graphs for Components (ages 14-15)

Measuring current against potential difference for a fixed resistor, a filament lamp and a diode, then reading each graph's shape. A straight line means constant resistance, and a bend means the resistance is changing.

Ready when they can: Builds a test circuit with an ammeter in series and a voltmeter across the component; Plots current against potential difference for both directions and describes the shape; Explains the lamp's curve by its filament heating up, and the diode's shape by current in one direction only.

https://lightmysky.com/learn/science/current-voltage-graphs-for-components-mt_n_CiOa-05J

#### Resistance in Series and Parallel (ages 14-16)

Resistances in series add, while adding a parallel branch lowers the total resistance and raises the current drawn from the supply. Each rule is checked against measurements rather than taken on trust.

Ready when they can: Calculates the total resistance of resistors in series and predicts the current; Explains why two identical resistors in parallel halve the total resistance; Predicts what happens to supply current when a lamp is added in parallel, and checks it in a circuit.

https://lightmysky.com/learn/science/resistance-in-series-and-parallel-mt_B29m3h5B75

#### Thermistors, Light-Dependent Resistors and Sensing Circuits (ages 15-16)

A thermistor's resistance falls as it warms and a light-dependent resistor's falls as light on it rises, so either one placed in a potential divider turns a physical change into a changing voltage. That voltage is what a heating controller or a street light switches on.

Ready when they can: Sketches how the resistance of a thermistor and of a light-dependent resistor change with temperature and with light; Predicts which way the output voltage of a two-resistor divider moves when one of the two changes; Designs a circuit that switches something on when a room gets cold or dark, and says which component senses what.

https://lightmysky.com/learn/science/thermistors-light-dependent-resistors-and-sensing-circuits-mt_d92v1CiqIG

#### Resistivity and What Sets a Wire's Resistance (ages 16-17)

A wire's resistance grows with its length and falls with its cross-section, and dividing out both leaves a number belonging to the material alone. That number is why copper is used for cables and why a strain gauge works at all.

Ready when they can: Predicts how resistance changes when a wire is stretched, doubled in length or swapped for a thicker one; Calculates a resistivity from measurements of resistance, length and diameter, with the diameter squared handled correctly; Compares two materials by resistivity and says which suits a heating element and which a connecting lead.

https://lightmysky.com/learn/science/resistivity-and-what-sets-a-wires-resistance-mt_A4f8THP-xm

#### Speed and energy (ages 9-10)

Use evidence to construct an explanation relating the speed of an object to the energy of that object

Ready when they can: Explain that a moving object has energy, and the faster it moves the more energy it has; Provide evidence from observations (e.g. faster ball causes more damage/movement); Use the term 'kinetic energy' or 'energy of motion' appropriately.

Needs first: Naming types of energy, Pushes & Pulls.

https://lightmysky.com/learn/science/speed-and-energy-mt_2Um22lTBZV

#### What happens when things collide (ages 9-10)

Ask questions and predict outcomes about the changes in energy that occur when objects collide

Ready when they can: Predict the outcome of a collision based on the speeds and sizes of the objects; Explain that energy transfers from one object to another during a collision; Describe observable changes: one object speeds up, the other slows down, sound is produced.

Needs first: Speed and energy.

https://lightmysky.com/learn/science/what-happens-when-things-collide-mt_1MLi55bPnt

#### Electromagnetic Induction and Generators (ages 12-14)

Explain how moving a coil of wire in a magnetic field produces a current (the generator effect), how power-station generators use spinning coils to make alternating current, and how Faraday's experiments led to the electric generator

Ready when they can: Describe that a current is produced when a wire or coil moves through a magnetic field, or the field around it changes; Predict how to induce a bigger current (move faster, add turns to the coil, use a stronger magnet) and what happens when the motion stops; Explain why a generator produces alternating current, linking it to a real example such as a bike dynamo or a power-station turbine.

Needs first: Electromagnets, Current, voltage, and what they measure, Motors & the Motor Effect.

https://lightmysky.com/learn/science/electromagnetic-induction-and-generators-mt_e0jgUKANT-

#### Energy stores and transfers (ages 11-12)

Identify the main energy stores (kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, electromagnetic) and the pathways by which energy is transferred between stores (mechanically, electrically, by heating, by radiation)

Ready when they can: Names and describes at least five energy stores with a real-world example of each; Identifies the energy stores at the start and end of a given process (e.g. a falling ball, a burning match); Describes the transfer pathway connecting two energy stores in a given scenario; Traces energy through a system identifying all stores and transfers involved.

Needs first: Speed and energy, Naming types of energy, Greenhouse Gas Science, How energy travels around.

https://lightmysky.com/learn/science/energy-stores-and-transfers-mt_Jvg_r4yWaY

#### Energy can't be created or destroyed (ages 11-12)

Explain the principle of conservation of energy (energy cannot be created or destroyed, only transferred between stores), and describe how energy is dissipated as thermal energy to the surroundings in all real processes

Ready when they can: States the law of conservation of energy; Explains why the total energy in a closed system is always the same even though it changes form; Explains what dissipation means and why it happens in real machines (friction, air resistance); Gives an example showing why 'wasted' energy is not lost but transferred to the surroundings.

Needs first: Naming types of energy, Energy stores and transfers.

https://lightmysky.com/learn/science/energy-cant-be-created-or-destroyed-mt_68pIoiiG4g

#### Efficiency, Sankey diagrams, and work done (ages 12-13)

Calculate energy efficiency as the ratio of useful output energy to total input energy, construct and interpret Sankey diagrams, and calculate work done using work = force × distance

Ready when they can: Calculates efficiency as a percentage from given input and useful output energy values; Draws a Sankey diagram to represent energy transfers in a device, with arrow widths proportional to energy amounts; Uses W = Fd to calculate work done when a force moves through a distance; Identifies which energy transformations in a Sankey diagram are useful and which are wasted.

Needs first: Energy can't be created or destroyed, Resultant Forces, Calculating Percentages.

https://lightmysky.com/learn/science/efficiency-sankey-diagrams-and-work-done-mt_JyfLtl_nhw

#### Heating experiments and Q = mcΔT (ages 12-13)

Plan and carry out experiments to measure energy transferred during heating, including using the equation Q = mcΔT, recording temperature changes over time, and evaluating sources of error

Ready when they can: Uses a thermometer and stopwatch to record temperature change over time in a heating experiment; Applies Q = mcΔT to calculate the energy transferred to a substance being heated; Identifies sources of energy loss in a heating experiment (e.g. heat to surroundings) and suggests improvements; Plots a temperature-time graph and identifies the energy transfer rate from its gradient.

Needs first: Efficiency, Sankey diagrams, and work done.

https://lightmysky.com/learn/science/heating-experiments-and-q-mc-t-mt_DI1cyAyGyN

#### Power: watts and energy per second (ages 12-13)

Define power as the rate of energy transfer (power = energy ÷ time, measured in watts), and compare energy transfer rates in different everyday contexts

Ready when they can: States the definition of power and gives its unit (watt); Uses P = E/t to calculate power, energy, or time given the other two quantities; Compares the power ratings of common appliances and explains what the rating means; Explains why a higher-powered device does the same job faster but uses more energy.

Needs first: Energy can't be created or destroyed.

https://lightmysky.com/learn/science/power-watts-and-energy-per-second-mt_ckpA3oZQ44

#### Electrical Power and the Cost of Running Appliances (ages 14-15)

Power in a circuit is potential difference times current, and also current squared times resistance. Energy transferred is power times time, which is what the kilowatt-hour on an electricity bill counts.

Ready when they can: Calculates the power of an appliance from its voltage and current, or from its current and resistance; Works out energy transferred in joules and in kilowatt-hours over a stated time; Costs a week of using an appliance given a price per kilowatt-hour.

https://lightmysky.com/learn/science/electrical-power-and-the-cost-of-running-appliances-mt_099G0drIbk

#### Calculating Work Done and Power (ages 15-16)

Work done is force times the distance moved along the force, measured in joules, and power is the work done each second, measured in watts. For steady motion the two combine as power equals force times speed.

Ready when they can: Calculates work done when a force drags, lifts or pushes something a stated distance; Converts between joules, watts and seconds to find any missing quantity; Explains why carrying a bag horizontally does no work against the lifting force.

https://lightmysky.com/learn/science/calculating-work-done-and-power-mt_udulQxseg1

#### Kinetic and Gravitational Potential Stores (ages 15-16)

Two energy stores get equations: half times mass times speed squared for movement, and mass times gravitational field strength times height for position. Falls, ramps and swings are then tracked as energy moving between the two.

Ready when they can: Calculates the kinetic store of a moving object and the gravitational store of a raised one; Equates the two stores to find a landing speed or a rise height; Explains why doubling the speed makes the kinetic store four times larger.

https://lightmysky.com/learn/science/kinetic-and-gravitational-potential-stores-mt_uD3jklaZCw

#### Work Done by a Force at an Angle (ages 16-18)

Only the part of a force along the displacement does work, which gives W = Fs cos theta. A force at right angles to the motion, such as the string tension on a whirled object, does none at all.

Ready when they can: Calculates work done when the force and the displacement are not in line; States the work done by a perpendicular force as zero and gives a worked example of one; Reads work done off a force-displacement graph as the area beneath it.

https://lightmysky.com/learn/science/work-done-by-a-force-at-an-angle-mt_OvBtur6dW5

#### Electromotive Force, Internal Resistance and the Potential Divider (ages 17-18)

A real source has resistance of its own, so the voltage across its terminals drops as it delivers more current and the missing part heats the source. Two resistors across a supply share that voltage in the ratio of their resistances, which is how a fixed supply is turned into whatever voltage a circuit needs.

Ready when they can: Explains why terminal potential difference falls as current rises and gets the internal resistance from a graph of the two; Calculates the output of a potential divider and predicts how it moves when one resistance changes; Says where the energy lost inside a source goes and why a battery warms when it is heavily loaded.

https://lightmysky.com/learn/science/electromotive-force-internal-resistance-and-the-potential-divider-mt_g3zYJ9qC53

#### Power as Force Times Velocity, and Efficiency (ages 17-18)

Dividing work by time when the force is steady gives P = Fv, which reads power straight off a speed. Efficiency then compares the useful output with the total input for the same machine.

Ready when they can: Uses P = Fv for a vehicle held at constant speed against a stated resistive force; Moves between the work-over-time and force-times-velocity forms and says when each is easier; Calculates efficiency as a ratio and names where the rest of the input went.

https://lightmysky.com/learn/science/power-as-force-times-velocity-and-efficiency-mt_2FFGLIjgV6

#### Work as a Line Integral Along a Path (ages 18-19)

When force varies along the route, work is the integral of the force component along the displacement rather than a product. The work-energy theorem then follows from the equation of motion instead of being quoted.

Ready when they can: Computes the work done by a varying force as an integral along a stated path; Derives the work-energy theorem from Newton's second law; Explains why only the component of force along the motion contributes.

https://lightmysky.com/learn/science/work-as-a-line-integral-along-a-path-mt_UFuQUPGAt7

#### Conservative Forces and the Potential Energy Function (ages 18-19)

A force whose work depends only on the endpoints defines a potential energy, and the force is recovered as minus the derivative of that function. Friction fails the test, which is why no friction potential exists.

Ready when they can: Tests whether a stated force is conservative by comparing work along different paths; Builds the potential energy function for gravity and for a spring by integrating the force; Recovers a force from a potential energy function by differentiating.

https://lightmysky.com/learn/science/conservative-forces-and-the-potential-energy-function-mt__053R9wrQy

#### Potential Energy Curves, Turning Points and Stability (ages 18-20)

A plot of potential energy against position tells the whole story of one-dimensional motion: turning points where the curve meets the total energy, and minima that are stable equilibria. The curvature at a minimum sets how fast small oscillations run.

Ready when they can: Marks the turning points and the allowed region on a potential energy curve for a given total energy; Classifies equilibria as stable or unstable from the shape of the curve; Predicts the direction of the force at any point from the slope of the curve.

https://lightmysky.com/learn/science/potential-energy-curves-turning-points-and-stability-mt_ZgRbrDaQzh

#### Specific Heat Capacity as a Material Property (ages 15-16)

Specific heat capacity is a number belonging to a material, and rearranging Q = mc times temperature change turns it into predictions. It explains storage heaters, why water is used as a coolant, and why the sea warms slowly.

Ready when they can: Rearranges the equation to find energy, mass, capacity or temperature change; Compares two materials of equal mass given the same energy and says which warms more; Justifies a material choice for a heater, a coolant or a cooking pan using its capacity.

https://lightmysky.com/learn/science/specific-heat-capacity-as-a-material-property-mt_mXC9IKom3P

#### Internal Energy, Absolute Zero and the Kelvin Scale (ages 16-17)

Internal energy is the total kinetic and potential energy of the particles in a body, counted over their random motion rather than the motion of the body as a whole. Absolute zero is where that random kinetic energy is as low as it can go, and the kelvin scale starts there.

Ready when they can: Separates internal energy from the kinetic energy of the whole object; Converts between degrees Celsius and kelvin and explains why a difference is the same size in both; Says which part of the internal energy changes during melting, when the temperature does not.

https://lightmysky.com/learn/science/internal-energy-absolute-zero-and-the-kelvin-scale-mt_n4Ku8ZDy1U

#### Specific Heat Capacity and Specific Latent Heat in Calculations (ages 15-17)

Warming a substance takes m c delta theta, while changing its state takes m L with no temperature change at all. A heating curve is read as a run of these two calculations taken in order.

Ready when they can: Works a multi-stage problem that both warms and melts a sample; Reads a temperature-time graph and names the flat sections as changes of state; Uses a heater's power and running time as the energy supplied, and comments on losses to the surroundings.

https://lightmysky.com/learn/science/specific-heat-capacity-and-specific-latent-heat-in-calculations-mt_GKNPAJgroW

#### Conduction, convection, and radiation (ages 12-13)

Describe and compare the three mechanisms of heat transfer — conduction (particle vibration through solids), convection (fluid movement in liquids/gases), and radiation (infrared waves) — and explain that the rate of transfer depends on temperature difference

Ready when they can: Explains the particle-level mechanism for conduction and why metals are good conductors; Describes a convection current using particle theory and gives a real-world example; Explains that all objects emit and absorb infrared radiation and how surface colour affects this; States that a greater temperature difference increases the rate of heat transfer.

Needs first: The Particle Model, Energy stores and transfers.

https://lightmysky.com/learn/science/conduction-convection-and-radiation-mt_ySnOkVIu22

#### Renewable vs non-renewable energy (ages 12-14)

Distinguish between renewable energy resources (solar, wind, hydroelectric, tidal, geothermal, biomass) and non-renewable resources (coal, oil, gas, nuclear), comparing their advantages, disadvantages, and environmental impacts

Ready when they can: Lists at least four renewable and three non-renewable energy resources; Explains what makes a resource renewable or non-renewable; Compares the environmental impact of at least two different energy sources (e.g. wind vs coal); Discusses trade-offs between cost, reliability, and environmental impact in choosing energy resources.

Needs first: Energy stores and transfers, Earth's Atmosphere & CO2.

https://lightmysky.com/learn/science/renewable-vs-non-renewable-energy-mt_w2A8D76ymp

#### Building shade from the sun (ages 5-6)

Use tools and materials to design and build a structure that will reduce the warming effect of sunlight on an area, such as a shade or shelter

Ready when they can: Design a structure intended to reduce the warming effect of sunlight on an area; Build the structure using available materials and test whether it reduces temperature; Compare the temperature in the shaded area vs an unshaded area as evidence of effectiveness.

Needs first: Modelling with Sketches, Sunlight warms things up.

https://lightmysky.com/learn/science/building-shade-from-the-sun-mt_2agkUcdah9

#### Mains Electricity: a.c., Earthing and Fuses (ages 14-15)

Mains supply is alternating, changing direction many times a second, unlike the direct current from a cell. The live, neutral and earth wires each have a job, and a fuse or breaker cuts the circuit when the current climbs too high.

Ready when they can: States the difference between alternating and direct current and names the mains voltage and frequency; Describes what each of the three wires in a plug does and why the live one is dangerous even when a switch is off; Chooses a suitable fuse rating for an appliance from its power and explains how earthing plus a fuse work together.

https://lightmysky.com/learn/science/mains-electricity-a-c-earthing-and-fuses-mt_jKTotBL78P

#### Transformers and the National Grid (ages 14-16)

A transformer uses a changing magnetic field to raise or lower an alternating voltage, in the ratio of the turns on its two coils. The grid steps voltage up for transmission because a smaller current wastes less energy heating the cables.

Ready when they can: Uses the turns ratio to find an output voltage, and states why a transformer does nothing with direct current; Applies power in equals power out for an ideal transformer to find the secondary current; Explains why transmitting at high voltage and low current cuts the energy wasted in the cables.

https://lightmysky.com/learn/science/transformers-and-the-national-grid-mt_ExV4Kc_7_P

#### Static Charge and Electric Fields (ages 14-16)

Rubbing moves electrons between surfaces, leaving one negative and the other positive, and like charges push apart. Around any charge is a field, and a strong enough field makes the air itself conduct, which is the spark.

Ready when they can: Explains a charged object in terms of electrons moved, never protons; Draws field lines around a positive and a negative charge with arrows the right way; Links a large potential difference across a small gap to a strong field and a spark, and gives an everyday example.

https://lightmysky.com/learn/science/static-charge-and-electric-fields-mt_6ii6CVOTI5

#### Coulomb's Law and the Electric Field of a Point Charge (ages 16-17)

Two point charges push or pull with a force that also falls off as the inverse square, but this one comes with two signs. Field strength is the force per coulomb on a small positive test charge.

Ready when they can: Calculates the force between two point charges and reads its direction from the signs; Finds E as force per coulomb and as kQ over r squared, and gives both units it is quoted in; Compares the electric and gravitational forces between two protons and comments on the ratio.

https://lightmysky.com/learn/science/coulombs-law-and-the-electric-field-of-a-point-charge-mt_p7FuzIsQch

#### Electric Potential and the Uniform Field Between Plates (ages 16-18)

Between parallel plates the field is uniform and equals V over d, so a charge crossing the gap gains energy QV. Around a point charge the potential is kQ over r, and it takes the sign of the charge.

Ready when they can: Uses E = V over d for the field between plates and states the unit volts per metre; Calculates the work done moving a charge through a potential difference as QV; Sketches equipotentials for plates and for a point charge and says how they meet the field lines.

https://lightmysky.com/learn/science/electric-potential-and-the-uniform-field-between-plates-mt_LKTfeYxNde

#### Capacitance and the Energy Stored in a Capacitor (ages 16-18)

Capacitance is the charge a component holds per volt across it. Because the charge builds as the voltage rises, the stored energy is half of QV, the area under the charge-voltage line.

Ready when they can: Uses C = Q over V and works comfortably in microfarads and nanofarads; Finds the stored energy from the area under a charge-voltage graph and from half CV squared; Explains why the energy is not QV, arguing from the graph rather than from the formula.

https://lightmysky.com/learn/science/capacitance-and-the-energy-stored-in-a-capacitor-mt_j1Eltr9z6l

#### Discharging a Capacitor and the Time Constant (ages 17-18)

A capacitor discharging through a resistor loses charge at a rate set by the charge still on it, so voltage, charge and current all fall exponentially. The product RC is the time taken to fall to about 37 per cent.

Ready when they can: Predicts the voltage after a stated number of time constants and reads RC off a decay curve; Uses the exponential form to find either a remaining charge or an elapsed time; Plots the natural log of voltage against time and takes RC from the gradient of the straight line.

https://lightmysky.com/learn/science/discharging-a-capacitor-and-the-time-constant-mt_5sjDPudyad

#### Magnetic Flux, Flux Linkage and Faraday's Law (ages 17-18)

Flux is the amount of field passing through an area, and flux linkage counts that once for every turn of a coil. The induced emf is equal to the rate at which the linkage changes.

Ready when they can: Calculates flux as BA cos theta and flux linkage as the number of turns times the flux; Finds an induced emf from the gradient of a flux linkage against time graph; Explains why a coil turning in a steady field still has a changing linkage.

https://lightmysky.com/learn/science/magnetic-flux-flux-linkage-and-faradays-law-mt_ZoN5JePCpt

#### Lenz's Law and the Alternating-Current Generator (ages 17-18)

An induced current always flows so as to oppose the change that produced it, which is conservation of energy written out for induction. A coil turning steadily in a field therefore gives an emf that varies as a sine curve.

Ready when they can: Predicts the direction of an induced current and names the change it opposes; Argues that the opposite sign would let a machine make energy from nothing; Relates the peak emf and the frequency of a generator output to how the coil is turning.

https://lightmysky.com/learn/science/lenzs-law-and-the-alternating-current-generator-mt_69u-fTOSku

### Weather & Climate

https://lightmysky.com/learn/science/areas/weather-and-climate

#### Temperature & Thermometers (ages 5-7)

Understand temperature as how hot or cold something is, that a thermometer measures temperature, and use words like hot, warm, cool, and cold to describe how the air feels on different days

Ready when they can: Explain that temperature describes how hot or cold something is; Identify a thermometer as the tool used to measure temperature; Use words like hot, warm, cool, and cold appropriately to describe air temperature.

https://lightmysky.com/learn/science/temperature-and-thermometers-mt_PrWc-HZzDl

#### Types of Weather (ages 5-7)

Identify and describe different types of weather — sunny, rainy, windy, snowy, cloudy, foggy, stormy — and describe what the weather is like today using simple vocabulary

Ready when they can: Name at least five types of weather; Describe today's weather accurately using appropriate vocabulary; Match weather types to simple pictures or symbols.

https://lightmysky.com/learn/science/types-of-weather-mt_jc9k_HJQGd

#### Dressing for the Weather (ages 5-7)

Choose appropriate clothing and equipment for different weather conditions — coat and umbrella for rain, sun hat and sunscreen for hot sun, warm layers for cold — understanding that weather affects what we do and how we prepare each day

Ready when they can: Select appropriate clothing for at least three different weather conditions; Explain why certain clothes or equipment are needed for specific weather; Describe how weather affects daily activities like playtime, walking to school, or outdoor events.

Needs first: Types of Weather, Temperature & Thermometers.

https://lightmysky.com/learn/science/dressing-for-the-weather-mt_Dj2xr8CoI0

#### Rain & Puddles (ages 5-7)

Know that rain falls from clouds in the sky, that puddles disappear because water goes back into the air, and that this is part of how water moves around — up into the sky and back down again

Ready when they can: State that rain falls from clouds; Explain that puddles disappear because the water goes into the air; Describe the basic idea that water goes up and comes back down in a repeating process.

Needs first: Types of Weather.

https://lightmysky.com/learn/science/rain-and-puddles-mt_TlLE4cZgOr

#### Seasons & Weather Patterns (ages 5-7)

Know that weather changes with the seasons — spring brings rain and new growth, summer is warmest with long days, autumn brings cooling and falling leaves, winter is coldest with short days — and that this pattern repeats every year

Ready when they can: Name the four seasons and describe typical weather for each; Explain that days are longer in summer and shorter in winter; State that the seasonal pattern repeats every year.

Needs first: Seasonal changes, Types of Weather.

https://lightmysky.com/learn/science/seasons-and-weather-patterns-mt_fI-8iqf_Id

#### Storm Safety (ages 5-7)

Know basic storm safety: during thunder and lightning, go indoors or into a car, stay away from trees and water; understand that storms can be frightening but there are ways to stay safe

Ready when they can: State at least two safety rules for thunderstorms; Explain why going indoors is the safest option during lightning; Describe that storms are natural events and there are ways to stay safe.

Needs first: Types of Weather.

https://lightmysky.com/learn/science/storm-safety-mt_4pLvMN8uzL

#### Weather Forecasting & Safety (ages 5-6)

Ask questions to obtain information about the purpose of weather forecasting and how people prepare for and respond to severe weather

Ready when they can: Explain that weather forecasts help people plan and stay safe; Describe how people prepare for at least two types of severe weather (storm, flood, heat wave, blizzard); Ask relevant questions about weather hazards and find answers from appropriate sources.

Needs first: Seasonal changes.

https://lightmysky.com/learn/science/weather-forecasting-and-safety-mt_URezjbU-6f

#### What Is Wind? (ages 5-7)

Know that wind is moving air, that it can be gentle (a breeze) or very strong (a gale), and that wind can move things like leaves, kites, flags, and even push people

Ready when they can: Define wind as air that is moving; Describe the difference between a gentle breeze and a strong wind; Give examples of things that wind can move or affect.

https://lightmysky.com/learn/science/what-is-wind-mt_j7cj9eWN7w

#### Cloud Types (ages 7-9)

Identify the three main cloud types — cumulus (fluffy, fair weather), stratus (flat layers, overcast or drizzle), and cirrus (thin wisps, high up) — and understand that clouds form when water vapour in the air cools and condenses into tiny droplets

Ready when they can: Name and describe the three main cloud types: cumulus, stratus, cirrus; Explain that clouds form when water vapour cools and condenses; Use cloud type to make a simple prediction about the weather.

Needs first: Rain & Puddles.

https://lightmysky.com/learn/science/cloud-types-mt_IhWzO4sQPg

#### Geography & Local Weather (ages 7-9)

Know that different places around the world have very different typical weather — tropical places are hot and wet all year, deserts are very dry, polar regions are freezing cold — and that geography (distance from the equator, altitude, nearness to the sea) affects local weather

Ready when they can: Describe typical weather in at least three different climate types; Explain that places near the equator tend to be hotter; Name at least one factor that affects a place's weather besides latitude.

Needs first: Seasons & Weather Patterns, Types of Weather.

https://lightmysky.com/learn/science/geography-and-local-weather-mt_hjJkBWruO6

#### Thunder & Lightning (ages 7-9)

Know that thunder and lightning happen during thunderstorms: lightning is a giant spark of electricity that forms in clouds, thunder is the sound the lightning makes, and we see lightning before hearing thunder because light travels faster than sound

Ready when they can: Describe lightning as a large electrical discharge in clouds; Explain that thunder is the sound caused by lightning; State that we see lightning before hearing thunder because light travels faster than sound.

Needs first: Storm Safety, Cloud Types.

https://lightmysky.com/learn/science/thunder-and-lightning-mt_BO_AHGLCk0

#### Using Weather Instruments (ages 7-9)

Use weather instruments to measure and record weather data: thermometers for temperature in °C, rain gauges for rainfall, wind vanes for direction, and anemometers for wind speed — and keep a weather diary over time

Ready when they can: Name at least three weather instruments and explain what each measures; Read a thermometer and record the temperature in degrees Celsius; Record weather data in a table or diary over several days.

Needs first: Local weather patterns, What Is Wind?, Types of Weather, Temperature & Thermometers.

https://lightmysky.com/learn/science/using-weather-instruments-mt_sA0RvWXSYY

#### Weather Forecasting (ages 7-9)

Know that meteorologists are scientists who study and forecast the weather using satellites, radar, weather balloons, and computer models, and that weather forecasts help people plan their activities and prepare for dangerous weather

Ready when they can: Define a meteorologist as a scientist who studies and predicts weather; Name at least three tools meteorologists use; Explain why weather forecasting is useful for safety and daily planning.

Needs first: Cloud Types, Using Weather Instruments, Weather Forecasting & Safety.

https://lightmysky.com/learn/science/weather-forecasting-mt_AghN5YcCHX

#### Weather vs Climate (ages 7-9)

Distinguish between weather and climate: weather is what the atmosphere is doing right now or today (it can change hour to hour), while climate is the typical pattern of weather in a place over many years

Ready when they can: Define weather as short-term atmospheric conditions; Define climate as the long-term pattern of weather in a place; Give an example showing the difference: a cold day doesn't change the overall climate.

Needs first: Seasons & Weather Patterns, Geography & Local Weather, Types of Weather.

https://lightmysky.com/learn/science/weather-vs-climate-mt_AB-TEMXSGJ

#### What Causes Wind (ages 7-9)

Understand what causes wind: the Sun heats the Earth's surface unevenly, warm air rises because it is lighter, and cooler air rushes in to take its place — this movement of air is wind

Ready when they can: Explain that the Sun heats Earth's surface unevenly; State that warm air rises and cooler air moves in to replace it; Define this air movement as wind.

Needs first: What Is Wind?.

https://lightmysky.com/learn/science/what-causes-wind-mt_-UAxilUtUt

#### Designing for Weather Hazards (ages 8-9)

Make a claim about the merit of a design solution that reduces the impacts of a weather-related hazard such as flooding, wind damage, or extreme temperatures

Ready when they can: Identify a specific weather-related hazard and its impacts on people; Describe at least two design solutions intended to reduce those impacts; Make a claim supported by evidence about which solution is most effective and why.

Needs first: Climates around the world, Weather Forecasting & Safety.

https://lightmysky.com/learn/science/designing-for-weather-hazards-mt_JmMtZCifJB

#### Reading Weather Maps (ages 9-11)

Read and interpret weather maps, data tables, and graphs — identifying symbols for sun, rain, wind, and temperature; spotting trends and patterns in weather data over weeks, months, or seasons; and using data to make simple predictions

Ready when they can: Interpret common weather map symbols for temperature, precipitation, and wind; Read a data table or graph of weather data and identify patterns; Use weather data to make a simple prediction about upcoming conditions.

Needs first: Weather vs Climate, Weather Forecasting, Graphing seasonal weather data.

https://lightmysky.com/learn/science/reading-weather-maps-mt_3pgTpuetKi

#### The Atmosphere (ages 9-11)

Know that Earth is surrounded by a layer of air called the atmosphere, that air has weight and exerts pressure, that the atmosphere protects us from harmful radiation and keeps the planet warm enough for life, and that weather happens in the lowest layer (troposphere)

Ready when they can: Define the atmosphere as the layer of air surrounding Earth; State that air has weight and exerts pressure; Explain that weather occurs in the troposphere, the lowest layer of the atmosphere.

Needs first: What Causes Wind.

https://lightmysky.com/learn/science/the-atmosphere-mt_fkcxpeYP85

#### The Water Cycle (ages 7-9)

Understand the water cycle: the Sun heats water in oceans and lakes causing it to evaporate into water vapour, the vapour rises and cools to form clouds (condensation), and water falls back to Earth as rain, snow, or hail (precipitation) — then the cycle repeats

Ready when they can: Name the three main stages: evaporation, condensation, precipitation; Explain the Sun's role in driving the water cycle; Describe the water cycle as a continuous loop with no beginning or end.

Needs first: Cloud Types, Where water is found on Earth, Heating & Cooling Changes, Temperature & Thermometers, Rain & Puddles.

https://lightmysky.com/learn/science/the-water-cycle-mt_fhqVdj4BYr

#### Extreme Weather Events (ages 9-11)

Know about extreme weather events — hurricanes (spinning storms over warm ocean), tornadoes (violent rotating columns of air), floods, droughts, and blizzards — how they form, where they typically occur, and their effects on people and the environment

Ready when they can: Describe how at least two types of extreme weather form; Explain where hurricanes and tornadoes typically occur and why; Describe the effects of extreme weather on communities and landscapes.

Needs first: Thunder & Lightning, The Water Cycle, What Causes Wind.

https://lightmysky.com/learn/science/extreme-weather-events-mt_6EfevRyeFW

#### Sun-Driven Weather Systems (ages 9-11)

Understand how the Sun drives weather: the Sun heats Earth's surface unevenly (land heats faster than water, equator gets more heat than poles), creating differences in air pressure that cause wind patterns, ocean currents, and large-scale weather systems

Ready when they can: Explain that the Sun heats land and water at different rates; Describe how temperature differences create air pressure differences that drive wind; Connect uneven heating to large-scale weather patterns.

Needs first: Weather vs Climate, The Water Cycle, Sunlight warms things up, What Causes Wind.

https://lightmysky.com/learn/science/sun-driven-weather-systems-mt_-YYnLLIZh5

#### Climate Zones (ages 9-11)

Understand that Earth has distinct climate zones — tropical (hot and wet near the equator), temperate (moderate, with four seasons), polar (freezing cold), arid/desert (very dry), and mountain (cold at high altitude) — and that each zone supports different ecosystems and ways of life

Ready when they can: Name and describe at least four climate zones; Explain what determines which zone a place belongs to (mainly latitude and geography); Give an example of how a climate zone affects the plants, animals, or people living there.

Needs first: Weather vs Climate, Sun-Driven Weather Systems.

https://lightmysky.com/learn/science/climate-zones-mt_TMOzMCE17H

#### Weather-Resistant Engineering (ages 9-11)

Understand that engineers design buildings, flood defences, and warning systems to protect communities from extreme weather — hurricane-resistant roofs, flood barriers, tornado shelters, and early-warning alert systems — and evaluate the merits of these solutions

Ready when they can: Describe at least two engineering solutions designed to protect against extreme weather; Explain how a specific design feature reduces damage from a weather hazard; Evaluate the advantages and limitations of a weather protection solution.

Needs first: Extreme Weather Events, Designing for Weather Hazards, Sun-Driven Weather Systems.

https://lightmysky.com/learn/science/weather-resistant-engineering-mt_iiUdDUEEGY

#### Global Wind Patterns (ages 11-13)

Explain that unequal solar heating drives large-scale atmospheric circulation: Hadley cells (0-30°), Ferrel cells (30-60°), and polar cells (60-90°) produce the trade winds, westerlies, and polar easterlies; describe how the Coriolis effect from Earth's rotation deflects winds rightward in the Northern Hemisphere; explain the jet stream as a fast high-altitude wind that steers weather systems; connect jet stream waviness and Arctic amplification to prolonged extreme weather

Needs first: Climate Zones.

https://lightmysky.com/learn/science/global-wind-patterns-mt_iYOcfzFqMw

#### Greenhouse Gas Science (ages 11-12)

Describe the electromagnetic spectrum and distinguish between short-wave solar radiation and long-wave infrared radiation emitted by Earth; explain how greenhouse gas molecules (CO2, CH4, N2O, H2O) absorb and re-emit infrared through molecular vibration while O2 and N2 do not; distinguish the natural greenhouse effect (which makes Earth habitable) from the enhanced greenhouse effect driven by human emissions; evaluate the relative potency of different greenhouse gases

Needs first: Global Wind Patterns, Sun-Driven Weather Systems.

https://lightmysky.com/learn/science/greenhouse-gas-science-mt_EQQWKz03P8

#### Natural resources (ages 9-10)

Obtain and combine information to describe that energy and fuels are derived from natural resources and that their uses affect the environment

Ready when they can: Name natural resources used for energy and fuels (coal, oil, gas, wind, sun, water); Describe how extracting and using these resources affects the environment (pollution, habitat loss, climate change); Distinguish between renewable (wind, solar) and non-renewable (fossil fuels) energy sources.

Needs first: Changing Environments, How energy travels around, Human impact on environments.

https://lightmysky.com/learn/science/natural-resources-mt_VI5kdtf28e

#### Climate Change Basics (ages 9-11)

Understand the basics of climate change: Earth’s atmosphere traps some of the Sun's heat (the greenhouse effect), burning fossil fuels adds extra greenhouse gases (especially CO₂), this is making Earth gradually warmer, and this warming changes weather patterns, melts ice, and raises sea levels

Ready when they can: Describe the greenhouse effect: the atmosphere traps heat from the Sun; Explain that burning fossil fuels increases CO₂ in the atmosphere; Name at least two consequences of global warming: changing weather patterns, melting ice, rising seas.

Needs first: Weather vs Climate, The Atmosphere, Oceans & Climate, Climate Zones, Natural resources, Sun-Driven Weather Systems.

https://lightmysky.com/learn/science/climate-change-basics-mt_DbI1kNg_0R

#### Reading Ancient Climate Records (ages 12-14)

Explain how ice cores preserve ancient air bubbles, isotope ratios, and volcanic markers allowing reconstruction of temperature and CO2 going back 800,000 years; describe tree rings, ocean sediment cores, coral skeletons, and pollen records as additional climate proxies; explain how climate models are built and validated against the palaeoclimate record; describe the IPCC process of synthesising scientific evidence across thousands of studies to produce consensus assessments

Needs first: Climate Change Basics, Earth's Frozen Water, Reconstructing Ancient Ecosystems.

https://lightmysky.com/learn/science/reading-ancient-climate-records-mt_olFzbawexJ

#### Hurricanes, Tornadoes & Monsoons (ages 12-13)

Explain how hurricanes form and intensify over warm ocean water (latent heat release, low-pressure spiral); describe tornado formation within supercell thunderstorms; explain monsoon mechanics driven by temperature differences between land and sea; introduce attribution science — how scientists use climate models to calculate whether and by how much climate change increased the probability or intensity of a specific extreme weather event

Needs first: Extreme Weather Events, Global Wind Patterns, Reading Ancient Climate Records, Reading Weather Maps.

https://lightmysky.com/learn/science/hurricanes-tornadoes-and-monsoons-mt__wWHVvqMWb

#### Net Zero & Energy Transition (ages 13-14)

Evaluate the energy transition required to reach net zero: renewable energy scaling, electrification of transport and heat, green hydrogen; describe carbon capture and storage (CCS) and direct air capture (DAC); introduce proposed solar radiation management techniques (stratospheric aerosol injection, marine cloud brightening) and their potential risks and governance challenges; critically evaluate the role of individual behaviour change versus systemic policy in reducing emissions

Needs first: Reading Ancient Climate Records, Renewable vs non-renewable energy.

https://lightmysky.com/learn/science/net-zero-and-energy-transition-mt_Wzj1RETm9A

### Rainforests

https://lightmysky.com/learn/science/areas/rainforests

#### What Is a Rainforest? (ages 5-7)

Know that a rainforest is a thick, tall forest found in hot, wet places near the Equator where it rains almost every day, creating a warm, damp environment where plants and animals thrive

Ready when they can: Describe a rainforest as a forest that is hot and wet, located near the Equator; Explain that it rains very often in a rainforest, which is why the plants grow so tall and thick; Point to the Equator on a globe and say that rainforests are found in the hot belt near it.

https://lightmysky.com/learn/science/what-is-a-rainforest-mt_FZ_ixwU1p1

#### Everyday Foods from Rainforests (ages 5-7)

Know that many everyday foods come from rainforests — chocolate is made from cacao beans, bananas grow in tropical forests, coffee berries ripen in forest shade, and Brazil nuts fall from giant trees — connecting our daily lives to faraway forests

Ready when they can: Name at least three foods that come from rainforests, such as chocolate (cacao), bananas, and Brazil nuts; Explain that cacao beans grow on trees in the rainforest and are made into chocolate; Connect their own food choices to rainforest origins by identifying a product they eat that comes from the forest.

Needs first: What Is a Rainforest?.

https://lightmysky.com/learn/science/everyday-foods-from-rainforests-mt_s08-QxASd2

#### Indigenous Rainforest Peoples (ages 5-7)

Know that indigenous peoples such as the Yanomami have lived in rainforests for thousands of years, building homes from forest materials, finding food by hunting, fishing, and gathering, and knowing the forest and its plants and animals deeply

Ready when they can: Explain that indigenous peoples like the Yanomami have lived in rainforests for thousands of years; Describe how they use the forest for shelter, food, and medicine; Show respect for indigenous knowledge by explaining that these communities understand the forest very deeply.

Needs first: What Is a Rainforest?.

https://lightmysky.com/learn/science/indigenous-rainforest-peoples-mt_2zJ1NrGgYm

#### Inside a Rainforest (ages 5-7)

Describe what it feels like inside a rainforest — hot and sticky (humid), dark on the ground because the treetops block the light, loud with animal calls and insect buzzing, and dripping with water from rain and condensation

Ready when they can: Describe the air inside a rainforest as hot and sticky (humid); Explain that the forest floor is dark because tall trees block most of the sunlight; Name at least two sounds you would hear in a rainforest, such as bird calls, insect buzzing, or rain dripping.

Needs first: What Is a Rainforest?.

https://lightmysky.com/learn/science/inside-a-rainforest-mt_ntxlccnYzB

#### Rainforest Layers (ages 5-7)

Know that a rainforest has four layers from ground to sky — the forest floor (dark, damp, full of decomposing leaves), the understory (small trees and shrubs in the shade), the canopy (a thick roof of treetops where most animals live), and the emergent layer (the tallest trees poking above the canopy into bright sunlight)

Ready when they can: Name the four rainforest layers in order from ground to sky: forest floor, understory, canopy, emergent; Describe one key feature of each layer, such as the canopy being a thick roof of leaves or the forest floor being dark and damp; Explain that most rainforest animals live in the canopy because that is where there is food and light.

Needs first: What Is a Rainforest?.

https://lightmysky.com/learn/science/rainforest-layers-mt_-0cjwyYhce

#### Iconic Rainforest Animals (ages 5-7)

Name and recognise iconic rainforest animals — jaguars, toucans, sloths, poison dart frogs, howler monkeys, macaws, and butterflies — and know which layer of the rainforest each lives in

Ready when they can: Name at least five iconic rainforest animals such as jaguars, toucans, sloths, poison dart frogs, and howler monkeys; Match at least three animals to the rainforest layer where they live (e.g. monkeys in the canopy, jaguars on the forest floor); Describe one distinctive feature of each named animal.

Needs first: Rainforest Layers.

https://lightmysky.com/learn/science/iconic-rainforest-animals-mt_xVW5U41tbp

#### Rainforest Insects (ages 5-7)

Know that rainforests are home to millions of insects — leaf-cutter ants that farm fungus, giant beetles, jewel-coloured butterflies, enormous spiders, and stick insects — and that insects are the most numerous animals in the rainforest

Ready when they can: Name at least three types of insect or minibeast found in the rainforest, such as leaf-cutter ants, morpho butterflies, and giant beetles; Explain that insects are the most numerous animals in the rainforest; Describe one interesting behaviour, such as leaf-cutter ants carrying leaf pieces back to grow fungus.

Needs first: Rainforest Layers, What is a minibeast?, Iconic Rainforest Animals.

https://lightmysky.com/learn/science/rainforest-insects-mt_XL2gqdKJfu

#### Rainforest Plants (ages 5-7)

Know that rainforests contain an enormous variety of plants — towering kapok and Brazil nut trees, climbing vines called lianas, colourful orchids that grow on tree branches, giant water lilies, and huge leaves that funnel rainwater

Ready when they can: Name at least three types of rainforest plant, such as kapok trees, lianas (climbing vines), and orchids; Explain that rainforest plants grow very tall because they compete for sunlight; Describe one unusual feature, such as orchids growing on tree branches or lianas climbing up trunks.

Needs first: Rainforest Layers.

https://lightmysky.com/learn/science/rainforest-plants-mt_x5ZrQMAZ5v

#### Where Rainforests Are (ages 5-7)

Know that rainforests are found in a belt around the middle of the Earth — in South America (the Amazon), Central Africa (the Congo), and Southeast Asia — and that they appear on every continent except Antarctica and Europe

Ready when they can: Point to the Amazon, Congo, and Southeast Asian rainforest regions on a world map; Explain that rainforests grow near the Equator where it is hot and wet all year; Name at least two continents that have large rainforests.

Needs first: What Is a Rainforest?.

https://lightmysky.com/learn/science/where-rainforests-are-mt_0u3QNroZ34

#### Classifying Rainforest Organisms (ages 7-9)

Classify rainforest organisms into major groups — mammals (jaguars, monkeys, bats), birds (toucans, macaws, hummingbirds), reptiles (snakes, lizards, caimans), amphibians (tree frogs, poison dart frogs), insects (butterflies, ants, beetles), and plants (trees, epiphytes, ferns) — using observable features to sort them

Ready when they can: Sort at least eight rainforest organisms into correct groups: mammals, birds, reptiles, amphibians, insects, or plants; State the key feature that defines each group (e.g. mammals have fur and feed milk to their young); Explain why classification helps scientists understand and study the huge variety of life in rainforests.

Needs first: Rainforest Plants, Iconic Rainforest Animals.

https://lightmysky.com/learn/science/classifying-rainforest-organisms-mt_OtShuvs3x8

#### Indigenous Ecological Knowledge (ages 7-9)

Understand that indigenous peoples of the rainforest have developed deep ecological knowledge over thousands of years — using plants for medicine, food, and building materials, practising sustainable farming methods like shifting cultivation, and understanding animal behaviour and forest ecology in ways that modern science is only beginning to appreciate

Ready when they can: Give at least two examples of indigenous knowledge, such as using specific plants as medicine or practising sustainable farming; Explain what shifting cultivation is and why it is less harmful to the forest than permanent clearing; Describe how indigenous knowledge and modern science can work together to protect rainforests.

Needs first: Indigenous Rainforest Peoples.

https://lightmysky.com/learn/science/indigenous-ecological-knowledge-mt_m43jiOAOCt

#### Rainforest Animal Survival Tricks (ages 7-9)

Know how rainforest animals are adapted to their environment — camouflage helps leaf insects and tree frogs hide, bright warning colours (aposematism) signal that poison dart frogs are toxic, prehensile tails let monkeys grip branches, toucans' large beaks help reach distant fruit, and many animals are nocturnal to avoid daytime heat

Ready when they can: Describe at least three animal adaptations such as camouflage, warning colours, and prehensile tails; Explain how each adaptation helps the animal survive (e.g. camouflage hides prey from predators); Give a specific example for each adaptation, linking the animal to its rainforest layer.

Needs first: Rainforest Layers, Iconic Rainforest Animals.

https://lightmysky.com/learn/science/rainforest-animal-survival-tricks-mt_XxgU_91AXg

#### Rainforest Food Webs (ages 7-9)

Understand how energy and nutrients flow through a rainforest food web — from plants (producers) to herbivores (primary consumers) to predators (secondary consumers) — and that decomposers like fungi and insects break down dead material on the forest floor, recycling nutrients back into the soil for plants to use again

Ready when they can: Construct a simple rainforest food chain with at least three levels: producer → herbivore → predator; Explain the role of decomposers in breaking down dead material and returning nutrients to the soil; Use the terms producer, consumer, and decomposer correctly.

Needs first: Rainforest Plants, Iconic Rainforest Animals.

https://lightmysky.com/learn/science/rainforest-food-webs-mt_1LFVPjdGg-

#### Rainforest Plant Adaptations (ages 7-9)

Know how rainforest plants are adapted to their environment — drip-tip leaves channel water off quickly to prevent rot, buttress roots spread wide to support tall trees in thin soil, epiphytes (like orchids and bromeliads) grow on tree branches to reach sunlight without needing soil, and lianas climb trunks to reach the canopy

Ready when they can: Describe at least three plant adaptations: drip-tip leaves, buttress roots, and epiphytes; Explain the purpose of each adaptation (e.g. drip-tips shed water to prevent rot); Use the word adaptation to mean a feature that helps an organism survive in its environment.

Needs first: Rainforest Plants.

https://lightmysky.com/learn/science/rainforest-plant-adaptations-mt_Wx5m6mwkpj

#### Tropical Rainforest Climate (ages 7-9)

Understand that rainforests have a tropical climate — consistently hot (25–30°C) with over 2000 mm of rainfall per year — and that this combination of heat and moisture creates ideal conditions for rapid plant growth and extraordinary biodiversity

Ready when they can: State that tropical rainforests are hot (25–30°C) and wet (over 2000 mm rain per year) all year round; Explain that the constant heat and moisture create ideal growing conditions for plants; Compare tropical rainforest climate to the UK or local climate, noting key differences in temperature and rainfall.

Needs first: Where Rainforests Are, Geography & Local Weather.

https://lightmysky.com/learn/science/tropical-rainforest-climate-mt_v6CBCMuvz1

#### The Amazon Rainforest (ages 7-9)

Know that the Amazon is Earth's greatest rainforest — spanning nine countries across South America, containing the world's largest river by water volume, and home to an estimated 10% of all species on Earth including 40,000 plant species, 1,300 bird species, and 3,000 types of fish

Ready when they can: Locate the Amazon rainforest on a map of South America and name at least two countries it spans; State that the Amazon contains the world's largest river by volume and is home to roughly 10% of all species on Earth; Give at least two specific numbers showing the Amazon's biodiversity, such as 40,000 plant species or 1,300 bird species.

Needs first: Where Rainforests Are, Tropical Rainforest Climate.

https://lightmysky.com/learn/science/the-amazon-rainforest-mt_38d-k-dJPa

#### Nutrient Cycling in Thin Soil (ages 9-11)

Understand the paradox of nutrient cycling in rainforests — despite lush growth, rainforest soil is typically thin and nutrient-poor because most nutrients are locked in living organisms, not the soil; decomposition is rapid in the warm, wet conditions, and nutrients released from dead material are immediately absorbed by plant roots and fungi, creating a fast, closed-loop recycling system

Ready when they can: Explain that rainforest soil is thin and nutrient-poor despite the lush growth above; Describe the rapid decomposition cycle: dead material → decomposers → nutrients released → immediately absorbed by roots; Explain why clearing rainforest for farming fails after a few years — once the trees are gone, the nutrients are lost.

Needs first: Rainforest Food Webs, Rainforest Plant Adaptations.

https://lightmysky.com/learn/science/nutrient-cycling-in-thin-soil-mt_JcfP1hWKa_

#### Rainforest Biodiversity (ages 9-11)

Understand that rainforests are biodiversity hotspots — covering just 6% of Earth's land surface but containing over 50% of all known plant and animal species — and that this extraordinary richness makes them irreplaceable for global biodiversity and a priority for conservation

Ready when they can: State that rainforests cover about 6% of Earth's land but hold over 50% of all species; Explain why this concentration of species makes rainforests a conservation priority; Give specific examples of rainforest biodiversity, such as one hectare containing more tree species than all of northern Europe.

Needs first: The Amazon Rainforest, Classifying Rainforest Organisms.

https://lightmysky.com/learn/science/rainforest-biodiversity-mt_pPGaf8bR8r

#### Rainforest Water Cycle (ages 7-9)

Understand how the water cycle works in a rainforest — trees absorb water through their roots and release it through their leaves (transpiration), this moisture forms clouds above the canopy, and the clouds produce rain that falls back into the forest — creating a self-sustaining cycle that generates much of the rainforest's own rainfall

Ready when they can: Describe the sequence: trees absorb water → release it through leaves (transpiration) → moisture rises → clouds form → rain falls; Explain that rainforests generate much of their own rainfall through this cycle; Use the word transpiration correctly when describing how water leaves a plant through its leaves.

Needs first: The Water Cycle, Tropical Rainforest Climate, Rainforest Plants.

https://lightmysky.com/learn/science/rainforest-water-cycle-mt_ZWTk6eP1qF

#### Temperate Rainforests (ages 9-11)

Know that not all rainforests are tropical — temperate rainforests exist in cooler, wet regions like the Pacific Northwest of North America, western Scotland and Wales, southern Chile, and New Zealand — with similar features (high rainfall, moss-draped trees, dense canopy) but different species, including ancient oaks, giant redwoods, and tree ferns

Ready when they can: Name at least two locations of temperate rainforests, such as the Pacific Northwest, western Scotland, or southern Chile; Compare temperate and tropical rainforests: both have high rainfall and dense canopy, but differ in temperature and species; Name species found in temperate rainforests, such as ancient oaks, giant redwoods, or tree ferns.

Needs first: Rainforest Layers, Climate Zones, Tropical Rainforest Climate.

https://lightmysky.com/learn/science/temperate-rainforests-mt_hbDflQfW-U

#### Deforestation Causes & Scale (ages 9-11)

Understand the causes and scale of rainforest deforestation — cattle ranching (largest driver in the Amazon), soy and palm oil plantations, logging for timber, and mining — and know that approximately 10 million hectares of forest are lost globally each year, with devastating consequences for biodiversity, climate, and indigenous communities

Ready when they can: Name at least three major causes of deforestation: cattle ranching, palm oil, soy, logging, and mining; State that approximately 10 million hectares of forest are lost globally each year; Explain the impact of deforestation on at least two of: biodiversity, climate, and indigenous peoples.

Needs first: The Amazon Rainforest, Rainforest Biodiversity, Changing Environments.

https://lightmysky.com/learn/science/deforestation-causes-and-scale-mt_2OSTHTWDpa

#### Rainforest Conservation (ages 9-11)

Know the main approaches to rainforest conservation — protected areas and national parks, reforestation and rewilding programmes, sustainable certification schemes (Rainforest Alliance, FSC), recognition of indigenous land rights as the most effective form of forest protection, and international agreements like REDD+ that pay countries to keep forests standing

Ready when they can: Name at least three conservation approaches: protected areas, reforestation, sustainable certification, and indigenous land rights; Explain why protecting indigenous territories is one of the most effective ways to prevent deforestation; Describe what certification labels like Rainforest Alliance or FSC mean and how they help.

Needs first: Deforestation Causes & Scale, Indigenous Ecological Knowledge.

https://lightmysky.com/learn/science/rainforest-conservation-mt_kON8bYEHYl

#### Rainforest Products in Daily Life (ages 9-11)

Understand how rainforest products connect to everyday life through global supply chains — palm oil is in snacks, soap, and cosmetics; soy feeds livestock worldwide; cocoa becomes chocolate; rubber is in tyres and gloves; timber becomes furniture; and many medicines originate from rainforest plants — and that consumer choices can drive either destruction or sustainable practices

Ready when they can: Name at least four products linked to rainforests: palm oil, soy, cocoa, rubber, timber, and medicines; Explain how a product like palm oil travels from a rainforest region to a supermarket shelf; Describe how consumer choices (e.g. buying Rainforest Alliance certified products) can reduce deforestation pressure.

Needs first: Deforestation Causes & Scale, Everyday Foods from Rainforests.

https://lightmysky.com/learn/science/rainforest-products-in-daily-life-mt_xE_b3JiDZU

#### Rainforests & Global Climate (ages 9-11)

Understand the connection between rainforests and global climate — rainforests absorb carbon dioxide and release oxygen through photosynthesis, store enormous amounts of carbon in their biomass, and generate rainfall through transpiration; when forests are burned or cleared, stored carbon is released as CO₂, accelerating climate change and disrupting regional rainfall patterns

Ready when they can: Explain that rainforests absorb CO₂ and store carbon in their trees, acting as a carbon sink; Describe how deforestation releases stored carbon back into the atmosphere, accelerating climate change; Explain that transpiration from rainforest trees generates rainfall, and losing trees disrupts rain patterns.

Needs first: Deforestation Causes & Scale, Climate Change Basics, Rainforest Water Cycle.

https://lightmysky.com/learn/science/rainforests-and-global-climate-mt_HJd-8EEC6N

#### Rainforest Futures & Trade-Offs (ages 9-11)

Understand that the future of rainforests depends on balancing competing needs — economic development for local communities, indigenous peoples' rights to their ancestral lands, global biodiversity conservation, and climate stability — and that there are no simple answers, requiring cooperation between governments, businesses, scientists, indigenous leaders, and consumers worldwide

Ready when they can: Name at least three competing interests: economic development, indigenous rights, biodiversity, and climate stability; Explain why there is no single simple solution to rainforest protection; Suggest how different groups (governments, businesses, consumers, scientists) can each contribute to a better outcome.

Needs first: Deforestation Causes & Scale, Rainforests & Global Climate, Rainforest Conservation.

https://lightmysky.com/learn/science/rainforest-futures-and-trade-offs-mt_ZM7u9m-gS4

### Waves, Light & Sound

https://lightmysky.com/learn/science/areas/waves-light-and-sound

#### Light & Sound Vocabulary (ages 6-8)

Name and use vocabulary for how light and sound behave — light source, transparent, translucent, opaque, shadow, reflect, vibration, pitch, volume — and apply these terms correctly when describing observations about how light travels and how sounds are made and changed

Ready when they can: Correctly classify a set of materials as transparent, translucent, or opaque and explain each term; Explain what causes a shadow using the words 'opaque' and 'light source' correctly; Describe what changes the pitch or volume of a sound using vibration vocabulary.

https://lightmysky.com/learn/science/light-and-sound-vocabulary-mt_YPSx5pbpVl

#### Light & Seeing in the Dark (ages 6-8)

Observe that objects in darkness can be seen only when illuminated by a light source

Ready when they can: Explain that we need light to see objects — without any light source, it is completely dark; Describe an observation showing objects become visible only when light reaches them; Distinguish between light sources (sun, torch, lamp) and objects that just reflect light.

Needs first: Light & Sound Vocabulary.

https://lightmysky.com/learn/science/light-and-seeing-in-the-dark-mt_4i-FKXDDXh

#### Communication with Light & Sound (ages 6-7)

Design and build a device that uses light or sound to solve the problem of communicating over a distance

Ready when they can: Design a device that uses light or sound to communicate over a distance (e.g. string telephone, torch signals); Build and test the device, identifying what works and what could be improved; Explain how the device uses properties of light or sound to transmit information.

Needs first: Light & Seeing in the Dark.

https://lightmysky.com/learn/science/communication-with-light-and-sound-mt_ZL9qVVnpwN

#### Vibrations & Sound (ages 6-9)

Understand that vibrating materials can make sound, and that sound can make materials vibrate

Ready when they can: Describe that sounds are made when objects vibrate (move back and forth quickly); Give at least three examples of vibrating objects making sound (drum skin, guitar string, voice box); Demonstrate that sound can cause objects to vibrate (e.g. rice on a drum jumps when you shout near it).

Needs first: Light & Sound Vocabulary, Communication with Light & Sound.

https://lightmysky.com/learn/science/vibrations-and-sound-mt_VBl1T1sFCM

#### Protecting Eyes from Sunlight (ages 7-8)

Recognise that light from the sun can be dangerous and that there are ways to protect eyes

Ready when they can: State that looking directly at the sun can damage eyes permanently; Name at least two ways to protect eyes from bright sunlight (sunglasses, hat, shade); Explain that the sun is an extremely bright light source unlike any artificial light.

Needs first: Light & Seeing in the Dark.

https://lightmysky.com/learn/science/protecting-eyes-from-sunlight-mt_3yuqKww2tU

#### Reflecting Light (ages 7-8)

Notice that light is reflected from surfaces, and that shiny smooth surfaces reflect light best

Ready when they can: Explain that light bounces off surfaces, which is called reflection; Identify that smooth, shiny surfaces (mirrors, still water) reflect light best; Give everyday examples of reflection: mirror, puddle, polished floor.

Needs first: Light & Seeing in the Dark, Light & Sound Vocabulary.

https://lightmysky.com/learn/science/reflecting-light-mt_gLy3ZgZWiN

#### Pitch of Sounds (ages 8-9)

Find patterns between the pitch of a sound and features of the object that produced it

Ready when they can: Describe the pattern: shorter/thinner/tighter objects produce higher-pitched sounds; Demonstrate pitch changes using at least one instrument or everyday object; Explain pitch as how high or low a sound is, determined by how fast the object vibrates.

Needs first: Vibrations & Sound, Light & Sound Vocabulary.

https://lightmysky.com/learn/science/pitch-of-sounds-mt_KTSoXcO7OL

#### Sound Travels Through Materials (ages 8-9)

Recognise that vibrations from sounds travel through a medium (solid, liquid, or gas) to the ear

Ready when they can: Explain that sound vibrations need a material (medium) to travel through — they can't travel in a vacuum; Give examples of sound travelling through different media: air, water, solid objects; Describe how a string telephone works: voice vibrates the cup, vibrations travel along the string to the other cup.

Needs first: Vibrations & Sound, Light & Sound Vocabulary.

https://lightmysky.com/learn/science/sound-travels-through-materials-mt_ydtcIBwHB9

#### Sound Fading with Distance (ages 8-9)

Recognise that sounds get fainter as the distance from the sound source increases

Ready when they can: State that sound gets quieter as distance from the source increases; Describe an observation or investigation demonstrating this pattern; Explain that vibrations spread out and get weaker as they travel further from the source.

Needs first: Sound Travels Through Materials.

https://lightmysky.com/learn/science/sound-fading-with-distance-mt_Pau0aqLNgp

#### Volume & Vibrations (ages 8-9)

Find patterns between the volume of a sound and the strength of the vibrations that produced it

Ready when they can: Describe the pattern: stronger vibrations (larger movements) produce louder sounds; Demonstrate volume changes by varying the force applied to a sound-making object; Explain volume as how loud or quiet a sound is, determined by the size of vibrations.

Needs first: Vibrations & Sound.

https://lightmysky.com/learn/science/volume-and-vibrations-mt__00ZSLnB7p

#### Wave Behaviour Vocabulary (ages 9-11)

Use technical vocabulary for wave behaviour — refraction, absorption, reflection, scattering, amplitude, frequency, wavelength, echo, spectrum, angle of incidence, angle of reflection — and apply these when explaining how light and sound travel and interact with different materials

Ready when they can: Use 'refraction' correctly to explain why a straw appears bent in a glass of water; Distinguish 'reflection' from 'refraction' using the correct definitions; Explain what an echo is using the vocabulary of sound reflection correctly.

Needs first: Light & Sound Vocabulary.

https://lightmysky.com/learn/science/wave-behaviour-vocabulary-mt_SFOSbVnrJ8

#### Waves & How They Move (ages 9-10)

Develop a model of waves to describe patterns in terms of amplitude and wavelength, and understand that waves can cause objects to move

Ready when they can: Describe a wave using the terms amplitude (height) and wavelength (distance between peaks); Demonstrate that larger amplitude means more energy (bigger waves move objects more); Model wave patterns using a slinky, rope, or water and describe what they observe.

Needs first: Volume & Vibrations, Wave Behaviour Vocabulary, Sound Travels Through Materials.

https://lightmysky.com/learn/science/waves-and-how-they-move-mt_ph4xZVMiVq

#### Patterns & Codes for Information (ages 9-10)

Generate and compare multiple solutions that use patterns to transfer information, such as codes and signals

Ready when they can: Describe at least two systems that use patterns of light or sound to transfer information (e.g. Morse code, semaphore, drum signals); Design a simple code using light or sound patterns to send a message; Compare the advantages and disadvantages of different information transfer methods.

Needs first: Waves & How They Move, Communication with Light & Sound.

https://lightmysky.com/learn/science/patterns-and-codes-for-information-mt_n5_Jt4ExUd

#### Wave Properties & Types (ages 11-12)

Describe waves in terms of amplitude, wavelength, frequency, and wave speed; distinguish transverse waves (oscillation perpendicular to direction of travel) from longitudinal waves (oscillation parallel); and use the wave equation v = fλ

Ready when they can: Labels a wave diagram with amplitude, wavelength, crest, and trough; Distinguishes transverse and longitudinal waves and gives an example of each; Uses v = fλ to calculate wave speed, frequency, or wavelength given the other two; Explains what happens to wavelength if frequency increases while wave speed stays constant.

Needs first: Waves & How They Move, Wave Behaviour Vocabulary, Vibrations & Sound.

https://lightmysky.com/learn/science/wave-properties-and-types-mt_LxK9OKZQZX

#### Analog and Digital Signals (ages 11-14)

How information travels as signals in waves: analog signals vary continuously while digital signals encode information as patterns of on/off pulses, and digitised signals can be copied, stored and sent with far less loss and noise

Ready when they can: Explain the difference between an analog signal (continuously varying) and a digital one (a coded pattern of discrete values); Give reasons why digital transmission is more reliable (e.g., a 1-or-0 pulse can be cleaned up and recopied, while noise permanently distorts an analog wave); Trace how a real message gets digitised and sent (e.g., a voice becomes numbers, travels as pulses, and is rebuilt as sound).

Needs first: Wave Properties & Types, Patterns & Codes for Information.

https://lightmysky.com/learn/science/analog-and-digital-signals-mt_gg5-bUckYX

#### How Sound Waves Travel (ages 11-12)

Explain that sound is produced by vibrating objects and travels as a longitudinal pressure wave through solids, liquids, and gases; describe reflection of sound (echoes) and absorption; explain why sound cannot travel through a vacuum

Ready when they can: Explains how a vibrating object creates regions of compression and rarefaction in air; Explains why sound travels fastest in solids and cannot travel in a vacuum; Describes how an echo is produced and gives a practical application (sonar, ultrasound); Explains what sound absorption means and why soft furnishings reduce echoes.

Needs first: Wave Properties & Types, Sound Travels Through Materials, Pitch of Sounds, Sound Fading with Distance.

https://lightmysky.com/learn/science/how-sound-waves-travel-mt_DQk9oDE7gr

#### Drawing Ray Diagrams (ages 12-13)

Draw ray diagrams to show reflection at a plane mirror (angle of incidence = angle of reflection) and refraction at a boundary between media; use ray diagrams to locate images and explain how lenses and mirrors work

Ready when they can: Draw a ray diagram for a plane mirror showing the incident ray, normal, reflected ray, and virtual image; Draw a ray diagram showing a ray bending towards the normal when passing from air into glass; Use a ray diagram to locate the image formed by a convex lens and describe whether it is real or virtual.

Needs first: Measuring angles.

https://lightmysky.com/learn/science/drawing-ray-diagrams-mt_-2VNlwAR5z

#### Transparent, Translucent & Opaque (ages 6-7)

Investigate the effect of placing objects made of different materials in the path of a beam of light, discovering transparent, translucent, and opaque materials

Ready when they can: Test at least six materials and classify them as transparent, translucent, or opaque; Define transparent (light passes through clearly), translucent (some light passes, blurry), opaque (no light passes); Predict whether a given material will let light through based on its appearance.

Needs first: Light & Seeing in the Dark, Describing Material Properties, Light & Sound Vocabulary.

https://lightmysky.com/learn/science/transparent-translucent-and-opaque-mt_p6frRFuxS6

#### How Shadows Form (ages 7-8)

Recognise that shadows are formed when light from a source is blocked by an opaque object, and find patterns in how shadow size changes

Ready when they can: Explain that a shadow forms because an opaque object blocks light from reaching a surface; Describe the pattern: shadow gets larger when object moves closer to the light source; Predict the shape and relative size of a shadow given the position of light and object.

Needs first: Transparent, Translucent & Opaque.

https://lightmysky.com/learn/science/how-shadows-form-mt_Oru08pKlxd

#### How We See Objects (ages 9-11)

Develop a model to describe that light reflecting from objects and entering the eye allows objects to be seen

Ready when they can: Draw a diagram showing light source → light hits object → reflects into eye; Explain that we see objects because reflected light enters our eyes, not because our eyes send out light; Use this model to explain why we can't see in total darkness (no light to reflect).

Needs first: Reflecting Light, How Shadows Form, Wave Behaviour Vocabulary.

https://lightmysky.com/learn/science/how-we-see-objects-mt_6w2g7aoPgz

#### Light Travels in Straight Lines (ages 10-11)

Recognise that light appears to travel in straight lines and use this to explain how we see objects and why shadows have the same shape as the objects that cast them

Ready when they can: State and demonstrate that light travels in straight lines (e.g. can't see around corners, laser pointer); Use straight-line light to explain why shadows have the same outline shape as the object; Draw ray diagrams showing light travelling from source, being blocked by object, creating shadow on screen.

Needs first: How We See Objects, How Shadows Form, Wave Behaviour Vocabulary.

https://lightmysky.com/learn/science/light-travels-in-straight-lines-mt_qZro923zvz

#### Reflection & Refraction (ages 11-12)

State the law of reflection (angle of incidence = angle of reflection) and explain refraction as the change in speed and direction when light crosses a boundary between two media; apply ray diagrams for plane mirrors and refracting surfaces

Ready when they can: States the law of reflection and applies it to draw a reflected ray correctly; Draws a ray diagram for a plane mirror showing a virtual image; Explains why a pencil looks bent in a glass of water using refraction; Explains qualitatively why light bends towards the normal when entering a denser medium.

Needs first: Drawing Ray Diagrams, Reflecting Light, Light Travels in Straight Lines, Wave Behaviour Vocabulary.

https://lightmysky.com/learn/science/reflection-and-refraction-mt_PifbJOuXrG

#### White Light & Colour (ages 11-12)

Explain that white light is a mixture of all visible colours (ROYGBIV), describe dispersion through a prism, explain why objects appear coloured (selective reflection and absorption of wavelengths), and describe colour mixing with filters

Ready when they can: Lists the colours of the visible spectrum in order of increasing frequency; Explains why a prism disperses white light into a spectrum; Explains why a red object looks red under white light but black under blue light; Predicts the colour of an object seen through a colour filter.

Needs first: How We See Objects, Reflection & Refraction.

https://lightmysky.com/learn/science/white-light-and-colour-mt_qzGADV-NGe

#### Ray Diagrams & Images (ages 12-13)

Construct ray diagrams to show the formation of images by plane mirrors and converging lenses, identifying whether images are real or virtual, magnified or diminished, upright or inverted

Ready when they can: Draws an accurate ray diagram for a plane mirror showing a virtual, upright, same-size image; Draws a ray diagram for a converging lens to show image formation; Uses a ray diagram to determine whether the image is real or virtual and which side of the lens it forms; Applies ray diagram knowledge to explain how glasses, cameras, or projectors work.

Needs first: Reflection & Refraction, White Light & Colour.

https://lightmysky.com/learn/science/ray-diagrams-and-images-mt_FVERuBoCD1

#### The Electromagnetic Spectrum (ages 12-13)

Describe the full electromagnetic spectrum from radio waves to gamma rays, in order of increasing frequency and energy; explain that all EM waves travel at the same speed in a vacuum; and describe the uses and hazards of different regions

Ready when they can: Lists the seven regions of the EM spectrum in order of increasing frequency; States that all EM waves travel at 3 × 10⁸ m/s in a vacuum; Gives at least one use and one hazard for each region of the spectrum; Explains why some EM waves are more dangerous to living tissue than others (linked to frequency/energy).

Needs first: Wave Properties & Types, Reflection & Refraction, Observing with Light Waves.

https://lightmysky.com/learn/science/the-electromagnetic-spectrum-mt_XSp-S0wter

#### Waves & Different Materials (ages 12-13)

Explain how waves can be absorbed, transmitted, or reflected by different materials, and apply these interactions to explain colour perception, sight, communication technologies, and the effects of different surfaces on wave behaviour

Ready when they can: Explains the difference between absorption, transmission, and reflection of waves; Uses the three interactions to explain how we see coloured objects; Explains how radio waves, visible light, and infrared are used in different communication technologies; Describes how the properties of a surface (colour, texture, material) determine how it interacts with radiation.

Needs first: Wave Properties & Types, The Electromagnetic Spectrum.

https://lightmysky.com/learn/science/waves-and-different-materials-mt_w5HzPpOUmj

#### The Electromagnetic Spectrum: Uses and Dangers (ages 15-16)

The seven groups run from radio waves to gamma rays in order of increasing frequency, all travelling at the same speed through space. Each group has uses that follow from how it interacts with matter, and the high-frequency end is ionising.

Ready when they can: Puts the seven groups in order and pairs each with a use that fits its properties; Explains which groups are ionising and what harm ultraviolet, X-rays and gamma rays can do; Justifies a choice of radiation for a job, such as cooking, imaging or communication.

https://lightmysky.com/learn/science/the-electromagnetic-spectrum-uses-and-dangers-mt_P_NXNSo1zQ

#### Infrared Emission, Absorption and the Temperature of a Body (ages 15-16)

Every object emits infrared, and how much it emits rises steeply with its temperature and depends on its surface. A body settles at the temperature where what it emits matches what it absorbs, which is why a matt black surface heats and cools fastest and why the Earth has the average temperature it does.

Ready when they can: Predicts which of two surfaces will heat faster in sunlight and which will cool faster in the dark, and gives the same reason for both; Explains the steady temperature of an object as the point where emission and absorption balance; Applies the balance to the Earth and says what changes when the atmosphere absorbs more of the outgoing infrared.

https://lightmysky.com/learn/science/infrared-emission-absorption-and-the-temperature-of-a-body-mt_xwh9uZ8gCl

#### The Wave Equation (ages 15-16)

Wave speed is frequency times wavelength, used in either direction for sound, ripples and light. Measuring it means timing or counting something real, such as ripples crossing a tank or an echo returning.

Ready when they can: Calculates any one of speed, frequency and wavelength from the other two, with units; Measures the speed of ripples in a tank or of sound in air and reports the method; Explains why a higher frequency means a shorter wavelength when the speed is fixed.

https://lightmysky.com/learn/science/the-wave-equation-mt_wmKhTiXt1p

#### Refraction and Lenses (ages 15-16)

A wave changes direction at a boundary because its speed changes there, while its frequency stays the same. Converging and diverging lenses use that bending, and a ray diagram shows where the image forms and what it looks like.

Ready when they can: Explains bending at a boundary by the change in speed, and says which of speed, frequency and wavelength change; Draws a ray diagram for a converging lens with the object beyond and inside the focal length; Describes an image as real or virtual, upright or inverted, magnified or reduced.

https://lightmysky.com/learn/science/refraction-and-lenses-mt_u8GKuBMmzC

#### Ultrasound and Echo Sounding (ages 15-16)

Sound above the range a person can hear reflects at a boundary between two materials, and timing the return gives the depth of that boundary. The same measurement images a fetus, finds a crack in a casting and maps a sea floor.

Ready when they can: States the frequency range a human ear covers and places ultrasound above it; Calculates a depth or a thickness from a measured return time and a wave speed in the material; Explains why a reflection happens at a boundary between two materials and why a scan needs gel against the skin.

https://lightmysky.com/learn/science/ultrasound-and-echo-sounding-mt_nE1uPfjhX-

#### Progressive Waves: Phase and Path Difference (ages 16-17)

A progressive wave carries energy without carrying matter, and any two points on it differ by a phase measured in degrees or in wavelengths. Path difference then decides whether two waves arrive in step.

Ready when they can: Reads amplitude, wavelength and period off displacement-distance and displacement-time graphs and says which graph is which; States the phase difference between two points a stated fraction of a wavelength apart; Turns a path difference into a phase difference and says whether the two waves arrive in phase.

https://lightmysky.com/learn/science/progressive-waves-phase-and-path-difference-mt_RotpycCNF8

#### Polarisation as Evidence for Transverse Waves (ages 16-17)

Only a transverse wave can be restricted to one plane of oscillation, so light that a second filter can block must be transverse. The same test performed on sound gives nothing.

Ready when they can: Predicts the brightness through two filters as one is turned, including the fully blocked position; Names polarisation behind glare reduction in sunglasses and behind aerial alignment; Explains why sound cannot be polarised and what that shows about it.

https://lightmysky.com/learn/science/polarisation-as-evidence-for-transverse-waves-mt_mCbxv77qDA

#### Superposition and Stationary Waves (ages 16-18)

Two waves crossing add displacement to displacement, and a wave meeting its own reflection makes a pattern that does not travel. Nodes never move, antinodes swing hardest, and neighbouring nodes sit half a wavelength apart.

Ready when they can: Applies the superposition principle to two pulses meeting, including the case where they cancel; Marks nodes and antinodes on the first three harmonics of a string and gives each wavelength; Finds the frequency of a harmonic from the length of the string and the wave speed.

https://lightmysky.com/learn/science/superposition-and-stationary-waves-mt_AIxA2TYGJN

#### Coherence and Young's Double-Slit Fringes (ages 16-18)

Two coherent sources give evenly spaced fringes whose spacing follows w = lambda D over s. A bright fringe sits wherever the path difference is a whole number of wavelengths.

Ready when they can: Explains why the two slits must be lit from one source, and what coherent means here; Uses the fringe spacing equation to get a wavelength from measurements on a screen; Predicts what happens to the pattern when the slit separation, the screen distance or the colour changes.

https://lightmysky.com/learn/science/coherence-and-youngs-double-slit-fringes-mt_mONvXhPmwq

#### The Diffraction Grating and Measuring Wavelength (ages 17-18)

A grating with many slits throws light into sharp maxima at angles given by d sin theta = n lambda. The sharpness is what makes it a better wavelength measurement than two slits.

Ready when they can: Converts lines per millimetre into a slit spacing before using the grating equation; Finds a wavelength from a measured angle for a stated order; Works out the highest order a given grating and wavelength can produce.

https://lightmysky.com/learn/science/the-diffraction-grating-and-measuring-wavelength-mt_yIjB-uJuFt

#### Single-Slit Diffraction and the Limit of Resolution (ages 17-18)

One slit spreads light into a wide central maximum with weaker ones either side, and the narrower the slit the wider that spread. The same spreading fixes the smallest detail a telescope or an eye can separate.

Ready when they can: Describes how the pattern changes as the slit width or the wavelength changes; Contrasts the uneven single-slit pattern with the even fringes from two slits; Explains why a larger aperture separates finer detail.

https://lightmysky.com/learn/science/single-slit-diffraction-and-the-limit-of-resolution-mt_qiG0fGadBU

#### Photon Energy and the Electronvolt (ages 17-18)

Light delivers energy in packets of size hf, so the energy of a photon is fixed by its frequency alone. The electronvolt is the convenient unit at that scale: the energy one electron gains crossing one volt.

Ready when they can: Calculates photon energy from a frequency or a wavelength using E = hf together with c = f lambda; Converts between joules and electronvolts in both directions; Estimates how many photons a second a stated laser power delivers.

https://lightmysky.com/learn/science/photon-energy-and-the-electronvolt-mt_UfmDhGRaYT

#### The Photoelectric Effect and the Work Function (ages 17-18)

Electrons leave a metal surface only above a threshold frequency, however bright the light gets, which no wave picture accounts for. One photon frees one electron, giving hf equal to the work function plus the greatest kinetic energy.

Ready when they can: Names the observations a wave model of light cannot explain; Uses the photoelectric equation to find a threshold frequency or a maximum kinetic energy; Explains why brighter light frees more electrons but not faster ones.

https://lightmysky.com/learn/science/the-photoelectric-effect-and-the-work-function-mt_ADQK7WB2JN

#### Energy Levels and Line Spectra (ages 17-18)

An atom holds only certain electron energies, so a jump between two of them emits or absorbs a photon of one exact energy. That is why a hot gas gives bright lines and a cool gas in front of a lamp gives dark ones.

Ready when they can: Calculates the wavelength emitted by a jump between two stated levels; Reads an energy level diagram, including why the levels are given as negative numbers; Explains an absorption spectrum as the same set of jumps taken the other way.

https://lightmysky.com/learn/science/energy-levels-and-line-spectra-mt_RlMCSDxE5q

#### de Broglie Waves and Electron Diffraction (ages 17-18)

If light can behave as particles then particles can behave as waves, with wavelength h divided by momentum. Electrons fired at a thin crystal give diffraction rings, which nothing but a wave can produce.

Ready when they can: Calculates a de Broglie wavelength from a momentum or from an accelerating voltage; Explains why the wave nature of a cricket ball is never noticed; Names electron diffraction rings as the evidence and says what raising the voltage does to them.

https://lightmysky.com/learn/science/de-broglie-waves-and-electron-diffraction-mt_Y8NthsmPcv

#### The Wave Equation and Its Travelling-Wave Solutions (ages 18-19)

Any function of x minus vt keeps its shape while moving, and the second-order equation relating the curvature of a wave to its acceleration is what such functions satisfy. One equation covers strings, sound and light.

Ready when they can: Checks by differentiation that a given function satisfies the wave equation; Reads the speed of the wave off the equation; Explains why any shape, not only a sine, can travel without distortion.

https://lightmysky.com/learn/science/the-wave-equation-and-its-travelling-wave-solutions-mt_Ue-v1cSxNx

#### Wave Speed on a String from Tension and Linear Density (ages 18-19)

The speed of a wave on a stretched string comes from the restoring tension and the inertia per unit length, with no reference to how the wave was made. Tuning an instrument is a change to one of those two quantities.

Ready when they can: Calculates wave speed from tension and mass per unit length; Predicts how the note of a string changes when it is tightened or thickened; Explains why speed is set by the medium and frequency by the source.

https://lightmysky.com/learn/science/wave-speed-on-a-string-from-tension-and-linear-density-mt_83x7vwb7UU

#### Intensity: the Energy and Power Carried by a Wave (ages 18-19)

A wave carries power proportional to the square of its amplitude, and intensity is that power spread over area. Spreading in three dimensions is why intensity falls with the square of the distance.

Ready when they can: Relates the power carried by a wave to its amplitude and frequency; Applies the inverse square law to a source radiating into space; Converts between intensity and the decibel scale for sound.

https://lightmysky.com/learn/science/intensity-the-energy-and-power-carried-by-a-wave-mt_Hj-yG6g3CD

#### Normal Modes of a Bounded System (ages 18-20)

Fixing the ends of a string or closing a pipe allows only those wavelengths that fit, so the system rings at a fundamental and its harmonics. Which harmonics appear is set by the boundary conditions.

Ready when they can: Finds the allowed wavelengths and frequencies for a string fixed at both ends; Compares open and closed pipes and explains the missing harmonics of a closed pipe; Explains why the mixture of harmonics gives an instrument its timbre.

https://lightmysky.com/learn/science/normal-modes-of-a-bounded-system-mt_650O-YrqJs

#### The Doppler Effect and Shock Waves (ages 18-20)

Motion of the source or the observer changes the observed frequency, with the two cases giving different formulas that agree at low speed. When the source outruns its own waves the fronts pile into a cone.

Ready when they can: Applies the correct Doppler expression for a moving source and for a moving observer; Explains why the two cases differ and when the difference matters; Relates the angle of a shock cone to the speed of the source.

https://lightmysky.com/learn/science/the-doppler-effect-and-shock-waves-mt_UVfD_coqh6

#### Huygens's Principle and the Laws of Reflection and Refraction (ages 18-19)

Treating every point on a wavefront as a source of new wavelets reproduces reflection and refraction without any new assumption. Snell's law becomes a statement about wave speed in each material.

Ready when they can: Constructs a refracted wavefront from wavelets and derives Snell's law; Relates refractive index to the speed of light in the material; Explains why the frequency is unchanged on crossing a boundary but the wavelength is not.

https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w

#### Total Internal Reflection, Optical Fibres and Dispersion (ages 19-20)

Past the critical angle light cannot leave a dense material at all, which is what keeps a signal inside a fibre. Because refractive index depends on wavelength, a prism spreads white light and a long fibre smears a pulse.

Ready when they can: Calculates a critical angle from two refractive indices; Explains how a step-index fibre guides light and what limits its bandwidth; Links dispersion in a prism to the wavelength dependence of refractive index.

https://lightmysky.com/learn/science/total-internal-reflection-optical-fibres-and-dispersion-mt_ZNSZMLkOD_

#### Thin Lenses and the Lens Maker's Equation (ages 19-20)

Refraction at two curved surfaces gives a focal length set by the curvatures and the refractive index, and the thin lens equation then locates any image. Sign conventions carry most of the difficulty.

Ready when they can: Uses the lens equation and a consistent sign convention to locate an image and find its magnification; Relates focal length to surface curvature and refractive index; Distinguishes real from virtual images and says which can be caught on a screen.

https://lightmysky.com/learn/science/thin-lenses-and-the-lens-makers-equation-mt_FXOcC5mpIM

#### Curved Mirrors, the Mirror Equation and Real Images (ages 19-20)

A concave mirror brings parallel light to a focus at half its radius of curvature, and one equation then locates the image for any object distance. Sign conventions decide whether the image is real or virtual, upright or inverted, and they are where most of the difficulty sits.

Ready when they can: Locates an image by ray construction for concave and convex mirrors and checks it against the mirror equation; Relates focal length to radius of curvature and explains why a spherical mirror blurs light far off axis; Explains why a shaving mirror magnifies while a car wing mirror shrinks the view and widens it.

https://lightmysky.com/learn/science/curved-mirrors-the-mirror-equation-and-real-images-mt_7XqB2umthJ

#### Magnifiers, Microscopes and Telescopes (ages 19-21)

Instruments are built by putting lenses in sequence so that the image of one becomes the object of the next, and angular magnification is what the eye actually notices. A telescope trades field of view for resolution and light collected.

Ready when they can: Traces an object through a two-lens instrument and computes the overall magnification; Distinguishes linear from angular magnification and says which matters for a distant object; Explains why a large aperture helps a telescope in two separate ways.

https://lightmysky.com/learn/science/magnifiers-microscopes-and-telescopes-mt_f30rUsqYkN

#### Phasor Addition and the Mathematics of Interference (ages 19-21)

Representing each contributing wave as a rotating arrow turns interference into vector addition, so intensity comes from the length of the resultant. Two-slit, multi-slit and single-slit patterns all follow from the same picture.

Ready when they can: Adds two or more waves of equal frequency with a phasor diagram and reads off the resultant amplitude; Derives the intensity pattern of a two-slit interference figure; Explains how the pattern sharpens as the number of slits increases.

https://lightmysky.com/learn/science/phasor-addition-and-the-mathematics-of-interference-mt_dxh7HHbIUw

#### Thin-Film Interference and Anti-Reflection Coatings (ages 19-21)

Light reflected from the two faces of a thin film interferes, and whether the result is bright or dark depends on the film thickness and on a phase change at reflection. Lens coatings are that condition engineered on purpose.

Ready when they can: Works out the condition for constructive interference in a film, including the reflection phase change; Explains the colours of an oil film and of a soap bubble as it drains; Designs the thickness of an anti-reflection coating for a stated wavelength.

https://lightmysky.com/learn/science/thin-film-interference-and-anti-reflection-coatings-mt_3ugW-ZijzH

#### The Michelson Interferometer (ages 20-22)

Splitting a beam and recombining it after two paths turns a tiny difference in path length into a countable shift of fringes. The instrument measures displacement in units of the wavelength of its own light.

Ready when they can: Relates the number of fringes passing to the distance a mirror is moved; Explains how the instrument measures a refractive index by inserting a sample in one arm; Describes why coherence length limits the path difference that still shows fringes.

https://lightmysky.com/learn/science/the-michelson-interferometer-mt_Wlb1tZnJBi

#### Intensity in Single-Slit and Double-Slit Diffraction (ages 20-21)

Adding the contributions from every point across a slit gives the intensity as a function of angle, not only the positions of the minima. A real two-slit pattern is that single-slit envelope multiplied by the two-slit fringes.

Ready when they can: Derives the single-slit intensity pattern by adding contributions across the slit; Explains missing orders in a two-slit pattern using the diffraction envelope; Predicts how the pattern changes when the slit is widened.

https://lightmysky.com/learn/science/intensity-in-single-slit-and-double-slit-diffraction-mt_HURhzZdIkM

#### X-Ray Diffraction and the Bragg Condition (ages 20-22)

Planes of atoms reflect X-rays that reinforce only at angles satisfying the Bragg condition, so a diffraction pattern is a map of atomic spacing. Crystal structures, and the shape of DNA, were read this way.

Ready when they can: Applies the Bragg condition to get a plane spacing from a measured angle; Explains why X-rays rather than visible light are needed for atomic spacings; Describes what a diffraction pattern reveals about the arrangement of atoms.

https://lightmysky.com/learn/science/x-ray-diffraction-and-the-bragg-condition-mt_qEDplGeIkB

#### Fourier Analysis and the Wave Packet (ages 21-22)

Any repeating shape is a sum of sines, and a pulse is a sum over a continuous range of frequencies. The shorter the pulse, the wider the range of frequencies it needs.

Ready when they can: Writes a square wave as a sum of harmonics and describes what adding more terms does; Relates the width of a pulse in time to the spread of frequencies it contains; Applies the idea to bandwidth in a communication channel.

https://lightmysky.com/learn/science/fourier-analysis-and-the-wave-packet-mt_1ZaojWUZEw

#### Stimulated Emission and How a Laser Works (ages 21-22)

An excited atom hit by a photon of the right energy emits a second identical photon, and a population inversion plus a mirrored cavity turns that into a beam. Coherence, not brightness, is what separates a laser from a lamp.

Ready when they can: Distinguishes spontaneous from stimulated emission and states what makes the emitted photon identical; Explains why a population inversion is needed and how a three-level scheme reaches one; Says what the cavity mirrors contribute to the output beam.

https://lightmysky.com/learn/science/stimulated-emission-and-how-a-laser-works-mt_xgjD0mzEAV

### Forces & Motion

https://lightmysky.com/learn/science/areas/forces-and-motion

#### Forces Vocabulary (ages 5-8)

Name and describe forces using precise vocabulary — force, push, pull, twist, stretch, squash, contact force, non-contact force, gravity, weight, friction, air resistance, upthrust — and distinguish between forces that require physical contact and forces that act at a distance

Ready when they can: Correctly name the force acting in at least five given scenarios (e.g. 'friction slows the sledge', 'gravity pulls the apple'); Distinguish between contact forces (friction, upthrust) and non-contact forces (gravity, magnetism) using the correct terms; Use 'weight' correctly as a force — distinct from 'mass' — in descriptions.

https://lightmysky.com/learn/science/forces-vocabulary-mt_GBY8enpzO0

#### Drawing Force Diagrams (ages 7-12)

Draw and interpret force diagrams showing forces as labelled arrows — where the arrow's length represents the force's magnitude and its direction shows which way the force acts; show multiple forces on one object; identify from the diagram whether forces are balanced (equal arrows in opposite directions, no resultant) or unbalanced (arrows of different sizes, producing a resultant); represent the resultant with a single arrow

Ready when they can: Draw a force diagram with labelled arrows showing direction and relative size for at least two forces acting on an object; Use their diagram to explain whether forces are balanced or unbalanced and what will happen to the object; Add a resultant force arrow to a diagram and explain how they calculated it.

Needs first: Forces Vocabulary.

https://lightmysky.com/learn/science/drawing-force-diagrams-mt_k7GOtslF-x

#### Pushes & Pulls (ages 5-6)

Understand that pushes and pulls are forces that can change the speed or direction of an object's motion, and compare the effects of different strengths and directions

Ready when they can: Describe a push and a pull as types of force that make objects move, speed up, slow down, or change direction; Compare the effects of a gentle push versus a strong push on the same object; Predict the direction an object will move based on the direction of the applied force.

Needs first: Drawing Force Diagrams.

https://lightmysky.com/learn/science/pushes-and-pulls-mt_B3W5EfimJw

#### Testing Push & Pull Designs (ages 5-6)

Analyse data to determine if a design solution works as intended to change the speed or direction of an object with a push or pull

Ready when they can: Test a simple design (e.g. ramp, launcher) and collect data on whether it meets the goal; Analyse results to determine if the design works as intended; Suggest modifications based on the data to improve the design's performance.

Needs first: Pushes & Pulls.

https://lightmysky.com/learn/science/testing-push-and-pull-designs-mt_RlILL2sccX

#### Friction & Surfaces (ages 7-8)

Compare how things move on different surfaces, noticing that some surfaces create more friction than others

Ready when they can: Observe and compare how the same object moves on at least three different surfaces; Describe that rough surfaces slow objects down more than smooth surfaces; Use the word 'friction' to explain why movement differs on different surfaces.

Needs first: Pushes & Pulls, Forces Vocabulary.

https://lightmysky.com/learn/science/friction-and-surfaces-mt_-p_xp4hMvh

#### Contact & Non-Contact Forces (ages 7-8)

Notice that some forces need contact between two objects (contact forces) while magnetic forces can act at a distance (non-contact forces)

Ready when they can: Define contact forces as those needing objects to touch (e.g. push, pull, friction); Define non-contact forces as those acting at a distance (e.g. magnetism); Sort examples of forces into contact and non-contact categories.

Needs first: Drawing Force Diagrams, Friction & Surfaces.

https://lightmysky.com/learn/science/contact-and-non-contact-forces-mt_lcf8lx-LkZ

#### Balanced & Unbalanced Forces (ages 8-9)

Plan and conduct an investigation to provide evidence of the effects of balanced and unbalanced forces on the motion of an object

Ready when they can: Define balanced forces (equal in size, opposite in direction — no change in motion) and unbalanced forces (cause motion to change); Plan a fair test investigating how different force sizes affect an object's motion; Use results as evidence to explain when forces are balanced versus unbalanced.

Needs first: Drawing Force Diagrams, Friction & Surfaces.

https://lightmysky.com/learn/science/balanced-and-unbalanced-forces-mt_3WMADSy0mA

#### Force & Motion Vocabulary (ages 9-11)

Use technical vocabulary for force and motion — balanced forces, unbalanced forces, resultant force, acceleration, deceleration, speed, moment, lever, fulcrum, mechanical advantage — and apply these when explaining and predicting how forces affect the motion and position of objects

Ready when they can: Distinguish between balanced and unbalanced forces and describe the effect of each on an object's motion; Use 'resultant force' correctly when describing the net effect of two or more forces acting on an object; Apply 'moment', 'lever', and 'fulcrum' correctly when describing how simple machines work.

Needs first: Forces Vocabulary.

https://lightmysky.com/learn/science/force-and-motion-vocabulary-mt_F3ATPTCYm6

#### Gravity & Falling Objects (ages 9-11)

Explain that unsupported objects fall towards the Earth because of the force of gravity acting between the Earth and the falling object

Ready when they can: Define gravity as a force of attraction between the Earth and objects; Explain that unsupported objects fall because gravity pulls them towards the Earth; Give examples showing gravity in action (dropping objects, jumping, water flowing downhill).

Needs first: Balanced & Unbalanced Forces, Drawing Force Diagrams, Contact & Non-Contact Forces.

https://lightmysky.com/learn/science/gravity-and-falling-objects-mt_AvrQauS_zX

#### Air Resistance & Friction (ages 9-10)

Identify the effects of air resistance, water resistance, and friction, and understand that these forces act between moving surfaces to oppose motion

Ready when they can: Define air resistance, water resistance, and friction as forces that oppose motion; Give everyday examples of each force and explain how they slow things down; Describe how these forces depend on factors like speed, surface area, or surface texture.

Needs first: Gravity & Falling Objects, Drawing Force Diagrams, Friction & Surfaces.

https://lightmysky.com/learn/science/air-resistance-and-friction-mt_Y9k86G8BBT

#### Levers, Pulleys & Gears (ages 9-10)

Recognise that some mechanisms including levers, pulleys, and gears allow a smaller force to have a greater effect

Ready when they can: Describe how a lever works: effort at one end moves a load at the other, with a pivot in between; Explain how a pulley changes the direction of a force and can make lifting easier; Describe how gears transfer and change the size or direction of forces.

Needs first: Balanced & Unbalanced Forces, Gravity & Falling Objects, Force & Motion Vocabulary.

https://lightmysky.com/learn/science/levers-pulleys-and-gears-mt_Q2k3fSwyzQ

#### Reading Distance-Time Graphs (ages 10-13)

Read and plot distance-time graphs for moving objects; interpret the gradient (steepness) of a line as speed; identify stationary periods (horizontal sections), constant speed (straight diagonal lines), and relative speeds by comparing gradients; calculate average speed from the gradient of a straight-line segment using speed = distance ÷ time

Ready when they can: Read a distance-time graph and describe what is happening at each stage — moving, stopped, returning; Calculate speed from the gradient of a straight section of a distance-time graph; Sketch a distance-time graph from a written description of a journey with stops and speed changes.

Needs first: Compound Units, First Quadrant Coordinates.

https://lightmysky.com/learn/science/reading-distance-time-graphs-mt_OUv-QXmW7_

#### Predicting Motion Patterns (ages 8-9)

Make observations and measurements of an object's motion to provide evidence that a pattern can be used to predict future motion

Ready when they can: Measure an object's motion (distance, speed, direction) under different conditions; Identify a pattern in the data (e.g. steeper ramp = further roll); Use the pattern to make and test a prediction about future motion.

Needs first: Balanced & Unbalanced Forces, Reading Distance-Time Graphs.

https://lightmysky.com/learn/science/predicting-motion-patterns-mt_AlLYwCm92a

#### Mass vs Weight (ages 11-12)

Distinguish between mass (amount of matter, measured in kg) and weight (gravitational force, measured in N), use the equation weight = mass × gravitational field strength, and explain why g differs on other planets and stars

Ready when they can: Explains the difference between mass and weight with correct units for each; Calculates weight using W = mg with g = 10 N/kg on Earth; Predicts what would happen to an object's weight on the Moon or Jupiter; Explains why mass stays constant but weight changes in different gravitational fields.

Needs first: Gravity & Falling Objects.

https://lightmysky.com/learn/science/mass-vs-weight-mt_sUVeVXzRuq

#### Resultant Forces (ages 11-12)

Describe forces as vector quantities with both magnitude and direction, distinguish between balanced forces (zero resultant, no change in motion) and unbalanced forces (non-zero resultant, causes acceleration or deceleration)

Ready when they can: Explains what a vector quantity is and why force is a vector; Calculates the resultant force when two forces act in the same or opposite directions on an object; Explains what happens to an object's motion when forces are balanced vs unbalanced; Draws free body diagrams showing all forces on a stationary object (e.g. a book on a table).

Needs first: Pushes & Pulls, Force & Motion Vocabulary, Drawing Force Diagrams, Contact & Non-Contact Forces.

https://lightmysky.com/learn/science/resultant-forces-mt_AiWlJfvC3O

#### Speed & Distance-Time Graphs (ages 11-12)

Calculate average speed using the equation speed = distance ÷ time, represent journeys on distance-time graphs, and interpret gradient as speed and flat sections as stationary periods

Ready when they can: Uses speed = distance ÷ time to calculate average speed with correct units (m/s, km/h); Draws a distance-time graph for a given journey with correct axes and labels; Reads a distance-time graph to determine speed, stopping points, and direction of travel; Identifies which section of a distance-time graph represents the fastest speed.

Needs first: Compound Units, Reading Distance-Time Graphs.

https://lightmysky.com/learn/science/speed-and-distance-time-graphs-mt_q-1a86ydgU

#### Relative Motion (ages 11-12)

Explain relative motion — how the apparent speed and direction of an object depends on the observer's own motion — using everyday examples such as trains and cars passing

Ready when they can: Explains why a train moving at the same speed in the same direction as another appears stationary to passengers on that train; Calculates relative speed when two objects move towards or away from each other; Explains why the frame of reference matters when describing motion.

Needs first: Speed & Distance-Time Graphs.

https://lightmysky.com/learn/science/relative-motion-mt_-OndzpVsrv

#### Deformation & Fluid Pressure (ages 12-13)

Explain forces associated with deforming objects (elastic and inelastic deformation), thermal expansion and contraction of materials, and how fluid pressure acts in all directions and increases with depth

Ready when they can: Distinguishes elastic deformation (returns to shape) from inelastic/plastic deformation (permanently changed); Explains why bridges and railway tracks have expansion gaps; Explains why pressure increases with depth in a liquid (e.g. why deep-sea divers need pressure suits); Gives an everyday example of thermal expansion causing a problem or being used usefully.

Needs first: Resultant Forces.

https://lightmysky.com/learn/science/deformation-and-fluid-pressure-mt_fkwcCB5px7

#### Moments, Pressure & Hooke's Law (ages 12-14)

Calculate the turning effect (moment = force × perpendicular distance), explain how pressure is transmitted equally in liquids (Pascal's principle) and the concept of atmospheric pressure, and describe Hooke's Law (extension ∝ force up to the elastic limit)

Ready when they can: Calculates the moment of a force and uses the principle of moments to solve lever problems; Explains why hydraulic systems can multiply force (pressure transmitted equally); States Hooke's Law and plots force-extension graphs identifying the elastic limit; Calculates spring constant k from a force-extension graph (k = F/x).

Needs first: Resultant Forces, Levers, Pulleys & Gears.

https://lightmysky.com/learn/science/moments-pressure-and-hookes-law-mt_vuNjYx3qOy

#### Newton's First & Second Laws (ages 12-13)

State and apply Newton's First Law (an object stays at rest or constant velocity unless acted on by a resultant force) and Second Law (force = mass × acceleration), including the relationship between mass, force, and acceleration

Ready when they can: States Newton's First Law and gives a real example (e.g. why a moving spacecraft doesn't need engines in space); Uses F = ma to calculate force, mass, or acceleration given the other two quantities; Explains why a heavier object requires more force to achieve the same acceleration; Explains why seatbelts are needed in cars using Newton's First Law.

Needs first: Resultant Forces, Mass vs Weight, Air Resistance & Friction, Speed & Distance-Time Graphs.

https://lightmysky.com/learn/science/newtons-first-and-second-laws-mt_tXxxCFl32J

#### Investigating Forces (ages 12-13)

Plan and carry out investigations into forces, including measuring force with a newton meter, investigating Hooke's Law, and collecting and interpreting motion data to test Newton's laws

Ready when they can: Uses a newton meter correctly to measure forces in newtons; Sets up and conducts a Hooke's Law investigation, recording force and extension and plotting a graph; Identifies and controls variables in a force investigation; Calculates acceleration from force and mass data and compares with experimental results.

Needs first: Newton's First & Second Laws, Moments, Pressure & Hooke's Law, Predicting Motion Patterns.

https://lightmysky.com/learn/science/investigating-forces-mt_xkn2sf93WJ

#### Newton's Third Law (ages 12-13)

State and apply Newton's Third Law: every force has an equal and opposite reaction force acting on a different object, distinguishing action-reaction pairs from balanced forces

Ready when they can: States Newton's Third Law correctly, identifying both the action and reaction force and the objects they act on; Gives at least two real-world examples (e.g. rocket propulsion, swimmer pushing off a wall); Distinguishes a Newton's Third Law pair from balanced forces on the same object; Explains why a gun recoils when fired using Newton's Third Law.

Needs first: Newton's First & Second Laws.

https://lightmysky.com/learn/science/newtons-third-law-mt_fbYbe3YSVj

#### Vectors, Scalars and Free-Body Diagrams (ages 14-15)

Sorting quantities into scalars, which carry only a size, and vectors, which carry a direction too. Every force on one object is then drawn as an arrow whose length is its size, and the resultant is read off the diagram.

Ready when they can: Sorts distance, speed and mass from displacement, velocity, force and weight, saying which need a direction; Draws a free-body diagram for a hanging lamp, a towed sledge and a falling ball, with arrows to scale; Finds the resultant of two forces along one line, and of two forces at right angles by scale drawing.

https://lightmysky.com/learn/science/vectors-scalars-and-free-body-diagrams-mt_erzORFj2-1

#### Acceleration from Velocity-Time Graphs (ages 14-15)

Reading a velocity-time graph two ways: the gradient gives the acceleration, and the area under the line gives the distance travelled. A negative gradient shows slowing down.

Ready when they can: Calculates acceleration as a gradient and quotes it in metres per second squared; Finds distance travelled from the area under a velocity-time graph made of straight sections; Sketches the distance-time graph and the velocity-time graph of the same journey and says how they differ.

https://lightmysky.com/learn/science/acceleration-from-velocity-time-graphs-mt_nmvfbSgnOn

#### The Uniform Acceleration Equations (ages 14-16)

Using v = u + at and v squared = u squared + 2as when acceleration is steady, including picking which one fits the quantities given. The graph work becomes algebra that answers questions no graph was drawn for.

Ready when they can: Lists the known and wanted quantities of a problem and picks the equation that links them; Rearranges each equation to make any one of its quantities the subject; Uses a negative acceleration for a braking or rising object and reads the sign of the answer correctly.

https://lightmysky.com/learn/science/the-uniform-acceleration-equations-mt_yJMJQ8_KqR

#### Newton's Second Law with Numbers (ages 14-15)

Treating F = ma as a working equation: the resultant force sets the acceleration, and mass measures how strongly an object resists that change. Mass, not weight, is what appears in the calculation.

Ready when they can: Calculates any one of resultant force, mass or acceleration when the other two are given; Explains why a loaded trolley accelerates less than an empty one under the same push; Uses the resultant of several forces, not one single force, in the calculation.

https://lightmysky.com/learn/science/newtons-second-law-with-numbers-mt_Nn2MVJL7bO

#### Terminal Velocity (ages 14-16)

Drag grows as an object speeds up, so the resultant force shrinks and the acceleration fades to zero. From then on the object falls at a steady speed, which changes if its area or weight changes.

Ready when they can: Sketches the velocity-time graph of a skydiver before and after the parachute opens, and explains each section; States that terminal velocity happens when drag equals weight, not when the force disappears; Predicts how a larger surface area or a heavier load changes the terminal velocity.

https://lightmysky.com/learn/science/terminal-velocity-mt_3eNYHV-m-c

#### Momentum and Its Conservation (ages 14-16)

Momentum is mass times velocity, and it points the way the object moves. With no outside force, the total momentum of a group of objects is the same after a collision or explosion as before.

Ready when they can: Calculates momentum in kg m/s and gives its direction; Works out an unknown velocity after two trolleys collide and stay joined; Applies the same reasoning to an explosion, where two objects start at rest and move apart.

https://lightmysky.com/learn/science/momentum-and-its-conservation-mt_Nn5_DMbK1_

#### Impulse and Crash Safety (ages 15-16)

Force equals the change in momentum divided by the time it takes. Stretching a collision over a longer time lowers the force, which is what airbags, crumple zones and crash mats are for.

Ready when they can: Calculates the average force from a change in momentum and a contact time; Explains a safety feature by naming the quantity it changes and the one it leaves alone; Says why a longer stopping time gives a smaller force when the momentum change is fixed.

https://lightmysky.com/learn/science/impulse-and-crash-safety-mt_BjLAFw2zjU

#### Resolving Vectors into Components (ages 16-17)

Splitting one vector into two perpendicular parts with sine and cosine, then adding several vectors by adding their components. Scale drawing gives way to a method that stays exact however many forces act.

Ready when they can: Resolves a force or a velocity into components along any chosen pair of perpendicular axes; Adds three or more coplanar vectors by components and states the resultant as a size and an angle; Picks the axes that make a problem shortest and says why that choice is free.

https://lightmysky.com/learn/science/resolving-vectors-into-components-mt_tc698unGJG

#### Projectile Motion as Two Independent Motions (ages 16-17)

The horizontal and vertical motions of a projectile are worked separately: constant velocity across, uniform acceleration down, sharing nothing but the time. A ball rolled off a bench becomes two one-dimensional problems joined by t.

Ready when they can: Keeps a separate list of u, v, a, s and t for the horizontal and the vertical direction; Uses time as the only quantity the two directions share; Predicts where a ball rolled off a bench lands and says why its mass does not appear.

https://lightmysky.com/learn/science/projectile-motion-as-two-independent-motions-mt_OBgL97RFbb

#### Projectiles Launched at an Angle (ages 16-18)

An angled launch gives both directions a starting velocity, so flight time, greatest height and range all come from the same two lists. The symmetry of the path is a check on the answer rather than an extra rule.

Ready when they can: Resolves the launch velocity, then gets the time of flight from the vertical motion alone; Finds the range from the horizontal component and that time, without quoting a range formula; Explains why 45 degrees gives the longest range on level ground but not from a cliff top.

https://lightmysky.com/learn/science/projectiles-launched-at-an-angle-mt_MMuacyCqb8

#### Newton's Second Law on a Slope (ages 16-17)

Resolving weight along and perpendicular to a slope turns an inclined-plane problem into one equation of motion plus one balance. Friction enters as a force set by the normal contact force and the surfaces in contact.

Ready when they can: Resolves weight into components along and perpendicular to the surface; Balances the perpendicular direction to get the normal contact force, then applies F = ma along the slope; Uses the coefficient of friction to find the friction force and the angle at which sliding begins.

https://lightmysky.com/learn/science/newtons-second-law-on-a-slope-mt_OR_sKFelnP

#### Connected Bodies: Tension, Pulleys and Lifts (ages 16-18)

Two bodies joined by a rope share one acceleration, so each gets its own equation and the tension appears in both. Adding the pair of equations removes the tension, and substituting back returns it.

Ready when they can: Draws a separate free-body diagram for each body and writes F = ma for each; Solves the pair of equations for the shared acceleration and then for the tension; Explains the changing reading of a bathroom scale in a lift that starts and stops.

https://lightmysky.com/learn/science/connected-bodies-tension-pulleys-and-lifts-mt_qk2gn4tUoN

#### Moments, Couples and the Conditions for Equilibrium (ages 16-17)

A rigid body is in equilibrium when the resultant force is zero and the total moment about any point is also zero. A couple is the special case with no resultant force at all, only a turning effect.

Ready when they can: Takes moments about a chosen point to find an unknown support force on a loaded beam; Shows the answer is the same whichever point is chosen, and picks the point that removes an unknown; Separates a couple from a single force and gives its moment as one force times the separation.

https://lightmysky.com/learn/science/moments-couples-and-the-conditions-for-equilibrium-mt_EDsdTZ0BNO

#### Velocity and Acceleration as Derivatives (ages 18-19)

Velocity is the time derivative of the position vector and acceleration the derivative of velocity, taken one component at a time. Motion whose acceleration changes needs no new formulas once this is the definition.

Ready when they can: Differentiates a position function to get velocity and acceleration at any instant; Handles two-dimensional motion by differentiating each component separately; Says why the constant-acceleration equations stop applying as soon as acceleration depends on time.

https://lightmysky.com/learn/science/velocity-and-acceleration-as-derivatives-mt_RdhbiJ6CTk

#### Recovering Motion by Integrating Acceleration (ages 18-19)

Given acceleration as a function of time, integration returns velocity and then position, with the constants of integration fixed by the initial conditions. The constant-acceleration equations reappear as the case of a constant integrand.

Ready when they can: Integrates a given acceleration twice and uses initial position and velocity to fix both constants; Derives the constant-acceleration equations by integrating a constant; Reads a change in velocity as the area under an acceleration-time graph.

https://lightmysky.com/learn/science/recovering-motion-by-integrating-acceleration-mt_CXo7wKOA46

#### Newton's Second Law as a Differential Equation (ages 18-19)

Writing the second law as mass times the second derivative of position equals force turns a force rule into an equation whose solution is the whole future motion. The same statement covers a falling stone, a spring and a charged particle.

Ready when they can: Writes the equation of motion for a stated force and identifies what has to be solved for; Solves the equation for a constant force and for a force that depends only on time; Explains why two initial conditions are needed before a single trajectory is picked out.

https://lightmysky.com/learn/science/newtons-second-law-as-a-differential-equation-mt_LzSNSkEovH

#### Drag and Terminal Speed from the Equation of Motion (ages 18-19)

A drag force that grows with speed makes acceleration depend on velocity, and solving that equation gives an approach to a terminal speed. Linear and quadratic drag give different curves and different terminal values.

Ready when they can: Sets up the equation of motion for a body falling with linear or quadratic drag; Finds terminal speed by setting the acceleration to zero and says what that means physically; Sketches the velocity-time curve and explains why it flattens rather than crosses the terminal value.

https://lightmysky.com/learn/science/drag-and-terminal-speed-from-the-equation-of-motion-mt_In6VeoADzZ

#### Magnetic Materials (ages 7-8)

Observe how magnets attract or repel each other and attract some materials and not others

Ready when they can: Demonstrate that magnets attract some materials (iron, steel, nickel) but not others (wood, plastic, copper); Show that two magnets can either attract (pull together) or repel (push apart); Test at least six objects and correctly predict which are magnetic.

Needs first: Contact & Non-Contact Forces, Naming Everyday Materials.

https://lightmysky.com/learn/science/magnetic-materials-mt_9NvuqZKNiV

#### Magnetic Poles (ages 7-9)

Describe magnets as having two poles (north and south) and predict whether two magnets will attract or repel based on which poles face each other

Ready when they can: Identify and label the north and south poles of a magnet; State the rule: like poles repel, opposite poles attract; Predict the outcome of bringing two magnets together based on their pole orientation.

Needs first: Magnetic Materials.

https://lightmysky.com/learn/science/magnetic-poles-mt_jgNB2752b9

#### Magnetic Fields (ages 11-12)

Describe magnetic poles (north and south), explain attraction and repulsion between poles, describe magnetic field lines plotted using a compass, and explain the Earth's magnetic field and its practical uses

Ready when they can: States the rule for attraction and repulsion of magnetic poles; Draws the magnetic field pattern around a bar magnet from memory or compass readings; Explains why a compass needle points north; Explains that the Earth has a magnetic field and describes how it is used for navigation.

Needs first: Magnetic Poles.

https://lightmysky.com/learn/science/magnetic-fields-mt_56aspHjU19

#### Electromagnets (ages 12-13)

Describe the magnetic effect of an electric current (a current-carrying wire produces a magnetic field), and investigate how the strength of an electromagnet depends on current, number of coil turns, and core material

Ready when they can: Describes that a current-carrying wire produces a circular magnetic field; Lists three factors that affect electromagnet strength: current size, number of coil turns, and core material; Explains why an electromagnet can be switched on and off, unlike a permanent magnet.

Needs first: Current, voltage, and what they measure, Magnetic Fields.

https://lightmysky.com/learn/science/electromagnets-mt_2qkn8Lhc8e

#### Motors & the Motor Effect (ages 13-14)

Explain the motor effect as the force on a current-carrying conductor in a magnetic field, and describe how this principle is used in electric motors and loudspeakers

Ready when they can: Explains that a current-carrying conductor in a magnetic field experiences a force (the motor effect); Predicts how reversing the current or reversing the magnetic field affects the direction of the force; Describes how the motor effect is applied in an electric motor and in a loudspeaker.

Needs first: Electromagnets.

https://lightmysky.com/learn/science/motors-and-the-motor-effect-mt__7BVYUN180

#### Floating, Sinking and Upthrust (ages 8-9)

Water pushes up on anything placed in it, and whether an object floats depends on that upward push against its weight rather than on how heavy it feels in the hand. A heavy steel boat floats and a small steel nail sinks, which is the puzzle this stop settles.

Ready when they can: Predicts whether an object will float and gives the upward push from the water as the reason; Explains why a large hollow object can float when a small solid one of the same material sinks; Feels and describes an object becoming lighter as it is lowered into water, and names that change as upthrust.

https://lightmysky.com/learn/science/floating-sinking-and-upthrust-mt_TJI95Ot-qQ

#### Stopping Distances and Braking Energy (ages 15-16)

Stopping distance splits into thinking distance, set by reaction time and speed, and braking distance, set by the work the brakes must do to empty the kinetic store. Braking distance grows with the square of the speed.

Ready when they can: Calculates thinking distance from a reaction time and a speed; Uses the kinetic store and the braking force to work out a braking distance; Explains why doubling the speed roughly quadruples the braking distance, and lists what makes each part longer.

https://lightmysky.com/learn/science/stopping-distances-and-braking-energy-mt_nRNZS4jHoj

#### Newton's Law of Gravitation and Gravitational Field Strength (ages 16-17)

Any two masses attract with a force that falls off as the square of their separation. Dividing that force by the test mass leaves a field strength that belongs to the source alone.

Ready when they can: Uses F = GMm over r squared with r measured centre to centre; Shows that surface g follows from GM over R squared, and predicts g at a stated height; Sketches the radial field of a single mass and says what the spacing of the lines shows.

https://lightmysky.com/learn/science/newtons-law-of-gravitation-and-gravitational-field-strength-mt_uUYXl3L0oW

#### Gravitational Potential and Escape Speed (ages 16-18)

Gravitational potential is the work per kilogram needed to bring a mass in from infinity, which makes it negative everywhere near a source. Escape speed is the speed whose kinetic energy exactly fills that well.

Ready when they can: Calculates potential as minus GM over r and potential energy as minus GMm over r at a stated position; Explains the negative sign by naming infinity as the zero of the scale; Gets escape speed by setting kinetic energy equal to the depth of the well.

https://lightmysky.com/learn/science/gravitational-potential-and-escape-speed-mt_drqTwCD9W8

#### Elastic and Inelastic Collisions (ages 17-18)

Momentum is conserved in every collision, but kinetic energy is conserved only in an elastic one. Adding up the kinetic energy before and after is what sorts one kind from the other.

Ready when they can: Applies conservation of momentum in one dimension with signs that carry the directions; Totals the kinetic energy before and after and classifies the collision from the comparison; Says where the missing kinetic energy has gone in an inelastic collision.

https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq

#### Pressure in Liquids and the Atmosphere (ages 15-16)

Pressure is force spread over area, and in a fluid it grows with depth and with the density of the fluid. The same reasoning gives upthrust, tells whether an object floats, and explains why air pressure drops with height.

Ready when they can: Calculates pressure from force and area, and pressure at depth from depth, density and gravitational field strength; Explains upthrust as the pressure difference between the bottom and top of a submerged object; Predicts whether an object floats by comparing its density with the liquid's, and explains why air pressure falls with altitude.

https://lightmysky.com/learn/science/pressure-in-liquids-and-the-atmosphere-mt_eLGNkEJAZl

#### Continuity and Bernoulli's Equation for Ideal Flow (ages 19-20)

Mass cannot pile up in a pipe, so a narrower section carries the same flow at a higher speed. Applying the work-energy theorem to a moving element of fluid then ties pressure, speed and height into one statement that holds along a streamline.

Ready when they can: Uses continuity to get the speed in one section of a pipe from the speed and area in another; Derives Bernoulli's equation as work done on a fluid element rather than quoting it; Explains lift, a Venturi meter and the flow from a hole in a tank with the same relation, and states where the ideal assumptions fail.

https://lightmysky.com/learn/science/continuity-and-bernoullis-equation-for-ideal-flow-mt_pKxlVYTy0Y

#### Viscosity, Poiseuille Flow and the Reynolds Number (ages 20-21)

A real fluid drags on itself and on the pipe wall, which gives a parabolic speed profile and a flow rate that falls with the fourth power of the radius. Comparing inertial to viscous effects gives one dimensionless number that says whether the flow will stay smooth or break into turbulence.

Ready when they can: Explains why halving a pipe's radius cuts the flow rate by a factor of sixteen at fixed pressure difference; Builds the Reynolds number from the quantities in the problem and uses it to predict laminar or turbulent flow; Says which of two situations Bernoulli's equation may be applied to, and why viscosity rules the other one out.

https://lightmysky.com/learn/science/viscosity-poiseuille-flow-and-the-reynolds-number-mt_-1sWgkRtMs

#### Circular Motion: Angular Speed and Centripetal Force (ages 17-18)

An object going round at steady speed is still accelerating, because the direction of its velocity keeps changing. The resultant force points to the centre and has size mv squared over r, which is also m omega squared r.

Ready when they can: Converts between period, frequency, linear speed and angular speed in radians per second; Names the real force acting as the centripetal one in a given setup instead of adding a new force; Finds the greatest speed for a whirled mass before the string reaches its breaking tension.

https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq

#### Simple Harmonic Motion: the Defining Relation and Its Graphs (ages 17-18)

When the acceleration of an object is proportional to its displacement and points back towards the centre, the motion repeats with a period that does not depend on the amplitude. Displacement, velocity and acceleration then run as three sine curves each a quarter cycle ahead of the last.

Ready when they can: Tests whether a given motion is simple harmonic by checking the acceleration against the displacement; Reads amplitude, period and phase off displacement, velocity and acceleration graphs and says how the three line up; Predicts how the period of a mass on a spring and of a pendulum changes when mass, stiffness or length changes.

https://lightmysky.com/learn/science/simple-harmonic-motion-the-defining-relation-and-its-graphs-mt_NTDayHkdfh

#### Energy in Simple Harmonic Motion, Damping and Resonance (ages 17-18)

An oscillator trades its whole energy between a kinetic store and a potential one twice per cycle, and the total stays fixed only while nothing dissipates. Damping drains it, and driving at the natural frequency pumps the amplitude up until the losses catch the input.

Ready when they can: Sketches kinetic, potential and total energy against displacement for one oscillation and explains the shape of each; Distinguishes light, critical and heavy damping by what happens to a displaced system, and gives a use for each; Explains why amplitude peaks near the natural frequency and what heavier damping does to the height and width of that peak.

https://lightmysky.com/learn/science/energy-in-simple-harmonic-motion-damping-and-resonance-mt_3sh7E7k7j2

#### Simple Harmonic Motion as a Second-Order Equation (ages 18-20)

Any restoring force proportional to displacement gives the same differential equation, whose solutions are sines and cosines at one natural frequency. Amplitude and phase come from the initial conditions, never from the equation itself.

Ready when they can: Derives the harmonic equation for a mass on a spring and for a small-angle pendulum; Writes the general solution with amplitude and phase and fits both to given initial conditions; Shows that the natural frequency depends on the system, not on how hard it was started.

https://lightmysky.com/learn/science/simple-harmonic-motion-as-a-second-order-equation-mt_HHmR-uCvwO

#### Damped Oscillations and the Three Damping Regimes (ages 19-20)

Adding a velocity-dependent damping term splits the behaviour into underdamped, critically damped and overdamped, decided by the size of the damping against the natural frequency. Car suspensions and door closers are engineered choices between those regimes.

Ready when they can: Adds a damping term to the harmonic equation and identifies the three regimes from its coefficient; Sketches displacement against time for each regime and states which returns to rest fastest; Explains why the oscillation frequency of an underdamped system is slightly below the natural frequency.

https://lightmysky.com/learn/science/damped-oscillations-and-the-three-damping-regimes-mt_JCpYpFVn6s

#### Driven Oscillations, Resonance and the Quality Factor (ages 19-20)

A periodic driving force makes the steady-state amplitude peak when the driving frequency is near the natural one, and the sharpness of that peak is the quality factor. Light damping means a tall narrow peak and a long ring-down.

Ready when they can: Sketches amplitude against driving frequency for several damping strengths; Relates the quality factor to the sharpness of the peak and to how long free oscillations last; Names a case where resonance is wanted and one where it has to be suppressed, with the physical reason.

https://lightmysky.com/learn/science/driven-oscillations-resonance-and-the-quality-factor-mt_FmpOTEZFy4

#### Coupled Oscillators and Normal Modes (ages 19-20)

Two masses joined by springs no longer have one frequency: the motion splits into normal modes, each a pattern of the whole system oscillating at a single frequency. Any starting motion is a combination of those modes.

Ready when they can: Writes the coupled equations for two masses and springs and finds both normal mode frequencies; Describes the in-phase and out-of-phase patterns and which frequency belongs to each; Expresses a general starting condition as a sum of normal modes.

https://lightmysky.com/learn/science/coupled-oscillators-and-normal-modes-mt_vnTGOIqZzP

#### The Centre of Mass and the Motion of a System (ages 19-21)

The centre of mass of any system moves as if all the mass sat there and every external force acted on it, whatever the internal forces do. Internal forces cancel in pairs, which is why an exploding shell keeps its parabola.

Ready when they can: Locates the centre of mass of a set of particles and of a simple continuous body by integration; Shows that internal forces cancel and so cannot move the centre of mass; Predicts the path of the centre of mass of a body that breaks apart in flight.

https://lightmysky.com/learn/science/the-centre-of-mass-and-the-motion-of-a-system-mt_fHO_KrMNKo

#### Variable Mass and the Rocket Equation (ages 19-21)

A rocket accelerates by throwing mass backwards, so the second law has to be applied to a system whose mass is changing. Integrating gives a speed that depends on exhaust speed and the logarithm of the mass ratio.

Ready when they can: Sets up the momentum balance for a short interval in which a small mass is ejected; Derives the rocket equation and identifies exhaust speed and mass ratio in it; Explains why staging beats carrying one large tank.

https://lightmysky.com/learn/science/variable-mass-and-the-rocket-equation-mt_4IugclcEVi

#### Rotational Kinematics and the Angular Velocity Vector (ages 20-21)

Angular displacement, velocity and acceleration are defined by the same derivatives as their linear partners, and angular velocity points along the axis. Every point of a rigid body then has a linear speed set by its distance from that axis.

Ready when they can: Relates angular and linear speed, tangential acceleration and centripetal acceleration for a point on a rotating body; Uses the right-hand rule to give an angular velocity its direction; Solves constant angular acceleration problems with the rotational analogues of the constant-acceleration equations.

https://lightmysky.com/learn/science/rotational-kinematics-and-the-angular-velocity-vector-mt_2UqK-zViqf

#### Moment of Inertia by Integration and the Parallel-Axis Theorem (ages 20-21)

Moment of inertia is an integral of distance squared over the mass distribution, so it depends on the axis as well as the body. The parallel-axis theorem moves a known result to any parallel axis without redoing the integral.

Ready when they can: Sets up and evaluates the integral for a rod, a disc or a hoop about a stated axis; Applies the parallel-axis theorem and says why the moment of inertia is smallest about the centre of mass; Explains why the same body has different moments of inertia about different axes.

https://lightmysky.com/learn/science/moment-of-inertia-by-integration-and-the-parallel-axis-theorem-mt_VFRk1WIzAK

#### Rotational Dynamics and Rolling Without Slipping (ages 20-22)

Torque equals moment of inertia times angular acceleration, and a rolling body ties its rotation to its translation through one constraint. That constraint is what makes a hoop lose a race to a solid cylinder.

Ready when they can: Writes the translational and rotational equations for a rolling body and applies the rolling constraint; Predicts which of two shapes reaches the bottom of a slope first and justifies it by moment of inertia; Identifies the role of static friction in rolling and why it does no work.

https://lightmysky.com/learn/science/rotational-dynamics-and-rolling-without-slipping-mt_1mV6ukwDxK

#### Angular Momentum and Its Conservation (ages 20-22)

Angular momentum is defined for a particle by its position and momentum and for a rigid body by its moment of inertia and angular velocity, and it changes only when an external torque acts. A skater pulling in her arms and a gyroscope precessing are the same law seen twice.

Ready when they can: Computes the angular momentum of a particle about a stated point and of a rigid body about its axis; Uses conservation of angular momentum where the net external torque is zero; Explains gyroscopic precession as the response of an angular momentum vector to a torque.

https://lightmysky.com/learn/science/angular-momentum-and-its-conservation-mt_9v3S9-rhwc

#### Generalised Coordinates and the Lagrangian (ages 21-22)

Choosing coordinates that already respect the constraints removes the constraint forces from the problem, and the Lagrangian is kinetic minus potential energy written in those coordinates. A pendulum needs one angle rather than two coordinates and a tension.

Ready when they can: Picks a set of generalised coordinates for a constrained system and counts the degrees of freedom; Writes kinetic and potential energy in those coordinates and forms the Lagrangian; Explains why constraint forces do not appear once the coordinates respect the constraint.

https://lightmysky.com/learn/science/generalised-coordinates-and-the-lagrangian-mt_9QPk1zI9jE

#### The Euler-Lagrange Equation and Conserved Momenta (ages 21-22)

Applying the Euler-Lagrange equation to a Lagrangian returns the equation of motion, and any coordinate missing from the Lagrangian gives a conserved momentum straight away. Conservation laws stop being separate rules and become consequences of symmetry.

Ready when they can: Applies the Euler-Lagrange equation to recover a known equation of motion; Spots a cyclic coordinate and writes down the conserved momentum it implies; Connects a symmetry of the Lagrangian to the quantity it conserves.

https://lightmysky.com/learn/science/the-euler-lagrange-equation-and-conserved-momenta-mt_GSEFABbEXI

#### Hamilton's Principle and the Action (ages 22-23)

The path a system actually follows is the one that makes the action stationary, and the Euler-Lagrange equations are the condition for that. Stating mechanics as a claim about whole paths rather than about instants is what carries over to fields and to quantum theory.

Ready when they can: States Hamilton's principle and writes the action of a simple system; Shows that making the action stationary returns the equation of motion; Explains what varying a path means and which endpoints stay fixed.

https://lightmysky.com/learn/science/hamiltons-principle-and-the-action-mt_a273REeeGu

#### The Hamiltonian, Phase Space and the Canonical Equations (ages 22-23)

Trading velocities for momenta turns one second-order equation per coordinate into two first-order ones, and makes phase space the natural arena. The Hamiltonian equals the conserved energy whenever it carries no explicit time dependence.

Ready when they can: Constructs a Hamiltonian from a Lagrangian and identifies the conjugate momenta; Writes and solves the canonical equations for a simple system; Sketches a phase-space trajectory and reads the motion off it.

https://lightmysky.com/learn/science/the-hamiltonian-phase-space-and-the-canonical-equations-mt_9bMDXQiq_n

#### The Two-Body Problem, Orbital Energy and Kepler's First Two Laws (ages 20-21)

Two bodies bound by gravity both orbit their common centre of mass, and the problem reduces to one body moving in a central field. Conservation of angular momentum gives the equal-areas law directly, and the sign of the total energy decides whether the path closes into an ellipse or escapes.

Ready when they can: Derives the equal-areas law from angular momentum conservation rather than quoting it as an observation; Classifies an orbit as bound or unbound from the sign of the total energy and finds the speed at any radius; Explains why the Sun also moves, and how that wobble is what a radial-velocity planet search measures.

https://lightmysky.com/learn/science/the-two-body-problem-orbital-energy-and-keplers-first-two-laws-mt_CjHFftkB6M

#### Magnetic Flux Density and the Force on a Current-Carrying Wire (ages 16-18)

The strength of a magnetic field is defined by the force it produces: F = BIL when the wire is at right angles to the field, and BIL sin theta otherwise. One tesla is one newton per amp per metre.

Ready when they can: Uses the left hand rule to give the direction of the force on a current-carrying wire; Calculates the force for a wire set at an angle to the field and says when it becomes zero; Defines the tesla from the defining equation rather than quoting it from memory.

https://lightmysky.com/learn/science/magnetic-flux-density-and-the-force-on-a-current-carrying-wire-mt_zuqc4gjBVh

#### Charged Particles Moving in a Magnetic Field (ages 17-18)

A charge crossing a magnetic field feels a force BQv that stays at right angles to its velocity, so the path curves into a circle. Setting BQv equal to mv squared over r gives the radius.

Ready when they can: Gives the direction of the force on a positive and on a negative charge in the same field; Derives r = mv over BQ and uses it to compare particles of different mass or charge; Explains why a magnetic field changes a particle's direction but never its speed.

https://lightmysky.com/learn/science/charged-particles-moving-in-a-magnetic-field-mt_evuhZ6cSfI

#### Poisson Brackets and Constants of the Motion (ages 22-23)

The Poisson bracket of a quantity with the Hamiltonian gives its rate of change, so a conserved quantity is one whose bracket vanishes. The same algebra reappears as the commutator in quantum mechanics, which is not a coincidence.

Ready when they can: Computes a Poisson bracket and uses it to test whether a quantity is conserved; Recovers the canonical equations as brackets with the Hamiltonian; States the correspondence between a Poisson bracket and a quantum commutator.

https://lightmysky.com/learn/science/poisson-brackets-and-constants-of-the-motion-mt_UFzJyZRdOI

#### Noether's Theorem: Symmetry and Conserved Quantities (ages 22-24)

Every continuous symmetry of the action carries a conserved quantity, which is why translation gives momentum and rotation gives angular momentum. Conservation laws stop being a list of separate facts.

Ready when they can: Matches three continuous symmetries to the quantities they conserve; Shows a given action is unchanged under a transformation and extracts the conserved quantity; Explains what fails when the symmetry is only approximate.

https://lightmysky.com/learn/science/noethers-theorem-symmetry-and-conserved-quantities-mt_kAoOn8syBK

#### From Coordinates to Fields: the Lagrangian Density (ages 22-24)

A field has a value at every point, so the sum over coordinates becomes an integral of a Lagrangian density and the equations of motion become partial differential equations. The vibrating string is the case where the step can be checked against an answer already known.

Ready when they can: Writes a Lagrangian density for a continuous system and derives its field equation; Explains what replaces the index labelling a coordinate when the system becomes a field; Recovers the wave equation from a field Lagrangian.

https://lightmysky.com/learn/science/from-coordinates-to-fields-the-lagrangian-density-mt_fRZN3ZByjr

### Space Systems & Earth's History

https://lightmysky.com/learn/science/areas/space-systems-and-earths-history

#### Naming the Planets (ages 5-8)

Name the planets in our solar system in order from the Sun and use vocabulary for space — planet, star, sun, moon, satellite, orbit, solar system, galaxy, universe, asteroid, comet — applying these correctly when describing the structure of the solar system and objects we see in the sky

Ready when they can: Name the eight planets in order from the Sun without prompting; Use 'orbit' correctly to describe the movement of planets around the Sun and moons around planets; Distinguish between a planet, a moon, a star, and an asteroid using the correct vocabulary.

https://lightmysky.com/learn/science/naming-the-planets-mt_EHuU1ZeUFA

#### Why seasons change (ages 5-7)

Make observations at different times of year to relate the amount of daylight to the time of year, noticing longer days in summer and shorter days in winter

Ready when they can: Describe the pattern: more daylight hours in summer, fewer in winter; Compare sunrise/sunset times at different points in the year; Relate amount of daylight to seasonal changes in weather and nature.

Needs first: Naming the Planets, Seasonal changes.

https://lightmysky.com/learn/science/why-seasons-change-mt_K0mZxY2AM8

#### Sun, Moon, and stars (ages 6-7)

Use observations of the sun, moon, and stars to describe predictable patterns such as the sun rising and setting, the moon changing shape, and stars appearing at night

Ready when they can: Describe the daily pattern of sunrise and sunset; Describe the pattern of the moon's shape changing over about a month; Explain that stars are visible at night and describe any seasonal patterns observed.

Needs first: Naming the Planets, Why seasons change.

https://lightmysky.com/learn/science/sun-moon-and-stars-mt_fk33IEGP-T

#### Earth & Space Vocabulary (ages 8-11)

Use technical vocabulary for Earth's motion and the wider universe — rotation, revolution, axis, tilt, orbit, light year, gravitational force, atmosphere, lunar phases, waxing, waning, solstice, equinox, eclipse — and apply these when explaining day and night, the seasons, and the Moon's phases

Ready when they can: Use 'rotation' and 'revolution' correctly to describe Earth's two distinct types of movement and explain what each causes; Use 'waxing' and 'waning' to describe the Moon's phases and explain what causes them; Apply 'solstice' and 'equinox' correctly when explaining why seasons exist and why day length varies.

Needs first: Naming the Planets.

https://lightmysky.com/learn/science/earth-and-space-vocabulary-mt_LQt4vnKeB4

#### The solar system (ages 9-10)

Describe the sun, Earth, and moon as approximately spherical bodies, and describe the movement of the Earth and other planets orbiting the sun in the solar system

Ready when they can: State that the sun, Earth, and moon are approximately spherical; Name the planets in order from the sun and explain they all orbit the sun; Describe the moon orbiting the Earth while both orbit the sun.

Needs first: Naming the Planets, Sun, Moon, and stars.

https://lightmysky.com/learn/science/the-solar-system-mt_5l7iGkf1Tp

#### Earth's rotation and day/night (ages 9-11)

Use the idea of the Earth's rotation to explain day and night and the apparent movement of the sun across the sky

Ready when they can: Explain that the Earth rotates (spins) on its axis once every 24 hours; Describe how this rotation causes day (facing the sun) and night (facing away); Explain that the sun appears to move across the sky because we are rotating, not the sun.

Needs first: The solar system, Why seasons change, Earth & Space Vocabulary, Earth's Spin & Orbit.

https://lightmysky.com/learn/science/earths-rotation-and-day-night-mt_q15w--Fb5H

#### Star Brightness & Distance (ages 10-11)

Support an argument that the apparent brightness of the sun and stars is due to their relative distances from Earth, understanding the sun is a relatively close star

Ready when they can: Explain that the sun is a star, and it appears much brighter because it is much closer to Earth; Describe how a torch looks brighter close up and dimmer far away as an analogy; Argue that differences in apparent brightness of stars are mainly due to their different distances from Earth.

Needs first: The solar system, Why the Sun Looks Brightest.

https://lightmysky.com/learn/science/star-brightness-and-distance-mt_ZhKuYCbXz1

#### Phases of the Moon (ages 11-12)

Explain the phases of the Moon as the changing angle of sunlight on the lunar surface as seen from Earth, and describe how solar and lunar eclipses occur

Ready when they can: Explains that the phases of the Moon arise from the changing geometry of Sun, Earth, and Moon, not Earth's shadow; Describes the sequence of Moon phases over approximately 28 days; Distinguishes between a solar eclipse (Moon between Sun and Earth) and a lunar eclipse (Earth between Sun and Moon).

Needs first: The solar system, Earth & Space Vocabulary, Earth's rotation and day/night.

https://lightmysky.com/learn/science/phases-of-the-moon-mt_4V-vYhFUcm

#### The solar system (age 11+) (ages 11-12)

Describe the detailed structure of the solar system, including moons, asteroids, and comets, compare orbital periods and distances of the planets, and distinguish between planets, dwarf planets, and other bodies

Ready when they can: Names the eight planets in order and gives one distinguishing fact about each; Describes the difference between a planet, a dwarf planet, an asteroid, and a comet; Explains the relationship between distance from the Sun and orbital period (planets further out take longer).

Needs first: The solar system.

https://lightmysky.com/learn/science/the-solar-system-age-11-mt_33RrpbceZE

#### Why We Have Seasons (ages 11-12)

Explain that the seasons are caused by the tilt of Earth's axis during its orbit around the Sun, distinguishing this from the common misconception that seasons are caused by changing distance from the Sun

Ready when they can: Explains that Earth's axis is tilted at about 23.5° relative to its orbit; Describes how the tilted axis causes one hemisphere to receive more direct sunlight in summer and less in winter; Refutes the misconception that distance from the Sun causes seasons by noting Earth is actually slightly closer to the Sun in January.

Needs first: The solar system (age 11+), Earth & Space Vocabulary, Earth's rotation and day/night.

https://lightmysky.com/learn/science/why-we-have-seasons-mt_lFiDFPkVmH

#### Universal Gravitation (ages 12-13)

Describe gravity as a universal attractive force between all masses, explain that orbital motion arises because gravity provides the centripetal force keeping objects in orbit, and compare gravitational field strengths on different planets

Ready when they can: States that gravity is a universal attractive force acting between all objects with mass; Explains that orbital motion occurs because gravity continuously deflects the path of the orbiting object; Compares gravitational field strength on different planets and explains how this affects weight.

Needs first: The solar system (age 11+), Mass vs Weight.

https://lightmysky.com/learn/science/universal-gravitation-mt_oLjz18CxDg

#### Galaxies and the universe (ages 12-13)

Describe the scale of the universe, including the structure of galaxies, the position of the Sun in the Milky Way, and the use of light years as a unit of distance, and appreciate why space exploration requires enormous timescales

Ready when they can: Defines a light year as the distance light travels in one year; Describes the structure of a galaxy and states that the Sun is a star in the Milky Way galaxy; Compares the distances within the solar system with the distances between stars and between galaxies, expressing them in appropriate units.

Needs first: Earth & Space Vocabulary, Universal Gravitation, Star Brightness & Distance.

https://lightmysky.com/learn/science/galaxies-and-the-universe-mt_v9uYnIY5-B

#### Life Cycle of a Star (ages 13-14)

Describe the life cycle of a star from nebula through main sequence to its end state (white dwarf, neutron star, or black hole depending on mass), and relate the life cycle to the origin of elements heavier than hydrogen

Ready when they can: Describes the main stages in the life cycle of a star similar to the Sun: nebula → protostar → main sequence → red giant → planetary nebula → white dwarf; Explains that more massive stars end as a supernova followed by a neutron star or black hole; States that nuclear fusion inside stars produces heavier elements from hydrogen and helium.

Needs first: Galaxies and the universe.

https://lightmysky.com/learn/science/life-cycle-of-a-star-mt_lHasFmgvnT

#### Shadows (ages 10-11)

Represent data in graphical displays to reveal patterns of daily changes in shadow length and direction, day and night cycles, and seasonal star patterns

Ready when they can: Measure and record shadow length and direction at different times of day; Create a graph showing how shadow length changes throughout the day; Connect shadow patterns to the sun's apparent position and Earth's rotation.

Needs first: How Shadows Form, Earth's rotation and day/night.

https://lightmysky.com/learn/science/shadows-mt_tMLsTPQHwF

#### Rapid earth changes (ages 7-8)

Use information from several sources to provide evidence that Earth events can occur quickly (earthquakes, volcanic eruptions) or slowly (erosion, mountain building)

Ready when they can: Give at least two examples of rapid Earth events (earthquake, volcanic eruption, landslide, flood); Give at least two examples of slow Earth processes (erosion, mountain formation, canyon carving); Use evidence from text, images, or video to support the distinction between fast and slow changes.

Needs first: Preventing Erosion, Properties of materials.

https://lightmysky.com/learn/science/rapid-earth-changes-mt_ZJu8s-Q1xa

#### Orbits: Period, Speed and Kepler's Third Law (ages 17-18)

Setting the gravitational force equal to the centripetal requirement gives orbital speed and period from the central mass and the radius alone. Squaring the period and cubing the radius turns the relationship into a straight line.

Ready when they can: Gets orbital speed by equating GMm over r squared with mv squared over r; Shows that T squared is proportional to r cubed and uses it to compare two satellites; Says what a geostationary orbit has to fix and works out its radius.

https://lightmysky.com/learn/science/orbits-period-speed-and-keplers-third-law-mt_PLKLykGF8Z

#### Rock layers as evidence of change (ages 9-10)

Identify evidence from patterns in rock formations and fossils in rock layers to support an explanation for changes in a landscape over time

Ready when they can: Explain that rock layers (strata) form over time, with the oldest at the bottom; Describe how fossils in different layers provide evidence of organisms that lived at different times; Use patterns in rock formations to explain how a landscape has changed over millions of years.

Needs first: Types of rocks, How fossils form, Rapid earth changes.

https://lightmysky.com/learn/science/rock-layers-as-evidence-of-change-mt_GheLsWvrJ4

#### Red-Shift and the Expanding Universe (ages 15-16)

Light from distant galaxies arrives with its lines shifted towards longer wavelengths, and the shift is bigger the further away the galaxy is. The straightforward reading is that space itself is expanding from a hot, dense start.

Ready when they can: Explains red-shift as an increase in observed wavelength and links it to a galaxy moving away; States the pattern between distance and red-shift and what it implies about expansion; Names a second piece of evidence for the hot dense start and says why one observation alone would not settle it.

https://lightmysky.com/learn/science/red-shift-and-the-expanding-universe-mt_JeAfpxw49W

### Volcanoes & Earthquakes

https://lightmysky.com/learn/science/areas/volcanoes-and-earthquakes

#### Earth Is Made of Rock (ages 5-7)

Understand that Earth is made of rock and other solid materials

Ready when they can: State that the ground beneath us is made of rock; Identify rocks and stones as pieces of the Earth; Explain that Earth is solid and made of natural materials.

https://lightmysky.com/learn/science/earth-is-made-of-rock-mt_uUa6cgv8zV

#### What Is a Volcano (ages 5-7)

Know what a volcano is: an opening in Earth's surface where hot melted rock (lava) comes out

Ready when they can: Describe a volcano as a place where hot material comes out of the Earth; Explain that lava is rock so hot it has melted; Point to a volcano in a picture and describe what is happening.

https://lightmysky.com/learn/science/what-is-a-volcano-mt_S9SKah-yi_

#### Power of Eruptions (ages 5-7)

Appreciate that volcanic eruptions are powerful events that can change the landscape

Ready when they can: Describe an eruption as a powerful, dramatic event; Give examples of how an eruption changes the area around a volcano; Compare the landscape before and after an eruption using pictures.

Needs first: What Is a Volcano.

https://lightmysky.com/learn/science/power-of-eruptions-mt_BLQ2_OXPod

#### What Is an Earthquake (ages 5-7)

Know what an earthquake is: a sudden shaking of the ground that can be strong or weak

Ready when they can: Describe an earthquake as the ground shaking suddenly; Explain that earthquakes vary in strength from barely noticeable to very strong; Describe what it might feel like during an earthquake.

https://lightmysky.com/learn/science/what-is-an-earthquake-mt_e29VrLfmYt

#### Earthquake Safety (ages 5-7)

Know basic earthquake safety: drop, cover, and hold on; move away from windows; tell a trusted adult

Ready when they can: Demonstrate the drop, cover, and hold on procedure; Explain why to move away from windows and shelves during shaking; Name a trusted adult to tell if they feel an earthquake.

Needs first: What Is an Earthquake.

https://lightmysky.com/learn/science/earthquake-safety-mt__pMF-Xb0TE

#### Fast & Slow Earth Changes (ages 5-7)

Understand that Earth's surface changes: some changes are quick (eruptions, earthquakes) and some are slow (wind, water wearing away rock)

Ready when they can: Give an example of a quick change to Earth's surface like a volcanic eruption; Give an example of a slow change to Earth's surface like erosion by wind or water; Compare quick and slow changes and explain the difference.

Needs first: What Is an Earthquake, What Is a Volcano.

https://lightmysky.com/learn/science/fast-and-slow-earth-changes-mt_adpdEaKEBC

#### Active, Dormant & Extinct (ages 7-9)

Classify volcanoes as active (could erupt any time), dormant (sleeping but could wake up), or extinct (will not erupt again)

Ready when they can: Define active, dormant, and extinct volcanoes; Explain that a dormant volcano is not safe just because it has not erupted recently; Classify a given volcano based on its eruption history.

Needs first: Power of Eruptions, What Is a Volcano.

https://lightmysky.com/learn/science/active-dormant-and-extinct-mt_dSeFrAWE4v

#### Earth's Layers (ages 7-9)

Know that Earth has layers — a thin outer crust, a thick hot mantle, and a core at the centre — and that the inside of the Earth is extremely hot

Ready when they can: Name Earth's three main layers: crust, mantle, and core; Explain that the crust is thin compared to the other layers; State that Earth's interior is extremely hot — hot enough to melt rock.

Needs first: What Is a Volcano, Earth Is Made of Rock.

https://lightmysky.com/learn/science/earths-layers-mt_jwElFY7Syd

#### Inside a Volcano (ages 7-9)

Understand the inside of a volcano: magma is hot melted rock underground, lava is the same material after it reaches the surface, and volcanoes have a magma chamber, vent, and crater

Ready when they can: Explain that magma is melted rock underground and lava is the same material above ground; Label a magma chamber, vent, and crater on a volcano cross-section; Describe the path magma takes from underground to the surface during an eruption.

Needs first: Earth's Layers, What Is a Volcano.

https://lightmysky.com/learn/science/inside-a-volcano-mt_QtIAWOcoQT

#### Pompeii & Vesuvius (ages 7-9)

Know the story of Pompeii: a Roman city buried by the eruption of Mount Vesuvius in 79 AD, preserved under volcanic ash, and rediscovered by archaeologists centuries later

Ready when they can: Retell the key events: Vesuvius erupted, Pompeii was buried under ash; Explain that the ash preserved the city, its buildings, and even people's shapes; Describe how archaeologists uncovered the city and what we can learn from it.

Needs first: Power of Eruptions, Inside a Volcano, What Is a Volcano.

https://lightmysky.com/learn/science/pompeii-and-vesuvius-mt_XG4RqUIXm8

#### Why Earthquakes Happen (ages 7-9)

Understand that earthquakes happen when rocks underground suddenly move or break, releasing energy that shakes the ground

Ready when they can: Explain that earthquakes are caused by rocks underground suddenly moving; Describe how this movement sends shaking through the surrounding ground; Distinguish between the underground cause and the surface effects of an earthquake.

Needs first: What Is an Earthquake.

https://lightmysky.com/learn/science/why-earthquakes-happen-mt_NVr4AhsvIq

#### Ring of Fire (ages 7-9)

Recognise that volcanoes and earthquakes tend to happen in certain places — especially around the edges of the Pacific Ocean (Ring of Fire) — not randomly across the Earth

Ready when they can: Describe the pattern that volcanoes and earthquakes cluster in certain zones; Locate the Ring of Fire on a world map; Explain that the locations of earthquakes and volcanoes are not random.

Needs first: Fast & Slow Earth Changes, What Is an Earthquake, Shapes of land and water, Why Earthquakes Happen, What Is a Volcano.

https://lightmysky.com/learn/science/ring-of-fire-mt_bhwf_rDXQL

#### Tsunamis (ages 7-9)

Know what a tsunami is: a very large, fast ocean wave caused by an earthquake or volcanic eruption under the sea, which can cause great damage when it reaches land

Ready when they can: Explain that a tsunami is caused by an earthquake or eruption under the sea; State that tsunamis travel very fast across the ocean; Describe the damage a tsunami can cause when it reaches the coast.

Needs first: Power of Eruptions, What Is an Earthquake, Why Earthquakes Happen.

https://lightmysky.com/learn/science/tsunamis-mt_Wu-ftkzoiE

#### Measuring Earthquake Strength (ages 9-11)

Know that scientists measure earthquakes using seismometers, that earthquakes release energy that travels as waves through the ground, and that a magnitude scale describes their strength

Ready when they can: Explain that a seismometer is an instrument that detects and records ground shaking; Describe earthquake energy as waves that travel outward from where rocks broke; Interpret a magnitude number as a measure of an earthquake's strength.

Needs first: Ring of Fire, Why Earthquakes Happen.

https://lightmysky.com/learn/science/measuring-earthquake-strength-mt_mdZ3nBWChW

#### Seismic Waves & Earth's Interior (ages 11-13)

Distinguish between P-waves (compression, travel through solids and liquids) and S-waves (shear, cannot pass through liquids); explain why a seismic shadow zone exists on the far side of an earthquake; describe how seismologists use wave refraction and reflection to infer that Earth has a solid inner core, liquid outer core, mantle, and crust

Needs first: Measuring Earthquake Strength.

https://lightmysky.com/learn/science/seismic-waves-and-earths-interior-mt__kFxuAgs6d

#### Types of Rock (ages 7-9)

Know the three main types of rock — igneous (formed when lava or magma cools), sedimentary (formed from layers pressed together), and metamorphic — and that fossils are found in sedimentary rock

Ready when they can: Name the three main rock types: igneous, sedimentary, metamorphic; Explain that igneous rock forms when lava or magma cools and hardens; State that fossils are preserved in sedimentary rock because it forms in layers.

Needs first: Earth's Layers, Properties of materials, What Is a Volcano, Earth Is Made of Rock.

https://lightmysky.com/learn/science/types-of-rock-mt_NYA50DFcOO

#### How Rocks Change Over Time (ages 9-11)

Understand the rock cycle: rocks slowly change from one type to another over millions of years — igneous rock weathers into sediment, sediment becomes sedimentary rock, heat and pressure create metamorphic rock, and melting starts the cycle again

Ready when they can: Describe the rock cycle as a continuous process with no beginning or end; Trace at least one complete path through the cycle from igneous to sedimentary to metamorphic and back; Explain that the rock cycle operates over millions of years through weathering, pressure, heat, and melting.

Needs first: Earth's Layers, Types of Rock, Erosion and weathering.

https://lightmysky.com/learn/science/how-rocks-change-over-time-mt_z7AJZapsJj

#### Natural Disaster Solutions (ages 9-10)

Generate and compare multiple solutions to reduce the impacts of natural Earth processes on humans, such as earthquakes, floods, or volcanic eruptions

Ready when they can: Identify at least two natural hazards and their impacts on human life and property; Generate multiple solutions for reducing impacts (e.g. earthquake-resistant buildings, flood barriers, early warning systems); Compare solutions based on criteria like effectiveness, cost, and feasibility.

Needs first: Designing for Weather Hazards, Human impact on environments, Rapid earth changes.

https://lightmysky.com/learn/science/natural-disaster-solutions-mt_cpDpjJaE5u

#### Tectonic Plates (ages 9-11)

Understand that Earth's crust is broken into large pieces called tectonic plates that float on hotter, softer rock beneath and move very slowly — a few centimetres per year

Ready when they can: Describe Earth's crust as broken into large plates; Explain that the plates float on hotter, partially melted rock underneath; State that plates move very slowly, typically a few centimetres per year.

Needs first: Ring of Fire, Finding patterns in data, Earth's Layers.

https://lightmysky.com/learn/science/tectonic-plates-mt_XrvPx5kUfO

#### Plate Boundaries (ages 9-11)

Explain how plate boundaries cause earthquakes and volcanoes: plates pushing together, pulling apart, or sliding past each other create the forces that trigger these events, and mountains form where plates collide

Ready when they can: Describe three types of plate boundary movement: convergent, divergent, and transform; Explain that earthquakes occur when plates grind or collide at boundaries; Explain that volcanoes form where plates pull apart or one slides under another, allowing magma to rise.

Needs first: Why Earthquakes Happen, Tectonic Plates.

https://lightmysky.com/learn/science/plate-boundaries-mt_-JnOhdei6F

#### Earthquake-Resistant Design (ages 9-11)

Know that buildings can be designed to resist earthquakes, tsunami warning systems alert coastal communities, and communities prepare through evacuation plans and drills

Ready when they can: Describe at least one feature that makes buildings more earthquake-resistant; Explain how tsunami warning systems detect danger and alert communities; Describe how communities prepare for earthquakes and eruptions through drills and evacuation plans.

Needs first: Natural Disaster Solutions, Designing for Weather Hazards, Plate Boundaries, Measuring Earthquake Strength, Tsunamis.

https://lightmysky.com/learn/science/earthquake-resistant-design-mt_yDZbQODIwp

#### Eruption Types & Volcano Shape (ages 9-11)

Understand that not all volcanic eruptions are the same: some flow gently (effusive) and some explode violently (explosive), depending on the properties of the magma, and that volcano shape is related to eruption type

Ready when they can: Contrast effusive eruptions (gentle lava flows) with explosive eruptions (violent blasts of ash and rock); Explain that eruption type depends on properties of the magma such as thickness and gas content; Connect volcano shape to eruption style: shield volcanoes from runny lava, steep cones from thick explosive magma.

Needs first: Active, Dormant & Extinct, Plate Boundaries, Inside a Volcano.

https://lightmysky.com/learn/science/eruption-types-and-volcano-shape-mt_W4j7T_PnGH

#### Famous Eruptions & Pangaea (ages 9-11)

Know about famous eruptions and their global effects: Mount St Helens (1980), Eyjafjallajökull (2010), and how large eruptions can affect weather and climate worldwide; understand that continents were once joined (Pangaea) and have slowly drifted apart

Ready when they can: Describe at least one famous volcanic eruption and its key effects; Explain how volcanic ash and gases in the atmosphere can cool global temperatures; State that continents were once joined in a supercontinent and have slowly moved apart over millions of years.

Needs first: Plate Boundaries, Eruption Types & Volcano Shape, Pompeii & Vesuvius, Tectonic Plates.

https://lightmysky.com/learn/science/famous-eruptions-and-pangaea-mt_rML9unnd9x

#### Monitoring Volcanoes (ages 9-11)

Understand how volcanologists monitor volcanoes by looking for warning signs — gas emissions, ground swelling, small earthquakes — and that prediction involves evidence and uncertainty, not certainty

Ready when they can: Name at least two warning signs scientists look for before an eruption; Explain that volcanologists combine multiple types of evidence to assess risk; Discuss why volcanic prediction involves uncertainty and cannot guarantee exact timing.

Needs first: Active, Dormant & Extinct, Plate Boundaries, Inside a Volcano.

https://lightmysky.com/learn/science/monitoring-volcanoes-mt_ZRoQVXf_aD

#### How Tectonic Plates Move (ages 11-12)

Understand that convection currents in the molten mantle drive the movement of rigid tectonic plates; distinguish between convergent (collision/subduction), divergent (spreading ridges), and transform (sliding) plate boundaries; explain why volcanoes, earthquakes, and mountain chains cluster at boundaries; introduce the Wilson cycle of supercontinent assembly and breakup

Needs first: Seismic Waves & Earth's Interior, Famous Eruptions & Pangaea.

https://lightmysky.com/learn/science/how-tectonic-plates-move-mt_gv_uoHkdjR

#### Hazard Assessment & Evacuation (ages 12-14)

Explain probabilistic hazard assessment using eruption recurrence intervals and fault slip rates; describe how volcano observatories monitor ground deformation, gas emissions, and seismicity to issue alert levels; explore why communities remain near active hazards (fertile volcanic soil, poverty, cultural ties); discuss the ethics and politics of evacuation decisions and the social justice dimensions of disaster risk

Needs first: Earthquake-Resistant Design.

https://lightmysky.com/learn/science/hazard-assessment-and-evacuation-mt_edaoZRkK6M

#### Supervolcanoes & Volcanic Winter (ages 12-13)

Describe calderas such as Yellowstone and Toba as supervolcanoes capable of erupting thousands of cubic kilometres of ash; explain how sulphur dioxide aerosols in the stratosphere scatter sunlight and cause volcanic winter; discuss the Toba catastrophe theory and how giant eruptions have interacted with ice ages; contrast supervolcano eruptions with ordinary eruptions in scale and climate impact

Needs first: Hazard Assessment & Evacuation, Seismic Waves & Earth's Interior, Monitoring Volcanoes.

https://lightmysky.com/learn/science/supervolcanoes-and-volcanic-winter-mt_Am_iTzHjoe

#### Volcanoes & Mass Extinctions (ages 13-14)

Explain how large igneous provinces (LIPs) — massive outpourings of lava over millions of years — caused global warming and ocean acidification that drove mass extinctions; connect the Siberian Traps to the end-Permian extinction and the Deccan Traps to the end-Cretaceous event; explore how hydrothermal vents on the early Earth may have been the cradle of life; understand volcanoes as both destroyers and creators in the history of life

Needs first: Hazard Assessment & Evacuation, How Rocks Change Over Time, Supervolcanoes & Volcanic Winter.

https://lightmysky.com/learn/science/volcanoes-and-mass-extinctions-mt_QwWo6an9N1

### Matter & Materials

https://lightmysky.com/learn/science/areas/matter-and-materials

#### Objects vs Materials (ages 5-6)

Distinguish between an object and the material from which it is made, understanding that objects can be made from different materials

Ready when they can: Explain the difference between an object (e.g. a chair) and the material it is made from (e.g. wood); Give examples of the same object made from different materials (e.g. plastic cup, glass cup); Identify what material a given object is made from by looking at and touching it.

https://lightmysky.com/learn/science/objects-vs-materials-mt_5r47Pvstyn

#### Naming Everyday Materials (ages 5-6)

Identify and name a variety of everyday materials including wood, plastic, glass, metal, water, and rock

Ready when they can: Name at least six everyday materials: wood, plastic, glass, metal, water, rock; Identify the material of at least ten different objects around the home or classroom; Recognise that some objects are made from more than one material.

Needs first: Objects vs Materials.

https://lightmysky.com/learn/science/naming-everyday-materials-mt_ZAJvTcroFO

#### States of Matter Vocabulary (ages 5-7)

Name and distinguish the three states of matter — solid, liquid, and gas — using properties vocabulary: hard, rigid, runny, flows, keeps its shape, fills its container; use 'change of state' to describe what happens when materials are heated or cooled

Ready when they can: Correctly sort a set of everyday materials as solid, liquid, or gas and give a reason for each; Use the terms solid, liquid, and gas accurately when describing everyday substances; Use 'change of state' to describe what happens when ice melts or water boils.

https://lightmysky.com/learn/science/states-of-matter-vocabulary-mt_1JFUNQDwAJ

#### Describing Material Properties (ages 5-6)

Describe simple physical properties of everyday materials such as hard/soft, stretchy/stiff, shiny/dull, rough/smooth, waterproof/absorbent, transparent/opaque

Ready when they can: Use at least five property words correctly: hard, soft, stretchy, shiny, rough, smooth, transparent, waterproof; Describe the properties of three different materials using at least two property words each; Explain why a property matters (e.g. 'waterproof means water doesn't soak through').

Needs first: States of Matter Vocabulary, Naming Everyday Materials.

https://lightmysky.com/learn/science/describing-material-properties-mt_auVZZEuXjs

#### Grouping Materials (ages 5-6)

Compare and group everyday materials based on their simple physical properties

Ready when they can: Sort a set of materials into groups based on a chosen property (e.g. transparent vs opaque); Compare two materials and state which properties they share and which differ; Explain the reasoning behind a grouping decision using property vocabulary.

Needs first: Describing Material Properties.

https://lightmysky.com/learn/science/grouping-materials-mt_SwaNNdm_Ks

#### Changing Shapes of Solids (ages 6-7)

Investigate how the shapes of solid objects can be changed by squashing, bending, twisting, and stretching

Ready when they can: Demonstrate four ways to change the shape of a solid: squashing, bending, twisting, stretching; Compare how different materials respond to these forces (e.g. clay squashes easily, wood does not); Explain that the material itself stays the same even when the shape changes.

Needs first: Describing Material Properties.

https://lightmysky.com/learn/science/changing-shapes-of-solids-mt_wf-SJhZ1kC

#### Changes & Separation Vocabulary (ages 7-9)

Use process vocabulary for changes of state and material separation — dissolve, solution, soluble, insoluble, evaporate, condense, melt, freeze, filter, sieve, mixture, separate — and understand precisely what each term describes, including the important distinction between dissolving and melting

Ready when they can: Distinguish 'dissolve' from 'melt' correctly in context and explain the difference; Use 'soluble' and 'insoluble' accurately when describing whether a material dissolves in water; Explain the difference between evaporation and condensation using the correct terms.

https://lightmysky.com/learn/science/changes-and-separation-vocabulary-mt_ahSqW_kK1b

#### Classifying Materials (ages 7-8)

Plan and conduct an investigation to classify different kinds of materials by their observable properties

Ready when they can: Design a simple test to compare one property across several materials; Record observations in a table or chart during the investigation; Classify the tested materials into groups based on the results.

Needs first: Grouping Materials.

https://lightmysky.com/learn/science/classifying-materials-mt_zHnOGwHIEz

#### Drawing Particle Diagrams (ages 7-11)

Draw and interpret particle diagrams — dot representations showing the arrangement, spacing, and movement of particles in solids (close, regular, vibrating in place), liquids (close, random, flowing past each other), and gases (widely spaced, moving rapidly in all directions) — and use these diagrams to explain observable properties such as fixed shape, fixed volume, and compressibility

Ready when they can: Draw labelled particle diagrams for solids, liquids, and gases showing the correct arrangement and spacing of particles; Use their particle diagram to explain why solids keep their shape but liquids flow; Sketch what happens to particles during a change of state (e.g. melting) and explain the energy changes involved.

https://lightmysky.com/learn/science/drawing-particle-diagrams-mt_htAYR-iCFF

#### Heating & Cooling Changes (ages 7-9)

Observe and describe that some materials change state when heated or cooled, and measure the temperature at which changes occur in degrees Celsius

Ready when they can: Describe melting (solid to liquid) and freezing (liquid to solid) with everyday examples; State that water freezes at 0°C and boils at 100°C; Explain that heating adds energy causing particles to move more, leading to state changes.

Needs first: States of Matter Vocabulary, Drawing Particle Diagrams.

https://lightmysky.com/learn/science/heating-and-cooling-changes-mt_Pl-nsjYGZ3

#### Taking Apart & Rebuilding (ages 7-8)

Observe that an object made of a small set of pieces can be disassembled and made into a new object, understanding that the pieces still exist

Ready when they can: Explain that taking apart an object and rebuilding it uses the same pieces in a new arrangement; Describe how the pieces themselves don't change even though the object looks different; Give an everyday example of reusing materials to make something new.

Needs first: Objects vs Materials.

https://lightmysky.com/learn/science/taking-apart-and-rebuilding-mt_GQpqoR5YOc

#### Evaporation & the Water Cycle (ages 8-9)

Identify the role of evaporation and condensation in the water cycle, and associate the rate of evaporation with temperature

Ready when they can: Describe evaporation as liquid turning to gas and condensation as gas turning to liquid; Explain the water cycle: evaporation from seas/lakes → condensation into clouds → precipitation; Explain why evaporation happens faster at higher temperatures (e.g. puddles dry faster on hot days).

Needs first: Changes & Separation Vocabulary, The Water Cycle, Heating & Cooling Changes.

https://lightmysky.com/learn/science/evaporation-and-the-water-cycle-mt_Qkewo5M3_c

#### Solids, Liquids & Gases (ages 8-9)

Compare and group materials as solids, liquids, or gases based on their observable properties and behaviour

Ready when they can: Define solids (fixed shape, hard to compress), liquids (flow, take shape of container), gases (spread out, fill space); Sort at least eight everyday materials into solid, liquid, or gas categories; Explain tricky cases like sand (solid particles) or steam (gas, not visible water droplets).

Needs first: States of Matter Vocabulary, Drawing Particle Diagrams, Heating & Cooling Changes, Grouping Materials, Changing Shapes of Solids.

https://lightmysky.com/learn/science/solids-liquids-and-gases-mt_YQkUdIHO8L

#### Material Properties Vocabulary (ages 9-11)

Use technical vocabulary to describe and compare material properties — conductor, insulator, thermal, electrical, transparent, opaque, translucent, soluble, insoluble, magnetic, flexible, rigid, density — and apply these terms precisely when selecting and justifying materials for particular purposes

Ready when they can: Classify a set of materials as electrical conductors or insulators and explain why using the correct terms; Use 'transparent', 'translucent', and 'opaque' correctly and distinctly in descriptions; Apply at least four property terms correctly when justifying a material choice for a given purpose.

https://lightmysky.com/learn/science/material-properties-vocabulary-mt_MVovx37Xct

#### Choosing the Right Material (ages 6-8)

Identify and compare the suitability of everyday materials for particular uses, explaining why specific materials are chosen for specific purposes

Ready when they can: Explain why a specific material is chosen for a purpose based on its properties (e.g. glass for windows because it's transparent); Compare two materials and decide which is more suitable for a given use with reasoning; Suggest an alternative material for an object and explain why it would or wouldn't work.

Needs first: Material Properties Vocabulary, Grouping Materials.

https://lightmysky.com/learn/science/choosing-the-right-material-mt_rTn43s8RNX

#### Testing Materials for Uses (ages 7-10)

Give reasons, based on evidence from comparative and fair tests, for the particular uses of everyday materials including metals, wood, and plastic

Ready when they can: Design a fair test to compare a specific property of two or more materials; Present test results as evidence for why a material is suited to a particular use; Explain the link between a material's tested properties and its real-world application.

Needs first: Material Properties Vocabulary.

https://lightmysky.com/learn/science/testing-materials-for-uses-mt_e3-_toGuWf

#### Advanced Material Properties (ages 9-11)

Compare and group everyday materials based on advanced properties: hardness, solubility, transparency, electrical and thermal conductivity, and response to magnets

Ready when they can: Define and test for at least four properties: hardness, solubility, conductivity, magnetism; Group a set of materials based on test results for each property; Use results to explain why certain materials are chosen for specific uses (e.g. copper for wires because it conducts electricity).

Needs first: Testing Materials for Uses, Material Properties Vocabulary, Choosing the Right Material, Solids, Liquids & Gases, Classifying Materials.

https://lightmysky.com/learn/science/advanced-material-properties-mt_Ge4Wtg6QMM

#### Dissolving & Solutions (ages 9-10)

Understand that some materials dissolve in liquid to form a solution, and describe how to recover a substance from a solution by evaporation

Ready when they can: Explain that dissolving means a solid mixes completely into a liquid to form a solution; Describe how to recover a dissolved substance by evaporating the liquid; Distinguish between a mixture (can see separate parts) and a solution (looks clear, fully dissolved).

Needs first: Changes & Separation Vocabulary, Advanced Material Properties, Evaporation & the Water Cycle.

https://lightmysky.com/learn/science/dissolving-and-solutions-mt_Mf-T-fYRLX

#### Reversible Changes (ages 9-10)

Demonstrate that dissolving, mixing, and changes of state are reversible changes where no new materials are formed

Ready when they can: Define a reversible change as one where the original materials can be recovered; Give at least three examples of reversible changes: melting, freezing, dissolving, evaporating; Explain how to reverse each example (e.g. freeze melted chocolate, evaporate a solution).

Needs first: Changes & Separation Vocabulary, Dissolving & Solutions, Heating & Cooling Changes, Taking Apart & Rebuilding.

https://lightmysky.com/learn/science/reversible-changes-mt_UKmtuAsSLN

#### Irreversible Changes (ages 9-11)

Explain that some changes result in the formation of new materials and are not usually reversible, such as burning, rusting, and reactions with acid

Ready when they can: Define an irreversible change as one that creates new materials that cannot be changed back; Give at least three examples: burning, rusting, mixing bicarbonate of soda with vinegar; Describe observable signs of irreversible change: gas produced, colour change, heat given off, new substance formed.

Needs first: Reversible Changes.

https://lightmysky.com/learn/science/irreversible-changes-mt_rbPioPELM1

#### Separating Mixtures (ages 9-10)

Use knowledge of solids, liquids, and gases to decide how mixtures might be separated through filtering, sieving, and evaporating

Ready when they can: Choose the correct separation method for a given mixture (sieving for large particles, filtering for small, evaporating for dissolved); Describe a multi-step separation plan for a complex mixture like sand, salt, and water; Explain why each method works based on the properties of the materials.

Needs first: Changes & Separation Vocabulary, Dissolving & Solutions, Solids, Liquids & Gases.

https://lightmysky.com/learn/science/separating-mixtures-mt_2b6CB0w3Yx

#### Matter Is Made of Particles (ages 10-11)

Develop a model to describe that matter is made of particles too small to be seen, and that this explains properties of solids, liquids, and gases

Ready when they can: Describe matter as made of particles too small to see with the naked eye; Use a particle model to explain differences: particles tightly packed (solid), loosely arranged (liquid), spread far apart (gas); Use the particle model to explain a state change (e.g. heating makes particles move faster and spread apart).

Needs first: Drawing Particle Diagrams, Heating & Cooling Changes, Solids, Liquids & Gases.

https://lightmysky.com/learn/science/matter-is-made-of-particles-mt_ylruY6VhOf

#### Conservation of Mass (ages 10-11)

Measure and provide evidence that the total weight of matter is conserved regardless of the type of change (heating, cooling, or mixing)

Ready when they can: State the principle that matter is neither created nor destroyed during physical or chemical changes; Describe an investigation weighing materials before and after a change to show mass is conserved; Explain why dissolved sugar still contributes to the total weight even though it can't be seen.

Needs first: Irreversible Changes, Matter Is Made of Particles.

https://lightmysky.com/learn/science/conservation-of-mass-mt_ehC1wsdmUz

#### The Particle Model (ages 11-12)

Use the particle model to explain the properties of solids, liquids, and gases — including differences in arrangement, movement, and spacing — and apply the model to explain density, compressibility, and the anomalous expansion of water

Ready when they can: Draws particle diagrams for solids, liquids, and gases showing correct arrangement and spacing; Explains why gases are compressible but liquids and solids are not; Explains why ice floats on water using the anomalous expansion of water; Uses particle spacing to explain why gases are much less dense than solids and liquids.

Needs first: Drawing Particle Diagrams, Matter Is Made of Particles, Solids, Liquids & Gases.

https://lightmysky.com/learn/science/the-particle-model-mt_b6kZgqolEd

#### Atoms, Elements & Compounds (ages 11-12)

Explain the differences between atoms, elements, and compounds; describe the simple Bohr model of the atom (nucleus with protons and neutrons, electrons in shells); and write and interpret chemical symbols and simple formulae

Ready when they can: Defines atom, element, and compound and distinguishes between them with examples; Draws a simple Bohr model of an atom labelling nucleus (protons/neutrons) and electron shells; Reads a chemical formula to identify the elements and number of each atom (e.g. H₂O, CO₂, NaCl); Identifies the difference between a mixture and a compound.

Needs first: The Particle Model.

https://lightmysky.com/learn/science/atoms-elements-and-compounds-mt_Z_Wu_77ybI

#### How Materials Change State (ages 11-12)

Explain melting, freezing, boiling, condensing, and sublimation using the particle model, interpreting heating and cooling curves to identify melting and boiling points

Ready when they can: Describes what happens to particles during each change of state; Reads a heating/cooling curve and identifies the melting point and boiling point from the flat regions; Explains why temperature stays constant during a change of state; Distinguishes between evaporation (from surface, any temperature) and boiling (throughout liquid, at boiling point).

Needs first: The Particle Model, Drawing Particle Diagrams, Heating & Cooling Changes.

https://lightmysky.com/learn/science/how-materials-change-state-mt_CyV7crZ8hl

#### Physical vs Chemical Changes (ages 11-13)

Distinguish between physical changes (reversible, no new substances formed) and chemical changes (new substances formed, often irreversible), using conservation of mass to understand both types

Ready when they can: Classifies given changes as physical or chemical with justification; Explains what conservation of mass means and why mass is conserved in chemical reactions; Names observable signs that a chemical reaction has occurred (colour change, gas produced, temperature change, precipitate); Explains why dissolving is a physical change but burning is a chemical change.

Needs first: The Particle Model, Conservation of Mass, Irreversible Changes, Reversible Changes, Atoms, Elements & Compounds.

https://lightmysky.com/learn/science/physical-vs-chemical-changes-mt_1hgck6ucII

#### The Periodic Table (ages 11-12)

Describe the organisation of the periodic table into periods and groups, explain the contribution of Mendeleev, and use the table to identify metals, non-metals, and predict patterns in reactivity

Ready when they can: Explains why the periodic table is arranged into periods (rows) and groups (columns); States that elements in the same group have similar chemical properties; Locates metals, non-metals, and metalloids in the periodic table; Explains how Mendeleev ordered elements by atomic weight and predicted missing elements.

Needs first: Atoms, Elements & Compounds.

https://lightmysky.com/learn/science/the-periodic-table-mt_wfEfQuHOG-

#### Metals vs Non-Metals (ages 11-13)

Compare the physical and chemical properties of metals and non-metals, explaining metallic properties (malleability, lustre, conductivity) and how position in the periodic table predicts reactivity

Ready when they can: Lists physical properties typical of metals (shiny, malleable, good conductor) and non-metals; Explains why metals are used in wires, cookware, and construction based on their properties; Uses the periodic table to predict whether an element is likely to be reactive or unreactive; Explains what lustre and malleability mean in terms of real-world observations.

Needs first: The Periodic Table.

https://lightmysky.com/learn/science/metals-vs-non-metals-mt_Sc_SorJhXW

#### Acids, Alkalis & pH (ages 12-13)

Define acids and alkalis in terms of hydrogen ion concentration, describe the pH scale (0–14), and explain how indicators are used to identify and measure acidity or alkalinity

Ready when they can: States that acids have pH below 7, alkalis have pH above 7, and neutral is pH 7; Explains what hydrogen ions (H⁺) have to do with acidity; Names common indicators (litmus, universal indicator) and describes colour changes; Identifies everyday acids (vinegar, lemon juice) and alkalis (bleach, bicarbonate of soda).

Needs first: Atoms, Elements & Compounds.

https://lightmysky.com/learn/science/acids-alkalis-and-ph-mt_AN2kJE6I0s

#### The Rock Cycle (ages 12-14)

Explain the rock cycle: how igneous rocks form from magma, sedimentary rocks from compressed sediment, and metamorphic rocks from heat and pressure, and how all rock types can transform into one another over geological time

Ready when they can: Describes how each rock type (igneous, sedimentary, metamorphic) is formed; Gives an example of each rock type and its formation (e.g. granite, limestone, marble); Traces a rock sample through possible transitions in the rock cycle; Explains what geological time means and why rock cycle changes are slow.

Needs first: How Tectonic Plates Move, Properties of materials, Rocks and soil, How Rocks Change Over Time.

https://lightmysky.com/learn/science/the-rock-cycle-mt_NckKLZ3uCE

#### Types of Chemical Reaction (ages 12-13)

Identify and describe four types of chemical reaction: combustion (burning in oxygen), oxidation (gain of oxygen), thermal decomposition (breaking down by heat), and displacement (more reactive metal replaces less reactive one)

Ready when they can: Writes a word equation for each type of reaction with an example; Identifies the type of reaction from a given word equation or description; Explains what makes a displacement reaction happen (relative reactivity); Distinguishes complete combustion (CO₂ and H₂O) from incomplete combustion (CO and soot).

Needs first: Physical vs Chemical Changes, Metals vs Non-Metals.

https://lightmysky.com/learn/science/types-of-chemical-reaction-mt_v0K6GRi4ZL

#### Acid Reactions & Salts (ages 12-13)

Describe and write word equations for the reactions of acids with metals, alkalis (neutralisation), and metal oxides/hydroxides, identifying the salt produced in each case

Ready when they can: Writes word equations for: acid + metal → salt + hydrogen; acid + alkali → salt + water; acid + metal oxide → salt + water; Names the salt formed from a given acid and base (e.g. hydrochloric acid + sodium hydroxide → sodium chloride); Describes the test for hydrogen gas (squeaky pop); Explains what neutralisation means and gives a practical example (indigestion tablets, treating acidic soil).

Needs first: Acids, Alkalis & pH, Types of Chemical Reaction.

https://lightmysky.com/learn/science/acid-reactions-and-salts-mt_QKRYLwaOU8

#### Reactions That Release or Absorb Heat (ages 12-13)

Distinguish between exothermic reactions (release energy, temperature rises) and endothermic reactions (absorb energy, temperature falls), with everyday and industrial examples

Ready when they can: Defines exothermic and endothermic in terms of energy transfer to and from the surroundings; Gives two examples of each type from everyday life (e.g. combustion, hand warmers; photosynthesis, cold packs); Explains energy changes during changes of state (melting is endothermic, freezing is exothermic); Interprets a temperature change in an experiment to classify the reaction type.

Needs first: Energy can't be created or destroyed, How Materials Change State, Types of Chemical Reaction.

https://lightmysky.com/learn/science/reactions-that-release-or-absorb-heat-mt_UoqUPI_uNz

#### The Reactivity Series (ages 12-14)

Order common metals in the reactivity series and explain how a more reactive metal displaces a less reactive one; describe how carbon is used to extract metals from their oxides in industry

Ready when they can: Recalls the order of common metals in the reactivity series (potassium to gold); Predicts whether a displacement reaction will occur given two metals; Explains why carbon can be used to extract iron from iron oxide but not aluminium from aluminium oxide; Links the reactivity series to the history of metal use (gold found free, iron smelted, aluminium electrolytic).

Needs first: Metals vs Non-Metals, Types of Chemical Reaction.

https://lightmysky.com/learn/science/the-reactivity-series-mt_zsYW61cn_q

#### Ceramics, Polymers & Composites (ages 13-14)

Describe the properties and uses of ceramics (hard, brittle, heat-resistant), polymers (flexible, lightweight, variable), and composites (combine properties of constituent materials), giving real-world examples of each

Ready when they can: Gives the key properties of ceramics, polymers, and composites with examples of each; Explains why a composite material is used rather than a single material in a given application (e.g. carbon-fibre reinforced plastic in bikes); Identifies natural and synthetic polymers; Explains why polymer properties can be tailored during manufacturing.

Needs first: Metals vs Non-Metals.

https://lightmysky.com/learn/science/ceramics-polymers-and-composites-mt_w83U-_noVR

#### Inside the Atom: Protons, Neutrons and Electrons (ages 14-15)

Place protons, neutrons and electrons in the atom with their relative charges and masses. Read the atomic number and mass number off the periodic table and use them to count every particle in an atom.

Ready when they can: States the relative charge and relative mass of a proton, a neutron and an electron; Works out how many protons, neutrons and electrons an atom holds from its atomic number and mass number; Explains why an atom carries no overall charge even though it is built from charged particles; Describes how small the nucleus is compared with the whole atom, and where nearly all the mass sits.

Needs first: Atoms, Elements & Compounds, The Periodic Table.

https://lightmysky.com/learn/science/inside-the-atom-protons-neutrons-and-electrons-mt_WqDXAr2IkA

#### Isotopes and Relative Atomic Mass (ages 14-15)

Isotopes of an element differ in neutron count but behave the same chemically. Relative atomic mass is the weighted mean of an element's isotopes, which is why most table values are not whole numbers.

Ready when they can: Identifies two atoms as isotopes of the same element from their atomic and mass numbers; Explains why isotopes of one element react in the same way; Calculates a relative atomic mass from isotope masses and their percentage abundances; Explains why chlorine appears as 35.5 in the table when no single chlorine atom has that mass.

Needs first: Inside the Atom: Protons, Neutrons and Electrons, Proportion.

https://lightmysky.com/learn/science/isotopes-and-relative-atomic-mass-mt_NFoRZd6UN_

#### Electron Shells and the Shape of the Periodic Table (ages 14-15)

Fill electron shells for the first twenty elements and use the result to explain the table itself: the group number gives the outer-shell electrons, the period number gives how many shells are occupied.

Ready when they can: Writes the electronic structure of any of the first twenty elements, such as 2,8,1 for sodium; Links group number to outer-shell electrons and period number to the number of occupied shells; Explains why group 0 elements take part in almost no reactions; Predicts from an element's position whether it will lose or gain electrons when it reacts.

Needs first: Isotopes and Relative Atomic Mass, The Periodic Table.

https://lightmysky.com/learn/science/electron-shells-and-the-shape-of-the-periodic-table-mt__Sdcw4RnZF

#### Group 1, Group 7 and Group 0: Trends You Can Predict (ages 14-16)

Use outer-shell electrons to predict how alkali metals, halogens and noble gases behave, including why group 1 gets more reactive down the group while group 7 gets less.

Ready when they can: Predicts the products when a named group 1 metal meets water and writes the equation; Explains the reactivity trend down group 1 using distance from the nucleus and inner-shell shielding; Explains why the trend in group 7 runs the other way; Predicts whether one halogen will displace another from a solution of its salt.

Needs first: Electron Shells and the Shape of the Periodic Table, The Reactivity Series.

https://lightmysky.com/learn/science/group-1-group-7-and-group-0-trends-you-can-predict-mt_cy1OrVAjIo

#### Ionic Bonding: Electron Transfer and Charged Lattices (ages 14-16)

Metal atoms hand their outer electrons to non-metal atoms, and the ions that result pull on each other in a giant lattice. Work out ionic charges and formulas from the group numbers.

Ready when they can: Draws a dot-and-cross diagram for sodium chloride or magnesium oxide showing where the electrons go; Predicts the charge on an ion from the element's group; Writes the formula of an ionic compound so that the charges cancel; Explains the high melting point and why an ionic solid conducts only when molten or dissolved.

Needs first: Group 1, Group 7 and Group 0: Trends You Can Predict, Metals vs Non-Metals.

https://lightmysky.com/learn/science/ionic-bonding-electron-transfer-and-charged-lattices-mt_sf24C4YLtN

#### Covalent Bonding: Shared Pairs and Simple Molecules (ages 14-16)

Two non-metal atoms fill their outer shells by sharing electron pairs. The shared bond is strong, but the pull between separate molecules is weak, which sets the properties of simple molecular substances.

Ready when they can: Draws dot-and-cross diagrams for hydrogen, water, methane and oxygen, including the double bond; Separates the strong covalent bond inside a molecule from the weak forces between molecules; Explains why simple molecular substances melt and boil at low temperatures; Explains why they do not conduct electricity in any state.

Needs first: Ionic Bonding: Electron Transfer and Charged Lattices.

https://lightmysky.com/learn/science/covalent-bonding-shared-pairs-and-simple-molecules-mt_fn5Dq6qUjP

#### Dot-and-Cross Diagrams and Lone Pairs (ages 14-15)

A dot-and-cross diagram shows where every outer electron sits once a bond has formed, including the pairs that are not bonding anything. Those lone pairs are the part of the picture most people leave out, and they decide what the molecule does next.

Ready when they can: Draw a dot-and-cross diagram for a simple molecule and count bonding pairs and lone pairs separately; Explain why a diagram with the right number of electrons can still be wrong if the pairs sit on the wrong atom; Use the group number of an atom to predict how many bonds it usually forms.

https://lightmysky.com/learn/science/dot-and-cross-diagrams-and-lone-pairs-mt_ghK4a25usP

#### Naming Ionic and Simple Molecular Compounds (ages 14-15)

Chemical names are built from rules, not memorised one by one: ion charges fix the formula of an ionic compound, and Greek prefixes count atoms in a molecular one. Reading a name backwards to a formula is the skill that makes every later equation legible.

Ready when they can: Write the formula of an ionic compound from the charges of its ions, including common polyatomic ions; Name a binary molecular compound using counting prefixes and explain why ionic compounds do not use them; Use a Roman numeral correctly for a metal with more than one possible charge.

https://lightmysky.com/learn/science/naming-ionic-and-simple-molecular-compounds-mt_GJ267pzxCI

#### Redox: Oxidation and Reduction as Electron Transfer (ages 14-16)

Rewrite displacement and metal-with-acid reactions as electron transfer, where oxidation is loss of electrons and reduction is gain, and split a reaction into two half equations.

Ready when they can: Names which species is oxidised and which is reduced in a displacement reaction; Writes the two ionic half equations with electrons balanced; Explains the reactivity series as an order of how readily a metal gives up electrons; Relates the older gain-of-oxygen definition to the electron definition using the same reaction.

https://lightmysky.com/learn/science/redox-oxidation-and-reduction-as-electron-transfer-mt_NMTikR0FTM

#### Extracting Metals: Reduction with Carbon and Choosing a Method (ages 14-15)

A metal sits in its ore as a compound, and getting it out is a reduction. Where the metal falls in the reactivity series decides whether carbon is a strong enough reducing agent or whether electricity has to do the job, which is why aluminium stayed a precious metal long after iron was common.

Ready when they can: Use the reactivity series to predict whether a given metal can be extracted by reduction with carbon; Write the reduction of a metal oxide by carbon and identify what is oxidised and what is reduced; Explain why the extraction method for a metal is an economic argument as well as a chemical one.

https://lightmysky.com/learn/science/extracting-metals-reduction-with-carbon-and-choosing-a-method-mt_LRAEJa8OLr

#### Strong and Weak Acids and the pH Scale (ages 14-16)

An acid in water releases hydrogen ions. A strong acid ionises fully while a weak one only partly does, so strength and concentration are separate ideas, and pH shifts by one for every tenfold change in hydrogen ion concentration.

Ready when they can: Separates strong from weak and concentrated from dilute, and gives an example of each pairing; Predicts the pH change when an acid is diluted ten times; Explains why a weak acid reacts more slowly with magnesium than a strong acid of the same concentration; Writes what happens to hydrochloric acid and to ethanoic acid when each is added to water.

https://lightmysky.com/learn/science/strong-and-weak-acids-and-the-ph-scale-mt_Y4nSn5XH56

#### Density and How to Measure It (ages 15-16)

Density is mass per unit volume, found by weighing and by measuring volume, including displacement for an awkward shape. Particle spacing explains why the same substance has a much lower density as a gas.

Ready when they can: Calculates density in kg per cubic metre or g per cubic centimetre and rearranges for mass or volume; Measures the volume of an irregular solid by displacement and reports its density; Uses particle spacing to explain the density order of a solid, a liquid and a gas.

https://lightmysky.com/learn/science/density-and-how-to-measure-it-mt_HrKI1-UzfI

#### Giant Covalent Structures: Diamond, Graphite and Graphene (ages 15-16)

Some covalent substances never stop bonding. Explain diamond, graphite, graphene and silicon dioxide from how many bonds each atom makes and what is left over.

Ready when they can: Explains diamond's hardness and very high melting point from four covalent bonds per carbon atom; Explains why graphite conducts and why its layers slide, using the fourth electron and the weak forces between layers; Compares graphene and a single graphite layer and gives one use that follows from the structure; Explains why giant covalent substances do not dissolve in water and, apart from graphite, do not conduct.

Needs first: Covalent Bonding: Shared Pairs and Simple Molecules.

https://lightmysky.com/learn/science/giant-covalent-structures-diamond-graphite-and-graphene-mt_YTEj9srwPG

#### Metallic Bonding and Alloys (ages 15-16)

Metal ions sit in a regular lattice inside a sea of delocalised electrons. That one picture explains conduction, malleability, and why an alloy is harder than the pure metal.

Ready when they can: Describes the metallic bond as positive ions held by delocalised electrons; Explains electrical and thermal conduction using electrons that are free to move; Explains malleability by layers of ions sliding over each other; Explains why atoms of a different size in an alloy make the metal harder.

Needs first: Giant Covalent Structures: Diamond, Graphite and Graphene, Metals vs Non-Metals.

https://lightmysky.com/learn/science/metallic-bonding-and-alloys-mt_yXOGOwHmZ4

#### Molecular Shapes from Electron Pair Repulsion (ages 15-16)

Electron pairs around a central atom push each other as far apart as they can, and that alone predicts the shape. A lone pair pushes harder than a bonding pair, which is why water is bent and not straight.

Ready when they can: Predict the shape and bond angle of a simple molecule from the number of bonding and lone pairs; Explain why ammonia and water have smaller bond angles than methane; Draw a three-dimensional representation using wedges and dashes rather than a flat sketch.

https://lightmysky.com/learn/science/molecular-shapes-from-electron-pair-repulsion-mt_Of6ZxYjOsn

#### Electronegativity and the Polar Bond (ages 15-16)

Two bonded atoms rarely pull on the shared pair equally, and the difference in pull leaves one end slightly negative. Whether the whole molecule is polar then depends on its shape, because equal pulls in opposite directions cancel.

Ready when they can: Use a periodic trend to say which of two atoms pulls the shared pair harder; Mark partial charges on a bond and explain what the symbols mean; Decide whether a molecule is polar overall, given both its bond polarities and its shape.

https://lightmysky.com/learn/science/electronegativity-and-the-polar-bond-mt_TwSlh2VvUT

#### Reading Structure from Properties (ages 15-16)

Given melting point, conductivity and solubility for an unknown substance, decide whether it is ionic, simple molecular, giant covalent or metallic, and defend the choice.

Ready when they can: Sorts a table of unknown substances into the four structure types with a reason for each; Names the test that separates ionic from metallic, since both conduct but only one has to melt first; Explains what to do when one property points a different way from the others; Runs the argument backwards, predicting properties from a named structure.

https://lightmysky.com/learn/science/reading-structure-from-properties-mt_yCA66GjWRw

#### Forces Between Molecules (ages 15-16)

Melting and boiling a simple molecular substance breaks the forces between molecules, not the bonds inside them. Those forces come in a few strengths, and hydrogen bonding is the strong end of the range.

Ready when they can: Distinguish the energy needed to separate molecules from the energy needed to break a covalent bond; Rank substances by boiling point using molecular size, polarity and hydrogen bonding; Explain why water boils far above the temperature its molecular mass alone would suggest.

https://lightmysky.com/learn/science/forces-between-molecules-mt_0uBZWotvZB

#### Nanoparticles and Why Surface Area Changes Everything (ages 15-16)

Cut a lump into small enough pieces and the fraction of atoms sitting on a surface stops being negligible. That single geometric fact is why a nanoparticle can catalyse, absorb light or pass through a membrane in ways the bulk material never does, and it is also the reason for caution about them.

Ready when they can: Calculate how the surface area to volume ratio changes when a cube is subdivided; Explain one use of a nanoparticle in terms of the property that only appears at that scale; State a reason for testing nanoparticles for harm that does not apply to the same substance in bulk.

https://lightmysky.com/learn/science/nanoparticles-and-why-surface-area-changes-everything-mt_pTG4U3Hvdn

#### Relative Formula Mass and the Mole (ages 15-16)

Add relative atomic masses to get the relative formula mass of a substance, then use the mole as a fixed count of particles so a mass on the balance can be turned into a number of particles.

Ready when they can: Calculates the relative formula mass of a molecular and an ionic formula, including brackets; Converts between mass in grams and amount in moles for a named substance; States that one mole always contains the same number of particles, about 6.02 x 10^23; Explains why one mole of two different substances weighs two different amounts.

https://lightmysky.com/learn/science/relative-formula-mass-and-the-mole-mt_-SiMKJK4rH

#### Balancing Equations and Conservation of Mass (ages 15-16)

Balance a symbol equation so every element has the same atom count on both sides, add state symbols, and use the balance to explain why mass is conserved even when a reaction looks like it gained or lost some.

Ready when they can: Turns a word equation into a balanced symbol equation with correct formulas; Adds state symbols and says what each one tells a reader; Explains an apparent mass gain when a metal burns and an apparent loss when gas escapes an open flask; Checks a proposed equation and says which element is not balanced.

https://lightmysky.com/learn/science/balancing-equations-and-conservation-of-mass-mt_KUaPCEIA5f

#### Reacting Masses, Limiting Reactants and Yield (ages 15-16)

Use the mole ratio in a balanced equation to work out what mass of product a given mass of reactant can make, find which reactant runs out first, and compare the mass actually collected with the maximum.

Ready when they can: Runs a mass to moles to ratio to mass calculation for a named reaction; Identifies the limiting reactant from the moles available and the equation; Calculates percentage yield from the mass collected and the theoretical mass; Gives reasons a real yield falls short, such as losses on transfer, an incomplete reaction, or a side reaction.

https://lightmysky.com/learn/science/reacting-masses-limiting-reactants-and-yield-mt_C2K6kp5Chv

#### Concentration of Solutions in Moles per Cubic Decimetre (ages 15-16)

Express how much solute a solution carries in g/dm3 and in mol/dm3, convert between the two, and work out what dilution does to the figure.

Ready when they can: Converts a volume in cubic centimetres to cubic decimetres and calculates a concentration; Converts between grams per cubic decimetre and moles per cubic decimetre using the formula mass; Works out what mass to weigh out to make a stated volume of a stated concentration; Predicts the new concentration after adding a measured volume of water.

https://lightmysky.com/learn/science/concentration-of-solutions-in-moles-per-cubic-decimetre-mt_vRK78ynnXb

#### Empirical and Molecular Formulas from Composition (ages 15-16)

Masses or percentages from an analysis give the simplest whole-number ratio of atoms, and one extra measurement of relative mass turns that ratio into the real formula. It is the calculation that connects what a balance reads to what a molecule is.

Ready when they can: Convert masses or percentage composition into an empirical formula; Scale an empirical formula to a molecular formula given the relative molecular mass; Explain why two different compounds can share an empirical formula.

https://lightmysky.com/learn/science/empirical-and-molecular-formulas-from-composition-mt_4rN5MQaTf7

#### The Gas Laws and the Ideal Gas Equation (ages 15-17)

Boyle's law, Charles's law and the pressure law are three slices of one relationship, pV = nRT, once the temperature is in kelvin. The equation gives any one of the four quantities when the other three are known.

Ready when they can: Uses pV over T staying constant to compare one fixed mass of gas in two states; Applies pV = nRT with the amount in moles and the temperature in kelvin; Sketches p against V and p against T and says what the shape of each line shows.

https://lightmysky.com/learn/science/the-gas-laws-and-the-ideal-gas-equation-mt_G7DOTVl4KM

#### Titration: Finding an Unknown Concentration (ages 15-16)

Run an acid and alkali titration to a single indicator end point, then use the mole ratio in the equation to calculate the unknown concentration from concordant titres.

Ready when they can: Describes the apparatus and the steps, including rinsing, swirling, and repeating until titres agree; Selects the concordant titres and takes the mean, discarding the rough run; Calculates moles from concentration and volume and crosses the mole ratio to the other reactant; Names one source of error and says which way it pushes the calculated concentration.

https://lightmysky.com/learn/science/titration-finding-an-unknown-concentration-mt_7WLN35XxYx

#### Why Some Things Dissolve and Others Do Not (ages 15-16)

Dissolving replaces the forces holding a solute together with forces between solute and solvent, and it only happens when that trade is worth making. This is why salt and sugar go into water but oil does not.

Ready when they can: Explain dissolving as an exchange of interactions rather than a disappearance; Predict whether a given solute will dissolve in water or in a non-polar solvent, and say why; Read a solubility curve and use it to predict what crystallises when a solution cools.

https://lightmysky.com/learn/science/why-some-things-dissolve-and-others-do-not-mt__njIrlqqqL

#### Kinetic Theory: Pressure from Molecular Motion (ages 16-18)

Treating a gas as many small particles in random motion, pressure comes from their collisions with the walls, which gives pV as one third of N m times the mean square speed. Comparing that with pV = nRT shows temperature to be a measure of mean molecular kinetic energy.

Ready when they can: States the assumptions the model rests on and names one place a real gas departs from them; Uses the root mean square speed and explains why the mean velocity is zero; Links mean kinetic energy to three halves kT and compares two gases held at the same temperature.

https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu

#### Elastic Strain Energy and Force-Extension Graphs (ages 17-18)

The area under a force-extension graph is the work done stretching a sample, held as elastic strain energy while the material stays elastic. A loading curve that does not retrace on unloading shows energy that never came back.

Ready when they can: Finds strain energy as the area under a force-extension line, and as half of F times x for a spring; Reads a loading and unloading pair of curves and states how much energy was not returned; Predicts the launch speed of an object fired by a stretched spring from the energy stored.

https://lightmysky.com/learn/science/elastic-strain-energy-and-force-extension-graphs-mt_4WnFUmR13O

#### Stress, Strain and the Young Modulus (ages 17-18)

Dividing force by cross-sectional area and extension by original length removes the size of the sample, leaving numbers that describe the material itself. The gradient of the straight part of a stress-strain graph is the Young modulus.

Ready when they can: Calculates stress in pascals and strain as a ratio for a wire under a stated load; Finds the Young modulus as a gradient and quotes it with its unit; Explains why two wires of the same material but different thickness give the same modulus.

https://lightmysky.com/learn/science/stress-strain-and-the-young-modulus-mt_uWdqhWGT7Y

#### Pure Substances & Mixtures (ages 11-13)

Distinguish between pure substances and mixtures, identify formulations as useful mixtures with precise compositions, and use melting and boiling points to test for purity

Ready when they can: Explains why a pure substance has a sharp, fixed melting point but a mixture melts over a range; Identifies common formulations (medicines, alloys, paints, fuels) as deliberate mixtures; Explains what impurities do to melting and boiling points; Distinguishes mixtures from compounds at the particle level.

Needs first: Dissolving & Solutions, Atoms, Elements & Compounds, Salt Water vs Fresh Water.

https://lightmysky.com/learn/science/pure-substances-and-mixtures-mt_MBTVB-E-S7

#### Separating Mixtures: Distillation and Chromatography (ages 11-13)

Select and carry out appropriate separation techniques for different types of mixtures: filtration (insoluble solids), distillation (liquids by boiling point), crystallisation (dissolved solids), and chromatography (coloured substances)

Ready when they can: Selects the correct separation technique for a given mixture with justification; Describes the steps of simple distillation and explains why it works; Interprets a chromatography result (Rf values, number of components); Explains why filtration removes sand from water but not salt.

Needs first: Separating Mixtures, Pure Substances & Mixtures.

https://lightmysky.com/learn/science/separating-mixtures-distillation-and-chromatography-mt_U_tJvy3cbB

#### Paper Chromatography and the Rf Value (ages 14-15)

A mixture spotted on paper separates because each component divides differently between the paper and the moving solvent. The ratio of the distances travelled is a number that identifies a substance under fixed conditions, which is what makes the method analytical rather than merely pretty.

Ready when they can: Run a chromatogram with a baseline drawn in pencil above the solvent, and say why each of those details matters; Calculate an Rf value from a chromatogram and state what must be held constant for it to mean anything; Decide from a chromatogram whether a sample is a pure substance or a mixture.

https://lightmysky.com/learn/science/paper-chromatography-and-the-rf-value-mt_BAcCcz11ls

#### Testing for Ions and Gases (ages 15-16)

Identify unknown ions by flame colour and by the precipitate they form, test the common gases at the bench, and say why an instrument beats these tests on a tiny sample.

Ready when they can: Matches flame colours to the group 1 and group 2 metal ions that produce them; Predicts the precipitate formed when a halide or a sulfate solution meets its test reagent, and writes the ionic equation; Describes the bench tests for hydrogen, oxygen, carbon dioxide and chlorine and the result each gives; Explains a flame colour as electrons dropping back between shells, and gives one reason instruments are used instead.

https://lightmysky.com/learn/science/testing-for-ions-and-gases-mt_PDZjzQJdVt

#### Electrolysis: Half Equations at the Electrodes (ages 15-16)

A current through a molten ionic compound pulls it apart. Positive ions take electrons at the cathode and negative ions give them up at the anode, and each electrode gets its own half equation.

Ready when they can: Explains why an ionic solid does not conduct but the melt does; Predicts the product at each electrode for a named molten compound; Writes both half equations with the electrons balanced; Combines the two half equations back into the overall reaction.

https://lightmysky.com/learn/science/electrolysis-half-equations-at-the-electrodes-mt_6FvxaD8wTY

#### Potable Water and Treating Waste Water (ages 15-16)

Water fit to drink is not pure water, and the treatment chosen depends on what is in the source and how much energy the answer is allowed to cost. Sewage is the harder problem because most of what has to be removed is alive.

Ready when they can: Describe the steps that turn fresh water into potable water and say what each step removes; Explain why desalination is used only where fresh water is scarce, in terms of energy; Distinguish the aerobic and anaerobic stages of sewage treatment by what each one is for.

https://lightmysky.com/learn/science/potable-water-and-treating-waste-water-mt_5qsFZJSmMO

#### Earth's Atmosphere & CO2 (ages 12-14)

Describe the composition of Earth's atmosphere (mainly nitrogen and oxygen, with small amounts of CO₂ and other gases), explain how human activity increases CO₂, and describe the impact on global climate

Ready when they can: States the approximate percentages of nitrogen, oxygen, CO₂, and argon in the atmosphere; Explains how burning fossil fuels and deforestation increase atmospheric CO₂; Describes the greenhouse effect and how it leads to climate change; Discusses one specific consequence of climate change (e.g. rising sea levels, extreme weather).

Needs first: The Carbon Cycle, Greenhouse Gas Science, Earth's atmosphere.

https://lightmysky.com/learn/science/earths-atmosphere-and-co2-mt_mTpV-0rtkO

#### Finite Resources & Recycling (ages 12-14)

Explain that many raw materials (metals, fossil fuels, minerals) are finite resources, describe the environmental costs of extraction, and evaluate the benefits of recycling and the circular economy

Ready when they can: Identifies examples of finite natural resources and explains why they are finite; Describes the environmental impact of mining and fossil fuel extraction; Explains why recycling metals saves energy compared to extraction from ores; Discusses trade-offs between the cost of recycling and the benefit of resource conservation.

Needs first: Earth's Atmosphere & CO2, The Reactivity Series.

https://lightmysky.com/learn/science/finite-resources-and-recycling-mt_0e5rZxbAeR

#### Electrolysis of Solutions and Getting Reactive Metals Out of Ores (ages 15-16)

In a solution the water competes with the dissolved ions, so the products follow reactivity rules. Aluminium extraction and electroplating are the industrial cases, and both are energy-hungry.

Ready when they can: Predicts the products of electrolysing a named aqueous solution using the reactivity of the ions present; Explains why aluminium is extracted by electrolysis while iron is reduced with carbon; Explains why cryolite is added to the aluminium oxide and what it saves; Explains why recycling a metal uses far less energy than extracting it from ore.

https://lightmysky.com/learn/science/electrolysis-of-solutions-and-getting-reactive-metals-out-of-ores-mt_l-t_JxRR7f

#### Reaction Profiles and Activation Energy (ages 15-16)

Draw a reaction as energy against progress, marking reactants, products, the overall energy change and the activation energy hump that has to be climbed before anything happens.

Ready when they can: Draws and labels the profile for an exothermic and for an endothermic reaction; Reads the overall energy change and the activation energy off a given profile; Explains why an exothermic reaction still needs energy put in to start; Matches a temperature rise or fall measured in a beaker to the correct profile shape.

https://lightmysky.com/learn/science/reaction-profiles-and-activation-energy-mt_6LtFkXn_xQ

#### Bond Energies and the Overall Energy Change (ages 15-16)

Breaking bonds takes energy in and making bonds gives energy out. Use a table of bond energies to calculate the overall change for a reaction and check the sign against the profile.

Ready when they can: Totals the energy needed to break the bonds in the reactants and the energy released making the products; Gets the sign right and links a negative overall value to an exothermic reaction; Explains why burning a hydrocarbon in oxygen releases so much energy in terms of the bonds made; Gives a reason a calculated value differs from one measured in a school experiment.

https://lightmysky.com/learn/science/bond-energies-and-the-overall-energy-change-mt_VI0_1ogIOy

#### Alkanes and Alkenes: The First Homologous Series (ages 15-16)

Alkanes and alkenes are families whose members differ by one carbon at a time and share a general formula. The double bond in an alkene makes it react in ways an alkane will not.

Ready when they can: Writes the name and formula of the first four alkanes and the first three alkenes; States the general formula of each series and explains what makes a set of compounds a homologous series; Describes the bromine water test and the result it gives for each family; Writes the products of complete and of incomplete combustion of a named hydrocarbon.

https://lightmysky.com/learn/science/alkanes-and-alkenes-the-first-homologous-series-mt_mkLJDtBanL

#### Crude Oil, Fractional Distillation and Cracking (ages 15-16)

Crude oil is a mixture of hydrocarbons separated by boiling point in a fractionating column, and the long fractions nobody wants are cracked into shorter, more useful molecules.

Ready when they can: Explains how a column separates fractions by chain length and boiling point; Links chain length to viscosity, how easily a fraction evaporates, and how easily it burns; Describes the conditions for cracking and writes an equation showing a long chain becoming an alkane plus an alkene; Explains why refineries crack at all, in terms of what is produced against what is wanted.

https://lightmysky.com/learn/science/crude-oil-fractional-distillation-and-cracking-mt_Jg3O4EQ9Vz

#### Pollutants from Burning Fuels (ages 15-16)

Burning a fuel gives out more than carbon dioxide and water. Incomplete combustion produces carbon monoxide and soot, and sulfur and nitrogen end up as acidic or irritant gases.

Ready when they can: Names the products of complete and incomplete combustion and states the harm each one does; Explains where sulfur dioxide comes from and how it ends up as acid rain; Explains why nitrogen oxides form in an engine when nitrogen is normally unreactive; Evaluates one measure that cuts a named pollutant and says what it costs.

https://lightmysky.com/learn/science/pollutants-from-burning-fuels-mt_DDiyDBy6YW

#### Rates of Reaction: Collision Theory and What Changes a Rate (ages 15-16)

A reaction happens when particles collide often enough and hard enough. Concentration, surface area, temperature, pressure and catalysts each change one of those two things, and a rate is read as the gradient of a graph.

Ready when they can: Explains each factor in terms of how often particles collide or how much energy they bring; Works out a mean rate from a mass loss or gas volume graph, and says why the curve flattens; Explains how a catalyst speeds a reaction up without being used up, using the activation energy; Decides which of two curves on the same axes belongs to the faster run and justifies it.

https://lightmysky.com/learn/science/rates-of-reaction-collision-theory-and-what-changes-a-rate-mt_Ma2bOotr9g

#### Reversible Reactions, Dynamic Equilibrium and Le Chatelier (ages 15-16)

Some reactions run both ways at once. In a closed container the forward and backward rates settle equal, and changing temperature, pressure or a concentration shifts the position until the rates match again.

Ready when they can: Uses the reversible arrow and explains what is still happening at equilibrium; Explains why one direction is exothermic and the other endothermic, using a reversible example such as hydrated copper sulfate; Predicts the shift when temperature, pressure or a concentration is changed, and justifies it; Explains why an industrial process such as the Haber process runs at compromise conditions rather than the ones equilibrium alone would pick.

https://lightmysky.com/learn/science/reversible-reactions-dynamic-equilibrium-and-le-chatelier-mt_Zas-V3kTiR

#### The Haber Process and the Industrial Compromise (ages 15-16)

Making ammonia is the case where equilibrium theory meets a factory, and the chosen conditions are not the ones that give the best yield. A moderate temperature and a catalyst buy a rate that pays, and the unreacted gas is sent round again rather than wasted.

Ready when they can: Predict from Le Chatelier what temperature and pressure would maximise the yield of ammonia; Explain why the temperature actually used is higher than that, in terms of rate and cost; Say what the catalyst does and does not change about the position of equilibrium.

https://lightmysky.com/learn/science/the-haber-process-and-the-industrial-compromise-mt_J-JkijqnY5

#### Inside the Atom: the Nuclear Model (ages 15-16)

Firing alpha particles at thin gold foil sent a few of them straight back, which no spread-out pudding of charge could do. The nuclear model that replaced it puts almost all the mass and all the positive charge in a tiny centre.

Ready when they can: States what the scattering result was and why it ruled out the earlier model; Describes the nuclear model's parts with their charges, and the scale gap between atom and nucleus; Explains that a model is kept only while it fits the evidence, using this change as the example.

https://lightmysky.com/learn/science/inside-the-atom-the-nuclear-model-mt_B_PtnvyRIo

#### Radioactive Decay: Alpha, Beta and Gamma (ages 15-16)

An unstable nucleus throws out an alpha particle, a beta particle or a gamma ray, and each has its own range and stopping material. A nuclear equation tracks how the mass number and atomic number change.

Ready when they can: Names what each emission is made of and what absorbs it, from paper to lead; Completes a nuclear equation for alpha and beta decay with mass and atomic numbers balanced; Explains why an alpha emitter is the most dangerous kind to swallow but the least dangerous at arm's length.

https://lightmysky.com/learn/science/radioactive-decay-alpha-beta-and-gamma-mt_-AmjVwkR9t

#### Half-Life and Activity (ages 15-16)

Activity is the number of decays each second, measured in becquerels, and it falls by half in every half-life. Reading a half-life off a decay curve turns an unpredictable single nucleus into a reliable count for a large sample.

Ready when they can: Reads a half-life from a graph of activity against time; Calculates the fraction or the count rate left after a whole number of half-lives; Explains that a single nucleus decays at random while a large sample follows a steady pattern.

https://lightmysky.com/learn/science/half-life-and-activity-mt_S5snTqUjyi

#### Irradiation, Contamination and Dose (ages 15-16)

Being irradiated means radiation reached you; being contaminated means the radioactive material is on or inside you, and keeps emitting. Dose in sieverts is how the risk from either is compared.

Ready when they can: Uses irradiation and contamination correctly for a sorted set of everyday situations; Explains why contamination usually carries the longer-lasting risk; Reads a dose figure against background radiation and says what it does and does not tell you about harm.

https://lightmysky.com/learn/science/irradiation-contamination-and-dose-mt_WyxR7ZVEhi

#### Nuclear Fission and Fusion (ages 15-16)

Fission splits a large nucleus after it absorbs a neutron, releasing energy and more neutrons that can keep a chain reaction going, which a reactor controls with rods. Fusion joins small nuclei instead, and needs the temperature and pressure found in stars.

Ready when they can: Describes a fission chain reaction and the job of the control rods and moderator; Explains why fusion needs enormous temperature and pressure to start; Compares the two processes by what goes in, what comes out and the waste each leaves.

https://lightmysky.com/learn/science/nuclear-fission-and-fusion-mt_jkO89KodSb

#### Mass, Energy and the Unified Atomic Mass Unit (ages 17-18)

Mass and energy are one quantity written in two units, tied together by E = mc squared. On the nuclear scale that makes one atomic mass unit worth about 931 MeV, which is why nuclear energies dwarf chemical ones.

Ready when they can: Converts a mass in kilograms or atomic mass units into an energy in joules and in MeV; Compares the energy per particle from a nuclear change with that from a chemical one; Explains why the change in mass goes unnoticed in everyday energy transfers.

https://lightmysky.com/learn/science/mass-energy-and-the-unified-atomic-mass-unit-mt_GTfhALD90X

#### Mass Defect and Binding Energy per Nucleon (ages 17-18)

A nucleus weighs less than its separate nucleons, and that missing mass is the energy it would take to pull it apart. Dividing by the number of nucleons gives the curve that peaks near iron.

Ready when they can: Calculates the mass defect and the binding energy of a stated nuclide; Divides by nucleon number and places the nuclide on the binding energy curve; Reads the curve to say which changes release energy and which would absorb it.

https://lightmysky.com/learn/science/mass-defect-and-binding-energy-per-nucleon-mt_UdYE8hgXyl

#### The Decay Constant and the Exponential Decay Law (ages 17-18)

Every unstable nucleus of one kind has the same chance of decaying each second, so the number left falls exponentially. The decay constant is that chance per nucleus per second.

Ready when they can: Uses the exponential decay law to find either the number left or the time elapsed; Explains why decay is random for a single nucleus yet predictable for a large sample; Plots the natural log of the count against time and takes the decay constant from the gradient.

https://lightmysky.com/learn/science/the-decay-constant-and-the-exponential-decay-law-mt_VIydSAys1W

#### Activity, Half-Life and Radioactive Dating (ages 17-18)

Activity is the decay constant times the number of nuclei, so it falls on the same curve as the nuclei do, and the half-life is ln 2 divided by the decay constant. Comparing the activity left with the activity at the start dates a sample.

Ready when they can: Converts between half-life and decay constant in both directions; Calculates activity in becquerels from the number of nuclei present; Dates a sample from a measured carbon-14 activity and names one assumption the method makes.

https://lightmysky.com/learn/science/activity-half-life-and-radioactive-dating-mt_LvZw4h5wlu

#### Energy Released in Fission and Fusion (ages 17-18)

Splitting a heavy nucleus and joining two light ones both move the products up the binding energy per nucleon curve, and the mass lost turns up as energy. The size of the release follows straight from E = mc squared.

Ready when they can: Calculates the energy released from the mass difference across a stated reaction; Explains from the curve why fission suits heavy nuclei and fusion suits light ones; Says why fusion needs extreme temperature, in terms of electrostatic repulsion.

https://lightmysky.com/learn/science/energy-released-in-fission-and-fusion-mt_VrqLAATXQY

#### Particles, Antiparticles and Annihilation (ages 17-18)

Every particle has an antiparticle of the same mass and opposite charge. A pair meeting turns entirely into photons, and a photon of enough energy can create a pair, both governed by E = mc squared.

Ready when they can: Finds the least photon energy needed for pair production of a stated particle; Explains why annihilation gives two photons rather than one; Names positron emission tomography as a use built on annihilation.

https://lightmysky.com/learn/science/particles-antiparticles-and-annihilation-mt_-Ud20HRNJz

#### Quarks, Leptons and the Conservation Laws (ages 17-18)

Protons and neutrons are built from up and down quarks, while electrons and neutrinos are leptons with nothing smaller inside them. Whether a proposed reaction can happen is settled by checking charge, baryon number and lepton number.

Ready when they can: Gives the quark content of a proton and of a neutron and checks that the charges add up; Writes beta-minus decay at quark level, as a down quark turning into an up quark; Tests a proposed reaction against charge, baryon number and lepton number.

https://lightmysky.com/learn/science/quarks-leptons-and-the-conservation-laws-mt_kCGc5Neub_

#### Exchange Particles and Reading a Feynman Diagram (ages 17-18)

Every interaction between particles is carried by an exchanged boson, and which boson it is decides the range and the timescale. A Feynman diagram is the bookkeeping for that exchange, with the vertices doing the conserving and the internal line naming the force.

Ready when they can: Names the exchange particle for each of the four interactions and links its mass to the range of the force; Draws the diagram for beta-minus decay, beta-plus decay and electron capture, with the W labelled and the arrows right; Checks charge, baryon number and lepton number at each vertex of a diagram they did not draw.

https://lightmysky.com/learn/science/exchange-particles-and-reading-a-feynman-diagram-mt_7Ka5cVpTVL

#### Crystal Lattices, the Reciprocal Lattice and Bloch's Theorem (ages 23-24)

A perfect crystal repeats, so its electron states can be labelled by a wavevector and written as a plane wave times a function with the lattice's own period. The reciprocal lattice is the bookkeeping that makes diffraction and band structure the same statement.

Ready when they can: Constructs a reciprocal lattice from a simple direct lattice; States Bloch's theorem and says what the crystal wavevector labels; Connects the diffraction condition to the boundary of the first Brillouin zone.

https://lightmysky.com/learn/science/crystal-lattices-the-reciprocal-lattice-and-blochs-theorem-mt_nbNnHpGnZI

#### Phonons and the Heat Capacity of Solids (ages 23-24)

Lattice vibrations quantise into modes whose occupation follows the Bose distribution, so a solid's heat capacity falls away at low temperature instead of staying constant. Counting modes up to a cutoff gives the cubic law that measurements show.

Ready when they can: Explains why equipartition fails for a solid at low temperature; Counts vibrational modes to reach the low-temperature power law; Distinguishes acoustic from optical branches on a dispersion curve.

https://lightmysky.com/learn/science/phonons-and-the-heat-capacity-of-solids-mt_WXZPdz_JTd

#### Band Structure: Metals, Insulators and the Gap (ages 23-24)

A periodic potential opens gaps in the energy spectrum where the Bragg condition is met, and whether the highest occupied band is full or partly filled decides whether the solid conducts. The free electron gas is the limit where those gaps are ignored.

Ready when they can: Explains why gaps open at Brillouin zone boundaries; Predicts metallic or insulating behaviour from band filling; Places the free electron result as a limiting case of the band picture.

https://lightmysky.com/learn/science/band-structure-metals-insulators-and-the-gap-mt_9f74Vu6qnW

#### Semiconductors, Doping and the p-n Junction (ages 23-24)

A small gap lets thermal excitation put carriers into the conduction band, and impurities decide which carrier dominates. Joining two differently doped regions builds a field at the boundary that lets current pass one way.

Ready when they can: Relates carrier concentration to gap size and temperature; Explains what donor and acceptor doping do to the Fermi level; Describes the built-in field of a junction and why it rectifies.

https://lightmysky.com/learn/science/semiconductors-doping-and-the-p-n-junction-mt_iKlnfAqDAg

#### Superconductivity: the Meissner Effect and Cooper Pairs (ages 23-24)

Below a critical temperature some metals expel magnetic flux completely, which is a stronger claim than zero resistance. A weak attraction carried by the lattice binds electrons into pairs that share one quantum state, and a gap opens at the Fermi level.

Ready when they can: Distinguishes the Meissner effect from what a perfect conductor would do; Explains how a lattice-mediated attraction can outweigh Coulomb repulsion between electrons; Connects the energy gap to the disappearance of resistance.

https://lightmysky.com/learn/science/superconductivity-the-meissner-effect-and-cooper-pairs-mt_2H9bAiAAUV

### Ocean Life

https://lightmysky.com/learn/science/areas/ocean-life

#### Coasts & Beaches (ages 5-7)

Know what a coast or beach is — the place where land meets the ocean — and that different coasts can be sandy, rocky, or muddy, each with different plants and animals

Ready when they can: Define a coast as where land meets the ocean; Describe at least two types of coast: sandy, rocky, or muddy; Name an animal likely found at each type of coast.

https://lightmysky.com/learn/science/coasts-and-beaches-mt_4bJiGiMPmy

#### Ocean Animal Variety (ages 5-7)

Recognise that the ocean is home to an amazing variety of animals — from tiny seahorses and colourful clownfish to enormous whales and sharks — and that ocean animals come in many shapes and sizes

Ready when they can: Name at least five different ocean animals; Describe differences in size between small and large ocean creatures; Express curiosity or wonder about the variety of life in the ocean.

https://lightmysky.com/learn/science/ocean-animal-variety-mt_ytUG3yjCYt

#### Rock Pool Habitats (ages 5-7)

Explore rock pools (tide pools) as small ocean habitats where crabs, anemones, starfish, and small fish can be found, and understand that these creatures are adapted to survive crashing waves and changing water levels

Ready when they can: Name at least three creatures found in rock pools; Describe a rock pool as a small ocean habitat on the shore; Explain one way rock pool animals cope with waves or changing water levels.

Needs first: Coasts & Beaches, Ocean Animal Variety.

https://lightmysky.com/learn/science/rock-pool-habitats-mt_w2u9bXP9n7

#### Whales & Dolphins Are Mammals (ages 5-7)

Know that whales and dolphins are mammals, not fish — they breathe air, are warm-blooded, and feed their babies milk — even though they live in the ocean

Ready when they can: State that whales and dolphins are mammals, not fish; Give at least two reasons why: they breathe air and feed babies milk; Explain that living in water does not make an animal a fish.

Needs first: Ocean Animal Variety.

https://lightmysky.com/learn/science/whales-and-dolphins-are-mammals-mt_mRCPP_Ab2W

#### What Is the Ocean? (ages 5-7)

Know that oceans are huge bodies of salt water that cover most of Earth's surface, and that the ocean is home to an enormous number of living things

Ready when they can: State that oceans cover more of Earth than land does; Explain that ocean water is salty, unlike the fresh water in rivers and lakes; Describe the ocean as home to a huge variety of living things.

https://lightmysky.com/learn/science/what-is-the-ocean-mt_oAg79ju344

#### What Ocean Animals Need (ages 5-7)

Understand that ocean animals need food, shelter, and the right conditions to survive — just like land animals — and that different parts of the ocean provide for different animals' needs

Ready when they can: List basic needs of ocean animals: food, shelter, suitable water conditions; Give an example of how a specific ocean animal meets its needs; Compare an ocean animal's needs to a familiar land animal's needs.

Needs first: What Is the Ocean?.

https://lightmysky.com/learn/science/what-ocean-animals-need-mt_m31_gPS8F1

#### Ocean Food Chains (ages 5-7)

Describe a simple ocean food chain: tiny plants (phytoplankton) are eaten by small animals, which are eaten by bigger fish, which are eaten by top predators like sharks — showing that all ocean life depends on others for food

Ready when they can: Describe a food chain with at least three levels; Identify that ocean food chains start with tiny plants or algae; Explain that bigger animals eat smaller ones in a chain of dependence.

Needs first: What Ocean Animals Need, Ocean Animal Variety.

https://lightmysky.com/learn/science/ocean-food-chains-mt_l6OpmOKMuT

#### Classifying Ocean Animals (ages 7-9)

Classify ocean animals into major groups: fish (breathe through gills, have scales), marine mammals (breathe air, warm-blooded, feed milk), and invertebrates (no backbone — jellyfish, octopuses, crabs, starfish)

Ready when they can: Sort ocean animals into fish, marine mammals, and invertebrates; Give defining features of each group (gills vs lungs, backbone vs none); Correctly classify at least two animals in each group.

Needs first: Whales & Dolphins Are Mammals, Ocean Animal Variety.

https://lightmysky.com/learn/science/classifying-ocean-animals-mt__aHSZTm5k5

#### Coral Reefs (ages 7-9)

Know that coral reefs are built by tiny living animals called coral polyps, that reefs are home to more species than almost any other ocean habitat, and that they are sometimes called the 'rainforests of the sea'

Ready when they can: State that coral is built by tiny living animals called polyps, not made of rock; Describe coral reefs as one of the most biodiverse habitats in the ocean; Explain why reefs are compared to rainforests.

Needs first: What Ocean Animals Need, Rock Pool Habitats, Ocean Animal Variety.

https://lightmysky.com/learn/science/coral-reefs-mt_AxGPeVRm__

#### Ocean Animal Adaptations (ages 7-9)

Understand that ocean animals have special adaptations for their environment: streamlined bodies for fast swimming, camouflage to hide from predators, blubber to keep warm in cold seas, and tentacles or suckers to catch prey

Ready when they can: Name at least three different ocean animal adaptations; Explain how each adaptation helps the animal survive in its environment; Connect an adaptation to the specific challenge it addresses (cold, predators, catching food).

Needs first: What Ocean Animals Need, Ocean Animal Variety.

https://lightmysky.com/learn/science/ocean-animal-adaptations-mt_9EoS35vaYB

#### Ocean Depth Zones (ages 7-9)

Understand that the ocean has different zones depending on depth and light: the sunlight zone near the surface where most life lives, the twilight zone where light fades, and the midnight zone of total darkness

Ready when they can: Name the three main ocean zones: sunlight, twilight, and midnight; Explain that light decreases with depth until it disappears completely; State that most ocean life is found in the sunlight zone because plants need light to grow.

Needs first: What Is the Ocean?, Ocean Animal Variety.

https://lightmysky.com/learn/science/ocean-depth-zones-mt_sQpIV0-qY7

#### Ocean Food Webs (ages 7-9)

Understand ocean food webs: multiple interconnected food chains where energy flows from phytoplankton (producers) through zooplankton, small fish, and large predators, and that removing one species affects the whole web

Ready when they can: Distinguish a food web from a simple food chain; Trace at least two paths of energy through an ocean food web; Explain what could happen if one species in the web were removed.

Needs first: Classifying Ocean Animals, Ocean Food Chains.

https://lightmysky.com/learn/science/ocean-food-webs-mt_OnV_DTp5i8

#### The Five Oceans (ages 7-9)

Name and locate the five oceans — Pacific (largest), Atlantic, Indian, Southern, and Arctic (smallest and coldest) — on a world map, and understand that they are all connected as one global ocean

Ready when they can: Name all five oceans: Pacific, Atlantic, Indian, Southern, Arctic; Locate at least three oceans on a world map; Explain that the five named oceans are all connected as one continuous body of water.

Needs first: Where water is found on Earth, What Is the Ocean?.

https://lightmysky.com/learn/science/the-five-oceans-mt_8QOeG3CuKc

#### The Ocean Floor (ages 7-9)

Know that the ocean floor is not flat — it has mountains, valleys, and the deepest trenches on Earth — and that the deepest point is the Mariana Trench, deeper than Mount Everest is tall

Ready when they can: State that the ocean floor has varied terrain including mountains, ridges, and trenches; Name the Mariana Trench as the deepest point on Earth; Compare its depth to a familiar reference like Mount Everest's height.

Needs first: What Is the Ocean?, Ocean Depth Zones.

https://lightmysky.com/learn/science/the-ocean-floor-mt_yxL1v4LuqR

#### Tides, Waves & Currents (ages 7-9)

Know that the ocean has tides (water level rises and falls twice a day, caused mainly by the Moon's gravity), waves (caused by wind), and currents (rivers of water flowing through the ocean that carry warmth and nutrients around the world)

Ready when they can: Describe tides as the regular rise and fall of water level, caused by the Moon's gravity; Explain that waves are caused by wind blowing across the water surface; Describe ocean currents as large flows of water that carry heat and nutrients around the globe.

Needs first: Coasts & Beaches, What Is the Ocean?.

https://lightmysky.com/learn/science/tides-waves-and-currents-mt_kCSy3Lsgme

#### Deep-Sea Creatures (ages 9-11)

Explore life in the deep sea: animals that make their own light (bioluminescence), creatures adapted to crushing pressure and total darkness, and hydrothermal vents where life thrives without sunlight

Ready when they can: Define bioluminescence as the ability of some deep-sea creatures to produce their own light; Describe at least two adaptations deep-sea animals have for life in darkness and pressure; Explain that hydrothermal vents support life without sunlight through chemical energy.

Needs first: Ocean Animal Adaptations, Ocean Depth Zones, The Ocean Floor.

https://lightmysky.com/learn/science/deep-sea-creatures-mt_dRCnJEIwk4

#### Exploring the Ocean (ages 9-11)

Know that oceanographers and marine biologists study the ocean using submarines, remotely operated vehicles (ROVs), satellites, and diving, and that much of the ocean remains unexplored — we know more about the Moon's surface than the deep ocean floor

Ready when they can: Name at least two tools scientists use to explore the ocean: submarines, ROVs, satellites; State that most of the deep ocean remains unexplored; Explain why ocean exploration is difficult: darkness, pressure, vastness.

Needs first: Deep-Sea Creatures, The Ocean Floor.

https://lightmysky.com/learn/science/exploring-the-ocean-mt_1m5ItPiwUK

#### Deep-Sea Life Without Sunlight (ages 11-13)

Contrast photosynthesis (energy from sunlight) with chemosynthesis (energy from oxidising chemicals like hydrogen sulphide); describe hydrothermal vent communities: chemoautotrophic bacteria form the base of a food web supporting tube worms, giant clams, and vent crabs with no sunlight; explore what deep-sea life tells us about the origin of life on Earth; explain why NASA studies ocean vents as analogues for potential life around hydrothermal activity on Europa and Enceladus

Needs first: Deep-Sea Creatures.

https://lightmysky.com/learn/science/deep-sea-life-without-sunlight-mt_6Wx--Du8j3

#### Ocean Ecosystems (ages 9-11)

Understand ocean ecosystems as interconnected systems where living things (producers, consumers, decomposers) and non-living factors (temperature, salinity, light, currents) all interact, and that changes to one part affect the whole system

Ready when they can: Describe an ocean ecosystem as a system of living and non-living parts that interact; Name key non-living factors that affect ocean life: temperature, salinity, light, currents; Explain how a change in one factor (like temperature) cascades through the whole ecosystem.

Needs first: Ocean Food Webs, Ocean Depth Zones, Changing Environments.

https://lightmysky.com/learn/science/ocean-ecosystems-mt_w4OYcWJs6H

#### Ocean Pollution & Harm (ages 9-11)

Identify ways humans harm the ocean — plastic pollution, overfishing, oil spills, and ocean acidification from carbon dioxide — and understand that most ocean pollution comes from land-based activities, not just ships

Ready when they can: Name at least three ways humans harm the ocean; Explain that most ocean pollution originates on land, not from ships; Describe how plastic pollution or overfishing specifically harms marine animals.

Needs first: Ocean Food Webs, Ocean Ecosystems.

https://lightmysky.com/learn/science/ocean-pollution-and-harm-mt_J6uccv2Bo4

#### Oceans & Climate (ages 9-11)

Understand the connection between the ocean and climate: the ocean absorbs heat and carbon dioxide, drives weather patterns through evaporation, and ocean currents distribute warmth around the planet — making the ocean Earth's climate engine

Ready when they can: Explain that the ocean absorbs a large amount of the Sun's heat and atmospheric carbon dioxide; Describe the ocean's role in the water cycle through evaporation; Explain how ocean currents distribute warmth and affect weather patterns in distant places.

Needs first: The Five Oceans, Weather vs Climate, Tides, Waves & Currents, Ocean Ecosystems.

https://lightmysky.com/learn/science/oceans-and-climate-mt_KRNU0IOKfO

#### Protecting the Ocean (ages 9-11)

Understand how people protect the ocean: marine protected areas limit fishing and pollution, sustainable fishing prevents overharvesting, beach clean-ups reduce plastic, and international agreements aim to reduce carbon emissions that cause ocean acidification

Ready when they can: Explain what a marine protected area is and why it helps; Describe sustainable fishing as taking only what the ocean can replace; Name at least two actions people can take to protect oceans: reducing plastic, marine reserves, cutting emissions.

Needs first: Coral Reefs, Ocean Pollution & Harm, Oceans & Climate.

https://lightmysky.com/learn/science/protecting-the-ocean-mt_50SdpkNH49

#### Ocean Currents and Global Heat (ages 11-12)

Explain thermohaline circulation (the global conveyor belt) as driven by temperature and salinity differences that cause dense water to sink; describe how the Atlantic Meridional Overturning Circulation (AMOC) transfers heat from the tropics toward Europe; explain that oceans absorb more than 90% of excess heat and ~25% of CO2 from human emissions; explore what would happen to Northern European climates if circulation weakened

Needs first: Oceans & Climate.

https://lightmysky.com/learn/science/ocean-currents-and-global-heat-mt_Mp_CpVK6e-

#### Ocean Animal Migrations (ages 9-11)

Know that many ocean animals undertake remarkable migrations — humpback whales travel thousands of miles between feeding and breeding grounds, sea turtles return to the same beach where they hatched to lay eggs — and understand these journeys are linked to seasonal food supplies and reproduction

Ready when they can: Describe at least one example of marine animal migration in detail; Explain that migrations are driven by seasonal food availability and breeding needs; Estimate the scale of these journeys (thousands of miles).

Needs first: The Five Oceans, Ocean Animal Adaptations, Animal Migration, Ocean Food Webs.

https://lightmysky.com/learn/science/ocean-animal-migrations-mt_Te-ulgYMUd

#### Predator Loss and Ecosystem Effects (ages 12-14)

Quantify energy transfer efficiency through trophic levels (~10% rule); explain trophic cascades: how removing an apex predator triggers a chain of ecosystem changes (sea otters → sea urchin explosion → kelp forest collapse); define 'fishing down the food web'; evaluate evidence for ocean rewilding — shark reintroduction, whale recovery driving nutrient cycling; understand why ecosystem-based fisheries management is needed

Needs first: Ocean Pollution & Harm, Ocean Animal Migrations.

https://lightmysky.com/learn/science/predator-loss-and-ecosystem-effects-mt_NPTjGJIyb3

#### Coral Bleaching & Acidification (ages 12-13)

Explain the mutualistic symbiosis between coral polyps and photosynthetic zooxanthellae; describe how heat stress causes bleaching (corals expel zooxanthellae and turn white); explain ocean acidification chemistry: CO2 dissolves in seawater to form carbonic acid, lowering pH and dissolving calcium carbonate skeletons; connect reef loss to the collapse of habitat for ~25% of marine species; evaluate current reef restoration efforts

Needs first: Ocean Currents and Global Heat, Predator Loss and Ecosystem Effects, Ocean Ecosystems, Acids, Alkalis & pH.

https://lightmysky.com/learn/science/coral-bleaching-and-acidification-mt_EXO1bJ3G_v

#### Deep-Ocean Exploration Technology (ages 13-14)

Explain how crewed submersibles (Alvin, Deepsea Challenger) and remotely operated vehicles (ROVs) allow exploration of the deep; describe acoustic seafloor mapping using sonar and why only ~25% of the ocean floor has been mapped at high resolution; explore why the deep ocean is harder to explore than the surface of the Moon (pressure, cold, darkness, communication difficulties); survey astrobiology missions targeting ocean worlds in our solar system

Needs first: Exploring the Ocean, Predator Loss and Ecosystem Effects, Deep-Sea Survival.

https://lightmysky.com/learn/science/deep-ocean-exploration-technology-mt_kKxbPHi5Db

### Organisms & Life Processes

https://lightmysky.com/learn/science/areas/organisms-and-life-processes

#### Common Plants & Trees (ages 5-6)

Identify and name common wild and garden plants, including deciduous and evergreen trees

Ready when they can: Name at least five common wild or garden plants from direct observation; Sort trees into deciduous (loses leaves) and evergreen (keeps leaves) with examples; Match a plant to its name when shown a picture or real specimen.

https://lightmysky.com/learn/science/common-plants-and-trees-mt_j7cer_Nmor

#### Living Things Vocabulary (ages 5-7)

Name and use vocabulary for what makes something living — alive, dead, never been alive, movement, nutrition, growth, reproduction, sensitivity, excretion — and apply these terms when classifying objects and explaining why plants and animals count as living things

Ready when they can: Correctly classify objects as living, dead, or never been alive and give a reason using one of the life process terms; Name at least five life processes using the correct vocabulary; Explain why a plant is alive using at least two life process words.

https://lightmysky.com/learn/science/living-things-vocabulary-mt_zexbopQjG0

#### Naming Common Animals (ages 5-6)

Identify and name common animals from major groups: fish, amphibians, reptiles, birds, and mammals

Ready when they can: Name at least two animals from each group: fish, amphibians, reptiles, birds, mammals; Sort a set of animal pictures into the five groups; Explain one feature of each group (e.g. 'birds have feathers', 'fish have gills').

https://lightmysky.com/learn/science/naming-common-animals-mt_zVLOm6U7bh

#### Animal Body Groups (ages 5-7)

Describe and compare the external body structure of common animals across groups (fish, amphibians, reptiles, birds, mammals)

Ready when they can: Describe key structural features of at least three animal groups (e.g. scales, feathers, fur); Compare two animals from different groups, noting at least two differences; Use words like 'wings', 'fins', 'legs', 'tail' correctly when describing an animal.

Needs first: Naming Common Animals.

https://lightmysky.com/learn/science/animal-body-groups-mt_fDoE-pL6Jv

#### Body Parts & Senses (ages 5-6)

Identify, name, and locate basic parts of the human body and associate each body part with its sense

Ready when they can: Label eyes, ears, nose, mouth, and skin on a body outline; Match each sense organ to its sense: sight, hearing, smell, taste, touch; Describe a simple scenario for each sense (e.g. 'I use my nose to smell cookies baking').

Needs first: Animal Body Groups.

https://lightmysky.com/learn/science/body-parts-and-senses-mt_83gRQ9OPkc

#### Herbivores, Carnivores & Omnivores (ages 5-6)

Classify common animals as carnivores (eat meat), herbivores (eat plants), or omnivores (eat both)

Ready when they can: Define carnivore, herbivore, and omnivore in own words; Sort at least six common animals into the three diet groups; Give a reason for each sorting decision based on what the animal eats.

Needs first: Naming Common Animals.

https://lightmysky.com/learn/science/herbivores-carnivores-and-omnivores-mt_13CtLTcWUB

#### Parts of a Plant (ages 5-6)

Identify and describe the basic structure of common flowering plants (roots, stem, leaves, flowers) and trees (roots, trunk, branches, leaves)

Ready when they can: Label roots, stem, leaves, and flowers on a diagram of a flowering plant; Name the main parts of a tree: roots, trunk, branches, leaves; Explain that roots take in water and leaves catch sunlight.

Needs first: Common Plants & Trees.

https://lightmysky.com/learn/science/parts-of-a-plant-mt_xT6jPzyj92

#### What Living Things Need (ages 5-7)

Understand what plants and animals (including humans) need to survive: water, food, air, and suitable conditions

Ready when they can: List the basic needs of animals: water, food, air, shelter; List the basic needs of plants: water, light, air, suitable temperature; Explain what happens if one basic need is missing (e.g. 'the plant wilts without water').

Needs first: Common Plants & Trees, Living Things Vocabulary, Naming Common Animals.

https://lightmysky.com/learn/science/what-living-things-need-mt_L1469gt34A

#### Animal Life Stages (ages 6-7)

Recognise that animals, including humans, have offspring which grow into adults, and describe basic animal life stages

Ready when they can: Describe the basic life stages of a human: baby, child, teenager, adult; Give examples of other animals and their young (e.g. kitten → cat, chick → hen); Explain that offspring grow and change as they develop into adults.

Needs first: What Living Things Need, How Animals Have Babies, Naming Common Animals.

https://lightmysky.com/learn/science/animal-life-stages-mt_oR6dwRj2Ll

#### Seeds & Plant Growth (ages 6-7)

Observe and describe how seeds and bulbs grow into mature plants through stages of germination and growth

Ready when they can: Describe the stages: seed absorbs water → root appears → shoot pushes up → leaves open; Compare how a bulb and a seed start growing differently; Record observations of a growing plant over several days using drawings or a simple diary.

Needs first: What Living Things Need.

https://lightmysky.com/learn/science/seeds-and-plant-growth-mt_0B64gfJf7j

#### What Plants Need to Grow (ages 6-8)

Understand that plants need water, light, and a suitable temperature to grow and stay healthy

Ready when they can: Name three things plants need to grow: water, light, suitable temperature; Predict what happens to a plant kept in the dark, with no water, or in freezing cold; Describe the results of a simple test comparing plants grown in different conditions.

Needs first: What Living Things Need.

https://lightmysky.com/learn/science/what-plants-need-to-grow-mt_3v0VNkwquK

#### Animal Classification Vocabulary (ages 7-9)

Use vocabulary for classifying animals and describing life cycles — vertebrate, invertebrate, mammal, bird, reptile, amphibian, fish, insect, arachnid, larva, pupa, metamorphosis, gestation, offspring, complete metamorphosis, incomplete metamorphosis — and apply these correctly when sorting and comparing organisms

Ready when they can: Correctly classify a set of animals as vertebrates or invertebrates, then into more specific groups; Use 'metamorphosis' correctly to describe insect and amphibian life cycles and distinguish complete from incomplete metamorphosis; Compare a mammal's life cycle with an insect's using precise vocabulary.

https://lightmysky.com/learn/science/animal-classification-vocabulary-mt_1J5fwxNDxL

#### Animal Nutrition (ages 7-8)

Understand that animals, including humans, need the right types and amounts of nutrition, and that animals cannot make their own food

Ready when they can: Name the main food groups: carbohydrates, proteins, fats, vitamins, minerals, fibre, water; Explain that animals get energy from food they eat, unlike plants which make their own; Describe what happens with too much or too little of a food group (e.g. weak bones without calcium).

Needs first: Herbivores, Carnivores & Omnivores, What Living Things Need.

https://lightmysky.com/learn/science/animal-nutrition-mt_E1wR8IfCV6

#### Drawing Life Cycle Diagrams (ages 7-8)

Draw and interpret life cycle diagrams for flowering plants, insects (complete and incomplete metamorphosis), birds, and mammals — labelling stages, describing transitions, and comparing cycles across species

Ready when they can: Draw a labelled life cycle diagram for a flowering plant including seed, seedling, mature plant, and flower/fruit; Compare a butterfly life cycle (complete metamorphosis) with a grasshopper life cycle (incomplete metamorphosis) using diagrams; Label a blank life cycle diagram for a given organism correctly, including transitions between stages.

Needs first: Sorting into categories.

https://lightmysky.com/learn/science/drawing-life-cycle-diagrams-mt_7EqhgErJyU

#### How Plant Parts Work (ages 7-8)

Identify and describe the functions of different parts of flowering plants: roots absorb water and nutrients, stems transport materials, leaves make food, flowers enable reproduction

Ready when they can: Describe the function of roots (absorb water and minerals from soil); Explain that the stem transports water up and food around the plant; State that leaves use sunlight to make food and flowers produce seeds for new plants.

Needs first: Parts of a Plant.

https://lightmysky.com/learn/science/how-plant-parts-work-mt_6xsEXxKdUX

#### Pollination & Seed Dispersal (ages 7-8)

Understand the life cycle of flowering plants including pollination, seed formation, and seed dispersal

Ready when they can: Describe the stages: pollination → fertilisation → seed formation → seed dispersal; Explain at least two methods of seed dispersal (wind, animal, water, explosion); Describe pollination as the transfer of pollen from one flower to another, often by insects or wind.

Needs first: Seeds & Plant Growth, How Plant Parts Work.

https://lightmysky.com/learn/science/pollination-and-seed-dispersal-mt_WNBHZ1d94L

#### Life Cycles of Organisms (ages 7-9)

Develop models to describe that organisms have unique and diverse life cycles but all share the common stages of birth, growth, reproduction, and death

Ready when they can: Describe the life cycle of at least two different organisms (e.g. butterfly, frog, plant); Identify the common stages all life cycles share: birth, growth, reproduction, death; Explain how life cycles can look very different (metamorphosis vs gradual growth) but follow the same pattern.

Needs first: Animal Classification Vocabulary, Drawing Life Cycle Diagrams, Animal Life Stages, Pollination & Seed Dispersal.

https://lightmysky.com/learn/science/life-cycles-of-organisms-mt_4IVWRAZoNC

#### Water Transport in Plants (ages 7-8)

Investigate how water is transported within plants, using observations such as coloured water being drawn up through a stem

Ready when they can: Describe an investigation using coloured water to track water movement in a plant; Explain that water travels from roots through the stem to the leaves and flowers; Draw or label a diagram showing the path of water through a plant.

Needs first: How Plant Parts Work.

https://lightmysky.com/learn/science/water-transport-in-plants-mt_GF6L7J4MNN

#### What Plants Need to Thrive (ages 7-8)

Explore and compare the requirements of plants for life and growth: air, light, water, nutrients from soil, and room to grow

Ready when they can: List five requirements for plant growth: air, light, water, nutrients, space; Explain how needs vary between plants (e.g. cacti need less water than ferns); Predict what happens when one requirement is removed or limited.

Needs first: What Plants Need to Grow.

https://lightmysky.com/learn/science/what-plants-need-to-thrive-mt_lutxvMlkwS

#### Inheritance Vocabulary (ages 8-10)

Use vocabulary for variation and inheritance — inherited characteristic, acquired characteristic, variation, offspring, trait, species, breed, genetic, environment — and apply these when comparing organisms and explaining similarities and differences within and between species

Ready when they can: Distinguish between inherited and acquired characteristics with a correct example of each; Use 'variation' correctly to describe differences within a species and explain what causes variation; Use 'offspring', 'species', and 'trait' correctly in written descriptions of living things.

https://lightmysky.com/learn/science/inheritance-vocabulary-mt_h4abSktujo

#### Inherited characteristics (ages 8-9)

Analyse and interpret data to provide evidence that plants and animals have traits inherited from parents and that variation of these traits exists in a group of similar organisms

Ready when they can: Define inherited traits as characteristics passed from parents to offspring; Collect or interpret data showing variation within a group (e.g. different heights, colours, sizes); Explain that while traits are inherited, there is natural variation among individuals of the same species.

Needs first: Inheritance Vocabulary.

https://lightmysky.com/learn/science/inherited-characteristics-mt_1wxwg782yX

#### Offspring resemble parents (ages 8-11)

Observe that young plants and animals resemble their parents but are not identical, recognising inherited similarities and individual differences

Ready when they can: Describe at least three features that offspring inherit from parents (e.g. eye colour, petal colour, fur type); Explain that offspring are similar to parents but not identical copies; Give examples from both plants and animals showing resemblance with variation.

Needs first: Inherited characteristics, Animal Life Stages, How Animals Have Babies.

https://lightmysky.com/learn/science/offspring-resemble-parents-mt_cEzX5r7kp0

#### Traits: inherited and environmental (ages 8-9)

Use evidence to support the explanation that traits can be influenced by the environment as well as inheritance

Ready when they can: Explain that traits result from both inheritance and environmental factors; Give examples of environmental influence on traits (e.g. sunlight affects plant growth, diet affects animal size); Distinguish between inherited traits (e.g. eye colour) and environmentally influenced traits (e.g. muscle strength from exercise).

Needs first: Inherited characteristics, Inheritance Vocabulary.

https://lightmysky.com/learn/science/traits-inherited-and-environmental-mt_Tls5qJ4p0L

#### Organ Systems Vocabulary (ages 9-11)

Use technical vocabulary for the major organ systems — organ, organ system, circulatory system, digestive system, respiratory system, skeletal system, muscular system, nutrient, oxygen, carbon dioxide, blood vessel, artery, vein, capillary, enzyme — and describe the function of each system using these terms

Ready when they can: Name the main organs in at least two body systems and state their functions using the correct vocabulary; Use 'circulatory', 'digestive', and 'respiratory' correctly in written descriptions of the body; Explain the difference between an artery and a vein using the correct anatomical terms.

https://lightmysky.com/learn/science/organ-systems-vocabulary-mt_K8DJzqbksM

#### Human Life Stages (ages 9-10)

Describe the changes as humans develop to old age, including the stages of the human life cycle

Ready when they can: Name the main stages of human development: baby, toddler, child, teenager, adult, elderly; Describe key changes at puberty (growth spurt, body changes); Explain that old age brings changes like reduced strength, greying hair, and slower healing.

Needs first: Life Cycles of Organisms, Organ Systems Vocabulary.

https://lightmysky.com/learn/science/human-life-stages-mt_OSfCeIeBak

#### Senses, Brain & Responses (ages 9-10)

Use a model to describe that animals receive information through their senses, process it in their brain, and respond in different ways

Ready when they can: Describe the pathway: sense organ detects stimulus → brain processes information → body responds; Give examples of different animal senses (sight, smell, hearing, echolocation, vibration); Explain how the same stimulus can produce different responses in different animals.

Needs first: Body Parts & Senses.

https://lightmysky.com/learn/science/senses-brain-and-responses-mt_IzlVK0Eony

#### Evolution vocabulary (ages 10-11)

Use technical vocabulary for evolution and natural selection — adaptation, evolution, natural selection, extinct, extinction, fossil record, species, common ancestor, mutation, variation — and explain the mechanism of natural selection using these terms in the correct sequence

Ready when they can: Use 'adaptation' correctly to describe a feature that helps an organism survive in its environment; Explain natural selection using 'variation', 'selection pressure', and 'reproduction' correctly in sequence; Use 'extinct' and 'extinction' correctly and distinguish them from 'endangered'.

https://lightmysky.com/learn/science/evolution-vocabulary-mt_lWqmKn5Jvr

#### Plants Grow from Air & Water (ages 10-11)

Support an argument that plants get the materials they need for growth chiefly from air and water, not from the soil

Ready when they can: Explain that plants take in carbon dioxide from air and water from soil to make food (photosynthesis); Argue that most of a plant's mass comes from air (CO₂) and water, not soil minerals; Describe a simple investigation showing soil mass barely changes while a plant grows significantly.

Needs first: Water Transport in Plants, What Plants Need to Thrive.

https://lightmysky.com/learn/science/plants-grow-from-air-and-water-mt_3-ii06P4YS

#### Energy from Food & the Sun (ages 10-11)

Use models to describe that energy in animals' food was once energy from the sun, transferred through plants or other organisms

Ready when they can: Explain that plants capture energy from sunlight to make food (photosynthesis); Trace an energy pathway: sun → plant → animal → another animal; Explain that animals use food energy for body repair, growth, movement, and warmth.

Needs first: Plants Grow from Air & Water, Animal Nutrition.

https://lightmysky.com/learn/science/energy-from-food-and-the-sun-mt_PYPs2yD2sn

#### Cells Under the Microscope (ages 11-12)

Understand that all living organisms are made of cells and use a light microscope to observe, interpret, and record cell structure

Ready when they can: States that all living things are made of cells; Prepares or examines a slide of cells (e.g. onion skin, cheek cells) under a microscope; Draws and labels a diagram of cells observed; Identifies nucleus, cytoplasm, and cell membrane in a microscope image.

Needs first: Organ Systems Vocabulary.

https://lightmysky.com/learn/science/cells-under-the-microscope-mt_VfA4xo4kUv

#### Nutrients in a Healthy Diet (ages 11-13)

Identify the seven components of a healthy diet — carbohydrates, lipids, proteins, vitamins, minerals, dietary fibre, and water — and explain the role of each in the body

Ready when they can: Names all seven dietary components and a food source for each; Explains what each nutrient does in the body (e.g. proteins for growth and repair); Identifies which nutrients provide energy and which do not.

Needs first: Animal Nutrition.

https://lightmysky.com/learn/science/nutrients-in-a-healthy-diet-mt_sDmrVCfzqt

#### Calculating Dietary Energy (ages 11-13)

Calculate and evaluate energy intake and requirements in a healthy daily diet, interpreting food labels and nutritional data

Ready when they can: Reads and interprets a nutritional information label (kJ and kcal); Estimates daily energy requirements for a person of a given age/activity level; Compares the energy content of different diets and identifies surpluses or deficits.

Needs first: Nutrients in a Healthy Diet.

https://lightmysky.com/learn/science/calculating-dietary-energy-mt_83KkBCtVyR

#### Diet Imbalance & Deficiency (ages 11-13)

Explain the health consequences of an imbalanced diet including obesity (excess energy), starvation (severe energy deficit), and deficiency diseases (lack of specific nutrients, e.g. scurvy, rickets)

Ready when they can: Defines obesity, starvation, and deficiency disease and links each to dietary imbalance; Identifies at least two specific deficiency diseases and the missing nutrient causing each; Explains why the impact of poor diet can be long-term.

Needs first: Nutrients in a Healthy Diet.

https://lightmysky.com/learn/science/diet-imbalance-and-deficiency-mt_NZHFcEtTyI

#### Parts of Plant and Animal Cells (ages 11-12)

Describe the functions of the main components of plant and animal cells: cell wall, cell membrane, cytoplasm, nucleus, vacuole, mitochondria, ribosomes, and chloroplasts

Ready when they can: Names the main organelles in plant and animal cells; Explains the function of each organelle in their own words; Links organelle function to the needs of the whole cell (e.g. mitochondria produce energy for cell activities).

Needs first: Cells Under the Microscope.

https://lightmysky.com/learn/science/parts-of-plant-and-animal-cells-mt_bABr-c2DfV

#### Plant Cells vs Animal Cells (ages 11-12)

Compare plant and animal cells, identifying shared features and structures unique to plant cells (cell wall, vacuole, chloroplasts)

Ready when they can: Lists features common to plant and animal cells; Identifies structures found only in plant cells and explains why; Draws and annotates labelled diagrams of both cell types showing similarities and differences.

Needs first: Parts of Plant and Animal Cells.

https://lightmysky.com/learn/science/plant-cells-vs-animal-cells-mt_fhqBH9scsU

#### Cells to Organ Systems (ages 11-12)

Describe the hierarchical organisation of multicellular organisms: cells → tissues → organs → organ systems → organism

Ready when they can: Places cells, tissues, organs, and organ systems in the correct order of organisation; Gives a specific example of each level (e.g. muscle cell → muscle tissue → heart → circulatory system → human); Explains why specialised cells are needed in a multicellular organism.

Needs first: Plant Cells vs Animal Cells.

https://lightmysky.com/learn/science/cells-to-organ-systems-mt_7hB8s5eOP1

#### Photosynthesis (ages 11-12)

Explain photosynthesis as the process by which plants use light energy to convert carbon dioxide and water into glucose and oxygen, and describe how mineral nutrients are absorbed through roots

Ready when they can: Writes and explains the word equation for photosynthesis; Identifies the raw materials needed and the products made; Explains the role of chlorophyll in capturing light energy; Distinguishes between what plants get from the air (CO₂), soil (water and minerals), and light.

Needs first: Deep-Sea Life Without Sunlight, Plant Cells vs Animal Cells, What Plants Need to Thrive.

https://lightmysky.com/learn/science/photosynthesis-mt_zM5vu31jgl

#### Single-Celled Organisms (ages 11-12)

Explain how unicellular organisms such as bacteria and Amoeba carry out all the functions of life within a single cell

Ready when they can: Names examples of unicellular organisms; Lists the seven life processes (MRS NERG) and explains how a single cell performs each one; Contrasts how unicellular organisms meet their needs compared to multicellular organisms.

Needs first: Parts of Plant and Animal Cells, Cells Under the Microscope.

https://lightmysky.com/learn/science/single-celled-organisms-mt_g9RcQOhU5d

#### Using a Microscope (ages 11-12)

Use a light microscope correctly to prepare, focus, and examine biological specimens, including making accurate labelled drawings at an appropriate magnification

Ready when they can: Sets up a light microscope safely and correctly (course focus then fine focus); Prepares a wet mount slide with a biological specimen (e.g. onion skin); Calculates the magnification of an image (magnification = image size ÷ actual size); Draws an accurate labelled diagram of observed cells with a scale.

Needs first: Cells Under the Microscope.

https://lightmysky.com/learn/science/using-a-microscope-mt_lMLeNLDRO8

#### How Diffusion Works (ages 12-13)

Explain diffusion as the net movement of particles from a region of higher concentration to lower concentration, and describe its role in moving materials (oxygen, carbon dioxide, glucose) in and between cells

Ready when they can: Defines diffusion using particle theory; Explains the direction of diffusion of oxygen and carbon dioxide at the alveoli; Explains how cells get glucose from the blood using diffusion; Identifies factors that affect the rate of diffusion (concentration gradient, surface area, distance).

Needs first: Parts of Plant and Animal Cells.

https://lightmysky.com/learn/science/how-diffusion-works-mt_i80I-1MLP2

#### Gas Exchange & Breathing (ages 12-13)

Describe the structure of the human gas exchange system (trachea, bronchi, bronchioles, alveoli) and explain how the mechanism of breathing — using pressure changes from rib and diaphragm movement — moves air in and out of the lungs

Ready when they can: Labels a diagram of the lungs showing trachea, bronchi, bronchioles, and alveoli; Explains that breathing in lowers air pressure in the chest and air rushes in; Describes how the structure of alveoli (large surface area, thin walls, good blood supply) aids gas exchange.

Needs first: Cells to Organ Systems, How Diffusion Works.

https://lightmysky.com/learn/science/gas-exchange-and-breathing-mt_V9SQS9gLFw

#### Aerobic Respiration (ages 12-13)

Explain aerobic respiration as the process by which organisms release energy from glucose using oxygen, producing carbon dioxide and water; write and interpret the word equation: glucose + oxygen → carbon dioxide + water

Ready when they can: Writes and explains the word equation for aerobic respiration; Explains where in the cell aerobic respiration takes place (mitochondria); Links aerobic respiration to why breathing rate and heart rate increase during exercise; Explains that respiration is not the same as breathing.

Needs first: How Diffusion Works, Gas Exchange & Breathing.

https://lightmysky.com/learn/science/aerobic-respiration-mt_mquPi2IP-J

#### Anaerobic Respiration (ages 12-14)

Explain anaerobic respiration in animals as the incomplete breakdown of glucose to lactic acid when oxygen is in short supply, causing muscle fatigue; contrast this with aerobic respiration in terms of energy yield and products

Ready when they can: Writes the word equation for anaerobic respiration in animals; Explains why lactic acid causes muscle pain and fatigue; Compares the energy released by aerobic and anaerobic respiration; Explains oxygen debt and recovery after vigorous exercise.

Needs first: Aerobic Respiration.

https://lightmysky.com/learn/science/anaerobic-respiration-mt_TKZefYXaVS

#### Human Reproduction (ages 12-13)

Describe the structure and function of the male and female human reproductive systems, and explain the processes of fertilisation, gestation, and birth including the role of the placenta

Ready when they can: Labels diagrams of the male and female reproductive systems; Explains the roles of gametes (sperm and egg) in sexual reproduction; Describes what happens during fertilisation and where it occurs; Explains the function of the placenta and the impact of maternal lifestyle on foetal development.

Needs first: Animal Life Stages.

https://lightmysky.com/learn/science/human-reproduction-mt_tQkCzRcWG7

#### Pathogens & the Immune System (ages 12-14)

Explain how pathogens (bacteria, viruses, and fungi) cause disease and describe how the immune system responds, including the roles of white blood cells (phagocytosis, antibody production) and the concept of immunity

Ready when they can: Distinguishes between bacteria, viruses, and fungi as pathogens with examples of each; Explains two ways white blood cells destroy pathogens (engulfing and antibodies); Explains how vaccination works and why it prevents disease; Explains the difference between being infected and being ill.

Needs first: Cells to Organ Systems, Single-Celled Organisms.

https://lightmysky.com/learn/science/pathogens-and-the-immune-system-mt_1VIE8FlZvL

#### Prokaryotic and Eukaryotic Cells (ages 14-15)

Compare a bacterial cell with plant and animal cells: a free loop of DNA and plasmids on one side, a nucleus and membrane-bound organelles on the other. Sets the size scale the rest of cell biology works in.

Ready when they can: Names the parts a bacterial cell has and the parts it does not, and says which structures a plant cell adds to the animal set.; Places a bacterium, an animal cell and a plant cell in size order using micrometres.; Says why plasmids matter to a bacterium even though they sit outside the main chromosome..

https://lightmysky.com/learn/science/prokaryotic-and-eukaryotic-cells-mt_vlL4GinuH6

#### Magnification and Scale Calculations (ages 14-15)

Use magnification as image size divided by actual size, and convert between millimetres, micrometres and nanometres without losing a factor of a thousand. Includes reading a scale bar and choosing a light or electron microscope by the detail needed.

Ready when they can: Rearranges the magnification relation to find any one of the three quantities.; Converts a length between millimetres, micrometres and nanometres and keeps the units on the answer.; Uses a scale bar on a micrograph to state the real width of a cell..

https://lightmysky.com/learn/science/magnification-and-scale-calculations-mt_0Iowx29ddQ

#### Osmosis in Plant and Animal Cells (ages 14-15)

Water crosses a partially permeable membrane from the more dilute solution towards the more concentrated one. Explains turgid, flaccid and plasmolysed plant cells, and why an animal cell in pure water can burst.

Ready when they can: Predicts which way water moves given the two solution concentrations.; Explains why a plant cell holds its shape in pure water while a red blood cell does not.; Calculates percentage change in mass for potato pieces left in sugar solutions of different strength..

https://lightmysky.com/learn/science/osmosis-in-plant-and-animal-cells-mt_XciCLO69xG

#### Active Transport Against the Gradient (ages 14-15)

A cell can move substances from a low concentration to a high one by spending energy released in respiration. Covers mineral ion uptake by root hairs and glucose absorption from the small intestine.

Ready when they can: States the direction of movement that separates active transport from diffusion and osmosis.; Links the number of mitochondria in a cell to how much active transport it does.; Explains why a root that cannot respire stops taking up minerals even though the water keeps coming in..

https://lightmysky.com/learn/science/active-transport-against-the-gradient-mt_BQf1bgo9oM

#### Surface Area to Volume Ratio and Exchange Surfaces (ages 14-16)

Work out surface area to volume ratios for cubes and simple shapes and show that the ratio falls as size rises. That falling ratio is why a large organism needs lungs, gills or a folded gut lining.

Ready when they can: Calculates the surface area to volume ratio for cubes of different side length and states the trend.; Names the features an effective exchange surface has and says what each one does to the rate.; Uses the ratio to argue why a single-celled organism manages with no lungs at all..

https://lightmysky.com/learn/science/surface-area-to-volume-ratio-and-exchange-surfaces-mt_1TclgVUxfa

#### The Cell Cycle and Mitosis (ages 14-16)

A cell copies its DNA, then divides into two cells with identical chromosomes. Covers the stages of the cycle, what mitosis produces, and where in the body it is happening now.

Ready when they can: Puts the stages of the cell cycle in order and says what happens to the chromosome number in each.; States how many cells mitosis produces and how their genetic content compares with the parent cell.; Names a place in the body where mitosis is going on and says what it is for..

https://lightmysky.com/learn/science/the-cell-cycle-and-mitosis-mt_gllZOZEzW7

#### Gas Exchange Surfaces Across Taxa (ages 16-17)

Insects, fish, leaves and mammals solve one problem with different surfaces, and every solution ends up thin, large and moist. Comparing them shows which features are forced by physics rather than by ancestry.

Ready when they can: Names the exchange surface in an insect, a fish, a leaf and a mammal.; Explains what each surface does to keep the diffusion distance short.; Says why a large active animal cannot rely on its outer body surface..

https://lightmysky.com/learn/science/gas-exchange-surfaces-across-taxa-mt_gCcrXUH0aP

#### Fick's Law and What Sets the Rate of Exchange (ages 16-18)

Rate of diffusion rises with surface area and with the concentration difference, and falls with the distance crossed. The relationship turns comparisons between exchange surfaces into arithmetic.

Ready when they can: States the three quantities in the relationship and which way each one pushes the rate.; Predicts the effect on the rate of doubling the diffusion distance.; Uses the relationship to explain why an alveolus wall is one cell thick..

https://lightmysky.com/learn/science/ficks-law-and-what-sets-the-rate-of-exchange-mt_6JreZAFeb-

#### Ventilation in Insects, Fish and Mammals (ages 16-18)

Ventilation keeps the concentration difference high by replacing the medium at the exchange surface. Tracheal pumping, countercurrent flow in gills and pressure changes in the thorax are three answers to one demand.

Ready when they can: Explains what ventilation does to the gradient rather than to the surface itself.; Describes why countercurrent flow holds a gradient along the whole gill lamella.; Traces the pressure changes that drive air into and out of a mammalian lung..

https://lightmysky.com/learn/science/ventilation-in-insects-fish-and-mammals-mt_Thd06O06Vr

#### Water and Hydrogen Bonding in Living Systems (ages 16-17)

Hydrogen bonds between water molecules give water its cohesion, its high heat capacity and its behaviour as a solvent. Every one of those properties traces back to the same charge separation across the molecule.

Ready when they can: Explains cohesion and surface tension from bonds between neighbouring molecules rather than from water being sticky.; Links the high specific heat capacity to what hydrogen bonds do when heat is added.; Predicts which solutes dissolve readily in water and says what about the molecule decides it..

https://lightmysky.com/learn/science/water-and-hydrogen-bonding-in-living-systems-mt_79dzlo6fD5

#### Condensation, Hydrolysis and the Polymers of Life (ages 16-17)

Carbohydrates, proteins and nucleic acids are all polymers joined by condensation and taken apart by hydrolysis. One bond-making rule covers three families of molecule.

Ready when they can: States what a condensation reaction removes and what a hydrolysis reaction adds.; Names the monomer and the bond for a carbohydrate, a protein and a nucleic acid.; Works out how many water molecules were released when a chain of a given length formed..

https://lightmysky.com/learn/science/condensation-hydrolysis-and-the-polymers-of-life-mt_v-M8zHd22C

#### Lipids: Built by Condensation but Not Polymers (ages 16-17)

Triglycerides and phospholipids form by condensation yet have no repeating monomer, so they sit outside the polymer rule. The phospholipid has one end attracted to water and one repelled, which is what later builds a membrane.

Ready when they can: Explains why a triglyceride is not called a polymer even though condensation built it.; Describes what makes a phospholipid behave differently from a triglyceride in water.; Relates the energy stored per gram in a lipid to the bonds it contains..

https://lightmysky.com/learn/science/lipids-built-by-condensation-but-not-polymers-mt_8-JYrLwjCw

#### Protein Structure from Primary to Quaternary (ages 16-18)

A protein's shape is described in four levels, from the order of amino acids up to several chains held together. Each level is kept by named bonds, and the finished shape decides what the protein can do.

Ready when they can: Names the bond type that holds each level of structure together.; Traces a change in the amino acid order through to a change in the folded shape.; Explains why heat and pH change the shape without altering the primary structure..

https://lightmysky.com/learn/science/protein-structure-from-primary-to-quaternary-mt_bMdQS2lqSI

#### Protists: The Eukaryotes That Are Not Plants, Animals or Fungi (ages 18-19)

Most eukaryotic diversity sits outside the three familiar kingdoms, in lineages that photosynthesise, hunt, or do both depending on the light. Their organelles record a history of one cell taking up another, which is why they are the evidence for endosymbiosis rather than an afterthought to it.

Ready when they can: Explain the endosymbiotic origin of mitochondria and plastids and state the evidence for each; Describe two contrasting protist lifestyles and the cell structures each depends on; Say why the word protist describes a grade of organisation rather than a natural group.

https://lightmysky.com/learn/science/protists-the-eukaryotes-that-are-not-plants-animals-or-fungi-mt_CHb8H727nW

#### Variation & Survival Advantage (ages 8-9)

Use evidence to explain how variations in characteristics among individuals of the same species may provide advantages in surviving, finding mates, and reproducing

Ready when they can: Explain that variation within a species means some individuals have traits better suited to their environment; Give examples of advantageous variations (e.g. camouflage, speed, drought resistance in plants); Connect variation to survival advantage: individuals with beneficial traits are more likely to survive and reproduce.

Needs first: Inherited characteristics, Habitats & Basic Needs.

https://lightmysky.com/learn/science/variation-and-survival-advantage-mt_UR5LvBeyF1

#### How animals adapt to environments (ages 8-11)

Identify how animals and plants are adapted to suit their environment and understand that adaptation may lead to evolution over time

Ready when they can: Define adaptation as a feature that helps an organism survive in its environment; Give at least three examples of adaptations in different organisms and explain how each helps survival; Explain that over many generations, organisms with helpful adaptations survive and reproduce more, leading to evolution.

Needs first: Ocean Animal Adaptations, Life Changed Over Time, Evolution vocabulary, Variation & Survival Advantage, Changing Environments.

https://lightmysky.com/learn/science/how-animals-adapt-to-environments-mt_LRzjbo1Fn6

#### Plant Reproduction (ages 12-13)

Describe the structure of a flower and explain the processes of wind and insect pollination, fertilisation, seed and fruit formation, and seed dispersal in plants

Ready when they can: Labels the main parts of a flower (sepals, petals, stamens, carpel, ovary, ovule); Compares wind-pollinated and insect-pollinated flowers and explains adaptations of each; Traces the journey from pollination to seed dispersal; Identifies and explains at least two methods of seed dispersal.

Needs first: Pollination & Seed Dispersal, Plant & Animal Reproduction.

https://lightmysky.com/learn/science/plant-reproduction-mt_ck57CDFGet

#### Communities: Interdependence, Competition and Abiotic Factors (ages 14-15)

An organism in a community depends on others for food, shelter and reproduction, and competes with them for whatever is scarce. Alongside that sit the non-living conditions of the place, and separating the two kinds of factor is what makes an ecological explanation testable.

Ready when they can: Sort the influences on a named population into abiotic and biotic factors; Explain what two species are competing for and predict what happens when one is removed; Describe an adaptation of an organism and link it to a specific factor in its habitat.

https://lightmysky.com/learn/science/communities-interdependence-competition-and-abiotic-factors-mt_su-CNKV8hK

#### Human Impact on Ecosystems: Land, Waste and a Warming World (ages 15-16)

Growing population and rising standards of living take more land and leave more waste, and both show up in ecosystems as lost habitat and changed conditions. The arguments about what to do are trade-offs between real costs, not a single right answer.

Ready when they can: Trace one human activity through to a measurable change in a named ecosystem; Explain why a warming climate shifts where a species can live rather than simply killing it; Weigh one conservation measure against what it costs, and say who bears that cost.

https://lightmysky.com/learn/science/human-impact-on-ecosystems-land-waste-and-a-warming-world-mt_BiYCyohfyI

#### Skeletons & Muscles (ages 7-8)

Identify that humans and some other animals have skeletons and muscles for support, protection, and movement

Ready when they can: Name the three functions of the skeleton: support, protection, movement; Identify that muscles are attached to bones and pull to create movement; Give examples of bones protecting organs (skull protects brain, ribs protect heart and lungs).

Needs first: Body Parts & Senses, Animal Body Groups, Bones & Muscles.

https://lightmysky.com/learn/science/skeletons-and-muscles-mt_g4YSiOCS8g

#### The Human Skeleton (ages 11-13)

Describe the structure and four main functions of the human skeleton: support, protection, movement, and production of blood cells in bone marrow

Ready when they can: Lists and explains the four functions of the skeleton with examples; Names key bones and identifies which organs they protect (e.g. ribcage protects heart and lungs); Explains what bone marrow is and where blood cells are made.

Needs first: Cells to Organ Systems, Skeletons & Muscles.

https://lightmysky.com/learn/science/the-human-skeleton-mt_Qkl46lyris

#### Joints, Tendons & Ligaments (ages 11-13)

Explain biomechanics — the interaction between skeleton and muscles at joints, including the roles of tendons (attach muscle to bone) and ligaments (attach bone to bone)

Ready when they can: Distinguishes between tendons and ligaments and gives the function of each; Describes how a synovial joint works (e.g. the knee or elbow); Explains how force is transmitted from muscle through tendon to bone to produce movement.

Needs first: The Human Skeleton.

https://lightmysky.com/learn/science/joints-tendons-and-ligaments-mt_yefw2CQT4x

#### Muscles Work in Pairs (ages 11-13)

Explain that muscles work in antagonistic pairs — one contracts while the other relaxes — to produce movement, using the bicep and tricep as a key example

Ready when they can: Explains why muscles can only pull, not push; Describes what happens to the bicep and tricep when the arm is bent and straightened; Gives another example of an antagonistic muscle pair.

Needs first: Joints, Tendons & Ligaments.

https://lightmysky.com/learn/science/muscles-work-in-pairs-mt_lm0usBAF53

#### Structures for Survival (ages 9-10)

Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behaviour, and reproduction

Ready when they can: Give examples of external structures and their survival functions (e.g. thorns for protection, claws for catching prey); Give examples of internal structures and their functions (e.g. heart pumps blood, lungs take in air); Construct a reasoned argument linking a specific structure to how it helps the organism survive or reproduce.

Needs first: How Plant Parts Work, Cells, Tissues & Organs, Skeletons & Muscles.

https://lightmysky.com/learn/science/structures-for-survival-mt_8VA40Tumth

#### The Digestive System (ages 8-9)

Describe the simple functions of the basic parts of the human digestive system: mouth, oesophagus, stomach, small intestine, large intestine

Ready when they can: Name the main organs in order: mouth, oesophagus, stomach, small intestine, large intestine; Describe the function of each (mouth chews, stomach breaks down, small intestine absorbs nutrients); Draw or label a simple diagram of the digestive system.

Needs first: Animal Nutrition, The Digestive Journey.

https://lightmysky.com/learn/science/the-digestive-system-mt_Ruk2-lyGPZ

#### Digestion & Enzymes (ages 11-13)

Describe the organs of the human digestive system and how food is physically and chemically digested, including the role of enzymes as biological catalysts

Ready when they can: Traces the journey of food from mouth to large intestine, naming each organ and its role; Explains what enzymes do and names where they are produced (salivary glands, stomach, small intestine); Distinguishes physical digestion (chewing, churning) from chemical digestion.

Needs first: Cells to Organ Systems, The Digestive System, Nutrients in a Healthy Diet.

https://lightmysky.com/learn/science/digestion-and-enzymes-mt_0NlbulkB5P

#### Gut Bacteria & Digestion (ages 12-13)

Explain the role of gut microbiome bacteria in digestion, including breaking down dietary fibre and contributing to a healthy gut environment

Ready when they can: Explains that many gut bacteria are beneficial, not harmful; Describes what gut bacteria do that human digestive enzymes cannot (e.g. break down fibre); Explains what might happen if the gut microbiome is disrupted.

Needs first: Digestion & Enzymes.

https://lightmysky.com/learn/science/gut-bacteria-and-digestion-mt_fCvmdI6xGO

#### The Circulatory System (ages 10-11)

Identify and name the main parts of the human circulatory system and describe the functions of the heart, blood vessels, and blood

Ready when they can: Name the main components: heart, arteries, veins, capillaries, blood; Describe the heart as a pump that pushes blood around the body in a continuous loop; Explain that blood carries oxygen and nutrients to cells and removes waste products like carbon dioxide.

Needs first: Skeletons & Muscles, Heart & Blood Circulation, Organ Systems Vocabulary, The Digestive System.

https://lightmysky.com/learn/science/the-circulatory-system-mt_BX4D8cCFtQ

#### Nutrient Transport in Animals (ages 10-11)

Describe how nutrients and water are transported within animals, including the role of the circulatory system in delivering nutrients from digestion

Ready when they can: Describe how nutrients from digested food pass through the wall of the small intestine into the blood; Explain that blood transports dissolved nutrients and water to all parts of the body; Connect the digestive system and circulatory system as working together to deliver nourishment.

Needs first: The Circulatory System, Organ Systems Vocabulary.

https://lightmysky.com/learn/science/nutrient-transport-in-animals-mt_YSyjTZfjvv

#### Heart Structure & Double Circulation (ages 12-13)

Describe the structure of the heart (four chambers, valves, coronary arteries) and explain how it pumps deoxygenated blood to the lungs and oxygenated blood to the body in a double circulatory system

Ready when they can: Labels a diagram of the heart showing atria, ventricles, valves, aorta, vena cava, and pulmonary vessels; Traces the route of blood through the double circulatory system; Explains the role of valves in preventing backflow; Compares arteries, veins, and capillaries.

Needs first: The Circulatory System, Gas Exchange & Breathing, Nutrient Transport in Animals.

https://lightmysky.com/learn/science/heart-structure-and-double-circulation-mt_TR2oTy9c2M

#### Diet, Exercise & Lifestyle (ages 10-11)

Recognise the impact of diet, exercise, drugs, and lifestyle on the way human bodies function

Ready when they can: Describe how a balanced diet provides energy and nutrients the body needs; Explain the positive effects of regular exercise on the heart, muscles, and mental health; Describe harmful effects of drugs, alcohol, or tobacco on the body.

Needs first: Healthy Lifestyle Choices, The Circulatory System, Animal Nutrition.

https://lightmysky.com/learn/science/diet-exercise-and-lifestyle-mt_2x-EwdBsgl

#### Effects of Drugs & Alcohol (ages 13-14)

Explain the effects of recreational drugs including alcohol, tobacco, and illegal substances on behaviour, health, and body systems, and distinguish between depressants, stimulants, and hallucinogens

Ready when they can: Categorises common recreational drugs as depressants, stimulants, or hallucinogens; Explains specific effects of alcohol and tobacco on the body (e.g. liver damage, lung cancer); Discusses the difference between physical and psychological dependence.

Needs first: Digestion & Enzymes, Diet, Exercise & Lifestyle.

https://lightmysky.com/learn/science/effects-of-drugs-and-alcohol-mt_2R3xRpYhMa

#### Body Temperature Regulation (ages 12-14)

Explain how the human body detects and responds to environmental changes including temperature, including the role of the skin in temperature regulation (sweating, shivering, vasodilation, vasoconstriction)

Ready when they can: Explains what homeostasis means in the context of body temperature; Describes at least two mechanisms the body uses to cool down and two to warm up; Explains why maintaining a constant core body temperature is important for enzyme activity.

Needs first: Aerobic Respiration, The Nervous System.

https://lightmysky.com/learn/science/body-temperature-regulation-mt_zaXr5wcJD2

#### Differentiation and Stem Cells (ages 14-16)

An unspecialised cell switches on part of its genes and becomes a cell with a job. Compares embryonic, adult and plant meristem stem cells, with the medical uses and the objections that come with them.

Ready when they can: Explains what differentiation changes inside a cell, given that every cell holds the same genes.; Compares what embryonic and adult stem cells can turn into.; Gives one medical use of stem cells and one objection people raise to it..

https://lightmysky.com/learn/science/differentiation-and-stem-cells-mt_UmLJgmcCjO

#### Enzyme Action and the Active Site (ages 14-16)

An enzyme speeds up one reaction because its active site fits one substrate shape. Covers the lock and key model, specificity, and why an enzyme is not used up by the reaction it runs.

Ready when they can: Explains specificity in terms of the shape of the active site rather than the strength of the enzyme.; States what happens to an enzyme once its reaction has finished.; Predicts what a change in active site shape does to the reaction..

https://lightmysky.com/learn/science/enzyme-action-and-the-active-site-mt__ozLTPNN0H

#### The Digestive System and Testing Food for Nutrients (ages 14-15)

Digestion is a sequence of organs each doing one job to a food molecule too big to absorb, with enzymes and bile doing the chemistry. Simple colour tests let a learner check which nutrient classes are actually present in a sample.

Ready when they can: Follow a named food molecule through the gut and say which organ and which enzyme acts on it; Explain what bile does and why it is not an enzyme; Carry out and interpret tests for starch, sugar, protein and fat, including a negative result.

https://lightmysky.com/learn/science/the-digestive-system-and-testing-food-for-nutrients-mt__mBJCQEqPS

#### Measuring the Rate of an Enzyme Reaction (ages 15-16)

Find how fast an enzyme works as amount per unit time, or as 1000 divided by the time taken, and describe how temperature and pH change that rate. The curve rises to an optimum and then falls away for good.

Ready when they can: Calculates a rate from a time with consistent units.; Sketches rate against temperature, marks the optimum, and marks where denaturing starts.; Explains the fall after the optimum through the active site changing shape, not through the enzyme being used up..

https://lightmysky.com/learn/science/measuring-the-rate-of-an-enzyme-reaction-mt_Rmz54ICmRC

#### Photosynthesis and Limiting Factors (ages 15-16)

Light intensity, carbon dioxide concentration and temperature each set a ceiling on the rate of photosynthesis, and at any moment one of them is the limiting factor. Includes the inverse square relation between lamp distance and light intensity.

Ready when they can: Reads a rate graph and names the limiting factor in each region of the curve.; Uses the inverse square relation to say what moving a lamp twice as far away does to light intensity.; Explains why a greenhouse grower may add carbon dioxide rather than more light..

https://lightmysky.com/learn/science/photosynthesis-and-limiting-factors-mt_PDn831oIih

#### Respiration Rate, Oxygen Debt and Metabolism (ages 15-16)

Aerobic respiration releases far more energy per glucose molecule than anaerobic respiration, which is why hard exercise builds an oxygen debt. Covers lactic acid, the recovery period, and fermentation in yeast.

Ready when they can: Writes both word equations and says which releases more energy per glucose molecule.; Explains what the oxygen debt is and what the body does afterwards to repay it.; Compares anaerobic respiration in muscle with fermentation in yeast, including the different products..

https://lightmysky.com/learn/science/respiration-rate-oxygen-debt-and-metabolism-mt_mvnCjThdTH

#### Transpiration and Transport in Plants (ages 15-16)

Water pulled up the xylem replaces what evaporates from the leaves, while phloem carries dissolved sugar to where it is used or stored. Covers stomata, guard cells, and what changes the transpiration rate.

Ready when they can: Says what xylem carries and what phloem carries, and in which direction each one moves it.; Predicts the effect of higher temperature, wind or humidity on transpiration rate.; Explains why closing the stomata saves water and costs photosynthesis..

https://lightmysky.com/learn/science/transpiration-and-transport-in-plants-mt_AqN0vL8QRu

#### Chloroplast Structure and the Light-Dependent Reactions (ages 16-17)

Thylakoid membranes hold the pigments that trap light, and the trapped energy splits water, reduces NADP and makes ATP. Those two products are the input to the reactions that fix carbon.

Ready when they can: Places the light-dependent reactions in the thylakoid membrane and says why they happen there.; Names what water is split into and where each product goes.; Lists the two products that carry energy and reducing power onward..

https://lightmysky.com/learn/science/chloroplast-structure-and-the-light-dependent-reactions-mt_3Ooq3BfmpX

#### Digestion and Absorption in the Mammalian Gut (ages 16-17)

Absorption is a transport problem set by surface area, gradient and the specific carriers in the membrane, and the small intestine is shaped by that problem. Co-transport of glucose with sodium is the case where the whole argument comes together.

Ready when they can: Explain the structure of a villus in terms of the quantities in Fick's law; Describe glucose absorption as sodium-linked co-transport and say what supplies the gradient; Account for the symptoms of a named absorption disorder from the mechanism that fails.

https://lightmysky.com/learn/science/digestion-and-absorption-in-the-mammalian-gut-mt_xZ2-3ZClDa

#### Enzyme Kinetics: Vmax and the Michaelis Constant (ages 16-18)

Rate plotted against substrate concentration flattens to a maximum because the active sites become saturated. Vmax and Km are read off that curve and used to compare enzymes.

Ready when they can: Reads Vmax and Km from a rate against substrate concentration curve.; Explains the shape of the curve in terms of how many active sites are occupied.; Compares two enzymes by their Km and says which binds its substrate more tightly..

https://lightmysky.com/learn/science/enzyme-kinetics-vmax-and-the-michaelis-constant-mt_ooF8eZ1Gzy

#### The Calvin Cycle and Carbon Fixation (ages 16-18)

Rubisco joins carbon dioxide to RuBP, and the ATP and reduced NADP from the light reactions turn the product into triose phosphate. Most of that triose phosphate is spent regenerating RuBP.

Ready when they can: Traces one carbon atom from carbon dioxide into a triose phosphate.; Explains what the ATP and the reduced NADP are used for inside the cycle.; Says why the cycle stalls quickly once the light-dependent stage stops..

https://lightmysky.com/learn/science/the-calvin-cycle-and-carbon-fixation-mt_zGOCx9mNrx

#### Glycolysis and the Link Reaction (ages 16-18)

Glucose is split into two pyruvate molecules in the cytoplasm, with a small net ATP gain and no oxygen involved. Pyruvate then enters the mitochondrion and becomes acetyl coenzyme A.

Ready when they can: Explains why glycolysis spends ATP before it yields any.; States the net ATP and reduced NAD yield per glucose molecule.; Says what is removed from pyruvate in the link reaction and where that happens..

https://lightmysky.com/learn/science/glycolysis-and-the-link-reaction-mt_crbadbBvqB

#### Enzyme Inhibition and Metabolic Control (ages 17-18)

Competitive and non-competitive inhibitors change the rate curve in different ways. Cells use the same effect on purpose, switching a pathway off when its end product builds up.

Ready when they can: Predicts what each kind of inhibitor does to Vmax and to Km.; Explains where a non-competitive inhibitor binds and why raising the substrate does not rescue the rate.; Describes end-product inhibition as a control loop rather than as damage..

https://lightmysky.com/learn/science/enzyme-inhibition-and-metabolic-control-mt_8VYolkJ_wR

#### The Fluid Mosaic Model of the Cell Membrane (ages 16-18)

The membrane is a phospholipid bilayer with proteins, cholesterol and glycoproteins set into it, and the parts drift. The model is what explains which molecules cross unaided and which need a protein.

Ready when they can: Places each named component in the bilayer and says what it does there.; Explains why small non-polar molecules cross the bilayer while ions do not.; Says what cholesterol does to fluidity as the temperature changes..

https://lightmysky.com/learn/science/the-fluid-mosaic-model-of-the-cell-membrane-mt_-xnAIG5hFc

#### The Krebs Cycle and the Reduced Carriers (ages 17-18)

Acetyl coenzyme A enters a cycle that releases carbon dioxide and loads electrons onto NAD and FAD. The cycle makes almost no ATP directly; its real output is the reduced carriers.

Ready when they can: Counts the carbon dioxide molecules released per turn and per glucose molecule.; Explains what reduced NAD and reduced FAD are carrying.; Says why the cycle is described as the main source of reduced carriers rather than of ATP..

https://lightmysky.com/learn/science/the-krebs-cycle-and-the-reduced-carriers-mt_eviWcVke2x

#### Oxidative Phosphorylation and Chemiosmosis (ages 17-18)

Electrons from the reduced carriers pass along a chain, and the energy released pumps protons across the inner membrane. Protons flowing back through ATP synthase make most of the cell's ATP.

Ready when they can: Explains what the electron transfer chain does with the energy it releases.; Describes the proton gradient and says where ATP synthase sits in it.; Says what oxygen does at the end of the chain and what happens without it..

https://lightmysky.com/learn/science/oxidative-phosphorylation-and-chemiosmosis-mt_1wP3-14Y4V

#### Anaerobic Routes and the ATP Yield Compared (ages 17-18)

Without oxygen the chain backs up, so cells reduce pyruvate to lactate or to ethanol purely to regenerate NAD. The ATP arithmetic shows how much a cell gives up by doing it.

Ready when they can: Explains that the anaerobic pathways exist to regenerate NAD rather than to make ATP.; Compares the ATP yield per glucose for the aerobic and the anaerobic route.; Names the anaerobic product in a muscle cell and in a yeast cell..

https://lightmysky.com/learn/science/anaerobic-routes-and-the-atp-yield-compared-mt_LBZ4laMfqb

#### Ecosystem Energy Budgets: GPP, NPP and Transfer Efficiency (ages 17-18)

Gross primary production is what producers capture, net primary production is what remains after their own respiration, and only a small share reaches the next trophic level. The numbers are why food chains stay short.

Ready when they can: Calculates net primary production from gross production and respiratory loss.; Works out percentage energy transfer between two trophic levels from given data.; Explains where the energy that fails to transfer actually goes..

https://lightmysky.com/learn/science/ecosystem-energy-budgets-gpp-npp-and-transfer-efficiency-mt_D81CKcOdBI

#### Water Potential and Osmosis Quantified (ages 17-18)

Water potential puts a number on the tendency of water to move, made from solute potential and pressure potential. Cells are then predicted to gain or lose water from the numbers alone.

Ready when they can: Adds solute potential and pressure potential to get the water potential of a cell.; Predicts the direction of net water movement between two solutions from their water potentials.; Explains why pure water sits at zero and every solution sits below it..

https://lightmysky.com/learn/science/water-potential-and-osmosis-quantified-mt_dFBz-cE6W0

#### Co-transport and Coupled Movement Across Membranes (ages 17-18)

A pump spends ATP to build an ion gradient, and a second protein then uses that gradient to drag another molecule in with the ion. Glucose uptake at the gut wall is the standard case.

Ready when they can: Separates the step that spends ATP from the step that rides the gradient.; Traces sodium and glucose through the two proteins in the right order.; Explains why blocking the pump stops glucose uptake although glucose transport uses no ATP directly..

https://lightmysky.com/learn/science/co-transport-and-coupled-movement-across-membranes-mt_pzQ8n3FWNV

#### Cell Cycle Checkpoints, Control and Cancer (ages 17-18)

Checkpoints hold a cell back at set points in the cycle until conditions and DNA are sound. Tumours follow when the genes that run those checkpoints stop working.

Ready when they can: Names what each checkpoint is testing before the cell is allowed on.; Distinguishes a gene that drives division from one that holds it back.; Links a mutation in a control gene to uncontrolled division rather than to a faulty protein in general..

https://lightmysky.com/learn/science/cell-cycle-checkpoints-control-and-cancer-mt_nwNmCVnZ7O

#### Cohesion-Tension and Water Movement in the Xylem (ages 17-18)

Evaporation from leaf cells pulls a continuous column of water up the xylem, held together by hydrogen bonds. The column is under tension, which is why a trunk narrows slightly on a hot day.

Ready when they can: Explains where the pulling force comes from and where in the plant it acts.; Links cohesion in the column back to hydrogen bonding between water molecules.; Uses the theory to predict what happens to the flow when the stomata close..

https://lightmysky.com/learn/science/cohesion-tension-and-water-movement-in-the-xylem-mt_9_TORolYIl

#### Translocation and the Mass Flow Hypothesis (ages 17-18)

Sugars are loaded into the phloem at a source, water follows by osmosis, and the pressure built there pushes sap towards a sink. The hypothesis is judged against ringing experiments and tracer evidence.

Ready when they can: Separates the loading step, the pressure step and the unloading step.; Explains why phloem transport needs energy while xylem transport does not.; Weighs one piece of evidence for the hypothesis against one difficulty with it..

https://lightmysky.com/learn/science/translocation-and-the-mass-flow-hypothesis-mt_WZ8id0kou4

#### Plant Growth Responses: Tropisms and the Hormones Behind Them (ages 17-18)

A plant that cannot move still responds to light and gravity, by growing unevenly. The uneven growth is caused by a hormone redistributing across the tip, which is one of the oldest experiments in plant biology and still the clearest.

Ready when they can: Explain phototropism and gravitropism as differential growth, not movement; Describe the classic shoot-tip experiments and say what each control ruled out; Name a commercial use of a plant hormone and the response it exploits.

https://lightmysky.com/learn/science/plant-growth-responses-tropisms-and-the-hormones-behind-them-mt_q1N7OG2_6j

#### Fertilisation and the First Cleavages (ages 19-20)

Fertilisation has to admit exactly one sperm and then start a programme of divisions that add no mass. The blocks against a second sperm and the pattern of those early cleavages already differ between animal groups, and both differences matter later.

Ready when they can: Describe the fast and slow blocks to polyspermy and what each one physically does; Explain why cleavage divisions shorten the cell cycle and skip growth; Compare two cleavage patterns and relate the difference to yolk.

https://lightmysky.com/learn/science/fertilisation-and-the-first-cleavages-mt_9BXQsdP8fI

#### Decomposers and the Rate of Decay (ages 15-16)

Bacteria and fungi break dead material down and return carbon to the air and mineral ions such as nitrates to the soil. Decay speeds up with temperature, water and oxygen, which is what a compost heap and a fridge each work on.

Ready when they can: Names what decomposers return to the soil and what they return to the air.; Predicts the effect of temperature, water or oxygen on decay rate and explains it through the decomposers' own respiration.; Explains why a compost heap is turned and why a fridge slows food going off..

https://lightmysky.com/learn/science/decomposers-and-the-rate-of-decay-mt_4152TrzD6A

#### Fertilisers, Leaching and Eutrophication (ages 15-16)

Nitrate added to a field does not stay in the field, and once it reaches a river it feeds algae rather than crops. The damage is done by the decomposers that follow, because the oxygen they use is the oxygen the fish needed.

Ready when they can: Trace the sequence from fertiliser application through leaching to an algal bloom to fish death; Explain why the oxygen falls after the algae die rather than while they are growing; Suggest a change to farming practice that reduces leaching and say what it costs the farmer.

https://lightmysky.com/learn/science/fertilisers-leaching-and-eutrophication-mt_9lTF20DWOZ

#### Food Security: What Limits Yield and What It Costs to Raise It (ages 15-16)

Every way of getting more food out of the same land moves a cost somewhere else, usually onto soil, water or biodiversity. Working out which limit is actually binding on a given farm is what separates a real answer from a slogan.

Ready when they can: Name the main biological threats to food supply and say which are getting worse; Explain why feeding animals is an inefficient route to human food, in terms of energy transfer; Evaluate one intensive farming method by what it gains and what it costs.

https://lightmysky.com/learn/science/food-security-what-limits-yield-and-what-it-costs-to-raise-it-mt_SprRvGuyrK

#### The Nitrogen Cycle and the Microbes That Drive It (ages 17-18)

Nitrogen moves between air, soil and organisms through fixation, ammonification, nitrification and denitrification, each run by particular bacteria. Unlike energy, the atoms get used again and again.

Ready when they can: Names the process at each arrow of the cycle and the type of microbe that runs it.; Contrasts a nutrient that cycles with the one-way flow of energy.; Explains what waterlogged soil does to the balance between nitrification and denitrification..

https://lightmysky.com/learn/science/the-nitrogen-cycle-and-the-microbes-that-drive-it-mt__K1J47NhWj

#### Population Growth Curves and Carrying Capacity (ages 17-18)

A population grows slowly, then fast, then levels off as limiting factors bite. Carrying capacity is read off the curve, and density-dependent factors are told from density-independent ones by how they scale.

Ready when they can: Labels the phases of a growth curve and explains what limits each one.; Distinguishes a density-dependent factor from a density-independent one with an example of each.; Estimates carrying capacity from a plotted curve..

https://lightmysky.com/learn/science/population-growth-curves-and-carrying-capacity-mt_KX6rhHF5kj

#### Succession from Pioneer to Climax Community (ages 17-18)

Pioneer species change a bare habitat until it suits other species better, and each stage is replaced by the next. Conservation often means holding succession back rather than letting it run.

Ready when they can: Explains how a pioneer species makes the habitat less suitable for itself.; Describes what happens to species diversity and biomass across the stages.; Says what deflected succession is and gives a case where it is deliberate..

https://lightmysky.com/learn/science/succession-from-pioneer-to-climax-community-mt_3s3dVLP0Lf

#### Protein Targeting and the Signal Sequence (ages 18-20)

A short stretch of the growing chain decides where the protein ends up: the endoplasmic reticulum, a mitochondrion, the nucleus or the cytosol. Removing or moving that stretch sends the protein to the wrong compartment.

Ready when they can: Predicts the destination of a protein from the presence and type of its targeting sequence.; Explains why the cell needs sorting at all, given every protein starts on a cytosolic ribosome.; Says what happens to a secreted protein whose signal sequence is deleted..

https://lightmysky.com/learn/science/protein-targeting-and-the-signal-sequence-mt_wVFZq8cZgn

#### Vesicle Traffic: Coats, Adaptors and Fusion (ages 18-20)

Cargo leaves one compartment in a coated bud and arrives at another by fusing with its membrane. Coat proteins choose the cargo, and matched proteins on the two membranes decide which vesicle fuses where.

Ready when they can: Traces a secreted protein from the endoplasmic reticulum to the outside, naming what happens at each hand-off.; Explains what gives traffic its direction when every step is a bud and a fusion.; Predicts the effect of blocking one coat type on the cargo that uses it..

https://lightmysky.com/learn/science/vesicle-traffic-coats-adaptors-and-fusion-mt_uq8R0bdB_L

#### Membrane Lipid Composition, Asymmetry and Fluidity (ages 19-20)

The two leaflets of a membrane hold different lipids, and enzymes spend energy to keep them different. Chain length, double bonds and sterol content set how fluid the bilayer is at a given temperature.

Ready when they can: Predicts how a change in fatty acid saturation shifts membrane fluidity, and says why an organism would make that change.; Explains what leaflet asymmetry is for, using one example such as the signal that marks a dying cell.; Distinguishes fluidity from permeability rather than treating them as the same property..

https://lightmysky.com/learn/science/membrane-lipid-composition-asymmetry-and-fluidity-mt_PIk59MG-gN

#### Ion Channels: Selectivity, Gating and the Evidence from Single Channels (ages 19-20)

A channel passes one ion species far better than another because of the chemistry lining its narrowest point, and it opens in response to voltage, a ligand or a mechanical pull. Recording one channel at a time shows it flicking between full open and shut rather than easing part way.

Ready when they can: Explains selectivity from the pore lining rather than from the size of the hole alone.; Reads a single-channel trace as open and closed states, and links their proportions to a whole-cell current.; Names the three gating cues and gives a cell that uses each..

https://lightmysky.com/learn/science/ion-channels-selectivity-gating-and-the-evidence-from-single-channels-mt_2xPzPeXZZ_

#### Ligand Binding: Dissociation Constants and Receptor Occupancy (ages 19-20)

Binding of a ligand to a receptor reaches an equilibrium set by the dissociation constant, and the fraction of receptors occupied follows a saturating curve. A smaller dissociation constant means tighter binding, so half occupancy is reached at a lower concentration.

Ready when they can: Calculates fractional occupancy from a ligand concentration and a dissociation constant.; Reads a binding curve to get the dissociation constant, and compares two ligands from their curves.; Explains why raising the concentration far above the constant gains almost nothing..

https://lightmysky.com/learn/science/ligand-binding-dissociation-constants-and-receptor-occupancy-mt_i-v79OaM0n

#### G-Protein-Coupled Receptors and Second Messengers (ages 19-21)

A bound ligand changes the receptor shape so that it activates a G protein, which switches on an enzyme that floods the cytosol with a small messenger. One bound molecule outside becomes thousands of messenger molecules inside.

Ready when they can: Traces the path from ligand to second messenger to a changed enzyme activity.; Explains where the amplification comes from and roughly at which steps.; Says what turns the pathway off, and why that has to be an active step..

https://lightmysky.com/learn/science/g-protein-coupled-receptors-and-second-messengers-mt_7ozcs_sUOJ

#### Plant Hormone Signalling and How a Plant Decides (ages 19-20)

A plant has no nervous system, so every decision about when to grow, when to stop and when to drop a leaf is made by the balance between a handful of small molecules. Most of these hormones do nothing alone, and the response depends on the ratio between two of them rather than the amount of either.

Ready when they can: Name the main plant hormone classes and the developmental decision each one dominates; Explain a response that depends on the ratio of two hormones rather than on the level of one; Describe how a hormone signal reaches the nucleus and changes which genes are transcribed.

https://lightmysky.com/learn/science/plant-hormone-signalling-and-how-a-plant-decides-mt_Zg2xpsb-p_

#### Receptor Tyrosine Kinases and Phosphorylation Cascades (ages 19-21)

Growth factor receptors pair up when a ligand binds, then phosphorylate each other on tyrosine residues. Those phosphates become docking sites, and the proteins that dock there start a kinase cascade that reaches the nucleus.

Ready when they can: Explains why dimerisation is the switch rather than just a consequence of binding.; Says how a phosphate on a receptor recruits a specific partner rather than any protein.; Predicts the effect of a receptor that dimerises without a ligand present..

https://lightmysky.com/learn/science/receptor-tyrosine-kinases-and-phosphorylation-cascades-mt_EvIwqsLVGA

#### Signal Integration: Cross-talk, Feedback and Termination (ages 20-21)

A cell rarely receives one signal at a time, and the same messenger can mean different things depending on what else is active. Feedback loops, phosphatases and receptor removal decide how fast a response stops.

Ready when they can: Explains how two pathways can converge on one target and give a response neither gives alone.; Names three ways a signal is switched off and says which acts fastest.; Predicts what a cell does when termination fails, without treating it as more of the same signal..

https://lightmysky.com/learn/science/signal-integration-cross-talk-feedback-and-termination-mt_Io2P-l38Xq

#### Apoptosis: Caspase Cascades and the Decision to Die (ages 20-21)

A cell can dismantle itself in an ordered way using a cascade of proteases that are already present but inactive. Death signals from outside and damage signals from inside both converge on the same execution step.

Ready when they can: Distinguishes apoptosis from uncontrolled cell death by what happens to the contents and the neighbours.; Explains why the machinery is kept in the cell in an inactive form rather than made on demand.; Links a failure of the death pathway to tumour growth without treating it as extra division..

https://lightmysky.com/learn/science/apoptosis-caspase-cascades-and-the-decision-to-die-mt_Pi6c9yoT7w

#### Actin Filaments: Polarity, Treadmilling and Cell Shape (ages 20-21)

Actin filaments have two different ends, so subunits can add at one end and leave at the other while the filament length stays the same. Regulating that turnover lets a cell push out a leading edge and crawl.

Ready when they can: Explains treadmilling in terms of different critical concentrations at the two ends.; Links filament growth at the front of a cell to the direction it moves.; Predicts what a drug that blocks subunit addition does to a crawling cell..

https://lightmysky.com/learn/science/actin-filaments-polarity-treadmilling-and-cell-shape-mt_sJlYoA-BnA

#### Microtubules, Dynamic Instability and the Spindle (ages 20-22)

Microtubules grow and shrink in sudden switches rather than smoothly, which lets them search space until an end is captured and held. That search is how a spindle finds every chromosome.

Ready when they can: Describes dynamic instability as switching between growth and rapid shrinking, and says what triggers the switch.; Explains how search and capture attaches a spindle fibre to a chromosome without aiming.; Predicts what a drug that freezes microtubules does to a dividing cell..

https://lightmysky.com/learn/science/microtubules-dynamic-instability-and-the-spindle-mt_RWhMJxOmUu

#### Motor Proteins and Directed Movement Along Tracks (ages 20-22)

Myosins, kinesins and dyneins burn ATP to take steps along a filament, and each motor walks towards one particular end. Cargo is carried where it needs to go because the track has a direction and the motor knows it.

Ready when they can: Links one round of ATP binding and hydrolysis to one step of the motor.; Predicts which way a cargo travels given the motor and the track polarity.; Explains why a cell needs motors moving in both directions along the same track..

https://lightmysky.com/learn/science/motor-proteins-and-directed-movement-along-tracks-mt_TUTmILr7y0

#### Junctions, Adhesion and the Extracellular Matrix (ages 20-22)

Cells hold onto each other and onto the matrix around them through junctions that are anchored to the cytoskeleton. The matrix is not filler: its stiffness and composition feed back into how the cell behaves.

Ready when they can: Matches a junction type to the job it does: sealing, anchoring or letting small molecules pass.; Explains why an anchoring junction is useless unless it connects to filaments inside the cell.; Gives one example of matrix stiffness changing what a cell does..

https://lightmysky.com/learn/science/junctions-adhesion-and-the-extracellular-matrix-mt_Sjcd3kQUmw

#### What a Cell Has to Break to Become a Tumour (ages 22-23)

Growth control, replicative limits, programmed death, metabolic supply and immune surveillance each constrain a cell, and a tumour has to defeat several of them. This stop treats the hallmark list as a set of constraints rather than a catalogue to memorise.

Ready when they can: Name the constraint that a stated genetic lesion removes; Explain why one lesion is rarely enough to produce a tumour; Map an experimental observation onto the constraint it was designed to test.

https://lightmysky.com/learn/science/what-a-cell-has-to-break-to-become-a-tumour-mt_cjg3DtLHQL

#### Fungi: Hyphae, Spores and Digestion Outside the Body (ages 18-19)

A fungus grows as a network of threads that secretes enzymes into its surroundings and takes back what dissolves, which is why the body plan is all surface. That habit makes fungi the main decomposers on land and, with the same machinery, serious pathogens of plants.

Ready when they can: Relate hyphal growth to the demands of external digestion; Compare a mycorrhizal partnership with a fungal infection and say what differs mechanically; Explain why antifungal drugs are harder to make selective than antibacterial ones.

https://lightmysky.com/learn/science/fungi-hyphae-spores-and-digestion-outside-the-body-mt_qfp2nuk1IH

#### Land Plants: Vascular Tissue and a Life Cycle That Alternates (ages 19-20)

Moving onto land forced plants to solve support, water transport and reproduction without water, and the fossil sequence from mosses to flowering plants is a record of those solutions. Every land plant alternates between a spore-producing and a gamete-producing generation, and which one you notice is what changed across the group.

Ready when they can: Draw the alternation of generations and say which generation dominates in a moss, a fern and a flowering plant; Link three land-plant innovations to the physical problem each solved; Explain why seeds and pollen together released plants from needing surface water to reproduce.

https://lightmysky.com/learn/science/land-plants-vascular-tissue-and-a-life-cycle-that-alternates-mt_DFtQ2mCZSm

#### Animal Body Plans: Symmetry, Cavities and the Deep Splits (ages 19-20)

The major animal groups are told apart by a handful of features fixed early in development: how many tissue layers form, whether there is a body cavity, and which opening the gut makes first. Those features are why a sea urchin is a closer relative of a fish than of a clam.

Ready when they can: Use symmetry, tissue layers and body cavity to place an unfamiliar animal in a major group; Explain the protostome and deuterostome split in terms of what happens in the embryo; Give a case where similar body form evolved twice and say how the tree shows it.

https://lightmysky.com/learn/science/animal-body-plans-symmetry-cavities-and-the-deep-splits-mt_hEC72cvFQF

#### Gastrulation and Laying Down the Body Axes (ages 19-20)

Gastrulation is where a ball of cells becomes an animal with an inside, an outside and three germ layers, by cells moving rather than dividing. The axes are set at the same time, and grafting experiments showed that one small region can organise a whole second axis.

Ready when they can: Name the three germ layers and one adult tissue derived from each; Describe the cell movements of gastrulation as distinct from cell division; Explain what an organiser graft demonstrated and why the control mattered.

https://lightmysky.com/learn/science/gastrulation-and-laying-down-the-body-axes-mt_PABfw_4RPs

#### Morphogen Gradients and Positional Information (ages 20-21)

A cell can work out where it is from the local concentration of a diffusible signal, and respond by switching on a different set of genes at different thresholds. This is how a smooth gradient produces sharp stripes, and why the same signal means different things in different tissues.

Ready when they can: Explain how a graded signal is read as discrete cell fates through thresholds; Predict the effect of doubling or removing a morphogen source on the resulting pattern; Say why the same morphogen can specify different structures in two tissues.

https://lightmysky.com/learn/science/morphogen-gradients-and-positional-information-mt_EbOK5M7V6Y

#### Organogenesis and the Model Organisms That Made It Visible (ages 20-21)

Organs form by a small repertoire of moves repeated in different places: fold a sheet, make a tube, branch it, then kill the cells in between. Most of what is known came from a handful of organisms chosen because they are transparent, fast, or easy to mutate, and that choice shapes what is known.

Ready when they can: Describe how a flat sheet of cells becomes a tube, and name one organ built that way; Explain the role of programmed cell death in shaping a structure; Say what a named model organism is good for and what it cannot answer.

https://lightmysky.com/learn/science/organogenesis-and-the-model-organisms-that-made-it-visible-mt_MXqKNdT519

#### The Tumour Microenvironment: Stroma, Hypoxia and Immune Exclusion (ages 22-24)

A tumour is a tissue rather than a bag of cancer cells, and its stroma, blood supply and immune infiltrate change how it grows and what a drug can reach. This stop reads a tumour section as a habitat with its own gradients.

Ready when they can: Explain how hypoxia changes gene expression and limits drug delivery inside a tumour; Distinguish an immune-infiltrated from an immune-excluded tumour and say why the difference matters; Argue how stromal cells can support tumour growth without carrying driver mutations themselves.

https://lightmysky.com/learn/science/the-tumour-microenvironment-stroma-hypoxia-and-immune-exclusion-mt_OIrMAjomX_

#### Targeted Therapy and the Resistance That Follows It (ages 22-24)

A drug aimed at a driver works for as long as the driver is required and the target is unchanged. This stop works through the routes back: mutation of the target, bypass signalling, and selection of a clone that was already present.

Ready when they can: Explain oncogene dependence and where the therapeutic window comes from; Classify a stated resistance mechanism as on-target or bypass, and say what evidence separates them; Argue from clonal structure why resistance can appear faster than mutation rates alone suggest.

https://lightmysky.com/learn/science/targeted-therapy-and-the-resistance-that-follows-it-mt_HrU1DfZhGz

### Polar Regions

https://lightmysky.com/learn/science/areas/polar-regions

#### Where Are the Poles? (ages 5-7)

Know that Earth has a North Pole and a South Pole — the two coldest places on the planet — and be able to find them on a globe, understanding that they are at the very top and very bottom of the Earth, as far from the Equator as possible

Ready when they can: Point to the North Pole and South Pole on a globe or world map; Explain that the poles are the coldest places on Earth because they are farthest from the Equator; State that the North Pole is at the top and the South Pole is at the bottom of the Earth.

https://lightmysky.com/learn/science/where-are-the-poles-mt_4uPnLieBPN

#### Arctic vs Antarctic (ages 5-7)

Know that the Arctic (North Pole) and Antarctic (South Pole) are very different — the Arctic is a frozen ocean surrounded by land where people and polar bears live, while the Antarctic is a huge ice-covered continent surrounded by ocean where penguins live but no people live permanently

Ready when they can: State that the Arctic is a frozen ocean surrounded by land, while the Antarctic is a continent covered in ice surrounded by ocean; Explain that polar bears live in the Arctic and penguins live in the Antarctic, not the other way around; Know that people (like the Inuit) live in the Arctic but nobody lives permanently in Antarctica.

Needs first: Where Are the Poles?.

https://lightmysky.com/learn/science/arctic-vs-antarctic-mt_aO018DkCun

#### Brave Polar Explorers (ages 5-7)

Know simple stories of brave polar explorers — Robert Falcon Scott and Roald Amundsen who raced to the South Pole, and Ernest Shackleton whose ship Endurance was crushed by ice but who brought all his men home safely — and understand that polar exploration required incredible courage and endurance

Ready when they can: Name at least two polar explorers: Scott, Amundsen, or Shackleton; Tell the basic story of Scott and Amundsen's race to the South Pole in simple terms; Describe what happened to Shackleton's ship Endurance and how he brought his crew home safely.

Needs first: Where Are the Poles?.

https://lightmysky.com/learn/science/brave-polar-explorers-mt_22XbXTRq50

#### Ice & Snow (ages 5-7)

Know that water can be solid (ice and snow) or liquid, that snow is made of tiny frozen ice crystals, that icebergs are huge chunks of ice floating in the ocean with most of their bulk hidden underwater, and that ice floats because it is lighter than liquid water

Ready when they can: Explain that ice and snow are frozen water (solid) and that water can change between solid and liquid; Describe an iceberg as a huge piece of ice floating in the ocean with most of it hidden below the surface; State that ice floats because frozen water is lighter than liquid water.

Needs first: Where Are the Poles?.

https://lightmysky.com/learn/science/ice-and-snow-mt_SrmHaJXKrX

#### Midnight Sun & Polar Night (ages 5-7)

Know that at the poles, daylight and darkness are extreme — in summer the Sun never fully sets (midnight sun) and in winter the Sun never rises (polar night lasting months) — and that this is very different from what we experience at home, where every day has both daylight and darkness

Ready when they can: Describe midnight sun: in polar summer, the Sun stays above the horizon all day and night; Describe polar night: in polar winter, the Sun stays below the horizon for weeks or months; Compare this to normal day-night patterns at home, noting the dramatic difference.

Needs first: Where Are the Poles?.

https://lightmysky.com/learn/science/midnight-sun-and-polar-night-mt_3duNkf6Qmr

#### Penguins (ages 5-7)

Know key facts about penguins — they live in the Antarctic and Southern Hemisphere, they cannot fly but are excellent swimmers, Emperor penguins are the largest and huddle together in winter to keep warm, and penguin parents take turns keeping their egg warm on their feet in freezing temperatures

Ready when they can: State at least three facts about penguins: they can't fly, they're excellent swimmers, and Emperor penguins are the biggest; Describe how Emperor penguins huddle together in winter to keep warm; Explain that penguin parents take turns keeping their egg warm on their feet in freezing temperatures.

Needs first: Arctic vs Antarctic.

https://lightmysky.com/learn/science/penguins-mt_CK2orHetl3

#### Polar Bears (ages 5-7)

Know key facts about polar bears — they live only in the Arctic (not the Antarctic), they have thick white fur and a layer of fat (blubber) to keep warm, they are excellent swimmers, and they hunt seals by waiting at holes in the sea ice

Ready when they can: State that polar bears live in the Arctic, not the Antarctic; Describe at least two ways polar bears stay warm: thick white fur and a layer of blubber (fat); Explain how polar bears hunt seals by waiting at breathing holes in the sea ice.

Needs first: Arctic vs Antarctic.

https://lightmysky.com/learn/science/polar-bears-mt_O9dH94NFae

#### More Polar Animals (ages 5-7)

Know about other polar animals besides penguins and polar bears — seals that swim under ice, walruses with long tusks, Arctic foxes that turn white in winter, snowy owls, narwhals with their unicorn-like tusk, and whales that migrate to polar waters to feed — and that all these animals have special features to survive extreme cold

Ready when they can: Name at least four polar animals beyond penguins and polar bears, such as seals, walruses, Arctic foxes, snowy owls, or narwhals; Describe one way each named animal survives the cold (e.g. walrus blubber, Arctic fox white winter coat); State that narwhals have a long spiral tusk and live in Arctic waters.

Needs first: Arctic vs Antarctic, Penguins, Polar Bears.

https://lightmysky.com/learn/science/more-polar-animals-mt_7OJjLOl0fz

#### Cold-Weather Adaptations (ages 7-9)

Understand how polar animals are adapted to survive extreme cold — blubber (thick fat layer) insulates seals and whales, hollow fur traps air for warmth in polar bears, counter-current heat exchange in penguin flippers prevents heat loss, Arctic foxes grow thick white winter coats for camouflage and warmth, and some animals migrate to avoid the harshest months

Ready when they can: Describe at least three cold-weather adaptations: blubber, hollow fur, counter-current heat exchange, white winter coats, or migration; Explain the purpose of each adaptation (e.g. blubber insulates against cold water, white fur provides camouflage in snow); Use the word adaptation correctly to mean a feature that helps an animal survive in its environment.

Needs first: More Polar Animals, Polar Bears.

https://lightmysky.com/learn/science/cold-weather-adaptations-mt_kDKo4lxRKi

#### Comparing Arctic & Antarctic (ages 7-9)

Compare the Arctic and Antarctic in detail — the Arctic is an ocean covered by floating sea ice with surrounding land masses (Canada, Russia, Greenland, Scandinavia), while Antarctica is a continent larger than Europe buried under ice up to 4 km thick; polar bears, Arctic foxes, and walruses live only in the Arctic while penguins, leopard seals, and albatrosses are found only in the Antarctic

Ready when they can: State that the Arctic is a frozen ocean surrounded by land (name at least two bordering countries), while Antarctica is a continent covered by ice sheet up to 4 km thick; Correctly assign at least three animals to the Arctic and three to the Antarctic; Name at least two differences in human presence: indigenous peoples in the Arctic vs research stations only in Antarctica.

Needs first: More Polar Animals, Arctic vs Antarctic.

https://lightmysky.com/learn/science/comparing-arctic-and-antarctic-mt_z9jn9HogfE

#### Ice & States of Matter (ages 7-9)

Understand ice in different forms and states of matter — sea ice forms when ocean water freezes (it's salty and relatively thin), glacial ice forms from compacted snow over centuries (fresh water, very thick), and icebergs break off from glaciers and float in the sea; know that water exists as solid (ice), liquid (water), and gas (water vapour), and that salt lowers the freezing point of water

Ready when they can: Distinguish between sea ice (frozen ocean, salty, thin) and glacial ice (compacted snow, fresh water, thick); Explain that icebergs break off from glaciers and float because ice is less dense than liquid water; Describe the three states of water (solid, liquid, gas) and explain that salt lowers the freezing point.

Needs first: Ice & Snow.

https://lightmysky.com/learn/science/ice-and-states-of-matter-mt_scbDHJZZHK

#### Inuit & Sami Peoples (ages 7-9)

Know that indigenous peoples have lived in the Arctic for thousands of years — the Inuit across Canada, Alaska, and Greenland, and the Sami in northern Scandinavia — developing remarkable knowledge of the environment, using dog sleds and kayaks for transport, wearing animal-skin clothing for warmth, and building igloos as temporary shelters, with a deep respect for the animals and land they depend on

Ready when they can: Name the Inuit (Canada, Alaska, Greenland) and Sami (northern Scandinavia) as Arctic indigenous peoples; Describe at least three aspects of traditional Arctic life: dog sleds, kayaks, animal-skin clothing, igloos, or hunting practices; Explain that indigenous Arctic peoples have deep knowledge of their environment developed over thousands of years.

Needs first: Comparing Arctic & Antarctic.

https://lightmysky.com/learn/science/inuit-and-sami-peoples-mt_rqalOvjkj3

#### Polar Food Chains (ages 7-9)

Understand polar food chains — in the Antarctic, phytoplankton are eaten by krill, krill are eaten by fish and penguins, and penguins are eaten by leopard seals and orcas; in the Arctic, algae under ice feeds zooplankton, which feeds fish, which feeds seals, which feeds polar bears — and that tiny organisms like krill and plankton are the foundation of all polar life

Ready when they can: Construct an Antarctic food chain: phytoplankton → krill → penguin → leopard seal or orca; Construct an Arctic food chain: algae → zooplankton → fish → seal → polar bear; Explain why krill and plankton are critical — without them, the entire food chain collapses.

Needs first: More Polar Animals, Penguins.

https://lightmysky.com/learn/science/polar-food-chains-mt_7nduoLvoB1

#### The Arctic Tundra (ages 7-9)

Know what the Arctic tundra is — a vast, treeless landscape with permafrost (permanently frozen ground) just below the surface, a very short growing season in summer when mosses, lichens, and tough grasses burst into life, and home to caribou/reindeer, musk oxen, lemmings, and snowy owls

Ready when they can: Describe the tundra as a treeless landscape with permafrost (permanently frozen ground) beneath the surface; Explain that the tundra has a very short summer growing season when mosses, lichens, and grasses grow quickly; Name at least three tundra animals: caribou/reindeer, musk oxen, lemmings, or snowy owls.

Needs first: Comparing Arctic & Antarctic.

https://lightmysky.com/learn/science/the-arctic-tundra-mt_X4CJpPRxae

#### The Race to the South Pole (ages 7-9)

Know the story of the race to the South Pole in detail — Norwegian Roald Amundsen and British Robert Falcon Scott both set out in 1911, Amundsen arrived first on 14 December using dog sleds and careful planning, Scott arrived 34 days later using man-hauled sledges and tragically died with his team on the return journey; also know about Ernest Shackleton's 1914 Endurance expedition where the ship was trapped and crushed by ice, and Shackleton's extraordinary boat journey to South Georgia to rescue his crew

Ready when they can: Describe the Scott vs Amundsen race: Amundsen arrived 14 December 1911 using dog sleds; Scott arrived 34 days later and died on the return; Explain at least two reasons Amundsen succeeded: better planning, dog sleds, polar experience, and lighter supplies; Narrate the key events of the Endurance expedition: ship crushed, camps on ice, boat journey to South Georgia, all crew rescued.

Needs first: Brave Polar Explorers, Comparing Arctic & Antarctic.

https://lightmysky.com/learn/science/the-race-to-the-south-pole-mt_islVn_P28Z

#### Why Polar Seasons Are Extreme (ages 7-9)

Understand why the poles have extreme seasons — Earth's axis is tilted at about 23.5°, so as it orbits the Sun, each pole spends half the year tilted toward the Sun (continuous daylight, warmer summer) and half tilted away (continuous darkness, bitter winter); this tilt also drives the annual cycle of sea ice expanding in winter and retreating in summer, and triggers animal behaviours like migration and breeding

Ready when they can: Explain that Earth's axis is tilted at about 23.5° and this tilt causes the extreme polar seasons; Describe how the tilt means each pole faces toward the Sun for half the year (summer/daylight) and away for the other half (winter/darkness); Connect the seasonal cycle to at least one animal behaviour, such as migration or sea ice retreat affecting hunting.

Needs first: Midnight Sun & Polar Night, Ice & States of Matter.

https://lightmysky.com/learn/science/why-polar-seasons-are-extreme-mt_f9syMry-0S

#### Antarctic Treaty & Research (ages 9-11)

Know that Antarctica is governed by the Antarctic Treaty (signed 1959, in force since 1961) — which sets Antarctica aside for peaceful purposes and scientific research, bans military activity and mining, and is signed by over 50 countries; understand that international research stations study climate, astronomy, biology, and geology, and that Antarctica is the closest thing on Earth to a continent for science rather than politics

Ready when they can: State that the Antarctic Treaty (1959) sets Antarctica aside for peace and science, banning military activity and mining; Know that over 50 countries have signed the treaty and that many operate research stations; Name at least two areas of scientific research conducted in Antarctica: climate, astronomy, biology, or geology.

Needs first: The Race to the South Pole, Comparing Arctic & Antarctic.

https://lightmysky.com/learn/science/antarctic-treaty-and-research-mt_itldWmVItr

#### Glaciers & Ice Sheets (ages 9-11)

Understand how glaciers and ice sheets form and behave — snow accumulates over centuries and compresses into dense ice, glaciers flow slowly downhill under their own weight carving U-shaped valleys and depositing moraines; the Greenland and Antarctic ice sheets together hold enough ice to raise sea levels by over 65 metres; and ice cores drilled from these sheets contain trapped air bubbles that reveal Earth's climate history going back 800,000 years

Ready when they can: Describe how glaciers form: snow accumulates, compresses, and becomes dense ice that flows slowly under its own weight; Explain that the Greenland and Antarctic ice sheets hold enough water to raise sea levels dramatically if melted; Describe how ice cores reveal climate history through trapped air bubbles from hundreds of thousands of years ago.

Needs first: Ice & States of Matter.

https://lightmysky.com/learn/science/glaciers-and-ice-sheets-mt_5_kErPeeNu

#### Polar Climate Zone (ages 9-11)

Understand that polar regions belong to the polar climate zone — one of Earth's five main climate zones (tropical, arid, temperate, continental, polar) — characterised by temperatures rarely above 10°C even in summer, low precipitation (polar deserts receive less rain than the Sahara), and strong winds; know that latitude is the key factor determining climate zones, with polar regions above 60°N/S

Ready when they can: Name the five main climate zones and place polar regions correctly within them; State that polar regions are above approximately 60° latitude and explain that distance from the Equator is the main reason they are cold; Describe polar climate characteristics: rarely above 10°C in summer, very low precipitation, strong winds.

Needs first: Why Polar Seasons Are Extreme, Geography & Local Weather, Climate Zones, Comparing Arctic & Antarctic.

https://lightmysky.com/learn/science/polar-climate-zone-mt_GbZFuGDFsa

#### Polar Ecosystems Compared (ages 9-11)

Compare Arctic and Antarctic ecosystems — the Arctic has both terrestrial (tundra) and marine ecosystems supporting large land mammals and indigenous human communities, while the Antarctic is almost entirely marine-based with virtually no land plants or mammals; both regions have short, intense food chains anchored by phytoplankton and krill, and both are disproportionately affected by climate change and human activity

Ready when they can: Compare Arctic (terrestrial + marine, land mammals, human communities) with Antarctic (almost entirely marine, no land mammals); Explain that both polar food chains depend on phytoplankton and krill at the base; Describe why polar ecosystems are particularly vulnerable to climate change (short food chains, specialised organisms).

Needs first: Polar Food Chains, Cold-Weather Adaptations, The Arctic Tundra.

https://lightmysky.com/learn/science/polar-ecosystems-compared-mt_kOYw43NPzr

#### Polar Exploration Then & Now (ages 9-11)

Compare historical polar exploration with modern polar science — the Heroic Age (1897–1922) relied on ships, dogs, and human endurance with many fatalities, while today's polar scientists use GPS, satellites, icebreaker ships, heated research stations, and aircraft; understand that modern challenges include studying climate change data, and that polar science now includes diverse international teams including women scientists like glaciologist Liz Thomas and marine biologist Sylvia Earle

Ready when they can: Compare Heroic Age exploration (dog sleds, man-hauling, many deaths) with modern science (GPS, satellites, icebreakers, heated stations); Name at least two technologies that make modern polar science possible; Name a modern polar scientist and explain that today's polar teams are diverse and international.

Needs first: The Race to the South Pole, Antarctic Treaty & Research.

https://lightmysky.com/learn/science/polar-exploration-then-and-now-mt_I_c57p0aGN

#### Polar Oceans and World Climate (ages 9-11)

Understand how polar oceans connect to the global climate system — cold, dense polar water sinks and drives thermohaline circulation (a global conveyor belt of ocean currents), sea ice reflects sunlight back to space (the albedo effect) helping regulate Earth's temperature, and the Southern Ocean around Antarctica is one of the most productive marine ecosystems on Earth due to upwelling nutrients

Ready when they can: Explain that cold, dense polar water sinks and drives global ocean circulation (thermohaline circulation); Describe the albedo effect: white ice reflects sunlight back to space, while dark ocean absorbs heat; State that the Southern Ocean is extremely productive because upwelling brings nutrients to the surface.

Needs first: Polar Food Chains, The Five Oceans, Oceans & Climate, Ice & States of Matter.

https://lightmysky.com/learn/science/polar-oceans-and-world-climate-mt_g1qgxmlJQ2

#### Climate Change at the Poles (ages 9-11)

Understand how climate change is affecting polar regions — Arctic sea ice is shrinking dramatically (losing about 13% per decade since 1979), the Greenland and Antarctic ice sheets are losing mass and contributing to sea level rise, permafrost is thawing and releasing methane (a powerful greenhouse gas), and these changes create positive feedback loops where melting leads to more warming which leads to more melting

Ready when they can: State that Arctic sea ice has been declining at roughly 13% per decade since 1979; Explain the positive feedback loop: warming → ice melts → dark ocean absorbs more heat → more warming → more melting; Describe at least two consequences of polar ice loss: sea level rise and permafrost thawing releasing methane.

Needs first: Glaciers & Ice Sheets, Climate Change Basics, Polar Oceans and World Climate, The Arctic Tundra.

https://lightmysky.com/learn/science/climate-change-at-the-poles-mt_Fqna9qHffr

#### Earth's Frozen Water (ages 9-11)

Understand the cryosphere and its role in Earth's water system — the cryosphere is all frozen water on Earth (ice sheets, glaciers, sea ice, permafrost, snow cover); polar ice sheets hold about 69% of Earth's fresh water; if all polar ice melted, sea levels would rise over 65 metres; and the water cycle connects polar ice to the global system through evaporation, precipitation, and meltwater flowing into oceans

Ready when they can: Define the cryosphere as all frozen water on Earth and name its components: ice sheets, glaciers, sea ice, permafrost, snow; State that polar ice sheets hold approximately 69% of Earth's fresh water; Explain how polar ice connects to the global water cycle and what would happen if it all melted (65m+ sea level rise).

Needs first: Glaciers & Ice Sheets, The Water Cycle, Polar Oceans and World Climate.

https://lightmysky.com/learn/science/earths-frozen-water-mt_cMmG8VLbAp

#### Polar Conservation & Future (ages 9-11)

Understand the conservation challenges facing polar regions — marine protected areas in the Southern Ocean aim to preserve Antarctic ecosystems, Arctic nations dispute sovereignty over northern sea routes and resources as ice retreats, indigenous peoples fight for land rights and voice in environmental decisions, and international cooperation (Paris Agreement, Antarctic Treaty) is essential but difficult to maintain as economic pressures grow

Ready when they can: Describe at least two conservation measures: marine protected areas in the Southern Ocean and the Antarctic Treaty; Explain why Arctic sovereignty is contested as ice retreats and shipping routes open; Describe the role of indigenous peoples in Arctic environmental decisions and why their knowledge matters.

Needs first: Climate Change at the Poles, Antarctic Treaty & Research, Inuit & Sami Peoples.

https://lightmysky.com/learn/science/polar-conservation-and-future-mt_7QeiS95TRC

### Chemistry

https://lightmysky.com/learn/science/areas/chemistry

#### Gas Volumes and the Ideal Gas Equation (ages 16-17)

Amount of substance stops being a mass calculation once the sample is a gas. The ideal gas equation ties pressure, volume, temperature and moles together, so a volume measured at the bench becomes a number of particles.

Ready when they can: Converts pressure to pascals, volume to cubic metres and temperature to kelvin before substituting anything; Calculates the amount in moles of a gas from measured pressure, volume and temperature; Finds the molar mass of an unknown gas from the mass of a measured volume of it; Says which assumptions of the ideal model break down at high pressure or low temperature.

https://lightmysky.com/learn/science/gas-volumes-and-the-ideal-gas-equation-mt_I1fz_6wjuD

#### Enthalpy Change, Standard Conditions and Calorimetry (ages 16-17)

Enthalpy change is the heat a reaction gives out or takes in at constant pressure, quoted per mole under agreed conditions. It is measured by tracking a temperature change and dividing by the amount that reacted.

Ready when they can: States what standard conditions fix and why a quoted value means nothing without them; Uses the mass of the solution, its specific heat capacity and the temperature change to find the heat transferred; Divides by the amount in moles to get a value per mole and attaches the right sign; Gives two reasons a bench value comes out well below the data book value.

https://lightmysky.com/learn/science/enthalpy-change-standard-conditions-and-calorimetry-mt_GPgwgyqyvN

#### Hess's Law and Enthalpy Cycles (ages 16-17)

The enthalpy change of a reaction does not depend on the route taken. Build a cycle out of enthalpies of formation or of combustion and you get a value for a reaction nobody can measure directly.

Ready when they can: States Hess's law and explains why it follows from conservation of energy; Draws a cycle with the arrows pointing the right way for formation data and for combustion data; Calculates an enthalpy change from standard enthalpies of formation of reactants and products; Explains why the enthalpy of formation of an element in its standard state is zero.

https://lightmysky.com/learn/science/hesss-law-and-enthalpy-cycles-mt_530V9czLOb

#### Ionisation Energy and the Evidence for Sub-Shells (ages 16-17)

Successive ionisation energies jump wherever the next electron has to come from closer in. Those jumps are the direct evidence for shells, and the smaller dips across a period are the evidence for sub-shells.

Ready when they can: Defines first ionisation energy with the state symbols that make the definition unambiguous; Reads an element's group off a graph of its successive ionisation energies; Explains the general rise across a period and the drop from the end of one period to the start of the next; Explains the small dips at aluminium and at sulfur and says what they reveal about sub-shells.

https://lightmysky.com/learn/science/ionisation-energy-and-the-evidence-for-sub-shells-mt__suwzd1kVQ

#### Naming Organic Compounds and the Formulas That Show Structure (ages 16-17)

Every organic name is built from a stem for the longest chain, a suffix for the main functional group and prefixes for whatever hangs off it. Molecular, structural, displayed and skeletal formulas each show a different amount of that structure.

Ready when they can: Names a branched alkane, an alcohol and a haloalkane with the locants as low as the rules allow; Converts between displayed, structural and skeletal formulas for the same molecule; Picks the functional group out of an unfamiliar molecule and names the family it belongs to; Explains what a homologous series is and what its general formula lets you predict.

https://lightmysky.com/learn/science/naming-organic-compounds-and-the-formulas-that-show-structure-mt_LCqg41gslT

#### Isomerism: Same Formula, Different Molecule (ages 16-17)

Two molecules can share a molecular formula and still be different substances. Chains, positions and functional groups give structural isomers, and a double bond that cannot rotate gives E and Z isomers.

Ready when they can: Draws and names every chain and position isomer of a given molecular formula; Recognises functional group isomerism between families such as alcohols and ethers; Explains why a double bond prevents rotation and what that produces; Assigns E or Z by comparing the priority of the groups on each carbon of the double bond.

https://lightmysky.com/learn/science/isomerism-same-formula-different-molecule-mt_DvD0coeKZe

#### Orbitals, Sub-Shells and Electron Configuration (ages 16-17)

Electrons fill orbitals that hold two each, grouped into s, p and d sub-shells. Writing configurations this way explains the block structure of the table and says exactly what an ion has lost.

Ready when they can: Writes the full electron configuration of any element up to krypton; Explains why the 4s sub-shell fills first and why its electrons also leave first when a transition metal forms an ion; Draws the arrows-in-boxes picture for a named element, including the half-filled cases; Links the s, p and d blocks of the table to the sub-shell being filled across them.

https://lightmysky.com/learn/science/orbitals-sub-shells-and-electron-configuration-mt_sRMo1f5PfJ

#### Trends Across Period 3: Radius, Ionisation Energy and Melting Point (ages 16-17)

Across a period the nuclear charge climbs while the outer shell stays the same, so atoms shrink and get harder to ionise. Melting point follows structure instead, which is why silicon towers over both of its neighbours.

Ready when they can: Explains the fall in atomic radius across period 3; Explains the general rise in first ionisation energy and accounts for the two dips; Explains the melting point pattern by naming the structure of each element in the row; Places an unknown period 3 element from two of its measured properties.

https://lightmysky.com/learn/science/trends-across-period-3-radius-ionisation-energy-and-melting-point-mt_stFFQ6GPIh

#### Period 3 Oxides and the Acid-Base Divide (ages 16-18)

Metal oxides on the left of period 3 give alkalis with water, non-metal oxides on the right give acids, and aluminium oxide does both. The bonding changes across the row and the reactions follow it.

Ready when they can: Writes equations for sodium oxide and for sulfur trioxide reacting with water; Links the change from ionic to covalent bonding across the row to the change from basic to acidic; Explains what amphoteric means using aluminium oxide with acid and with alkali; Predicts the approximate pH of the solution a named period 3 oxide makes.

https://lightmysky.com/learn/science/period-3-oxides-and-the-acid-base-divide-mt_3kC5hTavIQ

#### Group 2: Reactivity and Solubility Trends (ages 16-17)

Down group 2 the outer electrons come away more easily, so reactions with water get more vigorous. Hydroxide solubility rises down the group while sulfate solubility falls, and both trends get used.

Ready when they can: Explains the reactivity trend down the group in terms of ionisation energy; Writes equations for group 2 metals and their oxides reacting with water; States the opposite solubility trends of the hydroxides and of the sulfates; Explains a use such as barium sulfate in medical imaging or magnesium hydroxide in indigestion remedies from those trends.

https://lightmysky.com/learn/science/group-2-reactivity-and-solubility-trends-mt_Ch8FEkh-dV

#### Group 7: Oxidising Power, Displacement and Halide Tests (ages 16-17)

Down group 7 the halogens get worse at taking an electron, so oxidising power falls while the halide ions get better at giving one up. Displacement reactions and the reactions of solid halides with concentrated acid both follow from that.

Ready when they can: Explains the fall in oxidising power down the group using atomic radius and shielding; Predicts and writes the displacement reactions between halogens and halide solutions; Explains the different products when concentrated sulfuric acid meets sodium chloride, sodium bromide and sodium iodide; Identifies a halide with silver nitrate and ammonia and states the colours at each stage.

https://lightmysky.com/learn/science/group-7-oxidising-power-displacement-and-halide-tests-mt_li7olQ3dM9

#### Oxidation Numbers and Balancing Redox Equations (ages 16-18)

An oxidation number is a bookkeeping charge that records where the electrons are counted. With it, half equations can be balanced in acid solution and then combined into one ionic equation.

Ready when they can: Assigns oxidation numbers in a compound or a polyatomic ion using the standard rules; Identifies what is oxidised and what is reduced from the changes in oxidation number; Balances a half equation in acid solution using water and hydrogen ions; Combines two half equations so that the electrons cancel exactly.

https://lightmysky.com/learn/science/oxidation-numbers-and-balancing-redox-equations-mt_4xuYKYgUex

#### Lattice Enthalpy and Born-Haber Cycles (ages 17-18)

The energy released when gaseous ions come together as a lattice cannot be measured directly. It is found from a cycle built out of atomisation, ionisation, electron affinity and formation data.

Ready when they can: Puts the steps of a Born-Haber cycle in order and gives the sign of each; Calculates a lattice enthalpy from the other terms in the cycle; Explains why lattice enthalpy gets more exothermic for smaller ions and for larger charges; Compares a cycle value with one calculated from a perfect ionic model and says what a gap suggests about the bonding.

https://lightmysky.com/learn/science/lattice-enthalpy-and-born-haber-cycles-mt_pUku4iUjYa

#### Entropy and the Spread of Energy (ages 17-18)

Entropy measures how many ways a system's energy can be arranged. Changes that make more gas, or more particles, raise it, and that is why some endothermic changes happen at all.

Ready when they can: Ranks solid, liquid and gas by entropy and explains the order in terms of arrangements; Predicts the sign of the entropy change for a reaction from the states and the number of particles; Calculates an entropy change from standard entropy values; Explains why ammonium nitrate dissolving cools the water and still happens on its own.

https://lightmysky.com/learn/science/entropy-and-the-spread-of-energy-mt_a_2feH2gnE

#### Free Energy and Whether a Reaction Is Feasible (ages 17-18)

Free energy change combines enthalpy and entropy with temperature. Its sign says whether a reaction is feasible, and setting it to zero gives the temperature at which feasibility flips.

Ready when they can: Calculates a free energy change from enthalpy and entropy values with the units made consistent first; Reads the sign to say whether a reaction is feasible at that temperature; Finds the temperature at which a reaction becomes feasible by setting the free energy change to zero; Explains why a feasible reaction can still be far too slow to see.

https://lightmysky.com/learn/science/free-energy-and-whether-a-reaction-is-feasible-mt_o1kZgBYWoM

#### Rate Equations and Orders of Reaction (ages 17-18)

The rate equation says how the rate actually depends on the concentrations, and it comes from experiment rather than from the balanced equation. Each order says how much one concentration matters.

Ready when they can: Writes a rate equation from initial rate data by comparing runs where one concentration changes at a time; States the order with respect to each reactant and the overall order; Works out the units of the rate constant for a given overall order; Explains how a species in the balanced equation can turn out to be order zero.

https://lightmysky.com/learn/science/rate-equations-and-orders-of-reaction-mt_1x3ogDKGxC

#### Reading Orders and Half-Lives from Rate Graphs (ages 17-18)

A concentration-time curve and a rate-concentration graph each give the order away. A half-life that stays the same is the signature of first order.

Ready when they can: Takes tangents from a concentration-time curve to get rates and plots rate against concentration; Identifies zero, first and second order from the shape of a rate-concentration graph; Measures successive half-lives and uses their constancy to argue for first order; Finds the rate constant from a gradient or from a half-life.

https://lightmysky.com/learn/science/reading-orders-and-half-lives-from-rate-graphs-mt_gCToNUUYll

#### Standard Electrode Potentials and Predicting Redox Reactions (ages 17-18)

Each half reaction gets a potential measured against a standard hydrogen electrode. Put two half cells together and the difference says which way the electrons will flow, and whether a proposed reaction goes at all.

Ready when they can: Describes a half cell and explains what the standard hydrogen electrode is there for; States the conditions a standard electrode potential is measured under and why they are fixed; Calculates a cell potential from two standard values and identifies which species is oxidised; Predicts whether a named redox reaction happens, and gives one reason a feasible one may still not be seen.

https://lightmysky.com/learn/science/standard-electrode-potentials-and-predicting-redox-reactions-mt_LDI10CjoAI

#### Cells That Do Work: Batteries, Fuel Cells and Corrosion (ages 17-18)

A cell potential is only a prediction until current flows and the cell has to keep supplying it. Rechargeable cells, fuel cells and a rusting car body are all the same electrochemistry read in different directions.

Ready when they can: Write the electrode reactions for a familiar rechargeable cell in both charge and discharge directions; Explain what a fuel cell does differently from a battery, and what limits its voltage; Account for rusting as an electrochemical process and explain why sacrificial protection works.

https://lightmysky.com/learn/science/cells-that-do-work-batteries-fuel-cells-and-corrosion-mt_NQQzlecX4v

#### Redox Titrations with Manganate(VII) and Thiosulfate (ages 17-18)

A redox titration needs no separate indicator when one reagent changes colour as it reacts. Manganate(VII) against iron(II), and iodine against thiosulfate, are the two routines worth owning.

Ready when they can: Explains why manganate(VII) acts as its own indicator and describes the end point; Builds the full ionic equation from the two half equations before calculating anything; Calculates the concentration or the purity of a sample from the titre and the mole ratio; Explains why the iodine and thiosulfate route needs starch added only near the end.

https://lightmysky.com/learn/science/redox-titrations-with-manganate-vii-and-thiosulfate-mt_tKZTSfo0Ra

#### The Rate-Determining Step and Reaction Mechanisms (ages 17-18)

Most reactions run in several steps and the slowest one sets the pace. The orders in the rate equation say which species turn up in that step, which makes kinetics evidence about mechanism.

Ready when they can: Explains why only the slow step, and the steps before it, can affect the measured rate; Matches a proposed mechanism to a rate equation and rejects one that does not fit; Uses the orders to say which species, and how many of each, appear in the rate-determining step; Explains how a catalyst can change the mechanism rather than just push the same one along.

https://lightmysky.com/learn/science/the-rate-determining-step-and-reaction-mechanisms-mt_PM1Vo2CkVD

#### The Arrhenius Equation and Finding Activation Energy (ages 17-18)

The rate constant depends on temperature through the activation energy. Plotting the logarithm of the rate constant against one over temperature turns that dependence into a straight line whose gradient gives the barrier.

Ready when they can: Explains why a small temperature rise changes the rate so much, using the fraction of particles above the barrier; Rearranges the Arrhenius equation into straight-line form and says what to plot against what; Finds an activation energy from the gradient of that plot; Says what adding a catalyst does to the gradient and what it leaves alone.

https://lightmysky.com/learn/science/the-arrhenius-equation-and-finding-activation-energy-mt_QBQDSNwbXK

#### The Equilibrium Constant Kc (ages 16-18)

At equilibrium the concentrations settle into a ratio that is fixed for a given temperature. Kc puts a number on how far a reaction goes, where Le Chatelier could only say which way it moves.

Ready when they can: Writes the expression for Kc from a balanced equation, products over reactants, each raised to its coefficient; Works out the units of Kc for a given equation; Calculates Kc from equilibrium amounts and the volume of the container; Reads a very large or very small value of Kc as a statement about where the position lies.

https://lightmysky.com/learn/science/the-equilibrium-constant-kc-mt_3G8b6Hyz3u

#### Kp, Partial Pressures and Gas Equilibria (ages 17-18)

For gases the equilibrium constant is written in partial pressures. Each gas contributes its mole fraction of the total pressure, and the conditions chosen in industry are argued from there.

Ready when they can: Calculates mole fractions and partial pressures from equilibrium amounts and a total pressure; Writes Kp for a gas reaction and works out its units; Explains why raising the total pressure shifts the position while leaving Kp untouched; Uses Kp to argue the conditions picked for an industrial process such as ammonia synthesis.

https://lightmysky.com/learn/science/kp-partial-pressures-and-gas-equilibria-mt_1R8BpA2hfK

#### pH, Kw and Strong Acids and Bases (ages 17-18)

pH is a way of writing a hydrogen ion concentration as a small number using powers of ten. Water ionises a little itself, and that constant links the two ions, which is what makes the pH of an alkali calculable.

Ready when they can: Calculates pH from the concentration of a strong acid and works backwards from a pH to a concentration; Explains why a tenfold dilution changes pH by exactly one unit; Uses the ionic product of water to get the hydrogen ion concentration in a strong alkali; Explains why Kw changes with temperature and what that does to the pH of pure water.

https://lightmysky.com/learn/science/ph-kw-and-strong-acids-and-bases-mt_KJ4yc25Z_l

#### Solubility Equilibria and When a Precipitate Appears (ages 17-18)

A sparingly soluble salt sitting on the bottom of a beaker is at equilibrium with its ions, and one constant describes the whole situation. Comparing the ion product with that constant is how a chemist predicts a precipitate before mixing anything.

Ready when they can: Write the solubility product expression for a salt and relate it to the salt's solubility; Predict whether mixing two solutions produces a precipitate by comparing the ion product with the constant; Explain the common ion effect and use it to account for selective precipitation.

https://lightmysky.com/learn/science/solubility-equilibria-and-when-a-precipitate-appears-mt_IMdWLxIAFt

#### Transition Metals: Variable Oxidation State, Colour and Catalysis (ages 17-18)

A partly filled d sub-shell is what makes a transition metal a transition metal. It explains several oxidation states, coloured compounds, and why so many of these metals catalyse reactions.

Ready when they can: Defines a transition element by its d sub-shell and explains why scandium and zinc do not qualify; Gives the common oxidation states of a named transition metal with a compound of each; Explains colour as a d sub-shell split by ligands, with part of the visible spectrum absorbed; Names a heterogeneous and a homogeneous catalyst and explains the part the oxidation states play.

https://lightmysky.com/learn/science/transition-metals-variable-oxidation-state-colour-and-catalysis-mt_UIVC6d7wak

#### Complex Ions, Ligands and Their Shapes (ages 17-18)

A ligand donates a lone pair into a vacant orbital on a metal ion. How many fit, and how they arrange themselves, sets the shape of the complex and whether two mirror forms are possible.

Ready when they can: Defines a ligand and a coordination number and picks both out of a given formula; Predicts octahedral, tetrahedral or square planar geometry from the ligand and its size; Separates monodentate from bidentate ligands and explains why the larger ones hold on more tightly; Explains cis-trans isomerism in a named complex and why it matters for a drug such as a platinum complex.

https://lightmysky.com/learn/science/complex-ions-ligands-and-their-shapes-mt_xxWYYqgZp_

#### Weak Acids, Ka and pKa (ages 17-18)

A weak acid only partly ionises, so its hydrogen ion concentration has to come from an equilibrium constant. Ka measures how far the ionisation goes, and pKa puts that on the same kind of scale as pH.

Ready when they can: Writes the Ka expression for a named weak acid; Calculates the pH of a weak acid solution and names the two approximations the calculation makes; Converts between Ka and pKa and ranks acids by strength from either; Explains why a weak acid and a strong acid at the same concentration differ in pH yet need the same volume of alkali to neutralise.

https://lightmysky.com/learn/science/weak-acids-ka-and-pka-mt_q7fYb7qzMH

#### Buffers and Titration Curves (ages 17-18)

A weak acid mixed with its salt resists pH change, because whatever is added has something waiting to react with it. The same chemistry shapes the curve a pH meter draws during a titration and decides which indicator will work.

Ready when they can: Explains how a buffer absorbs added acid and added alkali, naming the species that does each job; Calculates the pH of a buffer from Ka and the ratio of acid to salt; Sketches the four titration curves and marks the equivalence point and the buffer region on each; Chooses an indicator by matching its range to the vertical section of the curve.

https://lightmysky.com/learn/science/buffers-and-titration-curves-mt_vevyEjNijM

#### Metal Aqua Ions: Acidity, Ligand Exchange and Precipitation (ages 17-18)

A metal ion in water is already a complex, and a highly charged one pulls hard enough on its water to make the solution acidic. Adding alkali, ammonia or an excess of either swaps ligands and drops or redissolves a hydroxide.

Ready when they can: Explains why a 3 plus aqua ion gives a more acidic solution than a 2 plus one; Writes the equation for a hydroxide precipitating when sodium hydroxide is added; Predicts which precipitates redissolve in excess alkali and which redissolve in excess ammonia; Identifies an unknown transition metal ion from the colours in a sequence of tests.

https://lightmysky.com/learn/science/metal-aqua-ions-acidity-ligand-exchange-and-precipitation-mt_jrsKwNq1Oi

#### Calibration, the Blank and What Makes a Measurement Trustworthy (ages 18-19)

An instrument reports a signal, not a concentration. Turning one into the other needs standards, a blank and a calibration line, and each of those is a place where a result can quietly go wrong.

Ready when they can: Prepares a calibration series and states why the standards must bracket the sample; Explains what the blank corrects for and what it cannot correct for; Chooses between external calibration, internal standard and standard addition for a stated sample; Names a matrix effect and explains how it biases a result even when the calibration line looks good.

https://lightmysky.com/learn/science/calibration-the-blank-and-what-makes-a-measurement-trustworthy-mt_UNkQFonlWJ

#### Molecular Orbital Theory for Homonuclear Diatomics (ages 18-19)

A shared pair between two atoms is a picture that fails for oxygen, which is magnetic. Combining atomic orbitals into orbitals that belong to the whole molecule gives a scheme that predicts bond order, magnetism and ionisation together.

Ready when they can: Combines two atomic orbitals into a bonding and an antibonding combination and explains the energy difference; Fills a diagram for a second-row diatomic, including the s and p mixing that reorders the levels before oxygen; Calculates bond order and links it to measured bond length and dissociation energy; Uses the diagram to predict that oxygen is paramagnetic and explains why the shared-pair picture cannot.

https://lightmysky.com/learn/science/molecular-orbital-theory-for-homonuclear-diatomics-mt_wRBDDmRYka

#### Heteronuclear Diatomics and Polarity in Orbital Terms (ages 18-19)

When the two atoms differ, their orbitals no longer sit at the same energy, so the shared orbitals lean towards one atom. Bond polarity stops being an arrow on a bond and becomes an unequal contribution to a molecular orbital.

Ready when they can: Places the atomic levels of two different atoms at different energies and explains which one dominates the bonding orbital; Links the size of the energy mismatch to the degree of ionic character; Builds the diagram for carbon monoxide and identifies the orbital that makes it a ligand; Explains why two orbitals must be close in both energy and symmetry to interact usefully.

https://lightmysky.com/learn/science/heteronuclear-diatomics-and-polarity-in-orbital-terms-mt_thdxFqyHJV

#### Molecular Symmetry: Elements, Operations and Point Groups (ages 18-19)

Every molecule has a set of movements that leave it looking unchanged. Cataloguing them gives the molecule a label, and that label turns out to decide which orbitals can mix and which spectra can appear.

Ready when they can: Finds the rotation axes, mirror planes, inversion centre and improper axes of a drawn molecule; Assigns a point group by working through a decision sequence rather than by recognition; Explains why a molecule with no improper axis of any kind can be chiral; Predicts from symmetry alone whether a molecule can have a permanent dipole.

https://lightmysky.com/learn/science/molecular-symmetry-elements-operations-and-point-groups-mt_KcofGO11tm

#### Signal, Noise and the Limit of Detection (ages 18-19)

Every instrument reads something when nothing is there. How much that reading wanders sets the smallest amount that can be claimed, and the difference between detecting and quantifying is a matter of how many multiples of the noise the signal reaches.

Ready when they can: Estimates noise from the spread of repeated blank readings; Calculates a limit of detection and a limit of quantitation and states the multiple used for each; Explains how averaging repeated scans improves the signal to noise ratio and at what cost; Explains why a result below the detection limit is reported as such rather than as a number.

https://lightmysky.com/learn/science/signal-noise-and-the-limit-of-detection-mt_NLtCWo_qlB

#### The Beer-Lambert Law and Quantitative Absorption (ages 18-19)

Absorbance is proportional to concentration and path length, which makes a spectrophotometer a concentration meter. The proportionality fails in predictable ways, and knowing where it fails is what keeps the numbers honest.

Ready when they can: Uses the law to find a concentration from an absorbance and a calibration line; Chooses the analytical wavelength from a spectrum and explains why the peak is chosen; Lists the reasons the law fails at high concentration and with stray light; Converts between transmittance and absorbance and explains the logarithmic relation.

https://lightmysky.com/learn/science/the-beer-lambert-law-and-quantitative-absorption-mt_JGdJxTKxav

#### Uncertainty in a Measurement and Where It Comes From (ages 18-19)

Every measured value carries a range, and quoting the value without it says nothing about whether two results agree. Some of that range is found by repeating the measurement and the rest is read off the equipment.

Ready when they can: Estimates an uncertainty from repeated readings and states the number of readings used; Estimates an uncertainty from a manufacturer's tolerance when repeating is not possible; Distinguishes a random contribution from a systematic one and names an experiment that would reveal each; Quotes a result with a matched number of significant figures in the value and its uncertainty.

https://lightmysky.com/learn/science/uncertainty-in-a-measurement-and-where-it-comes-from-mt_JXw4D9DReI

#### Propagating Uncertainty Through a Calculation (ages 18-19)

A result is usually calculated from several measurements, each with its own range. The rules for combining them show which measurement is worth improving and which is already good enough.

Ready when they can: Combines absolute uncertainties for a sum or difference and relative ones for a product or quotient; Handles a power correctly and explains why the exponent multiplies the relative uncertainty; Identifies the dominant contribution in a multi-step calculation and says what to improve first; Explains why a small difference between two large numbers carries a large relative uncertainty.

https://lightmysky.com/learn/science/propagating-uncertainty-through-a-calculation-mt_xssxg6NqQM

#### Significance Tests for Chemical Data (ages 18-20)

Two results that differ may differ only because measurements scatter. A significance test states how likely that scatter is to explain the difference, which turns an argument about numbers into a decision with a stated risk.

Ready when they can: Chooses between comparing a mean with a known value and comparing two means, and runs the right test; Compares two spreads with an F-test and says what a significant result implies about the methods; States a null hypothesis, quotes the confidence level and interprets the outcome in chemical terms; Applies an outlier test and explains why discarding a result needs a stated rule.

https://lightmysky.com/learn/science/significance-tests-for-chemical-data-mt_2-SDgPjOQk

#### Least-Squares Calibration and the Uncertainty of a Result Read From It (ages 19-20)

A calibration line is fitted, not drawn by eye, and the fit carries its own uncertainty into every result read off it. Knowing that uncertainty is what lets a result be quoted with a range rather than a number.

Ready when they can: Fits a line by least squares and explains what quantity the fit minimises; Uses the residuals to judge whether a straight line is the right model at all; Calculates the uncertainty in a concentration read from the line and says where on the line it is smallest; Explains why extrapolating beyond the standards is unsafe even when the line looks perfect.

https://lightmysky.com/learn/science/least-squares-calibration-and-the-uncertainty-of-a-result-read-from-it-mt_L08U-Extq_

#### Main-Group Chemistry: What Changes Down a p-Block Group (ages 19-20)

The p-block is the part of the periodic table a synthetic chemist actually reaches for, and its behaviour shifts systematically: bonds get longer and weaker, the lower oxidation state gets more stable, and the ability to expand past an octet appears only below the second row. Those three trends account for most of the reagents on a shelf.

Ready when they can: Explain the inert pair effect and predict which oxidation state a heavy p-block element prefers; Account for why silicon and phosphorus form compounds that carbon and nitrogen cannot; Compare the oxides and hydrides of one group and relate the pattern to bond strength and electronegativity.

https://lightmysky.com/learn/science/main-group-chemistry-what-changes-down-a-p-block-group-mt_wq15-pBrI5

#### Free-Radical Substitution in Alkanes (ages 16-17)

Ultraviolet light splits a halogen molecule into radicals, and those radicals attack an alkane in a chain that keeps itself going. The mechanism is why the product is always a mixture.

Ready when they can: Writes initiation, propagation and termination steps with the radical dots in the right places; Explains how one photon can lead to many product molecules; Explains why further substitution, and so a mixture, cannot be avoided; Connects the same radical chemistry to chlorine radicals breaking down ozone.

https://lightmysky.com/learn/science/free-radical-substitution-in-alkanes-mt_QkreYC9e2d

#### Electrophilic Addition to Alkenes (ages 16-17)

The double bond is a region of high electron density, so it attracts electrophiles and opens up. Curly arrows track the pair of electrons through a carbocation to the product.

Ready when they can: Draws the mechanism with curly arrows starting at the double bond and ending on the electrophile; Explains how a non-polar bromine molecule becomes polarised as it approaches; Compares primary, secondary and tertiary carbocations and uses their stability to predict the major product; Applies the same mechanism to hydrogen bromide, to bromine and to concentrated sulfuric acid.

https://lightmysky.com/learn/science/electrophilic-addition-to-alkenes-mt_1RB5nj8zR8

#### Nucleophilic Substitution in Haloalkanes (ages 16-18)

A carbon-halogen bond is polar, so the carbon can be attacked by a species carrying a lone pair. Which halogen is present decides the rate, because bond strength turns out to matter more than polarity.

Ready when they can: Draws the mechanism for hydroxide, for cyanide and for ammonia attacking a haloalkane; Explains why the carbon carries a partial positive charge in the first place; Ranks chloro, bromo and iodo compounds by rate and justifies the order using bond enthalpy; Names the product family for each nucleophile and says why the cyanide route lengthens the carbon chain.

https://lightmysky.com/learn/science/nucleophilic-substitution-in-haloalkanes-mt_QG-nKlnVvW

#### Elimination and Choosing Between Two Pathways (ages 16-18)

The same haloalkane and the same hydroxide can give an alcohol or an alkene. Concentration, solvent and temperature decide whether the hydroxide acts as a nucleophile or as a base.

Ready when they can: Draws the elimination mechanism, showing hydroxide taking a hydrogen and the double bond forming; States the conditions that favour substitution and those that favour elimination; Predicts the products, including which alkene isomers form when there is a choice; Explains what it means to call one species both a nucleophile and a base.

https://lightmysky.com/learn/science/elimination-and-choosing-between-two-pathways-mt_tRj_kiSS51

#### Alcohols: Classification, Oxidation and Dehydration (ages 16-17)

Primary, secondary and tertiary alcohols differ in how many carbons sit next to the one carrying the hydroxyl group, and that decides what oxidation does to each. Dehydration takes any of them back to an alkene.

Ready when they can: Classifies an alcohol as primary, secondary or tertiary from its structure; Predicts the oxidation product for each class and names the apparatus that stops the reaction at an aldehyde; Writes the dehydration of an alcohol to an alkene with the catalyst and conditions; Explains why alcohols boil far higher than alkanes of similar molecular mass.

https://lightmysky.com/learn/science/alcohols-classification-oxidation-and-dehydration-mt_FleYaf40y3

#### Aldehydes and Ketones: Nucleophilic Addition and the Tests That Separate Them (ages 17-18)

The carbonyl carbon carries a partial positive charge, so nucleophiles add across the double bond. Aldehydes oxidise further and ketones do not, which is exactly what the bench tests exploit.

Ready when they can: Draws the addition mechanism for cyanide, showing the carbonyl double bond breaking; Explains why the product of cyanide addition exists as two mirror-image forms; Predicts the result of Tollens' reagent and of Fehling's solution for an aldehyde and for a ketone; Names the reduction product of each and the reagent that gets there.

https://lightmysky.com/learn/science/aldehydes-and-ketones-nucleophilic-addition-and-the-tests-that-separate-them-mt_bVcJ0UaXk6

#### Carboxylic Acids, Esters and Hydrolysis (ages 17-18)

Carboxylic acids are weak acids that still fizz with carbonates, and with an alcohol they form an ester in a reaction that never quite finishes. Hydrolysis runs the ester back, in acid or in alkali.

Ready when they can: Writes the reactions of a carboxylic acid with a carbonate, with a metal and with an alkali; Explains why a carboxylic acid counts as weak and is still acidic enough to release carbon dioxide; Writes esterification with its catalyst and explains why the yield is limited; Compares acid hydrolysis with alkaline hydrolysis of an ester and gives a use for each.

https://lightmysky.com/learn/science/carboxylic-acids-esters-and-hydrolysis-mt_QLxUs5cOH2

#### Amines and Amides: Basicity and the Nitrogen Functional Groups (ages 17-18)

A nitrogen lone pair makes an amine basic and nucleophilic, and how available that pair is explains why some amines are far stronger bases than others. Acylating one gives an amide, the bond that later holds proteins and many polymers together.

Ready when they can: Rank primary, secondary and aromatic amines by base strength and justify the order; Give a route from a haloalkane or a nitrile to an amine and say why the product can react further; Write the formation of an amide from an acyl chloride and an amine, and explain why the amide is not basic.

https://lightmysky.com/learn/science/amines-and-amides-basicity-and-the-nitrogen-functional-groups-mt_cGP3ZJ8S6h

#### Benzene: Delocalisation and Electrophilic Substitution (ages 17-18)

Benzene's six electrons spread around the ring instead of sitting in three double bonds, which makes it much more stable than the alternative structure. That stability is why it substitutes rather than adds.

Ready when they can: Compares the enthalpy of hydrogenation of benzene with three times that of cyclohexene and says what the gap shows; Gives two further pieces of evidence against alternating double bonds, such as equal bond lengths and the failure to decolourise bromine water; Draws the mechanism for nitration, including how the electrophile is generated; Explains why the ring is restored at the end of the mechanism.

https://lightmysky.com/learn/science/benzene-delocalisation-and-electrophilic-substitution-mt_jFqF7cZ0Ij

#### Addition and Condensation Polymers (ages 17-18)

Alkenes join up by opening their double bonds and losing nothing at all, while diacids with diols or diamines join by losing a small molecule each time. What was lost decides whether the chain can be broken apart again.

Ready when they can: Draws the repeat unit of an addition polymer from its monomer, and the monomer back from the repeat unit; Draws the repeat unit of a polyester and of a polyamide and names the small molecule lost; Explains why condensation polymers can be hydrolysed while poly(alkenes) resist; Links the forces between chains to the strength and melting behaviour of a named polymer.

https://lightmysky.com/learn/science/addition-and-condensation-polymers-mt_klu208vTI1

#### Mass Spectra and Infrared: Identifying an Unknown (ages 17-18)

A mass spectrum gives the molecular mass from the molecular ion peak and hints at the structure from the fragments. An infrared spectrum shows which bonds are present by the frequencies they absorb.

Ready when they can: Reads the relative molecular mass off the molecular ion peak and accounts for the M plus 1 and M plus 2 peaks; Suggests the fragment lost from the gap between two peaks; Matches absorptions to hydroxyl, carbonyl and carbon-oxygen bonds using a data table; Combines both spectra to choose between two candidate structures.

https://lightmysky.com/learn/science/mass-spectra-and-infrared-identifying-an-unknown-mt_yotOEg9OTn

#### NMR Spectra: Counting Environments (ages 17-18)

Carbon-13 and proton NMR report how many different environments a molecule has and, for protons, how many hydrogens sit in each. Splitting patterns then say how many hydrogens are on the neighbouring carbon.

Ready when they can: Counts the carbon environments in a structure and matches the count to a carbon-13 spectrum; Uses integration to get the ratio of hydrogens in each proton environment; Applies the n plus one rule to predict or to read a splitting pattern; Explains why TMS is used as the reference and why the solvent is deuterated.

https://lightmysky.com/learn/science/nmr-spectra-counting-environments-mt_JquoiaxOMu

#### Hybridisation, Conjugation and Delocalisation in Organic Molecules (ages 18-19)

Organic structure has been drawn with lines that all look alike. This stop separates them: how orbitals mix to set geometry, when p orbitals line up to share electrons over several atoms, and what that sharing does to length, strength and reactivity.

Ready when they can: Assigns hybridisation at each carbon, nitrogen and oxygen in a drawn structure and predicts the bond angles; Identifies a conjugated system and explains why the arrangement has to be planar to work; Draws the significant resonance forms of an anion and ranks them by stability with reasons; Uses delocalisation to explain a measured bond length that lies between single and double.

https://lightmysky.com/learn/science/hybridisation-conjugation-and-delocalisation-in-organic-molecules-mt_Anv0MSQ4hq

#### Curly Arrows as the Language of Mechanism (ages 18-19)

A curly arrow is a claim about where a pair of electrons moves, not decoration on a scheme. Getting the tail, the head and the count right is what separates a mechanism that can be checked from a story.

Ready when they can: Starts every arrow at an electron source, a lone pair or a bond, and ends it where the pair arrives; Assigns formal charges before and after a step and checks that charge balances; Uses a single-headed arrow for radical steps and a double-headed arrow for pairs, without mixing them; Spots and corrects an arrow that would give an atom more bonds than it can have.

https://lightmysky.com/learn/science/curly-arrows-as-the-language-of-mechanism-mt_C0bq2Mu8HT

#### pKa as a Predictive Tool in Organic Chemistry (ages 18-19)

One tabulated number decides whether a proposed step will happen at all. Comparing the pKa of the acid formed with the acid consumed tells you which side an equilibrium sits on, and the reasons behind the numbers predict cases no table lists.

Ready when they can: Compares two pKa values to say whether a proposed proton transfer is favourable and by how many orders of magnitude; Explains an acidity difference using element, charge, hybridisation, induction and delocalisation in that order; Predicts which of several protons in a molecule is removed first and names the base strong enough to do it; Ranks the basicity of a set of nitrogen compounds and justifies the ranking.

https://lightmysky.com/learn/science/pka-as-a-predictive-tool-in-organic-chemistry-mt_fI03mNIC_m

#### Conformation: Newman Projections, Ring Strain and the Chair (ages 18-19)

Molecules with the same connectivity still differ in shape from moment to moment, and the shapes are not equally likely. Reading a molecule along a bond, or as a puckered ring, shows which arrangement it spends its time in.

Ready when they can: Draws a Newman projection for a named bond and identifies staggered and eclipsed arrangements; Sketches a rotation energy profile for butane and labels anti and gauche minima; Draws a cyclohexane chair, converts between the two chairs and tracks which positions become axial; Predicts the favoured chair for a substituted ring and explains the preference from steric interaction.

https://lightmysky.com/learn/science/conformation-newman-projections-ring-strain-and-the-chair-mt_N0_QpGF7Av

#### Chirality, R and S Assignment and Optical Activity (ages 18-20)

A carbon with four different groups makes a molecule that cannot be laid onto its mirror image. Assigning the descriptor is a fixed procedure, and the physical consequence, rotation of polarised light, is what first revealed the effect.

Ready when they can: Finds every stereocentre in a drawn structure, including ones inside rings; Applies the priority rules, including the duplication rule for double bonds, and assigns R or S with the lowest priority pointing away; Explains what a racemic mixture is and why it shows no net rotation; Calculates enantiomeric excess from a measured rotation and a known specific rotation.

https://lightmysky.com/learn/science/chirality-r-and-s-assignment-and-optical-activity-mt_-p-7uFBTDt

#### The Schrodinger Equation and What a Wavefunction Says (ages 18-19)

Orbitals have been used as pictures handed down from somewhere else. This stop names the equation those pictures solve and says what its answer, a wavefunction, does and does not tell you about an electron.

Ready when they can: States the time-independent equation as an energy statement: a kinetic term plus a potential term acting on the wavefunction returns the energy times the wavefunction; Explains why the square of the wavefunction, not the wavefunction itself, is the measurable quantity; Lists the conditions a physically acceptable wavefunction has to meet, and rejects a proposed function that breaks one; Says why an electron in an atom has no path, and what replaces the path in the quantum account.

https://lightmysky.com/learn/science/the-schrodinger-equation-and-what-a-wavefunction-says-mt_WCwbaO9rpR

#### The Particle in a Box: Where Quantised Levels Come From (ages 18-19)

The simplest bound system shows that quantisation is not an extra assumption. Fitting a wave into a fixed length forces whole numbers of half-waves, and the allowed energies follow from that alone.

Ready when they can: Applies the boundary conditions at the walls and shows why they select integer quantum numbers; Writes the energy expression and predicts how the spacing changes when the box is made longer or the particle heavier; Counts nodes for a given level and links node count to energy; Estimates an absorption wavelength for a conjugated chain treated as a box, and says why the estimate is rough.

https://lightmysky.com/learn/science/the-particle-in-a-box-where-quantised-levels-come-from-mt_rOCXlEi324

#### The Hydrogen Atom: Quantum Numbers and Orbital Shapes (ages 18-19)

One electron and one proton is the only atom the equation can be solved for exactly. Its solution produces the three spatial quantum numbers, and with them the shapes and sizes that orbital pictures have been standing in for.

Ready when they can: Says which quantum number controls energy, which controls shape and which controls orientation, and gives the allowed values of each; Reads a radial distribution plot and states where the electron is most likely to be found; Counts radial and angular nodes for a named orbital and checks the total against the principal quantum number; Explains why the hydrogen energy depends only on n while a many-electron atom breaks that pattern.

https://lightmysky.com/learn/science/the-hydrogen-atom-quantum-numbers-and-orbital-shapes-mt_zt9_eR1884

#### Many-Electron Atoms: Spin, Antisymmetry and Effective Charge (ages 18-20)

Add a second electron and the equation stops being solvable exactly. Two ideas rescue it: electrons repel each other into a screened, penetrating arrangement, and identical particles obey an exchange rule that the Pauli principle states.

Ready when they can: Explains screening and penetration and uses them to say why 4s fills before 3d in a neutral atom but ionises first; States the antisymmetry requirement and shows how the familiar orbital-filling rule follows from it; Estimates an effective nuclear charge for a valence electron and predicts a size or ionisation trend from it; Says why an orbital energy in a many-electron atom depends on both n and the shape quantum number.

https://lightmysky.com/learn/science/many-electron-atoms-spin-antisymmetry-and-effective-charge-mt_WPesw2f8T3

#### Atomic Absorption and Emission for Trace Metals (ages 19-20)

Break a sample into free atoms and each element absorbs or emits at wavelengths only it has. That makes atomic spectroscopy the standard route to metals at trace level, with the atom source doing most of the work.

Ready when they can: Explains why atomic lines are narrow while molecular bands are broad; Compares a flame and a plasma as atom sources on temperature and on the interferences each brings; Explains why a hollow cathode lamp of the same element is used as the source in absorption; Identifies a chemical or ionisation interference and states the usual fix.

https://lightmysky.com/learn/science/atomic-absorption-and-emission-for-trace-metals-mt_NfQWURds_H

#### Diastereomers, Meso Compounds and Fischer Projections (ages 19-20)

With more than one stereocentre the mirror-image rule stops being the whole story. Some pairs are mirror images and some are not, and telling them apart decides whether two samples can be separated by ordinary means.

Ready when they can: Counts the maximum number of stereoisomers for a molecule and explains when the count falls short; Classifies a pair as enantiomers or diastereomers and predicts which pair differs in melting point; Identifies a meso compound and explains why an internal mirror plane cancels the rotation; Converts between a wedge and dash drawing and a Fischer projection without losing the assignment.

https://lightmysky.com/learn/science/diastereomers-meso-compounds-and-fischer-projections-mt_1r5vCBK9zr

#### How a Chromatographic Separation Works (ages 19-20)

A mixture separates because each component divides itself differently between a moving phase and a stationary one. Retention time is the record of that division, and the plate model turns it into something that can be predicted.

Ready when they can: Defines the distribution constant and links it to retention factor and retention time; Explains why an unretained component marks the dead time and why it matters; Describes the plate model and what a plate stands for physically; Predicts the effect on retention of changing the stationary phase polarity.

https://lightmysky.com/learn/science/how-a-chromatographic-separation-works-mt_uKOPELqWzG

#### Molecular Mechanics: Force Fields and Conformational Searching (ages 19-20)

The cheapest way to model a molecule ignores electrons entirely and treats bonds as springs. It cannot describe a reaction, but it can search thousands of shapes for the one a molecule actually adopts.

Ready when they can: Names the terms of a force field and says what each is standing in for; Explains why a force field cannot model bond breaking and what that rules out; Describes a conformational search and explains why one minimisation is not enough; Judges whether a force field is appropriate for a stated problem and gives the reason.

https://lightmysky.com/learn/science/molecular-mechanics-force-fields-and-conformational-searching-mt_s4C0T3zFlf

#### Molecular Motion Quantised: The Oscillator and the Rotor (ages 19-20)

Molecules store energy in vibration and rotation as well as in electrons. Two solvable models, a spring between two masses and a rigid dumbbell, give the level patterns that every molecular spectrum is read against.

Ready when they can: Writes the vibrational level pattern as evenly spaced and the rotational pattern as widening with quantum number; Relates vibrational spacing to force constant and reduced mass, and predicts the shift on deuterium substitution; Relates rotational spacing to bond length through the moment of inertia; Explains what zero-point energy is and why a bond cannot be still even at absolute zero.

https://lightmysky.com/learn/science/molecular-motion-quantised-the-oscillator-and-the-rotor-mt_dHgi-i9pxc

#### Resolution, Efficiency and the van Deemter Curve (ages 19-20)

Two peaks are separated only if the distance between them beats their width. Width comes from three broadening processes with different dependences on flow rate, which is why every column has a best speed rather than a fastest one.

Ready when they can: Calculates resolution from retention times and peak widths and states the value needed for a clean separation; Names the three broadening contributions and says how each varies with flow rate; Reads a van Deemter curve to find the optimum flow and explains the shape at each end; Chooses between a longer column and a more selective phase to fix a stated separation, with a reason.

https://lightmysky.com/learn/science/resolution-efficiency-and-the-van-deemter-curve-mt_RUjdSb5Rgw

#### Gas Chromatography: Columns, Temperature Programming and Detectors (ages 19-20)

In gas chromatography the moving phase carries the sample and the temperature controls how long each component stays behind. Raising the temperature during a run is what lets one method handle both light and heavy components.

Ready when they can: States what limits which compounds can be run and how derivatisation extends the range; Explains why an isothermal run either loses early peaks or delays late ones, and how a programme fixes it; Compares two detectors on selectivity, sensitivity and whether the sample survives; Reads a chromatogram to identify overload or a leaking injector from the peak shapes.

https://lightmysky.com/learn/science/gas-chromatography-columns-temperature-programming-and-detectors-mt_C70HPdO2Dk

#### HPLC: Reversed Phase, Gradients and Method Development (ages 19-21)

Liquid chromatography moves the selectivity into the solvent, so the same column separates very different mixtures once the mobile phase is changed. Reversed phase, where the stationary phase is the non-polar one, is the default starting point.

Ready when they can: Explains what reversed phase means and predicts the elution order of a set of compounds on it; Describes a gradient and says which problem in an isocratic run it solves; Adjusts pH or adds a modifier to control the retention of an ionisable analyte and explains why; Works through a method development sequence and states what is changed at each stage.

https://lightmysky.com/learn/science/hplc-reversed-phase-gradients-and-method-development-mt_hlJl6nXQqT

#### Selection Rules and Why Some Transitions Never Appear (ages 19-20)

A spectrum is missing far more lines than it shows. Whether a transition appears depends on an integral over the two states and the light's interaction with the molecule, and that integral is often exactly zero.

Ready when they can: States the gross selection rule for infrared and for microwave absorption in terms of a changing dipole; Explains why homonuclear diatomics show no infrared absorption but do show Raman scattering; Applies the specific selection rules on vibrational and rotational quantum numbers to predict which lines occur; Distinguishes a forbidden transition from a weak one and gives an example of each.

https://lightmysky.com/learn/science/selection-rules-and-why-some-transitions-never-appear-mt_oJDr81W4fW

#### Character Tables and What Symmetry Predicts (ages 19-20)

A character table is a compact record of how things behave under a molecule's symmetry operations. Reading one tells you how many vibrations a molecule has, which are infrared active and which are Raman active, without solving anything.

Ready when they can: Reads a character table and states what each row and each column records; Reduces a reducible representation to its irreducible parts; Counts the vibrational modes of a small molecule and assigns each a symmetry label; Uses the table to predict infrared and Raman activity and applies the rule of mutual exclusion.

https://lightmysky.com/learn/science/character-tables-and-what-symmetry-predicts-mt_L8cTQjeKwf

#### Reading Bond Lengths and Force Constants from Spectra (ages 19-20)

Rotational and vibrational spectra are measured in wavenumbers and converted into molecular quantities. Line spacings give the moment of inertia and so the bond length; the band centre gives the force constant.

Ready when they can: Extracts the rotational constant from evenly spaced line spacings and converts it to a bond length; Converts a vibrational wavenumber into a force constant using the reduced mass; Identifies the P and R branches of a vibration-rotation band and explains the gap between them; States which measured quantity limits the precision of the derived bond length.

https://lightmysky.com/learn/science/reading-bond-lengths-and-force-constants-from-spectra-mt_5m7J1mFw68

#### Electronic Spectra, Franck-Condon and the Origin of Colour (ages 19-20)

An electronic transition happens far faster than the nuclei can move, so the molecule lands on the upper surface at the geometry it already had. That single fact explains band shapes, vibrational structure and why colour is a molecular property.

Ready when they can: States the Franck-Condon principle and draws the vertical transition on two potential energy curves; Explains why an electronic band is broad and structured rather than a single line; Links extent of conjugation to absorption wavelength and predicts the direction of a shift; Names the transition types available to a carbonyl compound and ranks their intensities.

https://lightmysky.com/learn/science/electronic-spectra-franck-condon-and-the-origin-of-colour-mt_y1hKy9nvAY

#### Stereochemistry as Mechanistic Evidence (ages 19-20)

The stereochemical outcome of a reaction is the strongest ordinary evidence about how it happened. Inversion, retention and loss of optical activity each point at a different arrangement of atoms at the moment of reaction.

Ready when they can: Explains what a planar intermediate does to the stereochemistry of a product and why; Distinguishes a stereospecific reaction from a stereoselective one with an example of each; Uses an observed inversion at a stereocentre to argue for a backside attack; States what partial racemisation with net inversion suggests about competing pathways.

https://lightmysky.com/learn/science/stereochemistry-as-mechanistic-evidence-mt_YtagP8C0Wi

#### SN1 and SN2: Kinetics, Stereochemistry and What Decides the Route (ages 19-20)

Two substitution mechanisms differ in whether the leaving group departs before or during the attack, and every observable follows from that. Substrate class, nucleophile, leaving group and solvent each push the choice one way.

Ready when they can: States the rate law each mechanism predicts and matches it to measured kinetics; Predicts the stereochemical outcome of each and explains it from the geometry of the step; Ranks primary, secondary and tertiary substrates for each route with the reason for the ranking; Explains how a polar protic solvent favours one route and a polar aprotic solvent the other.

https://lightmysky.com/learn/science/sn1-and-sn2-kinetics-stereochemistry-and-what-decides-the-route-mt_BiCjJw2eJF

#### Carbocations: Stability, Rearrangement and Neighbouring Groups (ages 19-20)

When a cation is the intermediate, it does not sit still waiting to be attacked. It can shift a hydrogen or an alkyl group to become more stable, and a group next door can reach in and take part.

Ready when they can: Ranks carbocations by stability and gives both the inductive and the hyperconjugative reason; Predicts a hydride or methyl shift and draws the product it leads to; Recognises an unexpected product as the fingerprint of a rearrangement; Explains how a neighbouring group changes the rate and the stereochemistry of a substitution.

https://lightmysky.com/learn/science/carbocations-stability-rearrangement-and-neighbouring-groups-mt_0r1d2u30PE

#### E1, E2 and E1cb: Three Ways to Lose Two Groups (ages 19-20)

Elimination has the same split as substitution, plus a third route through a carbanion. Each route sets its own requirement on geometry and on which proton is removed, so each gives a different alkene.

Ready when they can: Draws the anti-periplanar arrangement the concerted route needs and predicts which alkene it can give; Explains the Zaitsev preference and states the conditions under which the less substituted alkene wins; Identifies the substrates and bases that make the carbanion route available; Uses a ring system to show a case where the geometric requirement blocks the expected product.

https://lightmysky.com/learn/science/e1-e2-and-e1cb-three-ways-to-lose-two-groups-mt_vVq_xeZrKv

#### Substitution Against Elimination: Predicting the Major Product (ages 19-21)

Four mechanisms compete for the same substrate and the same reagent. Deciding which wins is a repeatable procedure over substrate class, base or nucleophile strength, bulk and temperature.

Ready when they can: Works through substrate class first and rules out the mechanisms it forbids; Separates nucleophile strength from base strength and uses each in the right place; Explains why a bulky base pushes a reaction towards elimination and towards the less substituted alkene; Predicts the effect of raising the temperature and gives the thermodynamic reason.

https://lightmysky.com/learn/science/substitution-against-elimination-predicting-the-major-product-mt_6WyFC9kQuu

#### Electrophilic Addition Revisited: Bridged Ions and Stereospecificity (ages 19-21)

Markovnikov's rule was a result to memorise. Once cations can be ranked, the rule becomes a prediction, and the cases where a bridged intermediate forms explain outcomes the rule alone cannot.

Ready when they can: Derives the Markovnikov outcome from the relative stability of the two possible cations; Draws a bromonium ion and uses it to explain anti addition across a double bond; Predicts the stereochemistry of halohydrin formation, including which carbon the hydroxyl lands on; Explains an anti-Markovnikov outcome by identifying the different intermediate involved.

https://lightmysky.com/learn/science/electrophilic-addition-revisited-bridged-ions-and-stereospecificity-mt_sbsBxFJyZy

#### Hydroboration, Oxidation and Cleavage of Alkenes and Alkynes (ages 19-21)

A double or triple bond is a handle for putting oxygen where you want it. Different reagents attack the same bond with different regiochemistry and different depth of oxidation, up to cutting the molecule in two.

Ready when they can: Predicts the anti-Markovnikov, syn product of hydroboration and oxidation and explains both features from the addition step; Distinguishes the products of cold dilute and hot concentrated oxidation of the same alkene; Uses ozonolysis products to work backwards to the position of the original double bond; Predicts whether an alkyne gives an aldehyde, a ketone or an acid under stated conditions.

https://lightmysky.com/learn/science/hydroboration-oxidation-and-cleavage-of-alkenes-and-alkynes-mt_Ny7vC57rqc

#### Radical Selectivity, Stability and Allylic Positions (ages 19-21)

Radicals attack whichever hydrogen is easiest to remove, and the ranking follows the same stability logic as cations. Where a double bond sits next door, the resulting radical is delocalised and dominates the product mixture.

Ready when they can: Ranks radical stability and links it to bond dissociation enthalpies; Explains why bromination is more selective than chlorination using the relative energies of the abstraction step; Predicts allylic and benzylic substitution and draws the delocalised radical that explains it; Calculates a product ratio from stated relative reactivities and the number of hydrogens of each type.

https://lightmysky.com/learn/science/radical-selectivity-stability-and-allylic-positions-mt_tgIlRLvc9x

#### Symmetry-Adapted Orbitals for Polyatomic Molecules (ages 19-20)

Building a molecular orbital diagram for more than two atoms means combining the outer atoms' orbitals into sets that match the symmetry of the central atom. Only matching sets interact, which cuts the problem down to something drawable.

Ready when they can: Forms symmetry-adapted combinations of ligand orbitals and labels them; Matches each combination with a central-atom orbital of the same label and rejects the mismatches; Builds and fills a diagram for a simple polyatomic such as water or methane; Explains what a non-bonding orbital is on the diagram and where the lone pairs went.

https://lightmysky.com/learn/science/symmetry-adapted-orbitals-for-polyatomic-molecules-mt_llEYzYuutf

#### Acid-Base Models Beyond Bronsted: Lewis, Solvents and Hard and Soft (ages 19-20)

Protons are only one way to be an acid. Widening the definition to electron pair acceptance covers metal ions, boron compounds and non-aqueous solvents, and a further split into hard and soft explains which partners actually pair up.

Ready when they can: Identifies the Lewis acid and base in a reaction where no proton moves; Classifies ions and molecules as hard or soft and predicts which pairs bind most strongly; Explains an ore's mineral form using the hard and soft preference of its metal; Applies the solvent-system definition to a named non-aqueous solvent.

https://lightmysky.com/learn/science/acid-base-models-beyond-bronsted-lewis-solvents-and-hard-and-soft-mt_jarui-9yfx

#### Coordination Compounds: Naming, Geometry and Isomerism (ages 19-20)

A complex is written and named by a strict convention that records the metal, its oxidation state, and every ligand in order. The same convention exposes the several ways two complexes can share a formula and differ.

Ready when they can: Names a complex from its formula and writes the formula back from the name; Works out the coordination number and the oxidation state of the metal for charged and neutral ligands; Draws cis and trans and fac and mer isomers for the appropriate geometries; Distinguishes linkage, ionisation and coordination isomerism with an example of each.

https://lightmysky.com/learn/science/coordination-compounds-naming-geometry-and-isomerism-mt_rkHM3jL3Ri

#### Crystal Field Theory and the Splitting of d Orbitals (ages 19-20)

Bringing charged or polar ligands up to a metal ion raises some d orbitals more than others. The size of that split explains the colour of a complex, its magnetism and part of its stability.

Ready when they can: Explains why the two sets of d orbitals separate in an octahedral field, from the direction each orbital points; Draws the splitting pattern for octahedral, tetrahedral and square planar fields and compares the gap sizes; Calculates crystal field stabilisation energy for a stated configuration; Links the gap to the wavelength absorbed and so to the colour observed.

https://lightmysky.com/learn/science/crystal-field-theory-and-the-splitting-of-d-orbitals-mt_YfIBGXj8su

#### The Spectrochemical Series, Spin State and Magnetism (ages 19-21)

Whether electrons pair up or spread out depends on which costs less, the pairing energy or the jump across the split. Ligands can be ordered by how large a split they cause, and that order predicts magnetic behaviour.

Ready when they can: Compares pairing energy with the splitting energy to assign a high or low spin configuration; Places common ligands in order of field strength and explains why the order does not follow charge; Predicts the number of unpaired electrons and converts it to a spin-only magnetic moment; Explains why tetrahedral complexes are almost always high spin.

https://lightmysky.com/learn/science/the-spectrochemical-series-spin-state-and-magnetism-mt_gfKL7W8kg-

#### What an Excited Molecule Does Next: Fluorescence and Phosphorescence (ages 19-21)

Absorption is only the first step. The excited molecule loses energy by several competing routes, and which one wins decides whether it glows at once, glows slowly, or heats its surroundings.

Ready when they can: Draws the states and arrows of a Jablonski diagram and labels radiative against non-radiative steps; Explains why fluorescence is emitted at longer wavelength than the light absorbed; Says why phosphorescence is slow and why a heavy atom in the molecule speeds it up; Predicts which of two compounds fluoresces more strongly from their rigidity and conjugation.

https://lightmysky.com/learn/science/what-an-excited-molecule-does-next-fluorescence-and-phosphorescence-mt_5AVF6uWed_

#### The Boltzmann Distribution over Molecular Levels (ages 19-21)

A sample holds an enormous number of molecules spread across the levels the quantum models produced. The Boltzmann expression says what fraction sits in each level at a given temperature, and it is where temperature enters molecular chemistry.

Ready when they can: Writes the ratio of populations of two levels in terms of their energy gap and the temperature; Calculates the fraction of molecules in the first excited vibrational state at room temperature and comments on the size; Explains why rotational levels are heavily populated while vibrational levels are barely populated at the same temperature; Uses degeneracy correctly when two levels of different degeneracy are compared.

https://lightmysky.com/learn/science/the-boltzmann-distribution-over-molecular-levels-mt_-DHIox6GBm

#### Hartree-Fock and What a Basis Set Decides (ages 20-21)

Treating electrons explicitly means solving for each one in the average field of the others, repeated until the answer stops changing. The orbitals are built from a chosen set of functions, and that choice limits the answer more than most users expect.

Ready when they can: Describes the self-consistent field cycle and says what convergence means; Explains what the mean-field approximation leaves out and names the missing energy; Compares a minimal, a split-valence and a polarised basis set on what each can describe; Says why adding diffuse functions matters for anions and for weak interactions.

https://lightmysky.com/learn/science/hartree-fock-and-what-a-basis-set-decides-mt_EYSTCPuRNx

#### Density Functional Theory and Choosing a Functional (ages 20-21)

Working with the electron density rather than the full wavefunction makes accurate calculations affordable for molecules of real size. The price is that part of the energy comes from an approximate functional, and different functionals disagree.

Ready when they can: Explains why the density is a smaller object to work with than a many-electron wavefunction; Says what the exchange-correlation functional accounts for and why it has to be approximated; Compares functional families on accuracy and cost and names what each is usually chosen for; Identifies a case where a common functional is known to fail and states the usual repair.

https://lightmysky.com/learn/science/density-functional-theory-and-choosing-a-functional-mt_mmuzLeA62V

#### Ligand Field Theory and Pi Bonding in Complexes (ages 20-21)

Treating ligands as point charges gets the pattern right and the reasons wrong. Rebuilding the same splitting from overlapping orbitals explains why carbon monoxide and cyanide sit at the strong end of the series while water and halides do not.

Ready when they can: Builds an octahedral orbital diagram from the ligand combinations and identifies where the split appears; Distinguishes pi donor from pi acceptor ligands and predicts the effect of each on the splitting; Explains the position of carbon monoxide in the series through back-donation; States what crystal field theory cannot explain and how the orbital picture repairs it.

https://lightmysky.com/learn/science/ligand-field-theory-and-pi-bonding-in-complexes-mt_Gq3JG7F7Nl

#### Electronic Spectra of Complexes and Tanabe-Sugano Diagrams (ages 20-22)

A complex often shows more than one absorption band, which a single splitting energy cannot explain. Labelling the electronic states of the whole ion, not the orbitals, gives a diagram that accounts for every band.

Ready when they can: Explains why several bands appear for one configuration and what each transition connects; Reads a Tanabe-Sugano diagram to extract the splitting energy from band positions; Distinguishes a weak d to d band from an intense charge transfer band and gives the selection-rule reason; Explains why manganate(VII) is intensely coloured although the metal has no d electrons.

https://lightmysky.com/learn/science/electronic-spectra-of-complexes-and-tanabe-sugano-diagrams-mt_GQFMqha0es

#### Nucleophilic Addition and the Tetrahedral Intermediate (ages 20-21)

The carbonyl group is polar and flat, which makes it the most attacked functional group in organic chemistry. Every reaction of it starts the same way, and what happens after the first step depends on whether the carbon carries a group that can leave.

Ready when they can: Draws the addition step with arrows and identifies the tetrahedral intermediate; Explains why aldehydes react faster than ketones using both electronic and steric arguments; Predicts whether the intermediate collapses back to a carbonyl or is protonated to an alcohol; Explains how acid catalysis and base catalysis each speed the same addition by different means.

https://lightmysky.com/learn/science/nucleophilic-addition-and-the-tetrahedral-intermediate-mt_N9Eydek3s7

#### Acetals, Imines and Protecting Groups (ages 20-21)

Adding two nucleophiles to a carbonyl and losing water gives a product that survives conditions the carbonyl would not. That is why the same reaction serves both as a route to new functional groups and as a way to hide one temporarily.

Ready when they can: Draws acetal formation from the hemiacetal onwards and explains why acid is needed at both stages; Explains how the equilibrium is driven each way by removing or adding water; Draws imine and enamine formation and states what decides which one forms; Chooses a protecting group for a stated transformation and justifies the choice of both the on and off conditions.

https://lightmysky.com/learn/science/acetals-imines-and-protecting-groups-mt_3dB99bKrMf

#### Nucleophilic Acyl Substitution and the Reactivity Ladder (ages 20-21)

When the carbonyl carbon carries a leaving group, the tetrahedral intermediate collapses forward instead of being protonated. The result is a ladder of acid derivatives on which every step can be taken downhill and none uphill.

Ready when they can: Orders acyl chlorides, anhydrides, esters and amides by reactivity and gives the electronic reason; Draws the addition then elimination sequence for a stated interconversion; Explains why an amide cannot be made into an ester directly and states what has to be done instead; Distinguishes acid and base hydrolysis of an ester by mechanism and by the fate of the product.

https://lightmysky.com/learn/science/nucleophilic-acyl-substitution-and-the-reactivity-ladder-mt_b60fq2aQ7r

#### Enols, Enolates and Alpha Substitution (ages 20-21)

A carbonyl compound has a second reactive site, the carbon next to the group, which becomes nucleophilic when a proton is removed. That flip from electrophile to nucleophile is what lets carbonyl compounds react with each other.

Ready when they can: Explains alpha acidity from delocalisation of the resulting anion onto oxygen; Draws keto and enol forms and predicts which dominates for a simple ketone and for a diketone; Chooses between a base that deprotonates completely and one that sets up a small equilibrium, with the consequence for the product; Predicts the site of alkylation or halogenation for an unsymmetrical ketone.

https://lightmysky.com/learn/science/enols-enolates-and-alpha-substitution-mt_EltcLAjnLC

#### Aldol and Claisen: Building Carbon Skeletons (ages 20-21)

Once one carbonyl compound can be made nucleophilic, it attacks another, and a new carbon to carbon bond appears. Which product forms depends on whether the electrophile can lose a group after the attack.

Ready when they can: Draws an aldol addition and the dehydration that follows it, with arrows throughout; Draws a Claisen condensation and explains why an ester gives a different outcome from a ketone; Predicts the products of a crossed reaction and states the conditions that make it useful rather than a mixture; Works backwards from an enone to the two carbonyl compounds that formed it.

https://lightmysky.com/learn/science/aldol-and-claisen-building-carbon-skeletons-mt_LYpEw4EpOX

#### Organometallic Nucleophiles: Grignard and Organolithium Reagents (ages 20-21)

Bonding carbon to a metal reverses the usual polarity and turns that carbon into a strong nucleophile. It is the most direct way to join two carbon fragments, and its weakness is that it reacts with almost anything acidic.

Ready when they can: Explains the polarity reversal from the electronegativity difference and marks the nucleophilic carbon; Predicts the alcohol formed from a stated reagent and carbonyl compound, including the double addition with esters; Explains why the reaction fails in the presence of water, alcohols or acidic protons; Chooses a protecting strategy that allows a Grignard reaction on a molecule with an acidic group.

https://lightmysky.com/learn/science/organometallic-nucleophiles-grignard-and-organolithium-reagents-mt_0X06qlyafO

#### Aromaticity: Huckel's Rule and Antiaromatic Systems (ages 20-21)

Benzene's stability is not a property of six-membered rings. It comes from a closed shell of delocalised electrons, and the same count explains stability in rings of other sizes and instability in some of them.

Ready when they can: States the conditions a ring must meet to be aromatic and tests a given structure against each; Applies the electron count to charged rings such as the cyclopentadienyl anion and the tropylium cation; Explains what antiaromatic means and why such rings distort to escape it; Identifies which lone pairs of a heterocycle count towards the delocalised system and which do not.

https://lightmysky.com/learn/science/aromaticity-huckels-rule-and-antiaromatic-systems-mt_2UmZKQozyN

#### Directing Effects in Electrophilic Aromatic Substitution (ages 20-22)

A substituted ring does not react evenly. The group already present decides both where the next one goes and how fast, and both effects come from the stability of the intermediate cation.

Ready when they can: Classifies a substituent as activating or deactivating and as ortho and para or meta directing; Draws the resonance forms of the intermediate to justify the directing outcome rather than reciting it; Explains why the halogens deactivate but still direct to ortho and para; Orders two substitutions correctly in a synthesis so that the second lands where it is wanted.

https://lightmysky.com/learn/science/directing-effects-in-electrophilic-aromatic-substitution-mt_KMRxS6s06f

#### Nucleophilic Aromatic Substitution, Diazonium Salts and Heterocycles (ages 20-22)

Rings can also be attacked by nucleophiles, but only when the intermediate anion has somewhere to put its charge. Diazonium chemistry then supplies a leaving group on a ring that nothing else can install.

Ready when they can: States what a ring needs before a nucleophile will attack it and names the intermediate; Contrasts the addition and elimination route with the benzyne route and gives the evidence that separates them; Draws the formation of a diazonium salt and lists three groups it can be replaced by; Predicts the position of attack on a named heterocycle and justifies it from the intermediate.

https://lightmysky.com/learn/science/nucleophilic-aromatic-substitution-diazonium-salts-and-heterocycles-mt_I4EtpYcrEq

#### Pericyclic Reactions: The Diels-Alder and Orbital Symmetry (ages 20-22)

Some reactions have no intermediate at all. Bonds break and form together in a ring of moving electrons, and whether that is allowed depends on whether the orbitals meeting each other have matching symmetry.

Ready when they can: Draws a Diels-Alder reaction with the diene in the required conformation and predicts the ring formed; Explains the effect of electron-donating and electron-withdrawing substituents on the rate; Predicts the stereochemistry of the adduct, including the endo preference, and explains where it comes from; Uses the symmetry of the interacting orbitals to say why a stated cycloaddition is allowed thermally but not photochemically.

https://lightmysky.com/learn/science/pericyclic-reactions-the-diels-alder-and-orbital-symmetry-mt_I4i9d6aDgD

#### The Molecular Partition Function (ages 20-21)

Summing the Boltzmann factors over every level of a molecule gives one number that counts how many levels are effectively in use. From that number the bulk properties of the sample can be calculated.

Ready when they can: Writes the partition function as a sum over levels and evaluates it for a two-level system; Sums the vibrational series as a geometric series and states the closed form; Explains what the limiting values at low and high temperature mean physically; Separates the total into translational, rotational, vibrational and electronic factors and says why the separation is allowed.

https://lightmysky.com/learn/science/the-molecular-partition-function-mt_-TPTlb7zQ2

#### Entropy from Counting: The Molecular Meaning of the Third Law (ages 20-21)

Entropy stops being a measured heat divided by a temperature and becomes a count of the arrangements a sample can adopt. The count also explains why a perfect crystal at absolute zero has none.

Ready when they can: States the Boltzmann entropy expression and applies it to a system with a known number of arrangements; Calculates the residual entropy of a disordered solid such as carbon monoxide and compares it with the measured value; Explains the third law in terms of a single accessible arrangement at absolute zero; Links a larger partition function to a larger entropy and gives the physical reason.

https://lightmysky.com/learn/science/entropy-from-counting-the-molecular-meaning-of-the-third-law-mt_ihl5fEjoLL

#### Steady-State and Pre-Equilibrium Approximations (ages 20-21)

A mechanism with a short-lived intermediate cannot be solved exactly, but two approximations turn it into an algebraic rate law. Which approximation is fair depends on how fast the intermediate is consumed.

Ready when they can: Sets the net rate of change of an intermediate to zero and eliminates it from the rate expression; Derives the rate law for the same mechanism under the pre-equilibrium assumption and compares the two results; States the condition on the rate constants under which each approximation holds; Recovers a fractional or mixed order from a proposed mechanism and matches it against measured data.

https://lightmysky.com/learn/science/steady-state-and-pre-equilibrium-approximations-mt_9ESWVl28-3

#### Chain Reactions, Branching and Explosion Limits (ages 20-21)

Some mechanisms regenerate their own reactive intermediate, so one initiation event drives many product-forming cycles. When a step makes more radicals than it consumes, the rate can run away.

Ready when they can: Labels initiation, propagation, branching and termination steps in a written mechanism; Derives a chain-reaction rate law using the steady-state approximation on the carrier; Defines chain length and calculates it from the rates of propagation and initiation; Explains the pressure limits of the hydrogen and oxygen reaction in terms of branching against wall termination.

https://lightmysky.com/learn/science/chain-reactions-branching-and-explosion-limits-mt_8SDv_5iRMu

#### Stability Constants and the Kinetics of Ligand Substitution (ages 20-21)

How tightly a ligand binds and how quickly it swaps are separate questions with separate answers. Stepwise constants measure the first, and substitution mechanisms measure the second, which is why some very stable complexes still exchange in seconds.

Ready when they can: Writes stepwise and overall stability constants and converts between them; Explains the chelate effect using entropy rather than bond strength; Distinguishes thermodynamic stability from kinetic inertness with an example of each combination; Assigns a substitution as associative or dissociative from the rate law and the effect of the entering group.

https://lightmysky.com/learn/science/stability-constants-and-the-kinetics-of-ligand-substitution-mt_XiuL697fut

#### Electron Counting and the Eighteen-Electron Rule (ages 20-21)

Organometallic compounds are stable when the metal's valence shell is full, which for a transition metal means eighteen electrons. Counting them is a bookkeeping procedure that predicts which formulas exist and which reactions are possible.

Ready when they can: Counts electrons by both the ionic and the neutral method and gets the same total; Assigns the contribution of common ligands, including bridging and multi-hapto ones; Predicts how many carbonyl ligands a given metal will carry in a neutral complex; Names classes of complex that break the rule and explains why square planar cases stop at sixteen.

https://lightmysky.com/learn/science/electron-counting-and-the-eighteen-electron-rule-mt_uab5c5pODY

#### Metals in Biology: Active Sites, Electron Transfer and Chelation (ages 20-21)

Roughly a third of proteins carry a metal, and the same crystal field and ligand arguments used for a synthetic complex explain why. Understanding the coordination environment is also how a chelating drug pulls a toxic metal out of a patient without stripping the useful ones.

Ready when they can: Relate the geometry and donor set of a metalloprotein active site to the reaction it catalyses; Explain how a protein tunes a metal's reduction potential without changing the metal; Use stability constants to argue why one chelator is selective for a target metal ion.

https://lightmysky.com/learn/science/metals-in-biology-active-sites-electron-transfer-and-chelation-mt_gKhjhRXfMU

#### Organometallic Ligands: Carbonyls, Phosphines and Hapticity (ages 20-21)

The ligands of organometallic chemistry are chosen for what they do to the metal, not just for binding. Carbon monoxide reports on electron density through its stretching frequency, phosphines are tuned by their substituents, and carbon chains can bind through several atoms at once.

Ready when they can: Explains back-donation into the carbonyl antibonding orbital and predicts the effect on its stretching frequency; Uses a measured carbonyl frequency to compare electron density at two metal centres; Assigns hapticity for alkene, allyl and cyclopentadienyl ligands and counts their electron contribution; Explains how changing a phosphine's substituents changes both its donor strength and its size.

https://lightmysky.com/learn/science/organometallic-ligands-carbonyls-phosphines-and-hapticity-mt_JXYSQDYlJ-

#### Elementary Steps of Catalysis: Oxidative Addition and Insertion (ages 20-22)

Almost every organometallic catalytic cycle is built from the same handful of steps. Each one changes the electron count and the metal's oxidation state in a fixed way, which is what makes cycles predictable.

Ready when they can: States the change in oxidation state and electron count for oxidative addition and for its reverse; Distinguishes migratory insertion from simple addition and identifies which ligand moves; Recognises beta-hydride elimination and explains what structural feature makes it possible; Explains what has to be true of a metal centre before oxidative addition can occur.

https://lightmysky.com/learn/science/elementary-steps-of-catalysis-oxidative-addition-and-insertion-mt_VVLGGh8QZ_

#### Transition State Theory and the Eyring Equation (ages 20-22)

Collision theory counts encounters and gets the size of a rate constant badly wrong. Treating the reacting pair as a species in equilibrium with the reactants, poised at the top of the barrier, gives a rate constant built from thermodynamic quantities.

Ready when they can: Writes the Eyring equation and identifies the enthalpy and entropy of activation in it; Explains what a large negative entropy of activation says about the geometry of the transition state; Compares an Arrhenius activation energy with an activation enthalpy and states how they differ; Extracts activation parameters from a plot of the appropriate function against reciprocal temperature.

https://lightmysky.com/learn/science/transition-state-theory-and-the-eyring-equation-mt_JVjDMcXds1

#### Chemical Potential and Gibbs Energy That Depends on Composition (ages 20-21)

Gibbs energy has been used as a fixed number per reaction. In a mixture it changes as the composition changes, and the partial derivative that describes it, the chemical potential, is what actually drives matter from one place or phase to another.

Ready when they can: Defines chemical potential as the change in Gibbs energy on adding a small amount of one component; Explains why matter flows from high chemical potential to low, and gives a phase-change example; Writes the composition dependence for an ideal mixture and derives the entropy of mixing from it; Shows how the equilibrium constant appears when the chemical potentials of products and reactants are set equal.

https://lightmysky.com/learn/science/chemical-potential-and-gibbs-energy-that-depends-on-composition-mt_Tdl6K-gFO3

#### Computed Geometries, Frequencies and Reaction Barriers (ages 20-22)

A calculation is run to answer a question, and the answer has to be checked. Optimising a structure, computing its vibrations and locating the point at the top of a barrier are the three jobs that make a computed mechanism worth quoting.

Ready when they can: Explains how a frequency calculation confirms that a structure is a minimum or a transition state; Compares a computed geometry with an experimental one and comments on the size of the difference; Extracts an activation barrier from computed energies and states which corrections were applied; Says why a single-point energy on a poor geometry is not worth reporting.

https://lightmysky.com/learn/science/computed-geometries-frequencies-and-reaction-barriers-mt_pdiFjK2wPe

#### Real Gases, Fugacity and Activity (ages 20-21)

Every thermodynamic expression so far assumed ideal behaviour. Fugacity and activity are the corrected quantities that keep the same equations working for real gases and real solutions.

Ready when they can: Reads a compression factor plot and says where attraction dominates and where repulsion does; Explains what each term of the van der Waals equation is correcting; Defines fugacity as an effective pressure and activity as an effective concentration, and states the standard state each refers to; Says which measurements go wrong if activities are replaced by concentrations in a concentrated solution.

https://lightmysky.com/learn/science/real-gases-fugacity-and-activity-mt_HzRqV-KXfN

#### Phase Diagrams, the Clapeyron Equation and the Phase Rule (ages 20-22)

A phase boundary is a line where two chemical potentials are equal. Setting them equal gives an equation for the slope of the line, and counting the constraints gives the number of variables that can still be changed freely.

Ready when they can: Reads a one-component phase diagram and names the triple point and critical point; Derives the slope of a boundary from equal chemical potentials and explains the unusual slope for water; Applies the Clausius-Clapeyron form to find an enthalpy of vaporisation from vapour pressure data; Uses the phase rule to say how many variables are free in a stated system.

https://lightmysky.com/learn/science/phase-diagrams-the-clapeyron-equation-and-the-phase-rule-mt_U-zj6r4WFM

#### Ideal and Real Solutions: Raoult, Henry and Excess Functions (ages 20-22)

A solution is ideal when every molecule feels the same neighbours it felt in the pure liquid. Two limiting laws describe the ends of that range, and the gap between measured and ideal behaviour is what excess functions record.

Ready when they can: Applies Raoult's law to a solvent and Henry's law to a dilute solute, and says which applies where; Reads a vapour pressure against composition plot and identifies positive or negative deviation; Links the sign of the deviation to the relative strength of the interactions involved; Explains why an azeotrope cannot be separated by simple distillation.

https://lightmysky.com/learn/science/ideal-and-real-solutions-raoult-henry-and-excess-functions-mt_DRHoU0yg3Z

#### Electrolyte Solutions and the Debye-Huckel Limiting Law (ages 20-22)

Ions in solution do not behave independently because each one gathers an atmosphere of opposite charge around it. That atmosphere lowers the effective concentration, and the limiting law predicts by how much.

Ready when they can: Calculates ionic strength for a mixed electrolyte and explains why charge is squared in it; Applies the limiting law to obtain a mean activity coefficient and states its range of validity; Explains why a measured pH drifts from the calculated value as salt is added; Says why single-ion activities cannot be measured and what is quoted instead.

https://lightmysky.com/learn/science/electrolyte-solutions-and-the-debye-huckel-limiting-law-mt_6wAcvWy0dv

#### Catalytic Cycles: Hydroformylation and Cross-Coupling (ages 21-22)

Chaining the elementary steps into a closed loop turns a metal complex into a catalyst that runs indefinitely. Reading a cycle means checking that every intermediate has a sensible count and that the loop closes back on the starting species.

Ready when they can: Traces a full cycle and names each elementary step in turn; Checks the electron count and oxidation state at every intermediate around the loop; Identifies the turnover-limiting step and explains what would raise the rate; Explains how ligand choice steers the selectivity of the product in a stated cycle.

https://lightmysky.com/learn/science/catalytic-cycles-hydroformylation-and-cross-coupling-mt_FmsXXdFRNC

#### Close Packing, Unit Cells and Ionic Lattice Types (ages 21-22)

A crystal is one small block repeated. Choosing that block, counting what it contains and finding where the holes are explains structure types, densities and why a given pair of ions adopts one arrangement rather than another.

Ready when they can: Counts atoms per unit cell for the cubic types and calculates a density from cell dimensions; Distinguishes hexagonal from cubic close packing by their stacking sequence; Locates tetrahedral and octahedral holes and links occupancy to a named structure type; Uses a radius ratio to predict a coordination number and states where the prediction fails.

https://lightmysky.com/learn/science/close-packing-unit-cells-and-ionic-lattice-types-mt_LzpVzwrDm3

#### Band Theory, Defects and Why Some Solids Conduct (ages 21-22)

Combining orbitals from a very large number of atoms produces bands rather than levels. Whether a band is full, empty or partly filled decides whether a solid is a metal, a semiconductor or an insulator, and small defects shift the answer.

Ready when they can: Explains how discrete orbitals become a band as the number of atoms grows; Uses band filling and gap size to classify a metal, a semiconductor and an insulator; Explains n-type and p-type doping in terms of where the extra levels appear; Links a point defect or a non-stoichiometric composition to ionic conductivity or to colour.

https://lightmysky.com/learn/science/band-theory-defects-and-why-some-solids-conduct-mt_RuPWyBzGOp

#### Retrosynthesis: Disconnections and Synthons (ages 21-22)

Planning a synthesis runs backwards from the target. Each disconnection is a bond you break on paper, chosen because a real reaction can make it, and the fragments it leaves tell you what starting materials to look for.

Ready when they can: Marks a disconnection on a target and names the reaction that would make that bond forwards; Converts a pair of synthons into real reagents with the right polarity at each carbon; Recognises a carbonyl compound as a two-carbon or three-carbon disconnection point and uses it; Compares two routes to the same target and argues for one on step count and available starting materials.

https://lightmysky.com/learn/science/retrosynthesis-disconnections-and-synthons-mt_0EJbkDPo2P

#### Planning a Multi-Step Synthesis: Order, Protection and Yield (ages 21-22)

A route that works on paper can still fail in a flask. Order of steps, groups that need hiding, and the way yields multiply decide whether a plan is worth running.

Ready when they can: Orders steps so that each reagent meets only the groups it tolerates; Inserts protection and deprotection where a reagent would otherwise attack the wrong site; Multiplies stage yields to get an overall figure and argues for a shorter route on that basis; Identifies the step most likely to fail on scale and proposes an alternative.

https://lightmysky.com/learn/science/planning-a-multi-step-synthesis-order-protection-and-yield-mt_3PYRELbNfu

#### Green Chemistry Metrics: Atom Economy, E-Factor and Solvent Choice (ages 20-21)

Percentage yield hides how much material a route throws away. Atom economy counts what ends up in the product on paper, the E-factor counts the waste actually produced, and solvent usually dominates both.

Ready when they can: Calculates atom economy from a balanced equation and contrasts it with percentage yield; Calculates an E-factor for a stated procedure and identifies the largest contributor; Compares an addition route with a substitution route on atom economy and explains the difference; Ranks candidate solvents on hazard, recovery and disposal for a stated reaction.

https://lightmysky.com/learn/science/green-chemistry-metrics-atom-economy-e-factor-and-solvent-choice-mt_sxO1hLpaUV

#### Carbohydrates: Anomers, Mutarotation and the Glycosidic Bond (ages 21-22)

Sugars are polyhydroxy carbonyl compounds that close onto themselves. The ring form is a cyclic hemiacetal, which explains the new stereocentre, the slow change in rotation on dissolving, and how sugars link into chains.

Ready when they can: Converts an open-chain sugar into its ring form and identifies the anomeric carbon; Explains mutarotation as an equilibrium through the open form and predicts the favoured anomer; Explains why a glycosidic bond is an acetal and why that makes it stable to base but not to acid; Distinguishes reducing from non-reducing sugars and links the difference to the free anomeric centre.

https://lightmysky.com/learn/science/carbohydrates-anomers-mutarotation-and-the-glycosidic-bond-mt_XpSBU8b0HN

#### Amino Acids and Peptides: Zwitterions and the Peptide Bond (ages 21-22)

An amino acid carries an acid and a base in one molecule, so in water it exists as an ion with charges at both ends. How those charges vary with pH sets its behaviour, and joining two of them makes a bond with unusual rigidity.

Ready when they can: Draws the dominant form of an amino acid at a stated pH and calculates its isoelectric point from the pKa values; Explains why the peptide bond is planar using delocalisation and predicts the preferred geometry; Explains why peptide synthesis needs both activation and protection, and where each is applied; Predicts the direction an amino acid moves during electrophoresis at a given pH.

https://lightmysky.com/learn/science/amino-acids-and-peptides-zwitterions-and-the-peptide-bond-mt_cXdg1yjq-n

#### Ion Exchange and Electrophoretic Separations (ages 20-21)

Charged species need a separation that works on charge. Ion exchange holds them on an oppositely charged phase and releases them with a competing ion, while electrophoresis moves them through a gel or a capillary under a field.

Ready when they can: Explains how an ion exchange resin retains an analyte and what an eluent competes for; Predicts how changing pH changes the retention of a weak acid on an exchanger; Explains what sets electrophoretic mobility and why size and charge both appear in it; Describes how a suppressor makes conductivity detection possible in ion chromatography.

https://lightmysky.com/learn/science/ion-exchange-and-electrophoretic-separations-mt_6xaiivXbAd

#### Mass Spectrometry: Ionisation Methods and Mass Analysers (ages 20-21)

A mass spectrometer has to make an ion, sort it by mass to charge ratio and count it. The choice of ionisation decides whether the molecule survives, and the choice of analyser decides how finely the sorting is done.

Ready when they can: Compares a hard and a soft ionisation method by what appears in the spectrum; Explains how a quadrupole, a time of flight and a magnetic sector each separate ions; Defines resolving power and says what it lets an analyst distinguish; Explains why multiply charged ions extend the mass range of an instrument.

https://lightmysky.com/learn/science/mass-spectrometry-ionisation-methods-and-mass-analysers-mt_JTTb7FM1L4

#### Accurate Mass and Isotope Patterns as Formula Evidence (ages 20-21)

Measured to enough decimal places, a mass belongs to only one molecular formula, because nuclides do not have whole-number masses. Isotope peak patterns add a second, independent check on which elements are present.

Ready when they can: Uses an accurate mass to choose between candidate formulas of the same nominal mass; Applies the rings and double bonds calculation to a candidate formula; Reads an isotope pattern to count chlorine, bromine or sulfur atoms; Applies the nitrogen rule and states when it holds.

https://lightmysky.com/learn/science/accurate-mass-and-isotope-patterns-as-formula-evidence-mt_68vjdAPNrc

#### Hyphenated Techniques: GC-MS, LC-MS and Tandem Fragmentation (ages 20-22)

Joining a separation to a mass spectrometer gives every peak in the chromatogram its own spectrum. Selecting one ion and breaking it again gives a second dimension of evidence, which is what makes trace work in dirty samples possible.

Ready when they can: Explains what an interface has to do to join a liquid separation to a vacuum instrument; Distinguishes a total ion chromatogram from an extracted ion chromatogram and says when each is used; Describes precursor selection and product scanning in a tandem experiment; Explains why selected reaction monitoring gives such low detection limits in a complex matrix.

https://lightmysky.com/learn/science/hyphenated-techniques-gc-ms-lc-ms-and-tandem-fragmentation-mt_wmKqp8HyTL

#### Reading a Proton NMR Spectrum: Shift, Integration and Multiplicity (ages 20-21)

Counting environments was the first step. A full reading uses where each signal sits, how many protons it represents and how it is split, and the three together usually fix the structure.

Ready when they can: Relates chemical shift to the electron density around a proton and predicts the shift for a named environment; Converts relative integrals into proton counts consistent with the molecular formula; Applies the splitting rule to predict a pattern and reads a pattern back to a neighbour count; Recognises exchangeable protons and explains what a deuterium oxide shake proves.

https://lightmysky.com/learn/science/reading-a-proton-nmr-spectrum-shift-integration-and-multiplicity-mt_WgxqHHf-YL

#### Carbon-13, DEPT and Coupling Constants (ages 20-21)

The carbon spectrum shows the skeleton directly, and an editing experiment says how many hydrogens sit on each carbon. Coupling constants, read carefully, then report on geometry rather than just on neighbours.

Ready when they can: Explains why a routine carbon spectrum shows singlets and why the integrals are not reliable; Reads a DEPT experiment to classify each carbon by the number of attached protons; Extracts a coupling constant in hertz and uses its size to argue for cis or trans geometry; Combines carbon and proton evidence to distinguish two candidate structures.

https://lightmysky.com/learn/science/carbon-13-dept-and-coupling-constants-mt_9K6GkAkqq1

#### Designing a Safer Process: Hazard, Scale and Waste (ages 21-22)

A reaction that is routine in a flask can be dangerous in a reactor, because heat and pressure do not scale the way volume does. Designing for scale means choosing reagents and conditions with the failure case in mind.

Ready when they can: Reads a safety data sheet and translates its entries into decisions about handling and containment; Explains why heat removal gets harder as a vessel grows and what that means for an exothermic step; Replaces a hazardous reagent or solvent in a stated route and defends the substitution; Identifies where a waste stream leaves a process and proposes a way to recover or reduce it.

https://lightmysky.com/learn/science/designing-a-safer-process-hazard-scale-and-waste-mt_5zhSYCYU_o

#### The Nernst Equation and Cells Away from Standard Conditions (ages 21-22)

A tabulated electrode potential applies only at one set of concentrations. The Nernst equation converts it to any composition, which turns a cell into an instrument for measuring concentration.

Ready when they can: Writes the reaction quotient for a cell reaction and substitutes it into the Nernst equation with the right electron count; Calculates the potential of a concentration cell and explains why it is not zero; Converts a standard cell potential into an equilibrium constant and states the link to Gibbs energy; Explains why the quotient should strictly contain activities and when the concentration form is good enough.

https://lightmysky.com/learn/science/the-nernst-equation-and-cells-away-from-standard-conditions-mt_yqmRqDaadR

#### Electrode Kinetics: Exchange Current and Overpotential (ages 21-22)

Thermodynamics says which way a cell reaction goes but not how fast, and the gap between the two is why an electrolysis needs more voltage than the calculation predicts. Overpotential is that gap, and it depends on the electrode material.

Ready when they can: Defines exchange current density and explains what a large value says about an electrode reaction; Explains overpotential as a kinetic cost and gives the reason platinum and mercury differ for hydrogen evolution; Reads a current against potential curve and identifies the kinetically controlled and diffusion-limited regions; Uses overpotential to explain a product of electrolysis that thermodynamics alone would not predict.

https://lightmysky.com/learn/science/electrode-kinetics-exchange-current-and-overpotential-mt__z7Y780pyo

#### Two-Dimensional NMR and Assigning a Whole Structure (ages 21-22)

A two-dimensional experiment shows which signals are connected rather than only where they sit. Using two or three of them together, a structure can be assigned atom by atom instead of guessed and checked.

Ready when they can: Reads a COSY map to trace a chain of coupled protons; Uses a one-bond correlation experiment to attach each proton to its own carbon; Uses a long-range correlation experiment to join fragments across a quaternary carbon; Assembles the evidence from several spectra into one assigned structure and states the weakest link in the argument.

https://lightmysky.com/learn/science/two-dimensional-nmr-and-assigning-a-whole-structure-mt_UEC4dilKT9

#### Potentiometry, Ion-Selective Electrodes and Voltammetry (ages 21-22)

An electrode can be a sensor as well as a site of reaction. Measuring its potential at near zero current reports concentration, while sweeping the potential and recording current reports both what is present and how it reacts.

Ready when they can: Explains how a glass electrode develops a potential that tracks pH and why a reference electrode is needed; Calibrates an ion-selective electrode and applies a selectivity coefficient to assess an interference; Reads a cyclic voltammogram and identifies a reversible couple from peak separation and peak ratio; Explains why stripping methods reach such low detection limits.

https://lightmysky.com/learn/science/potentiometry-ion-selective-electrodes-and-voltammetry-mt_7sLJXqFfWR

#### Method Validation: Accuracy, Precision, Recovery and Robustness (ages 21-22)

A method is not finished when it produces numbers. Validation is the evidence that the numbers are right, repeatable by someone else, unaffected by small changes, and correct on a sample of known content.

Ready when they can: Separates accuracy from precision and names the experiment that tests each; Designs a spike and recovery experiment and states what a recovery outside the accepted range implies; Distinguishes repeatability from reproducibility and explains why both are reported; Plans a robustness check by varying one method parameter at a time and reading the effect.

https://lightmysky.com/learn/science/method-validation-accuracy-precision-recovery-and-robustness-mt_ihmF2fl4OC

#### Reading a Paper and Its Supporting Information (ages 22-23)

The claim is in the paper and the evidence is usually in the supporting information. Reading well means checking the procedure, the characterisation and the controls against the claim, and noticing what has been left out.

Ready when they can: Extracts the central claim of a paper and lists what would have to be true for it to hold; Checks reported characterisation against the structure that was claimed; Identifies a missing control and says what alternative explanation it would have excluded; Separates what the data show from what the discussion asserts.

https://lightmysky.com/learn/science/reading-a-paper-and-its-supporting-information-mt_8t32DdAY44

#### Searching the Chemical Literature by Structure and by Reaction (ages 22-23)

Chemical searching is not keyword searching. A structure or substructure query finds compounds regardless of what they were called, and a reaction query finds precedent for a transformation, which is what tells you whether a planned step has ever worked.

Ready when they can: Turns a planned step into a reaction query with the right level of generality; Uses a substructure search to find precedent for a scaffold and narrows it sensibly; Traces a reported procedure back from a review to the paper that first published it; Judges whether a hit is real precedent or a superficially similar case.

https://lightmysky.com/learn/science/searching-the-chemical-literature-by-structure-and-by-reaction-mt_7vkNiUQ2uw

#### Characterisation Standards: What Counts as Proof of a New Compound (ages 22-24)

Reporting a new compound carries an evidential standard that the field agrees on: spectra that fit, a formula confirmed by mass or elemental analysis, and purity shown rather than asserted. Falling short of it is what makes results hard to repeat.

Ready when they can: Lists the data a new compound needs and says what each item rules out; Judges a purity claim against the method used to support it; Explains why an isolated yield reported without characterisation is not a result; Writes a procedure at the level of detail another group would need to repeat it.

https://lightmysky.com/learn/science/characterisation-standards-what-counts-as-proof-of-a-new-compound-mt_WKhYUq-eyd

#### Solid-State Synthesis: Controlling Phase, Defect and Dopant (ages 22-23)

Making a solid with a wanted property is mostly about which phase forms and what sits on the wrong site. Temperature, atmosphere and the route chosen decide both, and a dopant introduced on purpose is a defect used as a control.

Ready when they can: Chooses between a high-temperature ceramic route and a solution route for a stated target; Explains how oxygen partial pressure during firing changes the defect population; Predicts what substituting a lower-valent cation does to carrier concentration; Uses a powder diffraction pattern to say whether the wanted phase was obtained.

https://lightmysky.com/learn/science/solid-state-synthesis-controlling-phase-defect-and-dopant-mt_5gri5iZ0lV

#### Porous Frameworks: Zeolites, Metal-Organic Frameworks and What They Hold (ages 22-23)

Build a solid out of nodes and linkers and the empty space becomes the useful part. Pore size and the chemistry of the internal surface decide which guest goes in, how strongly it is held and whether the framework survives its removal.

Ready when they can: Predicts the topology a given node geometry and linker length would produce; Reads an adsorption isotherm and extracts pore volume and binding strength; Explains why some frameworks collapse when the solvent is removed and how that is avoided; Matches a separation or storage problem to a framework property that would address it.

https://lightmysky.com/learn/science/porous-frameworks-zeolites-metal-organic-frameworks-and-what-they-hold-mt_csqPeYIhN6

#### Chain Growth and Step Growth: Two Routes to a Polymer (ages 22-24)

Both routes end with long chains, but they get there differently. Chain growth builds full-length molecules from the start at active centres, while step growth couples everything with everything, so molar mass only climbs at very high conversion.

Ready when they can: Sketches how molar mass changes with conversion for each mechanism; Calculates degree of polymerisation from conversion for a step-growth reaction; Explains why a small excess of one monomer caps the achievable chain length; Reads a dispersity value and says what it implies about how the chains were made.

https://lightmysky.com/learn/science/chain-growth-and-step-growth-two-routes-to-a-polymer-mt_LADBgarlKs

#### Strategy in Retrosynthesis: Strategic Bonds and Convergent Routes (ages 22-23)

A target with several rings and stereocentres offers more disconnections than anyone can evaluate one at a time. Strategy narrows the field: cut the bonds that simplify the skeleton most, and arrange the route so that fragments of similar size meet late.

Ready when they can: Ranks candidate disconnections by how much skeletal simplification each one buys; Rewrites a linear route as a convergent one and compares the overall yield of the two; Uses a symmetry element in the target to cut the number of distinct steps; Names the functional group interconversion that opens a disconnection which is otherwise blocked.

https://lightmysky.com/learn/science/strategy-in-retrosynthesis-strategic-bonds-and-convergent-routes-mt_9ZRKVbdP72

#### Protecting Group Strategy: Orthogonality and the Order of Removal (ages 22-23)

On a molecule with three reactive groups, protection stops being a single decision and becomes a schedule. Orthogonal sets can be removed in any order under conditions that leave the others untouched, which is what lets a long route stay flexible.

Ready when they can: Selects an orthogonal pair of protecting groups for two hydroxyls that must be freed at different points; Reads a deprotection condition and says which other groups in the molecule would not survive it; Places protection and deprotection steps in a route so that no step is wasted; Explains what a global deprotection at the end costs in yield and why it is still often chosen.

https://lightmysky.com/learn/science/protecting-group-strategy-orthogonality-and-the-order-of-removal-mt_-TvfTGZ-_Z

#### Structure Elucidation from a Complete Data Set (ages 22-23)

In practice a structure is settled by several techniques at once, not one. Working from a molecular formula, an infrared spectrum and a full set of nuclear magnetic resonance experiments, each piece of evidence removes candidates until one structure survives.

Ready when they can: Derives degrees of unsaturation from an accurate mass formula and states what they permit; Orders the available experiments so that the cheapest evidence is used first; Builds fragments from correlation data and connects them into a single candidate; States which experiment would settle a remaining ambiguity and why.

https://lightmysky.com/learn/science/structure-elucidation-from-a-complete-data-set-mt_O2uungksMZ

#### Nuclear Magnetic Resonance Past Assignment: Relaxation, the Nuclear Overhauser Effect and Exchange (ages 22-23)

Once peaks are assigned, the same experiment reports on motion and distance. Relaxation times track how a molecule tumbles, cross-relaxation between nearby nuclei measures separation in space, and a line that broadens with temperature is a process happening on the timescale of the measurement.

Ready when they can: Explains what a short longitudinal relaxation time says about the environment of a nucleus; Uses a through-space enhancement to decide between two stereochemical assignments; Reads a set of variable-temperature spectra and extracts the barrier to an exchange process; Says why an experiment that fails at one field strength can succeed at another.

https://lightmysky.com/learn/science/nuclear-magnetic-resonance-past-assignment-relaxation-the-nuclear-overhauser-effect-and-exchange-mt_dCV2EbNlF2

#### Reducible Representations and Predicting Infrared and Raman Activity (ages 22-23)

Take the motions of a molecule as a basis, work out the characters of that basis under each symmetry operation, and reduce it into irreducible labels. The labels say directly which vibrations absorb infrared light and which scatter it.

Ready when they can: Builds the reducible representation for a chosen basis by counting unshifted contributions; Applies the reduction formula and subtracts translation and rotation to leave the vibrations; Assigns each remaining label as infrared active, Raman active, both or neither; Uses the predicted band count to choose between two candidate geometries.

https://lightmysky.com/learn/science/reducible-representations-and-predicting-infrared-and-raman-activity-mt_DP4JfkS6c0

#### Choosing Between Vibrational Methods: Infrared, Raman and Resonance Raman (ages 22-24)

Infrared absorption and Raman scattering see different motions and suit different samples. Tuning the laser onto an electronic absorption picks out only the vibrations coupled to that transition, which turns a crowded spectrum into a short list.

Ready when they can: Matches a sample type, including aqueous samples, to the vibrational technique that suits it; Explains why a symmetric stretch can be strong in one method and absent in the other; Says which vibrations are enhanced when the excitation lands on an electronic band, and why; Chooses a technique for a stated problem and defends the choice against one alternative.

https://lightmysky.com/learn/science/choosing-between-vibrational-methods-infrared-raman-and-resonance-raman-mt_YxLAvBIBAR

#### Single-Crystal Diffraction: From Reflections to a Refined Structure (ages 22-24)

A crystal gives intensities, not a picture. Turning them into atomic positions means finding the unit cell and space group, solving the phase problem, then refining a model until it accounts for the measured data within its uncertainty.

Ready when they can: Derives the unit cell and candidate space group from systematic absences; States what the phase problem is and how a solution method gets around it; Reads refinement statistics and displacement parameters and says whether the model is sound; Names two ways a structure can be wrong even when the refinement statistics look acceptable.

https://lightmysky.com/learn/science/single-crystal-diffraction-from-reflections-to-a-refined-structure-mt_7PjfoEu-WE

#### Substrate Control of Stereochemistry: Models for Facial Selectivity (ages 22-23)

When a reagent attacks a carbonyl next to an existing stereocentre, one face is easier to reach than the other. Which face wins is predicted by a small set of conformational models, and each model states the assumption it rests on.

Ready when they can: Applies the standard open-chain model to predict the major diastereomer from an alpha-substituted aldehyde; Says when a chelating metal changes the preferred conformation and reverses the outcome; Predicts attack direction on a rigid ring from axial and equatorial approach arguments; Names an experiment whose result would distinguish two competing facial models.

https://lightmysky.com/learn/science/substrate-control-of-stereochemistry-models-for-facial-selectivity-mt_qLBmyLq2ZU

#### Asymmetric Catalysis: Where Enantioselectivity Comes From (ages 22-23)

A chiral catalyst turns two mirror-image pathways into two diastereomeric transition states with different energies. A gap of about ten kilojoules per mole is enough for high enantiomeric excess, which is why small changes to a ligand matter so much.

Ready when they can: Converts an enantiomeric excess into a transition-state energy difference and back; Explains why raising the temperature usually lowers selectivity in a catalytic asymmetric reaction; Identifies the part of a chiral ligand that blocks one approach and says what changing it would do; Distinguishes a catalyst that sets stereochemistry from a chiral auxiliary that is consumed.

https://lightmysky.com/learn/science/asymmetric-catalysis-where-enantioselectivity-comes-from-mt_vFpTH27iHP

#### Organocatalysis: Enamine and Iminium Activation (ages 22-23)

A secondary amine condenses with a carbonyl and changes what that carbon can do: as an enamine it becomes nucleophilic, as an iminium ion it becomes more electrophilic. A chiral amine does both while holding one face of the intermediate shielded.

Ready when they can: Draws the enamine and iminium intermediates from a given amine and carbonyl and says which one activates which position; Predicts the sense of induction from the substituent that blocks one face of the intermediate; Explains why the catalyst is released unchanged and what makes turnover fast enough to matter; Compares an organocatalytic route with a metal-catalysed one on cost, air sensitivity and metal residue.

https://lightmysky.com/learn/science/organocatalysis-enamine-and-iminium-activation-mt_E3lmwAFuIO

#### Cross-Coupling in Practice: Choosing Ligand, Base and Conditions (ages 22-24)

The catalytic cycle of a cross-coupling is settled chemistry; getting one to work on a real substrate is not. Ligand bite angle and bulk, base strength, solvent and the choice of precatalyst decide whether the slow step turns over at all.

Ready when they can: Matches a coupling partner class to a coupling reaction and states why that partner suits it; Explains what a bulky electron-rich phosphine does to oxidative addition and to reductive elimination; Diagnoses a failed coupling from the recovered material and proposes the next condition to try; Says why a defined precatalyst often beats mixing metal source and ligand in the flask.

https://lightmysky.com/learn/science/cross-coupling-in-practice-choosing-ligand-base-and-conditions-mt_y2vF6EDb2X

#### Controlled Radical Polymerisation and Block Architecture (ages 23-24)

Ordinary radical polymerisation gives chains of many lengths because termination is fast and random. Holding most chains in a dormant state keeps them alive and growing together, which makes narrow distributions and block sequences possible.

Ready when they can: Explains how a dormant-active equilibrium suppresses termination without stopping growth; Predicts the dispersity and molar mass expected from an initiator-to-monomer ratio; Designs a two-stage addition that produces a block copolymer and says when to add the second monomer; Names a symptom in the data that shows control was lost partway through.

https://lightmysky.com/learn/science/controlled-radical-polymerisation-and-block-architecture-mt_nQKYR0yEEs

#### Electron Correlation and Methods Past Hartree-Fock (ages 23-24)

Hartree-Fock lets every electron feel an average of the others, so it misses the way they avoid each other. Recovering that missing energy is what perturbation and coupled-cluster methods do, at a cost that climbs steeply with system size.

Ready when they can: States what correlation energy is in terms of the approximation that omits it; Ranks a set of methods by cost scaling and by expected accuracy; Explains why a bond being broken needs a different treatment from a molecule at equilibrium; Chooses a method for a stated system and says what error it will still carry.

https://lightmysky.com/learn/science/electron-correlation-and-methods-past-hartree-fock-mt_3F5B8V7CGb

#### Excited States by Calculation and Simulated Electronic Spectra (ages 23-24)

Predicting where a molecule absorbs means treating a state that is not the ground state. Time-dependent methods give excitation energies and intensities cheaply, but they fail in known ways, and recognising those failures is part of using them.

Ready when they can: Reads computed excitation energies and oscillator strengths into a predicted spectrum; Identifies which orbitals a transition involves from the computed contributions; Names a class of excitation that common functionals describe badly and says why; Compares a computed band position with an experimental one and accounts for the difference.

https://lightmysky.com/learn/science/excited-states-by-calculation-and-simulated-electronic-spectra-mt_DsZ3wfCRkX

#### Functionalising a Carbon-Hydrogen Bond Without a Handle (ages 23-24)

Classical routes need a leaving group or a halide already in place. Direct functionalisation works on a carbon-hydrogen bond instead, and the problem becomes selectivity, usually solved by a directing group that holds the metal near one position.

Ready when they can: Explains why selectivity, not reactivity, is the hard part when every position carries a similar bond; Predicts which position a stated directing group would activate and draws the metallacycle it forms; Compares a directed route with a route that installs a halide first, on step count and waste; Names a case where sterics rather than a directing group decides the site.

https://lightmysky.com/learn/science/functionalising-a-carbon-hydrogen-bond-without-a-handle-mt_j0LaIeS2VP

#### Glass Transition, Crystallinity and Entanglement in Polymers (ages 23-24)

A polymer sample is not one thing: parts of it can be ordered, the rest frozen or rubbery depending on temperature. Chain stiffness, side groups and length above the entanglement threshold decide which, and that is what the material feels like.

Ready when they can: Explains what changes at the glass transition and why it is not a first-order transition; Predicts how a bulky side group or a polar backbone shifts the transition temperature; Relates the entanglement molar mass to the jump in melt viscosity above it; Reads a thermal trace and identifies glass transition, crystallisation and melting.

https://lightmysky.com/learn/science/glass-transition-crystallinity-and-entanglement-in-polymers-mt_vGEYO5ILqt

#### Molecular Recognition: Preorganisation, Complementarity and Binding Constants (ages 23-24)

Strong binding between two molecules comes from many weak contacts arranged to fit. A host that already holds the right shape pays less entropy on binding, which is why preorganisation shows up directly in the measured constant.

Ready when they can: Splits a measured binding free energy into enthalpic and entropic parts and interprets each; Explains why a macrocyclic host binds more strongly than its open-chain analogue; Designs a change to a host that would raise selectivity between two similar guests; Chooses a titration method suited to a stated binding strength and explains the limit.

https://lightmysky.com/learn/science/molecular-recognition-preorganisation-complementarity-and-binding-constants-mt_Ub84WUj1Gg

#### Olefin Metathesis and Ring-Closing Strategy (ages 23-24)

Metathesis exchanges the ends of two alkenes through a metallacyclobutane, and the equilibrium is usually driven by loss of a small volatile alkene. That single reaction turns a long diene into a ring, which changes how a synthesis is planned.

Ready when they can: Draws the metallacyclobutane and shows how it accounts for the exchanged fragments; Predicts the ring formed from a stated diene and names what drives the reaction forwards; Explains why high dilution favours ring closing over chain extension; Chooses between a metathesis disconnection and a carbonyl disconnection for a macrocyclic target.

https://lightmysky.com/learn/science/olefin-metathesis-and-ring-closing-strategy-mt_J9UAxKsgSk

#### Photoredox and Electrochemical Routes to Radical Intermediates (ages 23-24)

A single electron transfer makes an intermediate that two-electron chemistry cannot reach. Light absorbed by a photocatalyst and a controlled electrode potential are two ways to supply that electron, and both give the chemist a dial for how hard to push.

Ready when they can: Reads an excited-state reduction potential and predicts whether a given substrate will accept an electron; Distinguishes an oxidative quenching cycle from a reductive one on the order of the steps; Explains why an electrochemical version can replace a stoichiometric oxidant and what that saves; Names the side reaction that limits radical chemistry at high concentration.

https://lightmysky.com/learn/science/photoredox-and-electrochemical-routes-to-radical-intermediates-mt_YhqzHGcx31

#### Putting the Solvent Into a Calculation (ages 23-24)

A gas-phase result can be wrong by tens of kilojoules per mole for a charged species. A continuum treats the solvent as a polarisable medium and is cheap; explicit molecules are needed when specific interactions such as hydrogen bonds do real work.

Ready when they can: Explains what a continuum model represents and what it cannot represent; Decides when explicit solvent molecules must be included and how many; Compares computed and measured solvation energies for an ion and accounts for the gap; Says how solvent choice changes a computed reaction barrier and in which direction.

https://lightmysky.com/learn/science/putting-the-solvent-into-a-calculation-mt_3SCFfcvoei

#### Molecular Dynamics and Free Energy from Sampling (ages 23-24)

Integrating the equations of motion for a system of atoms produces a trajectory, and averages along that trajectory stand in for thermodynamic quantities. The result is only as good as the sampling, so the honest questions are about convergence and the force field.

Ready when they can: Explains what a thermostat does and why a raw trajectory needs one to represent a chosen ensemble; Judges whether a simulation is converged from the behaviour of a monitored quantity; Describes how biasing along a coordinate produces a free energy profile; States which errors come from the force field and which from too little sampling.

https://lightmysky.com/learn/science/molecular-dynamics-and-free-energy-from-sampling-mt_ajdYrZOzEd

#### Reaction Dynamics: Trajectories Across a Potential Energy Surface (ages 23-24)

Rate theory treats a reaction as a population crossing a barrier. Dynamics follows individual trajectories instead, and some of them do not behave: they recross the barrier, or they skip the expected intermediate and land somewhere else.

Ready when they can: Reads a two-dimensional surface and traces the path a trajectory would take across it; Explains what recrossing does to a rate constant predicted from a barrier height; Describes an outcome that a statistical theory predicts wrongly and says why; Names an experiment whose product ratio is evidence for dynamic rather than statistical control.

https://lightmysky.com/learn/science/reaction-dynamics-trajectories-across-a-potential-energy-surface-mt_6ctTUYqYtS

#### Risk Assessment for a Reaction Nobody Has Run Here (ages 23-24)

The reactions that hurt people are the unfamiliar ones. A written assessment forces the questions in advance: what is the worst credible failure, what would trigger it, what stops it spreading and what does the person doing the work need to know.

Ready when they can: Finds the hazard data for a reagent and translates it into handling and containment decisions; Identifies the worst credible failure for a stated procedure and the condition that would cause it; Specifies the controls in order, from substitution through containment to protective equipment; Writes a stop condition that says when to abandon the experiment rather than adjust it.

https://lightmysky.com/learn/science/risk-assessment-for-a-reaction-nobody-has-run-here-mt_CdotJQjdka

#### Self-Assembly: Templates, Reversibility and Error Correction (ages 23-24)

Components that bind reversibly can find the arrangement of lowest free energy on their own, so mistakes are undone rather than trapped. A template biases which structure that is, which is how a defined cage or a block copolymer phase forms.

Ready when they can: Explains why reversible bonding is needed for a defined product rather than an amorphous mixture; Predicts the assembly a stated metal geometry and ligand denticity would give; Describes how a template changes which structure is favoured and what happens on its removal; Relates block copolymer phase behaviour to the same balance of contacts.

https://lightmysky.com/learn/science/self-assembly-templates-reversibility-and-error-correction-mt_6y_SNmqwYX

#### Taking a Route into Flow and Onto Scale (ages 23-24)

A step that works in a flask can fail in a reactor because mixing, heat removal and residence time all change with size. Continuous flow keeps the reacting volume small, which makes some hazardous chemistry practical at output that a batch vessel could not reach.

Ready when they can: Identifies which step of a route is the one that resists scale-up and says why; Converts a batch procedure into a flow specification with residence time and concentration stated; Explains why a small reacting volume changes the risk of an unstable intermediate; Compares batch and flow for the same step on throughput, control and capital cost.

https://lightmysky.com/learn/science/taking-a-route-into-flow-and-onto-scale-mt_eOjBPoeZSf

#### Reading a Total Synthesis as an Argument (ages 23-24)

A published synthesis is a claim that a particular route was the right one, supported by yields, characterisation and comparison with earlier work. Reading it well means separating the strategic decisions from the steps that were forced.

Ready when they can: Reconstructs the retrosynthetic plan behind a published route from the forward scheme; Separates the steps chosen for strategy from the steps installed to fix a problem; Judges a stereochemical claim against the evidence given in the supporting information; Proposes an alternative disconnection and states honestly what it would cost.

https://lightmysky.com/learn/science/reading-a-total-synthesis-as-an-argument-mt_Eu3Id8NMrH

#### Writing a Research Proposal: Question, Feasibility and Milestones (ages 23-24)

A proposal argues that a question is worth answering and that this group can answer it. The hard part is feasibility: naming the step most likely to fail, saying how it will be tested early, and what the project becomes if that test goes badly.

Ready when they can: States a research question narrowly enough that an experiment could settle it; Identifies the riskiest step in a plan and schedules the experiment that tests it first; Sets milestones that a reader outside the group could check; Writes a fallback that keeps the project useful if the central idea fails.

https://lightmysky.com/learn/science/writing-a-research-proposal-question-feasibility-and-milestones-mt_RYEXqgkeEU

#### Reporting Chemical Data: Statistics, Figures and Data Availability (ages 23-24)

How results are reported decides whether anyone can build on them. That means stating replicates and uncertainty rather than a single number, drawing figures that show the data instead of hiding it, and depositing the raw files where they can be checked.

Ready when they can: Reports a result with the number of replicates and an uncertainty that matches how it was obtained; Redraws a figure so that the underlying points are visible rather than only their mean; Explains what selective reporting of successful runs does to a conclusion; Says which raw files should be deposited for a stated result and in what form.

https://lightmysky.com/learn/science/reporting-chemical-data-statistics-figures-and-data-availability-mt_P3RFmE6LzI

#### Ultrafast Spectroscopy and Watching a Reaction Happen (ages 23-24)

A pulse short enough to beat a vibration lets one experiment start a reaction and a second one look at it a known delay later. What comes back is a series of spectra against time, from which intermediates and their lifetimes are read.

Ready when they can: Explains why the pulse duration sets the shortest process the experiment can resolve; Reads a transient absorption map and identifies bleach, excited-state and product features; Extracts a lifetime from decay traces and states the model that fitting assumed; Connects a measured intermediate to a step in a proposed mechanism.

https://lightmysky.com/learn/science/ultrafast-spectroscopy-and-watching-a-reaction-happen-mt_wxQgetzzW5

#### From Hit to Lead: Structure-Activity Relationships (ages 23-24)

A screening hit is a starting point, not a drug. Making analogues one change at a time shows which parts of the molecule the target actually needs, and the pattern that emerges is what guides the next round of synthesis.

Ready when they can: Designs a set of analogues that isolates the contribution of one substituent; Reads a potency table and states which structural feature the target requires; Distinguishes a real potency gain from an artefact of assay conditions or compound aggregation; Explains what ligand efficiency measures and why potency alone is a poor guide.

https://lightmysky.com/learn/science/from-hit-to-lead-structure-activity-relationships-mt_p53KgFKAUg

#### Drug-Like Properties: Solubility, Permeability and Metabolic Fate (ages 23-24)

A potent compound is useless if it does not dissolve, does not cross a membrane or is cleared in minutes. Those three properties trade against each other, and most of the medicinal chemist's work is finding a structure that keeps all of them acceptable.

Ready when they can: Predicts how adding a polar group changes solubility and permeability in opposite directions; Uses the ionisation constant and the pH of a compartment to say what fraction is neutral; Names the common sites of oxidative metabolism in a structure and proposes a way to block one; Explains why a compound with excellent potency can still fail on exposure.

https://lightmysky.com/learn/science/drug-like-properties-solubility-permeability-and-metabolic-fate-mt_HGnGjBCLM6

#### Chemical Biology: Bioconjugation and Reporting on a Molecule in a Cell (ages 23-24)

Attaching a label to one protein inside a living cell needs a reaction that ignores everything else present. That is a narrow requirement: aqueous, near neutral pH, fast at low concentration, and blind to the amines and thiols that are everywhere.

Ready when they can: States the conditions a reaction must meet to be usable inside a cell and why each is needed; Compares labelling at a native residue with labelling at an installed unnatural handle; Chooses a reporter suited to a stated question and says what it can and cannot show; Designs a control that would distinguish a real signal from non-specific labelling.

https://lightmysky.com/learn/science/chemical-biology-bioconjugation-and-reporting-on-a-molecule-in-a-cell-mt_nsNwVhPRFN

### Quantum & Modern Physics

https://lightmysky.com/learn/science/areas/quantum-and-modern-physics

#### Blackbody Radiation and the Quantum of Energy (ages 18-19)

The measured spectrum of a hot body disagrees with classical physics at short wavelengths, and the disagreement disappears only if energy is exchanged in packets proportional to frequency. Planck's constant enters physics as the size of that packet.

Ready when they can: Describes how the observed blackbody curve shifts with temperature and where classical theory fails; Explains how quantised exchange of energy removes the short-wavelength failure; Uses Wien's displacement law to get a surface temperature from a peak wavelength.

https://lightmysky.com/learn/science/blackbody-radiation-and-the-quantum-of-energy-mt_B2Bk2IAOa9

#### The Compton Effect and Photon Momentum (ages 18-19)

X-rays scattered from electrons come back with a longer wavelength that depends only on the scattering angle, which is what a collision between two particles predicts. The photon therefore carries momentum h over lambda.

Ready when they can: Applies conservation of energy and momentum to a photon-electron collision; Predicts the wavelength shift from the scattering angle and shows it does not depend on the incident wavelength; Explains why the effect is invisible for visible light on a free electron.

https://lightmysky.com/learn/science/the-compton-effect-and-photon-momentum-mt_wt7kdaof_P

#### The Postulates of Special Relativity and the Loss of Simultaneity (ages 18-19)

Taking the laws of physics and the speed of light to be the same for every inertial observer forces two events simultaneous for one observer to be separated in time for another. Nothing else is assumed, and everything else follows.

Ready when they can: States both postulates and identifies what counts as an inertial frame; Uses a light-signal argument to show that simultaneity depends on the observer; Explains why a fixed speed of light is incompatible with adding velocities the ordinary way.

https://lightmysky.com/learn/science/the-postulates-of-special-relativity-and-the-loss-of-simultaneity-mt_kZqVQ18bbc

#### The Wavefunction and the Born Probability Rule (ages 18-20)

A particle is described by a complex wavefunction whose squared magnitude gives the probability of finding it in a small region. Position stops being a property the particle has and becomes something a measurement returns.

Ready when they can: States what the square of the wavefunction gives and over what interval it is read; Interprets an interference pattern built one particle at a time; Distinguishes the wavefunction itself from the probability density it produces.

https://lightmysky.com/learn/science/the-wavefunction-and-the-born-probability-rule-mt_elzmbBzmKE

#### Time Dilation and Length Contraction (ages 18-19)

A moving clock runs slow and a moving ruler is short, by the same factor, as measured from the frame the motion is relative to. Muons reaching the ground are the everyday evidence.

Ready when they can: Derives the time dilation factor from a light clock; Applies dilation and contraction consistently to the same situation from both frames; Explains the survival of atmospheric muons from either frame and gets the same answer.

https://lightmysky.com/learn/science/time-dilation-and-length-contraction-mt_7tpKiFWeG0

#### Normalisation and Expectation Values (ages 19-20)

Total probability must be one, which fixes the constant in front of any wavefunction, and averages of position or momentum are integrals weighted by the probability density. Expectation values are what a long run of measurements would average to.

Ready when they can: Normalises a given wavefunction over its allowed range; Computes the expectation value of position for a stated state; Explains why the expectation value need not be a value the measurement can return.

https://lightmysky.com/learn/science/normalisation-and-expectation-values-mt_6Y3DZ8P1qm

#### The Lorentz Transformation and Velocity Addition (ages 19-20)

One set of equations converts coordinates between frames and contains dilation and contraction as special cases. Adding velocities with it never gives a result above the speed of light.

Ready when they can: Transforms the coordinates of an event between two frames; Recovers time dilation and length contraction from the transformation; Adds two large velocities relativistically and checks the low-speed limit.

https://lightmysky.com/learn/science/the-lorentz-transformation-and-velocity-addition-mt_uG3_gArw19

#### Relativistic Momentum and Energy (ages 19-20)

Momentum and energy have to be redefined for conservation to hold in every frame, and the redefinition gives every mass a rest energy. Mass and energy become two readings of the same quantity.

Ready when they can: Computes relativistic momentum, kinetic energy and total energy for a fast particle; Relates energy, momentum and rest mass and applies the relation to a massless particle; Explains rest energy and where it shows up in nuclear reactions.

https://lightmysky.com/learn/science/relativistic-momentum-and-energy-mt_zBq87F-j3B

#### Spacetime Intervals and Four-Vectors (ages 19-20)

Observers disagree about distances and times but agree on the interval between two events, which is the invariant of spacetime. Grouping quantities into four-vectors makes that invariance automatic.

Ready when they can: Computes the interval between two events and classifies it as timelike, spacelike or lightlike; Shows that the interval is unchanged by a Lorentz transformation; Explains why causality survives even though the time order of some events is frame dependent.

https://lightmysky.com/learn/science/spacetime-intervals-and-four-vectors-mt_CYdi7Qpvrf

#### Properties of Nuclei and the Nuclear Force (ages 19-21)

Nuclear radius grows with the cube root of nucleon number, so nuclear density is nearly constant, and the force holding nucleons together is short ranged and blind to charge. Those two facts shape the binding energy curve.

Ready when they can: Estimates a nuclear radius and density from the nucleon number; Describes the range and charge independence of the strong force; Explains why the binding energy per nucleon peaks near iron.

https://lightmysky.com/learn/science/properties-of-nuclei-and-the-nuclear-force-mt_HdMS_muGWa

#### The Uncertainty Principle from Wave Packets (ages 19-20)

Localising a particle needs many wavelengths added together, so a narrow position spread forces a wide momentum spread. The limit is a property of waves, not a comment on clumsy apparatus.

Ready when they can: Explains how adding waves of many wavelengths makes a localised packet; Estimates a minimum momentum spread from a stated position spread; Argues why the limit is not caused by disturbance from the measuring instrument.

https://lightmysky.com/learn/science/the-uncertainty-principle-from-wave-packets-mt_DPYnoGksRd

#### The Time-Independent Schrödinger Equation (ages 19-20)

Energy conservation written for a wavefunction gives a differential equation whose solutions are the allowed stationary states. Solving a quantum problem means solving that equation with boundary conditions.

Ready when they can: Identifies kinetic, potential and total energy terms in the equation; States the conditions a physical solution has to satisfy at a boundary; Explains what makes a state stationary when the particle is still described by a wave.

https://lightmysky.com/learn/science/the-time-independent-schrodinger-equation-mt_zeBVPery5T

#### The Infinite Square Well and Energy Quantisation (ages 19-20)

A particle trapped between hard walls can only hold whole numbers of half wavelengths, so its energies form a discrete ladder that rises as the square of the quantum number. Quantisation comes from the boundary conditions, not from an extra rule.

Ready when they can: Solves the equation in the well and applies the boundary conditions to get the allowed energies; Sketches the first few wavefunctions and their probability densities; Predicts how the energy levels shift when the well is made narrower.

https://lightmysky.com/learn/science/the-infinite-square-well-and-energy-quantisation-mt_VV9ItoW7ew

#### Decay Modes, Decay Chains and Nuclear Reactions (ages 20-21)

Which decay a nucleus takes depends on where it sits relative to the line of stability, and a heavy nucleus usually needs a chain of steps to reach it. Reaction equations balance charge, nucleon number and energy.

Ready when they can: Predicts the likely decay mode of a nucleus from its neutron to proton ratio; Balances a nuclear reaction and computes its energy release from the mass difference; Follows a decay chain to a stable end point.

https://lightmysky.com/learn/science/decay-modes-decay-chains-and-nuclear-reactions-mt_b_imidwJeQ

#### Fission Reactors and Fusion in the Laboratory (ages 20-21)

A chain reaction is controlled by moderating neutrons and absorbing the surplus, while fusion needs temperatures high enough to beat the Coulomb barrier and confinement long enough to pay for itself. The physics of each explains the engineering.

Ready when they can: Explains the role of moderator, control rods and coolant in a reactor; States the conditions fusion needs and why confinement time enters; Compares the energy released per kilogram and the waste produced by each route.

https://lightmysky.com/learn/science/fission-reactors-and-fusion-in-the-laboratory-mt_iTwgXI0iBy

#### Nuclear Models: the Liquid Drop and the Semi-Empirical Mass Formula (ages 20-21)

Treating a nucleus as an incompressible charged drop gives volume, surface, Coulomb, asymmetry and pairing terms that reproduce the binding energy curve to within a per cent. The same formula says which nuclide in an isobaric chain is stable and why heavy nuclei fission at all.

Ready when they can: Names each term of the mass formula and says what physical picture it comes from; Predicts the most stable nuclide for a fixed nucleon number and compares it with the chart of nuclides; Uses the formula to argue that fission of a heavy nucleus releases energy while fission of a light one does not.

https://lightmysky.com/learn/science/nuclear-models-the-liquid-drop-and-the-semi-empirical-mass-formula-mt_-cTGNdUJLz

#### Particle Accelerators, Detectors and Cross-Sections (ages 20-21)

Finding structure at small scale needs high energy, because resolution is limited by the de Broglie wavelength of the probe. What comes out of a collision is counted as a cross-section rather than watched directly.

Ready when they can: Relates the energy of a probe to the size of structure it can resolve; Describes how a detector reconstructs a track and identifies a particle; Explains what a cross-section measures and why rates are quoted that way.

https://lightmysky.com/learn/science/particle-accelerators-detectors-and-cross-sections-mt_euJtxtxXyV

#### The Finite Well and Wavefunction Penetration (ages 20-21)

When the walls are of finite height the wavefunction does not stop at the edge but decays into the classically forbidden region. The well then holds only a limited number of bound states.

Ready when they can: Matches the wavefunction and its slope at the boundary of a finite well; Describes the exponential decay in the forbidden region and what sets its length; Explains why a finite well has a finite number of bound states.

https://lightmysky.com/learn/science/the-finite-well-and-wavefunction-penetration-mt_Vs4pWnXW7l

#### Quantum Tunnelling and the Transmission Probability (ages 20-21)

A particle meeting a barrier it cannot classically cross has a small chance of appearing on the far side, falling off exponentially with barrier width and height. Alpha decay and the scanning tunnelling microscope both live on that exponential.

Ready when they can: Relates transmission probability to barrier width, height and particle mass; Explains alpha decay as tunnelling out of the nuclear potential; Says why the tunnelling microscope resolves single atoms.

https://lightmysky.com/learn/science/quantum-tunnelling-and-the-transmission-probability-mt_tLdPJKx8Id

#### The Quantum Harmonic Oscillator and Zero-Point Energy (ages 20-21)

A parabolic potential gives evenly spaced energy levels, and the lowest of them sits above the bottom of the well. A quantum oscillator can never be brought completely to rest.

Ready when they can: States the level spacing of the quantum oscillator and contrasts it with the square well; Explains zero-point energy using the uncertainty principle; Identifies where the oscillator model applies, such as vibrating molecular bonds.

https://lightmysky.com/learn/science/the-quantum-harmonic-oscillator-and-zero-point-energy-mt_HyDxmqyReX

#### Operators, Eigenvalues and Measurement (ages 20-22)

Every observable is represented by an operator, and the values a measurement can return are that operator's eigenvalues. A state that is not an eigenstate gives one of those values with a probability set by the wavefunction.

Ready when they can: Applies the position, momentum and energy operators to a stated wavefunction; Identifies eigenstates and reads off the eigenvalue; Explains why a superposition returns one of several results rather than an average.

https://lightmysky.com/learn/science/operators-eigenvalues-and-measurement-mt_E9C_9DlwD2

#### Separating the Schrödinger Equation for Hydrogen (ages 20-22)

In a spherically symmetric potential the wavefunction splits into a radial part and an angular part, and each piece brings its own quantum number. The energy levels of hydrogen come out of the radial equation alone.

Ready when they can: Explains why spherical symmetry allows the wavefunction to be separated; Names the three quantum numbers the separation produces and what each restricts; Recovers the hydrogen energy levels and compares them with the measured spectrum.

https://lightmysky.com/learn/science/separating-the-schrodinger-equation-for-hydrogen-mt_Yk2qHB0_v2

#### The Standard Model and the Four Interactions (ages 20-22)

Matter is built from quarks and leptons in three generations, and forces are carried by exchange particles with characteristic ranges and strengths. The model states which interactions each particle feels.

Ready when they can: Places a given particle in the standard model and states which interactions it feels; Relates the range of a force to the mass of its exchange particle; Uses conservation rules to decide whether a proposed reaction can happen.

https://lightmysky.com/learn/science/the-standard-model-and-the-four-interactions-mt_GYB4UMS0D9

#### Orbital Angular Momentum and the Quantum Numbers (ages 21-22)

Angular momentum is quantised in both size and direction, so only certain projections along a chosen axis are allowed. The shapes labelled s, p and d are the angular solutions drawn out.

Ready when they can: States the allowed values of orbital angular momentum and its projection for a given level; Connects the angular quantum numbers to the shapes of the orbitals; Relates the orbital magnetic moment to the splitting of lines in a magnetic field.

https://lightmysky.com/learn/science/orbital-angular-momentum-and-the-quantum-numbers-mt_OXlbat0vat

#### Electron Spin and the Stern-Gerlach Experiment (ages 21-22)

A beam of silver atoms splits into exactly two in a non-uniform magnetic field, which no orbital motion can explain. Electrons carry an intrinsic angular momentum with only two possible projections.

Ready when they can: Describes the experiment and why two beams rule out a classical magnetic moment; States the allowed spin projections and the associated magnetic moment; Explains fine structure as a coupling between spin and orbital motion.

https://lightmysky.com/learn/science/electron-spin-and-the-stern-gerlach-experiment-mt_HVFLoNe6wk

#### The Exclusion Principle and Multi-Electron Atoms (ages 21-22)

No two electrons in an atom share all four quantum numbers, so electrons stack into shells instead of collapsing into the lowest state. The periodic table is that stacking rule made visible.

Ready when they can: Uses the four quantum numbers and the exclusion principle to fill the levels of a light atom; Explains why chemical behaviour repeats along a period; Describes how screening changes the order in which sub-shells fill.

https://lightmysky.com/learn/science/the-exclusion-principle-and-multi-electron-atoms-mt_4tLa-3Av0A

#### First-Order Perturbation Theory (ages 21-22)

Most potentials cannot be solved exactly, so a small extra term is treated as a correction to a solved problem. The first-order energy shift is the expectation value of that term in the unperturbed state.

Ready when they can: Splits a Hamiltonian into a solved part and a small perturbation; Computes a first-order energy shift as an expectation value; States when the method is trustworthy and what makes a perturbation small.

https://lightmysky.com/learn/science/first-order-perturbation-theory-mt_UsbiiQFOAt

#### The Nuclear Shell Model and the Magic Numbers (ages 21-22)

The drop model says nothing about why nuclei with 2, 8, 20, 28, 50 or 82 of either nucleon are unusually tightly bound. Putting nucleons in levels of a mean potential, with a strong spin-orbit term, produces exactly those gaps and predicts ground-state spins.

Ready when they can: Explains what a magic number is and gives the experimental evidence that singles those numbers out; Says why the spin-orbit term is needed and which levels it moves; Predicts the ground-state spin and parity of an odd-A nuclide from the last unpaired nucleon.

https://lightmysky.com/learn/science/the-nuclear-shell-model-and-the-magic-numbers-mt_1tiXMm0sA2

#### States as Vectors: Dirac Notation and the State Space (ages 22-23)

A quantum state is a vector in a complex space carrying an inner product, and the wavefunction is only its components in one particular basis. Bra-ket notation writes the same state in position, momentum or energy language without changing the state itself.

Ready when they can: Writes a state as a superposition of basis kets and reads off the amplitudes; Converts between a ket and the wavefunction that represents it in a chosen basis; Uses an inner product to compute an overlap and says what that number predicts.

https://lightmysky.com/learn/science/states-as-vectors-dirac-notation-and-the-state-space-mt_9g0aNMxQ8M

#### Observables as Hermitian Operators and Their Spectra (ages 22-23)

Every measurable quantity is a Hermitian operator whose eigenvalues are the possible results and whose eigenvectors span the state space. Continuous spectra need a different normalisation, which is why a momentum eigenstate is not an ordinary state.

Ready when they can: Shows that a Hermitian operator has real eigenvalues and orthogonal eigenvectors; Expands an arbitrary state in an operator's eigenbasis and predicts the measurement probabilities; Explains why a continuous spectrum forces a different normalisation convention.

https://lightmysky.com/learn/science/observables-as-hermitian-operators-and-their-spectra-mt_TXCN8uiWqs

#### Commutators, Compatible Observables and the General Uncertainty Relation (ages 22-23)

Two quantities can be known together only when their operators commute, and the commutator sets a floor on the product of their spreads. Position and momentum are one case of a relation that holds for any pair of observables.

Ready when they can: Evaluates a commutator and states whether the two observables share an eigenbasis; Derives the uncertainty bound for a general pair from their commutator; Applies the relation to a pair other than position and momentum.

https://lightmysky.com/learn/science/commutators-compatible-observables-and-the-general-uncertainty-relation-mt_TKoUwu74K9

#### Unitary Time Evolution and the Heisenberg Picture (ages 22-24)

Time evolution is a unitary operator generated by the Hamiltonian, which is what keeps total probability fixed. Putting the time dependence on the operators instead of the state gives identical predictions and often less algebra.

Ready when they can: Writes the evolution operator for a time-independent Hamiltonian and applies it to a superposition; Explains why unitarity is exactly what conserves total probability; Moves a problem between the Schrödinger and Heisenberg pictures and checks the answers agree.

https://lightmysky.com/learn/science/unitary-time-evolution-and-the-heisenberg-picture-mt_3JsTc9VYj8

#### Angular Momentum from Its Commutation Relations (ages 22-24)

The entire angular momentum spectrum follows from the commutation relations alone, using raising and lowering operators to step between states. Half-integer values fall out of the algebra, which is where spin belongs.

Ready when they can: Builds the ladder of states from the commutators without solving a differential equation; Explains why the eigenvalues step by one and may be half-integer; Matches the algebraic result to the spherical harmonics found the analytic way.

https://lightmysky.com/learn/science/angular-momentum-from-its-commutation-relations-mt_u0y20XJh-v

#### Adding Angular Momenta and the Coupled Basis (ages 23-24)

Two angular momenta combine into a total whose allowed values run from the difference to the sum, and the coupled basis is a change of basis from the product one. Atomic fine structure and nuclear spin states are read off this way.

Ready when they can: Lists the total angular momentum values available from two given ones; Counts states in both bases and checks the totals agree; Writes a coupled state as a combination of product states for a two-spin case.

https://lightmysky.com/learn/science/adding-angular-momenta-and-the-coupled-basis-mt_eSBNPKm9C4

#### Identical Particles and the Symmetry of a Many-Body State (ages 23-24)

Swapping two identical particles cannot change any prediction, which leaves only symmetric or antisymmetric states. That single requirement produces the exclusion principle for fermions and the crowding of bosons into one state.

Ready when they can: Builds symmetric and antisymmetric two-particle states from single-particle ones; Derives the exclusion principle from antisymmetry instead of stating it as a rule; Explains how exchange symmetry shifts the energy of a two-electron system.

https://lightmysky.com/learn/science/identical-particles-and-the-symmetry-of-a-many-body-state-mt_hns-eEGeHU

#### Degenerate Perturbation Theory and the Variational Method (ages 23-24)

When unperturbed states share an energy, the correction has to be found by diagonalising the perturbation inside that subspace. The variational method gives a second handle: any trial state puts an upper bound on the ground state energy.

Ready when they can: Explains why the first-order formula breaks down for degenerate levels and what replaces it; Diagonalises a small perturbation matrix to get the split levels; Uses a trial function to bound a ground state energy and judges how tight the bound is.

https://lightmysky.com/learn/science/degenerate-perturbation-theory-and-the-variational-method-mt_uov0PZ8vqy

#### The Path Integral and the Sum Over Histories (ages 23-24)

An amplitude can be written as a sum over every path from start to finish, each contributing a phase equal to its action in units of the Planck constant. Paths near the stationary one add in step and the rest cancel, which is why the classical path appears at all.

Ready when they can: Writes a propagator as a sum over paths weighted by the phase of the action and says what the weight means; Recovers the classical trajectory as the stationary-phase limit and states when that limit fails; Explains double-slit interference and tunnelling in the same language, without switching pictures between them.

https://lightmysky.com/learn/science/the-path-integral-and-the-sum-over-histories-mt_QRLheflB1O

#### Time-Dependent Perturbation Theory and Fermi's Golden Rule (ages 23-24)

A perturbation switched on in time drives transitions between states at a rate set by a matrix element and the density of final states. This is where absorption, emission and decay rates come from.

Ready when they can: Computes a first-order transition amplitude for a perturbation applied for a finite time; States the golden rule and identifies the matrix element and the density of states in a given problem; Explains why the rate depends on how many final states are available.

https://lightmysky.com/learn/science/time-dependent-perturbation-theory-and-fermis-golden-rule-mt_zDSASGF7SC

#### Scattering: Cross-Sections and the Born Approximation (ages 23-24)

A scattering experiment measures a cross-section, which is the area a target seems to present to an incoming beam. Treating the potential as a weak perturbation makes the scattering amplitude a Fourier transform of that potential, so the pattern maps the target.

Ready when they can: Defines a differential cross-section in terms of counts, beam flux and solid angle; Relates the Born amplitude to the Fourier transform of the potential; States when the approximation is trustworthy and what a partial-wave treatment adds.

https://lightmysky.com/learn/science/scattering-cross-sections-and-the-born-approximation-mt_xmN9KDfSp7

#### Density Matrices, Entanglement and the Bell Test (ages 23-24)

A state that is only known statistically needs a density matrix rather than a state vector, and the two situations it covers, ignorance and entanglement, look identical to anyone holding one half of the system. Bell's inequality turns the difference between quantum correlation and any local explanation into a number an experiment can measure.

Ready when they can: Writes density matrices for a pure and a mixed state and tells them apart; Shows that tracing out one particle of an entangled pair leaves a mixed state; States what a Bell inequality assumes and what its violation rules out.

https://lightmysky.com/learn/science/density-matrices-entanglement-and-the-bell-test-mt_qwUJ2qV0l3

#### Field Quantisation: Creation Operators and Particle Number (ages 23-24)

Treating each mode of a field as a harmonic oscillator makes its quantum number a count of particles, so particles become excitations rather than objects. Creation and annihilation operators then explain why identical particles are identical and why particle number need not be conserved.

Ready when they can: Maps the modes of a classical field onto independent oscillators and reads the quantum numbers as occupation numbers; Explains why exchange symmetry is automatic once states are built by creation operators; Says what changes when a process creates or destroys particles.

https://lightmysky.com/learn/science/field-quantisation-creation-operators-and-particle-number-mt_BJyZWQA5cb

#### The Klein-Gordon and Dirac Equations (ages 23-24)

Demanding a wave equation that treats space and time the way relativity does gives a second-order equation with negative-energy solutions and no positive probability density. Insisting on first order in time forces the wavefunction to carry four components, and spin and antiparticles arrive as consequences rather than as additions.

Ready when they can: Builds the Klein-Gordon equation from the relativistic energy-momentum relation and states the two problems it brings; Explains why first order in time forces matrices, and what the four components of a Dirac spinor stand for; Reads spin one half and the existence of antiparticles out of the equation rather than assuming either.

https://lightmysky.com/learn/science/the-klein-gordon-and-dirac-equations-mt_njCW9OEevW

### Electricity & Magnetism

https://lightmysky.com/learn/science/areas/electricity-and-magnetism

#### The Electric Field of a Continuous Charge Distribution (ages 18-19)

A charged rod or ring is treated as an infinite set of point charges, so the field becomes an integral of Coulomb contributions. Symmetry decides which components cancel before any integration starts.

Ready when they can: Sets up the field integral for a line or ring of charge with a stated charge density; Uses symmetry to argue that certain components cancel; Checks that the result reduces to a point charge far away.

https://lightmysky.com/learn/science/the-electric-field-of-a-continuous-charge-distribution-mt_IIcVqWapC1

#### Electric Flux and Gauss's Law (ages 18-19)

Flux counts how much field passes through a surface, and Gauss's law says the flux out of any closed surface is set only by the charge inside. The shape of the surface is free, which is what makes the law useful.

Ready when they can: Calculates the flux through a flat surface for a uniform field at any angle; States Gauss's law and explains why charge outside the surface contributes nothing; Chooses a closed surface whose symmetry matches a given charge distribution.

https://lightmysky.com/learn/science/electric-flux-and-gausss-law-mt_Z5dZQvik6o

#### Applying Gauss's Law to Symmetric Charge Distributions (ages 18-19)

For spherical, cylindrical or planar symmetry, Gauss's law gives the field in a line of algebra where the direct integral would be heavy. The work is all in choosing the surface and arguing the symmetry.

Ready when they can: Finds the field inside and outside a uniformly charged sphere; Derives the field of an infinite line and an infinite sheet of charge; States what symmetry a distribution needs before Gauss's law is any help.

https://lightmysky.com/learn/science/applying-gausss-law-to-symmetric-charge-distributions-mt_1LZboKPJ4D

#### Conductors, Shielding and Surface Charge (ages 18-20)

In electrostatic equilibrium the field inside a conductor is zero, all excess charge sits on the surface, and the field just outside is perpendicular to it. A closed conducting shell shields whatever is inside it.

Ready when they can: Argues from equilibrium that the field inside conducting material must vanish; Locates the induced charge on the inner and outer surfaces of a shell with a charge inside; Explains why a car body protects its occupants during a lightning strike.

https://lightmysky.com/learn/science/conductors-shielding-and-surface-charge-mt_2zmzTE-dgL

#### Calculating Electric Potential from a Charge Distribution (ages 18-19)

Potential is a scalar, so contributions add without any concern for direction, which usually makes it easier to compute than the field. For a continuous body it is again an integral over the charge.

Ready when they can: Adds the potentials of several point charges at a given place; Sets up and evaluates the potential integral for a line or ring of charge; Explains why the choice of zero potential is free and where it is normally put.

https://lightmysky.com/learn/science/calculating-electric-potential-from-a-charge-distribution-mt_B4WiVkpH4j

#### Recovering the Field from the Potential Gradient (ages 19-20)

The field is minus the gradient of the potential, so a map of potential contains the field everywhere. Equipotential surfaces are perpendicular to field lines, and the field is strongest where they crowd together.

Ready when they can: Differentiates a potential function to recover each field component; Sketches field lines on a given equipotential map and states the relation between them; Explains why no work is done moving a charge along an equipotential.

https://lightmysky.com/learn/science/recovering-the-field-from-the-potential-gradient-mt_EqCLB9bqG1

#### Dielectrics and the Polarisation of Matter (ages 19-20)

An insulator in a field develops aligned dipoles whose own field opposes the applied one, cutting the field inside by the dielectric constant. That is why filling a capacitor with plastic raises its capacitance.

Ready when they can: Explains polarisation for polar and non-polar molecules and the field it produces; Relates the dielectric constant to the reduction of the field inside the material; Predicts how capacitance, stored charge and voltage change when a dielectric is inserted.

https://lightmysky.com/learn/science/dielectrics-and-the-polarisation-of-matter-mt_OYRr_k3IW6

#### Current Density, Drift Velocity and the Microscopic Ohm's Law (ages 19-20)

Current is charge crossing an area per second, and inside a metal it comes from a slow drift superposed on fast random motion. Writing current density as conductivity times field turns Ohm's law into a statement about the material.

Ready when they can: Relates current, current density and drift velocity for a wire of known cross-section; Estimates a drift speed and contrasts it with the speed of the signal; Explains resistivity in terms of collisions and says why it rises with temperature in a metal.

https://lightmysky.com/learn/science/current-density-drift-velocity-and-the-microscopic-ohms-law-mt_QU-HkQrkFV

#### Kirchhoff's Rules for Multi-Loop Circuits (ages 19-20)

The junction rule is charge conservation and the loop rule is energy conservation, and together they give enough equations to solve any network. Sign conventions are the only real difficulty.

Ready when they can: Assigns currents and signs consistently, then writes independent junction and loop equations; Solves a two-loop circuit with two sources for every branch current; Interprets a negative current as a direction guessed the wrong way round.

https://lightmysky.com/learn/science/kirchhoffs-rules-for-multi-loop-circuits-mt_AS3KiGstGD

#### The Biot-Savart Law and the Field of a Current Element (ages 19-20)

Each short piece of current makes a magnetic field that circles it, falling off with the square of the distance, and the total field is the integral of those contributions. It is the magnetic counterpart of the Coulomb integral.

Ready when they can: Applies the Biot-Savart law to find the field of a straight wire and on the axis of a loop; Uses the cross product to fix the direction of each contribution; Finds the force between two parallel currents and says when it is attractive.

https://lightmysky.com/learn/science/the-biot-savart-law-and-the-field-of-a-current-element-mt_RRsHUaXrFq

#### Ampere's Law: Wires, Solenoids and Toroids (ages 19-21)

The line integral of the magnetic field around a closed loop equals the enclosed current, which gives the field of symmetric arrangements in a line of algebra. A long solenoid comes out uniform inside and near zero outside.

Ready when they can: States Ampere's law and chooses a loop that matches the symmetry of the current; Derives the field of a long straight wire, a solenoid and a toroid; Says why the law gives nothing useful without symmetry.

https://lightmysky.com/learn/science/amperes-law-wires-solenoids-and-toroids-mt_uTzRcSiUQ-

#### Induced Electric Fields and Motional EMF (ages 19-21)

A changing magnetic flux produces a real electric field that pushes charge round a loop, whether the flux changes because the field changes or because the circuit moves. Both readings give the same EMF for a rod sliding on rails.

Ready when they can: Computes the EMF of a rod moving on rails in two ways and shows they agree; Describes the induced electric field around a region of changing flux, with no conductor needed; Explains eddy current braking as induction plus Lenz's law.

https://lightmysky.com/learn/science/induced-electric-fields-and-motional-emf-mt_LpmHnz46tu

#### Magnetisation: Diamagnetism, Paramagnetism and Ferromagnetism (ages 20-21)

Matter in a magnetic field acquires a magnetisation of its own, weakly opposing the field, weakly aligning with it, or aligning strongly and staying that way. Ferromagnetic order comes from an interaction between neighbouring moments and disappears above the Curie temperature.

Ready when they can: Sorts materials by how their magnetisation responds to an applied field and gives the microscopic reason for each class; Explains why an iron core multiplies the field of a solenoid while a copper one does almost nothing; Reads a hysteresis loop and says what its area and its width cost in a transformer core.

https://lightmysky.com/learn/science/magnetisation-diamagnetism-paramagnetism-and-ferromagnetism-mt_1apyQ1_1gg

#### Self-Inductance and Energy Stored in a Magnetic Field (ages 20-21)

A coil opposes changes in its own current through the flux it links with itself, and the energy that opposition stores can be written as an energy density spread through the field. Inductance is the magnetic partner of capacitance.

Ready when they can: Calculates the self-inductance of a solenoid from its geometry; Finds the energy stored in an inductor and writes it as an energy density in the field; Describes the current growth in an RL circuit and identifies its time constant.

https://lightmysky.com/learn/science/self-inductance-and-energy-stored-in-a-magnetic-field-mt_BLyLSJT-Fr

#### Oscillations in LC and RLC Circuits (ages 20-21)

Charge sloshing between a capacitor and an inductor obeys the same equation as a mass on a spring, with resistance playing the part of damping. The electrical and mechanical problems share every solution.

Ready when they can: Derives the LC equation from the loop rule and identifies the resonant frequency; Matches charge, current, inductance and capacitance to displacement, velocity, mass and spring constant; Describes how resistance damps the oscillation and where the energy goes.

https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ

#### Impedance and Phasors in AC Circuits (ages 20-21)

Resistors, capacitors and inductors each set a different phase between current and voltage, and rotating phasors add those voltages without trigonometric identities. Impedance packages size and phase in one quantity.

Ready when they can: States the reactance of a capacitor and an inductor and how each shifts the phase; Adds voltages with a phasor diagram to get the impedance of a series RLC circuit; Reads the phase angle between supply voltage and current off the diagram.

https://lightmysky.com/learn/science/impedance-and-phasors-in-ac-circuits-mt_vQVlVWv2ln

#### Resonance and Power in AC Circuits (ages 20-22)

At the frequency where the two reactances cancel, the impedance is smallest and the current peaks, which is how a radio picks one station. Average power depends on the power factor, so a purely reactive load consumes nothing.

Ready when they can: Finds the resonant frequency of a series RLC circuit and describes the current peak; Calculates average power using root mean square values and the power factor; Explains why a capacitor or inductor alone takes no net energy from the supply over a cycle.

https://lightmysky.com/learn/science/resonance-and-power-in-ac-circuits-mt_wviaR0dJud

#### Displacement Current and Maxwell's Equations (ages 20-22)

Ampere's law fails for a charging capacitor until a term for changing electric flux is added, and with it the four equations close on each other. They say that changing fields of either kind make the other.

Ready when they can: Shows where Ampere's law breaks down between capacitor plates and what the extra term fixes; States all four equations in words and names the physical content of each; Explains why the set is symmetric except for the absence of magnetic charge.

https://lightmysky.com/learn/science/displacement-current-and-maxwells-equations-mt_YR8m8TNfyy

#### Plane Electromagnetic Waves from Maxwell's Equations (ages 21-22)

Combining the two induction equations in empty space gives a wave equation whose speed is fixed by two measured electric and magnetic constants. That speed came out equal to the measured speed of light, which is why light is an electromagnetic wave.

Ready when they can: Shows how the two curl equations combine into a wave equation for the fields; States the speed of the wave in terms of the electric and magnetic constants and evaluates it; Describes the geometry of a plane wave: fields perpendicular to each other and to the direction of travel.

https://lightmysky.com/learn/science/plane-electromagnetic-waves-from-maxwells-equations-mt_27tbaYcxCM

#### The Poynting Vector and Radiation Pressure (ages 21-22)

The cross product of the electric and magnetic fields gives the energy flowing through unit area per second, and the same wave carries momentum. Light therefore pushes on what absorbs it, twice as hard if the surface is a mirror.

Ready when they can: Computes the intensity of a wave from its field amplitudes; Relates the momentum carried by a wave to its energy and finds the pressure on a surface; Explains why a reflecting surface feels twice the pressure of an absorbing one.

https://lightmysky.com/learn/science/the-poynting-vector-and-radiation-pressure-mt_dwTbNlzBgE

#### Covariant Electrodynamics and the Field Tensor (ages 22-24)

Collecting the fields into one antisymmetric tensor turns Maxwell's four equations into two and makes the split between electric and magnetic a matter of frame. Charge density and current become a single four-vector.

Ready when they can: Assembles the field tensor from the electric and magnetic components; Shows how a purely electric field in one frame appears as a mixture in another; Writes Maxwell's equations in four-vector form and identifies which pair each one covers.

https://lightmysky.com/learn/science/covariant-electrodynamics-and-the-field-tensor-mt_RoxM9z6DfK

#### Gauge Freedom and the Potentials as the Working Variables (ages 22-24)

The potentials are not unique: a whole family of them gives the same fields, and choosing a gauge is choosing which member to work with. Once a gauge is fixed, Maxwell's equations become wave equations with sources.

Ready when they can: Shows that a gauge transformation leaves the measured fields unchanged; Picks a gauge condition and states what it simplifies; Writes the sourced wave equation for the potentials in a chosen gauge.

https://lightmysky.com/learn/science/gauge-freedom-and-the-potentials-as-the-working-variables-mt_BovDzq3WZm

#### Radiation from an Accelerating Charge (ages 23-24)

A charge that accelerates radiates power growing with the square of the acceleration, and it radiates sideways rather than along its motion. Antennas, synchrotron light and the reddening of a setting sun all rest on this result.

Ready when they can: States how radiated power depends on charge and acceleration; Describes the angular pattern of the radiation and the direction in which it vanishes; Applies the result to one named laboratory or astronomical source.

https://lightmysky.com/learn/science/radiation-from-an-accelerating-charge-mt_Qr0rMEOYAg

### Thermal & Statistical Physics

https://lightmysky.com/learn/science/areas/thermal-and-statistical-physics

#### The Maxwell-Boltzmann Distribution of Molecular Speeds (ages 18-19)

Molecules in a gas do not share one speed but a distribution with a peak, a mean and a longer tail at high speed. Raising the temperature flattens and widens the curve rather than shifting it rigidly.

Ready when they can: Sketches the speed distribution at two temperatures and describes how the peak and tail change; Distinguishes the most probable, mean and root mean square speeds and orders them; Explains evaporation and reaction rates by appealing to the high-speed tail.

https://lightmysky.com/learn/science/the-maxwell-boltzmann-distribution-of-molecular-speeds-mt_njr5r5YtuT

#### Equipartition and the Heat Capacities of Gases (ages 18-19)

Each way a molecule can store energy holds an average of half kT, so monatomic, diatomic and polyatomic gases have different heat capacities. Freezing out of modes at low temperature is the first hint that classical physics is incomplete.

Ready when they can: Counts the degrees of freedom of a monatomic and a diatomic molecule and predicts the heat capacity; Explains the difference between heat capacity at constant volume and at constant pressure; Describes why measured heat capacities fall below the classical prediction at low temperature.

https://lightmysky.com/learn/science/equipartition-and-the-heat-capacities-of-gases-mt_3OjJwVWlYD

#### Thermodynamic State Variables and PV Diagrams (ages 18-19)

Pressure, volume and temperature describe the state of a system regardless of how it got there, and a path on a PV diagram shows a process. The area under the path is the work done.

Ready when they can: Distinguishes state variables from path quantities such as work and heat; Reads the work done from the area under a path on a PV diagram; Explains why a closed cycle returns every state variable to its starting value.

https://lightmysky.com/learn/science/thermodynamic-state-variables-and-pv-diagrams-mt_G3EYx84GZK

#### The First Law of Thermodynamics for Any Process (ages 18-19)

Internal energy changes only by heat added and work done, whatever route the system takes. Applying it means being careful about signs and about which quantities depend on the path.

Ready when they can: States the first law with a consistent sign convention and applies it to a stated process; Explains why internal energy is a state function while heat and work are not; Traces energy round a complete cycle and shows the internal energy change is zero.

https://lightmysky.com/learn/science/the-first-law-of-thermodynamics-for-any-process-mt_LIWgeWSXHz

#### Work in Isothermal, Isobaric and Adiabatic Processes (ages 19-20)

Each idealised process fixes one variable and gives its own expression for the work, with the adiabatic case following a steeper curve than the isothermal one. Which curve applies decides how much a compressed gas heats up.

Ready when they can: Derives the work done in isothermal and isobaric expansion by integration; Uses the adiabatic relation between pressure and volume and says where the exponent comes from; Explains why an adiabatic compression raises the temperature and an isothermal one does not.

https://lightmysky.com/learn/science/work-in-isothermal-isobaric-and-adiabatic-processes-mt_WzVxwN3svc

#### Heat Engines and the Second Law (ages 19-20)

An engine takes heat from a hot reservoir, does work and dumps the rest cold, and no arrangement of parts can skip the dumping. The second law states that limit in terms of what cannot be built.

Ready when they can: Computes the efficiency of an engine from the heat taken in and rejected; States the engine and refrigerator forms of the second law and shows they say the same thing; Explains why a device converting heat entirely into work is impossible.

https://lightmysky.com/learn/science/heat-engines-and-the-second-law-mt_M7CDvIi4Vs

#### The Carnot Cycle and the Ceiling on Efficiency (ages 19-20)

A cycle built from two isothermal and two adiabatic legs is the most efficient possible between two temperatures, and its efficiency depends on those temperatures alone. Every real engine is measured against it.

Ready when they can: Traces the four legs of the Carnot cycle on a PV diagram and names the heat flow in each; Computes the Carnot efficiency from the two reservoir temperatures; Argues why no engine between the same reservoirs can do better.

https://lightmysky.com/learn/science/the-carnot-cycle-and-the-ceiling-on-efficiency-mt_aWH0BHM556

#### Entropy as a State Function (ages 19-21)

Heat divided by temperature, summed round a reversible path, returns to zero, which means entropy is a property of the state. Real processes only ever increase the entropy of the whole system and its surroundings.

Ready when they can: Computes the entropy change for a reversible isothermal process and for a heated solid; Shows that entropy returns to its starting value round a reversible cycle; Finds the entropy change of the surroundings and argues that the total cannot fall.

https://lightmysky.com/learn/science/entropy-as-a-state-function-mt_bg_K5nU-GZ

#### Microstates, Multiplicity and Boltzmann's Entropy (ages 20-21)

Counting the arrangements a system can take gives a multiplicity, and its logarithm times Boltzmann's constant is the entropy. The second law becomes a statement about which outcomes have overwhelmingly more arrangements.

Ready when they can: Counts microstates for a small system and identifies the most probable macrostate; Relates entropy to multiplicity with Boltzmann's formula; Explains why the second law is about probability rather than prohibition.

https://lightmysky.com/learn/science/microstates-multiplicity-and-boltzmanns-entropy-mt_55I3VvYMc6

#### The Boltzmann Factor and the Partition Function (ages 20-22)

The chance of a state falls exponentially with its energy divided by kT, and summing those factors over all states gives the partition function. Once it is known, the thermal properties follow by differentiation.

Ready when they can: Writes the Boltzmann factor for a two-level system and finds the ratio of populations; Sums the factors to build a partition function for a small set of states; Gets the mean energy of a system from its partition function.

https://lightmysky.com/learn/science/the-boltzmann-factor-and-the-partition-function-mt_u9MSoTgJkF

#### Free Energy and the Direction of Spontaneous Change (ages 20-22)

A system in contact with surroundings at fixed temperature settles where free energy is least, balancing low energy against high entropy. That is why some processes run even though they absorb heat.

Ready when they can: Writes the free energy as energy minus temperature times entropy and identifies the competing terms; Predicts the direction of a change from the sign of the free energy difference; Explains how the balance shifts as temperature rises.

https://lightmysky.com/learn/science/free-energy-and-the-direction-of-spontaneous-change-mt_ww43eqzupN

#### The Microcanonical and Canonical Ensembles (ages 21-22)

An isolated system at fixed energy and a system held at fixed temperature are described by different ensembles, and each has its own way of assigning probabilities. For large systems the two agree on everything measurable.

Ready when they can: States what is held fixed in each ensemble and how probabilities are assigned; Explains why the canonical ensemble suits a system in a heat bath; Argues why the two agree in the limit of a large number of particles.

https://lightmysky.com/learn/science/the-microcanonical-and-canonical-ensembles-mt_NSCYLK-brt

#### The Grand Canonical Ensemble and the Chemical Potential (ages 22-23)

Letting a system exchange particles as well as energy introduces a second multiplier, the chemical potential, which sets the free energy cost of one more particle. The grand partition function is what makes quantum gases tractable.

Ready when they can: States what is held fixed in each of the three ensembles and when each is the convenient one; Reads the chemical potential as a derivative of a free energy with respect to particle number; Builds a grand partition function for a system with a small number of states.

https://lightmysky.com/learn/science/the-grand-canonical-ensemble-and-the-chemical-potential-mt_sdrQrWhBAF

#### Fermi-Dirac and Bose-Einstein Statistics (ages 21-22)

Identical quantum particles cannot be labelled, and whether they may share a state splits them into fermions and bosons with different occupation rules. Classical counting is what both reduce to when states are plentiful.

Ready when they can: States the occupation rule for fermions and for bosons and links it to the exclusion principle; Sketches the Fermi-Dirac distribution at zero and at finite temperature; Explains when the classical Boltzmann count is an adequate approximation.

https://lightmysky.com/learn/science/fermi-dirac-and-bose-einstein-statistics-mt_rU5uPV4SB8

#### The Free Electron Gas and the Fermi Energy (ages 21-22)

Electrons in a metal fill states up to the Fermi energy even at absolute zero, which explains why they contribute so little to heat capacity. Only the few near the top of the stack can be excited.

Ready when they can: Estimates the Fermi energy of a metal from its electron density; Explains why the electronic heat capacity is far smaller than equipartition predicts; Connects the filled band picture to electrical conduction in metals.

https://lightmysky.com/learn/science/the-free-electron-gas-and-the-fermi-energy-mt_4oTalBcKpm

#### Ideal Quantum Gases and Bose-Einstein Condensation (ages 22-23)

Occupation numbers from the grand ensemble reproduce the Bose and Fermi distributions, and below a critical temperature a finite fraction of bosons collects in the single lowest state. The condensate comes from statistics rather than from any interaction.

Ready when they can: Derives an occupation number from the grand partition function; Explains why the ground state cannot be treated as one term among many below the critical temperature; Estimates a condensation temperature from particle density and mass.

https://lightmysky.com/learn/science/ideal-quantum-gases-and-bose-einstein-condensation-mt_wR2YnShTwJ

#### Fluctuations, Linear Response and the Fluctuation-Dissipation Relation (ages 22-24)

Equilibrium quantities fluctuate by an amount fixed by a derivative of the same free energy that gives their averages, so heat capacity measures the size of energy fluctuations. The same noise sets how strongly a system responds when it is pushed, which is why resistance and thermal noise are one measurement.

Ready when they can: Relates the variance of energy in the canonical ensemble to heat capacity; Explains why relative fluctuations shrink as system size grows; States what the fluctuation-dissipation relation connects and names one measurable case.

https://lightmysky.com/learn/science/fluctuations-linear-response-and-the-fluctuation-dissipation-relation-mt_Ibsvdyx7uP

#### Phase Transitions, Order Parameters and Broken Symmetry (ages 22-24)

A phase transition appears as a point where the free energy stops being smooth, and an order parameter measures which symmetry the ordered phase has given up. First-order and continuous transitions differ in whether that parameter jumps.

Ready when they can: Chooses an order parameter for a named transition and says what it measures; Separates first-order from continuous transitions by the behaviour of free energy derivatives; Explains which symmetry the ordered phase breaks and why the disordered one has it.

https://lightmysky.com/learn/science/phase-transitions-order-parameters-and-broken-symmetry-mt_3DQjfNJ-Ef

#### The Ising Model and the Mean-Field Approximation (ages 23-24)

Replacing the neighbours of a spin by their average turns an intractable interacting model into one self-consistent equation with a spontaneous solution below a critical temperature. The approximation gets the transition right and the exponents wrong, and knowing why is the point.

Ready when they can: Writes the self-consistency equation and solves it graphically; Finds the critical temperature the approximation predicts; Explains which fluctuations the approximation discards and when that matters.

https://lightmysky.com/learn/science/the-ising-model-and-the-mean-field-approximation-mt_wPwyBTVI0C

#### Critical Exponents, Scaling and Universality (ages 23-24)

Near a continuous transition the correlation length grows without bound and measured quantities follow power laws whose exponents depend on dimension and symmetry rather than on the material. A fluid at its critical point and a magnet at its own share the same numbers.

Ready when they can: Defines two critical exponents and states what each one measures; Explains universality through the correlation length swallowing microscopic detail; Says what the renormalisation idea does with short-distance degrees of freedom.

https://lightmysky.com/learn/science/critical-exponents-scaling-and-universality-mt_EaJOjyvjjj

### Astronomy & Astrophysics

https://lightmysky.com/learn/science/areas/astronomy-and-astrophysics

#### Flux, Magnitudes and the Distance Ladder (ages 20-21)

What reaches a telescope is a flux, and turning it into a luminosity needs a distance, which is why every astronomical number rests on a chain of distance measurements. Parallax calibrates the first rung, and each later rung is calibrated against the one below it.

Ready when they can: Converts between flux, luminosity and distance, and between apparent and absolute magnitude; Explains why the magnitude scale runs backwards and what a difference of five magnitudes means; Traces one rung of the ladder to the rung it is calibrated against and says what an error there does to everything above it.

https://lightmysky.com/learn/science/flux-magnitudes-and-the-distance-ladder-mt_q1vEUas3AY

#### Hydrostatic Equilibrium and the Structure of a Star (ages 20-21)

A star is a ball of gas where the pressure gradient balances gravity at every depth, which fixes how temperature and density rise towards the centre. The same balance explains why a heavier star burns hotter.

Ready when they can: States the hydrostatic condition and uses it to estimate a central pressure; Explains why temperature has to rise inwards for the star to hold itself up; Relates stellar mass to central temperature and to luminosity.

https://lightmysky.com/learn/science/hydrostatic-equilibrium-and-the-structure-of-a-star-mt_RKeMW8iX56

#### Energy Transport and Nuclear Burning in Stars (ages 20-22)

Energy made by fusion in the core leaves by radiation or by convection depending on how steeply temperature falls, and the proton-proton chain and the CNO cycle dominate in different mass ranges. Photons take a very long time to escape.

Ready when they can: Compares the proton-proton chain and the CNO cycle and says which suits which stellar mass; Distinguishes radiative from convective transport and states what decides between them; Explains why energy made in the core takes so long to reach the surface.

https://lightmysky.com/learn/science/energy-transport-and-nuclear-burning-in-stars-mt_2rc4UAMyl-

#### Stellar Spectra, Spectral Classes and Surface Composition (ages 20-21)

A star's spectrum is a continuum crossed by absorption lines, and which lines appear depends more on the surface temperature than on what the star is made of. Sorting stars by those lines gives the spectral sequence, and the shape of each line carries rotation, pressure and motion along the line of sight.

Ready when they can: Explains why hydrogen lines are strongest in intermediate stars rather than the hottest ones; Reads a temperature from the continuum and a composition from the line strengths, and says why the two are separate measurements; Names what broadens a spectral line and what shifts it, and distinguishes the two effects on a plotted profile.

https://lightmysky.com/learn/science/stellar-spectra-spectral-classes-and-surface-composition-mt_4FBh5G7Gdc

#### The Hertzsprung-Russell Diagram and Stellar Evolution (ages 21-22)

Plotting luminosity against surface temperature sorts stars into a main sequence, giants and white dwarfs, and a star's track across the diagram is its life story. Position on the main sequence is set almost entirely by mass.

Ready when they can: Places a star on the diagram from its temperature and luminosity; Explains why main sequence lifetime falls sharply as mass rises; Reads the age of a cluster from where its main sequence turns off.

https://lightmysky.com/learn/science/the-hertzsprung-russell-diagram-and-stellar-evolution-mt_zMZDIB5TGc

#### General Relativity: Curved Spacetime and Its Tests (ages 21-22)

Gravity is treated as the curvature of spacetime rather than as a force, starting from the observation that free fall and weightlessness cannot be told apart. Light bending, orbit precession and clock rates are the tests.

Ready when they can: States the equivalence principle and gives an experiment it explains; Describes gravitational time dilation and its effect on satellite navigation; Names the classical tests of the theory and what each one measured.

https://lightmysky.com/learn/science/general-relativity-curved-spacetime-and-its-tests-mt_-rZZxZwU2L

#### Stellar Death: White Dwarfs, Neutron Stars and Black Holes (ages 21-22)

When fusion stops, what remains is held up by degeneracy pressure or by nothing at all, and which happens depends on the mass left behind. The Chandrasekhar limit is quantum statistics setting an astronomical boundary.

Ready when they can: Explains degeneracy pressure and why it does not depend on temperature; Applies the mass limits that separate white dwarfs, neutron stars and black holes; Describes how a core-collapse supernova disperses heavy elements.

https://lightmysky.com/learn/science/stellar-death-white-dwarfs-neutron-stars-and-black-holes-mt_k1oUF3mJlu

#### Galaxies, Redshift and the Expanding Universe (ages 21-22)

Galaxy distances measured by standard candles and speeds measured by redshift give a linear relation whose slope sets the expansion rate. The expansion is of space itself, so there is no centre to point at.

Ready when they can: Builds a distance from a standard candle and a speed from a measured redshift; Estimates the age of the universe from the expansion rate; Explains why every observer sees the same recession and why that means no centre.

https://lightmysky.com/learn/science/galaxies-redshift-and-the-expanding-universe-mt_-POhqrng-Q

#### Galaxy Types, the Milky Way's Structure and Active Nuclei (ages 21-22)

Galaxies sort into spirals, ellipticals and irregulars, and our own is a barred spiral whose shape was worked out from inside it. A small fraction have centres far brighter than all their stars together, powered by accretion onto a massive black hole rather than by fusion.

Ready when they can: Classifies a galaxy from an image and links its type to its stellar ages and gas content; Explains how the Milky Way's spiral structure and central bar were mapped from a position inside the disc; Argues that an active nucleus cannot be stellar, using its output, its size and how fast it varies.

https://lightmysky.com/learn/science/galaxy-types-the-milky-ways-structure-and-active-nuclei-mt_Eps5CXEB5C

#### The Cosmic Microwave Background and the Light Elements (ages 21-22)

A hot dense start predicts both a cooled thermal glow filling the sky and fixed proportions of hydrogen, helium and lithium, and both are measured. Together they are the strongest evidence for the Big Bang.

Ready when they can: Explains why the background radiation has a blackbody spectrum and why it is so cold now; Relates the predicted helium fraction to conditions in the first minutes; Says what the small temperature ripples in the background correspond to.

https://lightmysky.com/learn/science/the-cosmic-microwave-background-and-the-light-elements-mt_oz0MJXiuVt

#### Dark Matter, Dark Energy and What the Universe Is Made Of (ages 21-22)

Galaxy rotation curves and cluster masses need far more matter than shines, and the expansion is speeding up rather than slowing. Ordinary matter turns out to be a small part of the total.

Ready when they can: Explains what a flat rotation curve implies about mass beyond the visible disc; Describes the supernova evidence that the expansion is accelerating; States the rough proportions of ordinary matter, dark matter and dark energy.

https://lightmysky.com/learn/science/dark-matter-dark-energy-and-what-the-universe-is-made-of-mt_GKKPGcHqJH

#### The Interstellar Medium and How Stars Form (ages 21-22)

The space between stars holds gas and dust in phases from cold molecular clouds to hot ionised bubbles, and dust reddens and dims everything seen through it. A cloud collapses when its own gravity beats its internal pressure, which sets a minimum mass for the collapse and starts the next generation of stars.

Ready when they can: Names the phases of the interstellar medium by temperature and density and says which wavelength each is observed at; Explains extinction and reddening by dust and what they do to a distance measured from brightness; Argues the collapse condition by comparing gravitational to thermal energy and says what happens to the excess angular momentum.

https://lightmysky.com/learn/science/the-interstellar-medium-and-how-stars-form-mt_i2HyLf_Emy

#### The Scale Factor, the Friedmann Equation and the Age of the Universe (ages 21-22)

Expansion is written as one function of time multiplying every distance, and the equation governing it comes from applying general relativity to a uniform universe. What the universe contains fixes how that function behaves, so the measured contents predict an age and a fate.

Ready when they can: Writes redshift as a ratio of scale factors and explains why that is not a Doppler shift through space; States how matter, radiation and a cosmological constant each dilute as the universe expands, and which dominates when; Estimates an age from an expansion rate and says why the simplest estimate is not the measured answer.

https://lightmysky.com/learn/science/the-scale-factor-the-friedmann-equation-and-the-age-of-the-universe-mt_v3VEzinvJe

#### The Sun as a Star: Photosphere, Corona and the Activity Cycle (ages 21-22)

The Sun is the one star whose surface can be resolved, and its layers, granulation and sunspots are read as a magnetic field wound up by differential rotation. The corona is hotter than the surface below it, which is the open problem the observations frame.

Ready when they can: Places photosphere, chromosphere and corona by temperature and density and says how each is observed; Ties sunspots, flares and the eleven-year cycle to a magnetic field that differential rotation twists; States why the corona being hotter than the photosphere is a problem and what would count as a solution.

https://lightmysky.com/learn/science/the-sun-as-a-star-photosphere-corona-and-the-activity-cycle-mt_AMIkiU7wRz

#### Tensors and the Metric on a Curved Manifold (ages 23-24)

Coordinates are labels with no physical content, so physics is written with objects whose components transform in a fixed way under a change of labels. The metric holds the geometry: distances, angles, and which vectors count as parallel.

Ready when they can: Distinguishes objects by how their components transform under a coordinate change; Raises and lowers indices with a given metric; Reads distances off a metric written in a non-Cartesian coordinate system.

https://lightmysky.com/learn/science/tensors-and-the-metric-on-a-curved-manifold-mt_9r9SG3NcZR

#### Parallel Transport, Christoffel Symbols and the Geodesic Equation (ages 23-24)

Comparing vectors at different points needs a rule for carrying one to the other, and the Christoffel symbols encode that rule for a given metric. A geodesic is a path that parallel-transports its own tangent, which is what free fall means.

Ready when they can: Computes Christoffel symbols from a simple metric; Explains why differentiating a vector field needs a correction term in curved coordinates; Writes the geodesic equation and identifies free fall as its solution.

https://lightmysky.com/learn/science/parallel-transport-christoffel-symbols-and-the-geodesic-equation-mt_bUEL2R91Vy

#### Curvature and the Einstein Field Equation (ages 23-24)

Curvature is measured by how a vector changes when it is carried around a closed loop, and the Riemann tensor records that. The field equation ties curvature to the energy and momentum present, so matter fixes the geometry that matter then moves through.

Ready when they can: Describes curvature operationally through transport around a closed loop; Names the two sides of the field equation and what each represents; Shows why the equation reduces to Newtonian gravity in the weak-field limit.

https://lightmysky.com/learn/science/curvature-and-the-einstein-field-equation-mt_1CxE6kRDt_

#### The Schwarzschild Solution: Orbits, Redshift and the Horizon (ages 23-24)

The geometry outside a spherical mass has one exact solution, and reading it gives orbital precession, light bending and the way clock rates depend on depth. At one radius the coordinates fail while the geometry does not, which is what a horizon is.

Ready when they can: Reads gravitational time dilation off the metric; Explains orbital precession as a departure from the inverse-square result; Separates a coordinate breakdown at the horizon from a genuine singularity.

https://lightmysky.com/learn/science/the-schwarzschild-solution-orbits-redshift-and-the-horizon-mt_dNZpRDeZUE

#### Linearised Gravity and Gravitational Waves (ages 23-24)

Small departures from flat spacetime obey a wave equation, so a changing mass distribution sends ripples of geometry that stretch one transverse direction while squeezing the other. Detectors measure that strain, and it is tiny because geometry couples weakly to matter.

Ready when they can: Explains why the linearised equations resemble electromagnetic radiation with a different source; Describes what a passing wave does to a ring of freely floating test masses; Says why there is no monopole or dipole gravitational radiation.

https://lightmysky.com/learn/science/linearised-gravity-and-gravitational-waves-mt_z0tMZDGMHi

### Scientific Inquiry

https://lightmysky.com/learn/science/areas/scientific-inquiry

#### Observation vs Interpretation (ages 6-7)

Notice the difference between what you observed and what you think it means — 'the ice melted' is an observation; 'the ice melted because of the heat' is an interpretation

Ready when they can: observation vs interpretation in primary science; BERA: children's observation skills in nature.

Needs first: Feeling of not understanding.

https://lightmysky.com/learn/science/observation-vs-interpretation-mt_Hw70LI5xza

#### Asking scientific questions (ages 5-8)

Ask simple scientific questions and recognise that they can be answered in different ways including observation, testing, and research

Ready when they can: Ask at least three 'how' or 'why' questions about the natural world; Suggest different ways to answer a question: observing, testing, asking an expert, reading a book; Choose an appropriate method to investigate a specific question.

Needs first: Asking Questions, Observation vs Interpretation, Feeling of not understanding, Persisting When It's Hard.

https://lightmysky.com/learn/science/asking-scientific-questions-mt_XirhnAB6Ye

#### Modelling with Sketches (ages 5-8)

Develop a simple sketch, drawing, or physical model to illustrate how the shape of an object helps it function as needed to solve a given problem

Ready when they can: Create a sketch, drawing, or physical model of a design solution; Explain how the shape or structure of the design helps solve the problem; Relate the model to the real-world problem it addresses.

Needs first: Asking scientific questions.

https://lightmysky.com/learn/science/modelling-with-sketches-mt_hi8cVycbwn

#### Observing with simple equipment (ages 5-7)

Observe closely using simple equipment such as hand lenses, and use observations to describe, compare, and identify things

Ready when they can: Use a hand lens or other simple equipment to make detailed observations; Describe observations using specific vocabulary (colour, shape, size, texture, pattern); Compare two objects based on careful observation, noting similarities and differences.

Needs first: Asking scientific questions.

https://lightmysky.com/learn/science/observing-with-simple-equipment-mt_vJO5Bxk4z-

#### Simple tests and experiments (ages 5-7)

Perform simple tests and use observations and ideas to suggest answers to questions

Ready when they can: Carry out a simple test with one thing changing at a time; Observe what happens and describe the result; Use the result to suggest an answer to the original question.

Needs first: Observing with simple equipment.

https://lightmysky.com/learn/science/simple-tests-and-experiments-mt_Wa44s-f8Ws

#### Recording Data (ages 5-7)

Gather and record data using simple methods such as tables, tally charts, and drawings to help answer questions

Ready when they can: Record observations and measurements in a simple table or tally chart; Use drawings or labelled diagrams to record what was observed; Explain how the recorded data helps answer the original question.

Needs first: Simple tests and experiments.

https://lightmysky.com/learn/science/recording-data-mt_ZFwPZaDJ0_

#### Comparing Design Solutions (ages 5-8)

Analyse data from tests of two objects designed to solve the same problem to compare the strengths and weaknesses of each design

Ready when they can: Test two designs that address the same problem and collect data on their performance; Compare the results, identifying strengths and weaknesses of each design; Use data as evidence to recommend which design works better and suggest improvements.

Needs first: Modelling with Sketches, Recording Data.

https://lightmysky.com/learn/science/comparing-design-solutions-mt_nNYo5A-7Bl

#### Changing Your Mind with Evidence (ages 6-8)

Be willing to change your mind when evidence doesn't support your prediction — a result that surprises you is more valuable than one that confirms what you already thought

Ready when they can: belief revision in children research (PMC 2020); hypothesis testing and argumentation from evidence in young children.

Needs first: Observation vs Interpretation, Analysing Your Own Errors.

https://lightmysky.com/learn/science/changing-your-mind-with-evidence-mt_obF-6VYRya

#### Could there be another explanation? (ages 7-9)

For any result, ask: is there another explanation? — the first explanation that fits isn't always the right one, and good scientists actively look for alternatives

Ready when they can: prompts to consider alternative possible worlds research (6-7 year olds); scientific thinking promotes critical thinking (MDPI 2025).

Needs first: Changing Your Mind with Evidence, Understanding Why.

https://lightmysky.com/learn/science/could-there-be-another-explanation-mt_QrVF5n7vci

#### Fair testing (ages 7-9)

Set up simple practical enquiries, comparative tests, and fair tests, understanding the importance of changing only one variable at a time

Ready when they can: Explain what makes a test 'fair' (only one variable changes, everything else stays the same); Identify the variable to change, the variable to measure, and the variables to keep the same; Set up and carry out a comparative or fair test with support.

Needs first: Simple tests and experiments.

https://lightmysky.com/learn/science/fair-testing-mt_qgb76wHN2X

#### Measuring accurately (ages 7-9)

Make systematic and careful observations, take accurate measurements using standard units and equipment including thermometers and data loggers

Ready when they can: Use at least three types of measuring equipment correctly (ruler, thermometer, measuring jug, scales); Read measurements in standard units (cm, ml, °C, g) with reasonable accuracy; Make systematic observations by following a planned method consistently.

Needs first: Measurable Attributes of Objects, Observing with simple equipment.

https://lightmysky.com/learn/science/measuring-accurately-mt_nUnowllzaN

#### Recording and presenting data (ages 7-9)

Gather, record, classify, and present data in a variety of ways including tables, bar charts, labelled diagrams, and keys

Ready when they can: Organise data into a clear table with appropriate headings; Create a bar chart or pictogram from collected data; Use labelled diagrams and classification keys to present findings.

Needs first: Pictograms and tally charts, Measuring accurately, Recording Data.

https://lightmysky.com/learn/science/recording-and-presenting-data-mt_7IFpDVNsmt

#### Drawing conclusions from evidence (ages 7-9)

Report on findings from enquiries using oral and written explanations, draw simple conclusions, make predictions, and suggest improvements

Ready when they can: Write or present a clear report of findings from an investigation; Draw a conclusion that answers the original question, supported by data; Make a prediction for a new situation based on the results, and suggest improvements to the method.

Needs first: Teaching It Back, Recording and presenting data, Building Writing Stamina, Fair testing.

https://lightmysky.com/learn/science/drawing-conclusions-from-evidence-mt_7VrR1GzhrN

#### Using evidence to answer questions (ages 7-9)

Identify differences, similarities, or changes related to scientific ideas and use straightforward scientific evidence to answer questions or support findings

Ready when they can: Identify at least one pattern (similarity, difference, or trend) in a set of scientific data; Explain how the pattern relates to the scientific idea being investigated; Use specific data points as evidence when answering a scientific question.

Needs first: Drawing conclusions from evidence, Reading between the lines, Could there be another explanation?, Spotting Patterns.

https://lightmysky.com/learn/science/using-evidence-to-answer-questions-mt_CVywzrjT_c

#### Correlation vs Causation (ages 8-10)

Two things happening together doesn't mean one caused the other — recognise the difference between correlation and causation before drawing conclusions

Ready when they can: developmental changes in children's recognition of evidence relevance to causal explanations; causal learning research.

Needs first: Describing Rules & Patterns, Could there be another explanation?.

https://lightmysky.com/learn/science/correlation-vs-causation-mt_X0Tr8IYaEd

#### Simple Design Problems (ages 8-11)

Define a simple design problem reflecting a need or want that includes specified criteria for success and constraints on materials, time, or cost

Ready when they can: Define a design problem by describing the need or want it addresses; Specify at least two criteria for a successful solution (e.g. must hold X weight, must cost less than Y); Identify constraints such as available materials, time limits, or cost.

Needs first: Comparing Design Solutions.

https://lightmysky.com/learn/science/simple-design-problems-mt_Z5-fSCOBep

#### Comparing Possible Solutions (ages 8-11)

Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints

Ready when they can: Generate at least three possible solutions to a defined design problem; Compare solutions against the specified criteria and constraints; Select the most promising solution with reasoning for the choice.

Needs first: Simple Design Problems.

https://lightmysky.com/learn/science/comparing-possible-solutions-mt_HveO1bOXpJ

#### Fair testing (age 8+) (ages 8-11)

Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved

Ready when they can: Plan a fair test of a prototype with clearly identified variables to control; Carry out the test and identify failure points or weaknesses in the design; Propose specific improvements based on test results and retest.

Needs first: Comparing Possible Solutions.

https://lightmysky.com/learn/science/fair-testing-age-8-mt_eoPcc4nrBE

#### Accurate Measurement (ages 9-11)

Take measurements with increasing accuracy and precision using a range of scientific equipment, taking repeat readings when appropriate

Ready when they can: Use scientific equipment (scales, thermometers, measuring cylinders, stopwatches) with increasing precision; Explain why repeat readings improve reliability and take at least three readings; Identify and deal with anomalous results (measurements that don't fit the pattern).

Needs first: Measuring accurately.

https://lightmysky.com/learn/science/accurate-measurement-mt_Psun-u_lPf

#### Controlling variables (ages 9-11)

Plan different types of scientific enquiries to answer questions, recognising and controlling variables where necessary

Ready when they can: Independently plan an investigation identifying the independent, dependent, and controlled variables; Choose the appropriate type of enquiry for the question (fair test, observation over time, pattern seeking, research); Explain why controlling variables is essential for valid results.

Needs first: Using evidence to answer questions, Fair testing (age 8+), Choosing a Strategy, Fair testing, Planning a Task.

https://lightmysky.com/learn/science/controlling-variables-mt_ArVBEpMAPk

#### Fair testing (age 9+) (ages 9-11)

Use test results to make predictions and set up further comparative and fair tests to investigate new questions

Ready when they can: Use results from an investigation to make a specific, testable prediction; Design a follow-up test to verify the prediction; Explain the reasoning linking the original results to the new prediction.

Needs first: Drawing conclusions from evidence, Controlling variables, Describing Rules & Patterns.

https://lightmysky.com/learn/science/fair-testing-age-9-mt_5PgQB0QkWi

#### Recording data with diagrams and graphs (ages 9-11)

Record data and results of increasing complexity using scientific diagrams, classification keys, tables, scatter graphs, bar and line graphs

Ready when they can: Choose and create an appropriate graph type for the data (bar chart, line graph, scatter graph); Draw graphs with correctly labelled axes, appropriate scales, and accurate plotting; Use classification keys and scientific diagrams to present complex findings.

Needs first: Recording and presenting data, Bar graphs.

https://lightmysky.com/learn/science/recording-data-with-diagrams-and-graphs-mt_rDjtmDogJr

#### Drawing conclusions from evidence (age 9+) (ages 9-11)

Report and present findings including conclusions, causal relationships, explanations, and a degree of trust in results using oral and written forms

Ready when they can: Present findings clearly in written and oral form with appropriate scientific vocabulary; Identify causal relationships (X caused Y because...) supported by evidence; Discuss the degree of trust in results, considering sample size, repeat readings, and possible errors.

Needs first: Fair testing (age 9+), Writing opinions, Planning Ideas Before Writing, Basic Informational Writing, Recording data with diagrams and graphs, Understanding Why.

https://lightmysky.com/learn/science/drawing-conclusions-from-evidence-age-9-mt_nyPMkeHlVJ

#### Science Can Be Revised (ages 9-11)

Scientific knowledge is provisional — it is the best current explanation based on available evidence, and it can and should be revised when better evidence arrives

Ready when they can: Give an example of a scientific idea that changed when new evidence was found — e.g. people once thought the Sun orbited the Earth; Explain that scientists update their ideas when experiments give unexpected results, and that this is a strength not a weakness; Describe why it is important to keep testing ideas rather than just accepting them because an expert said so.

Needs first: Could there be another explanation?, Reflecting After Learning, Correlation vs Causation.

https://lightmysky.com/learn/science/science-can-be-revised-mt_1GVAmcwAiO

#### Evidence Supporting Ideas (ages 9-11)

Identify scientific evidence that has been used to support or refute ideas or arguments, evaluating the strength of evidence

Ready when they can: Distinguish between a claim and the evidence supporting it; Evaluate whether evidence is strong (fair test, multiple trials) or weak (single observation, no controls); Identify when evidence supports or refutes a scientific idea and explain why.

Needs first: Science Can Be Revised, Drawing conclusions from evidence (age 9+), Analysing Your Own Errors, Inferring Characters' Feelings and Motives, Correlation vs Causation.

https://lightmysky.com/learn/science/evidence-supporting-ideas-mt_AstzvYDU2m

#### Assessing Hazards and Risks (ages 11-14)

Evaluate risks before and during practical work: identify hazards (a substance, flame or procedure that could cause harm), judge how likely and how serious the harm would be, and choose sensible control measures to reduce the risk

Ready when they can: Identify the hazards in a planned experiment (e.g., acid can burn skin, a beaker of hot water can scald); Distinguish a hazard from a risk, judging the risk by how likely harm is and how serious it would be; Choose sensible precautions for an experiment (e.g., wear goggles, tie hair back, heat gently, use a smaller amount).

Needs first: Fair testing (age 9+), Following Multi-Step Procedures.

https://lightmysky.com/learn/science/assessing-hazards-and-risks-mt_r66rs2EVkZ

#### Controlling variables (age 11+) (ages 11-12)

Form a testable scientific hypothesis linking an independent variable to a predicted outcome, plan a full investigation identifying independent, dependent, and control variables, sample size, and risk assessment

Ready when they can: Writes a hypothesis in the form 'I predict that [IV] will affect [DV] because...' supported by scientific reasoning; Identifies and labels the independent variable, dependent variable, and at least three control variables; Plans repeat readings and an appropriate sample size, and identifies relevant hazards with control measures.

Needs first: Controlling variables, Planning a Task, Structured Opinion Writing.

https://lightmysky.com/learn/science/controlling-variables-age-11-mt_Ae56umVlTT

#### Repeated tests for reliability (ages 11-12)

Distinguish between precision (consistency of repeated readings) and accuracy (closeness to true value), use significant figures and standard form correctly, and choose and use appropriate measuring instruments to minimise uncertainty

Ready when they can: Explains the distinction between precision and accuracy with examples; Rounds measurements to an appropriate number of significant figures; Selects a measuring instrument with appropriate resolution for the context (e.g. choosing a 10 ml measuring cylinder rather than a 1-litre measuring jug for a 5 ml measurement).

Needs first: Accurate Measurement.

https://lightmysky.com/learn/science/repeated-tests-for-reliability-mt_auJqTemMpI

#### Scientific Quantities and Units (ages 11-14)

Use scientific quantities with correct units: pair every measurement with its unit (metres, kilograms, seconds, newtons, joules), pick sensible prefixes like milli- and kilo-, convert between them, and call chemicals by their proper scientific names

Ready when they can: Record measurements with the correct unit and symbol (e.g., 2.5 kg, 30 s, 1.2 m); Convert between prefixed units when comparing or calculating (e.g., 2500 mL = 2.5 L, 0.4 km = 400 m); Use proper chemical names for common substances in written work (e.g., sodium chloride rather than just 'salt').

Needs first: Accurate Measurement, Converting measurement units (age 9+).

https://lightmysky.com/learn/science/scientific-quantities-and-units-mt_vdHqdaflog

#### Tables, charts, and graphs (ages 12-13)

Construct data tables with correct headings and SI units, plot appropriate graph types (bar chart, line graph, scatter graph), draw a line of best fit, and calculate the gradient of a straight-line graph

Ready when they can: Constructs a table with column headings that include quantity and unit (e.g. Mass / g); Selects the appropriate graph type for the data and plots it accurately with labelled axes and scales; Draws a line of best fit for linear data and correctly calculates its gradient using two points.

Needs first: Repeated tests for reliability, Bar graphs, Recording data with diagrams and graphs.

https://lightmysky.com/learn/science/tables-charts-and-graphs-mt_YHsUhi4Prc

#### Drawing conclusions from evidence (age 12+) (ages 12-13)

Identify patterns and trends in data, draw conclusions that directly address the hypothesis with quantitative reference to evidence, and evaluate the investigation by distinguishing between systematic and random errors and proposing targeted improvements

Ready when they can: Identifies the pattern or trend in a graph or data table using specific values; Writes a conclusion that references the hypothesis, states whether the prediction was supported, and quotes numerical evidence; Distinguishes between a systematic error (affects all readings in the same direction) and a random error, and proposes a specific procedural improvement to address each.

Needs first: Transferring Skills, Evidence Supporting Ideas, Seismic Waves & Earth's Interior, Drawing conclusions from evidence (age 9+), Tables, charts, and graphs, Evidence-Based Writing.

https://lightmysky.com/learn/science/drawing-conclusions-from-evidence-age-12-mt_3jmBpEepYX

#### Writing Science Reports (ages 13-14)

Communicate scientific findings in a structured report using appropriate scientific vocabulary, SI units, and standard notation; describe how peer review and replication contribute to the reliability of scientific knowledge

Ready when they can: Writes a structured scientific report including aim, hypothesis, method, results, conclusion, and evaluation using appropriate scientific vocabulary; Uses SI units and standard form consistently throughout a report; Explains what peer review is and why replication by independent researchers is essential for scientific claims to be accepted.

Needs first: Drawing conclusions from evidence (age 12+), Controlling variables (age 11+), Research & Source Evaluation, Developed Informational and Explanatory Writing.

https://lightmysky.com/learn/science/writing-science-reports-mt_ThTbUuNb3p

#### Uncertainty, Precision and Significant Figures in a Measurement (ages 16-17)

Every reading carries an uncertainty set by the instrument and by how the measurement was taken, and quoting a result means quoting that uncertainty with it. Repeating a reading shrinks the random part and leaves a zero error untouched, which is why precise and accurate are not the same word.

Ready when they can: Quotes a measurement with an absolute and a percentage uncertainty and rounds the value to match; Separates a random scatter from a systematic offset in a set of repeated readings and says what fixes each; Chooses an instrument and a method that make the dominant uncertainty smaller, and says which one it was.

https://lightmysky.com/learn/science/uncertainty-precision-and-significant-figures-in-a-measurement-mt_HPc3OahYoV

#### Combining Uncertainties and Reading a Result off a Graph (ages 17-18)

Uncertainties in a sum add in absolute terms and uncertainties in a product add as percentages, so the dominant one usually decides the answer. Plotted with error bars, the steepest and shallowest lines that still pass through them give the uncertainty in a gradient.

Ready when they can: Combines uncertainties through a multi-step calculation and names which measurement dominates the result; Draws error bars, then a best line and a worst acceptable line, and gets an uncertainty in the gradient from the pair; Decides whether two published values agree, using their stated uncertainties rather than their central values.

https://lightmysky.com/learn/science/combining-uncertainties-and-reading-a-result-off-a-graph-mt_kn8RhTDEOK

#### Dimensional Analysis, Scaling and the Order-of-Magnitude Estimate (ages 22-23)

Before solving anything, the dimensions of the quantities involved fix the form of the answer up to a factor near one. Physicists use that to check results, to guess how a quantity scales, and to decide whether a measurement is worth attempting at all.

Ready when they can: Builds a dimensionless group from the quantities in a problem and predicts the scaling; Estimates a physical quantity to within an order of magnitude and states every assumption used; Catches an error in an expression by checking its dimensions.

https://lightmysky.com/learn/science/dimensional-analysis-scaling-and-the-order-of-magnitude-estimate-mt_jXnXRMKnC3

#### Fitting a Model to Data: Least Squares, Chi-Square and Goodness of Fit (ages 22-23)

A fit chooses parameters that minimise a weighted sum of squared residuals, and the size of that sum says whether the model is believable at all. Without uncertainties on the points, neither the parameters nor the verdict means anything.

Ready when they can: Fits a straight line by weighted least squares and reports parameter uncertainties; Interprets a reduced chi-square value, including what too small a value suggests; Reads structure in the residuals and says what it implies about the model.

https://lightmysky.com/learn/science/fitting-a-model-to-data-least-squares-chi-square-and-goodness-of-fit-mt_NN0WYlp0md

#### Systematic Error, Controls and the Design of a Measurement (ages 22-24)

Repeating a measurement shrinks the random part and leaves the systematic part untouched, so the design has to attack systematics directly through calibration, null tests and blind analysis. Most disagreements between published results are arguments about the systematic budget.

Ready when they can: Separates random from systematic contributions in a described experiment; Proposes a null test or a blind analysis for a stated risk of bias; Builds an error budget and identifies which term dominates.

https://lightmysky.com/learn/science/systematic-error-controls-and-the-design-of-a-measurement-mt_rGjB_JcsLJ

#### Reading a Paper: the Claim, the Evidence and the Assumption (ages 23-24)

A research paper is read in a different order than it was written: the claim first, then the figure that carries it, then the method that produced the figure. The question that does the work is which assumption would have to fail for the conclusion to collapse.

Ready when they can: Extracts the central claim and the single figure that supports it; Identifies the assumptions the result depends on and how the authors tested them; Judges whether the stated uncertainty supports the strength of the claim.

https://lightmysky.com/learn/science/reading-a-paper-the-claim-the-evidence-and-the-assumption-mt_YFgMvbohC0

#### Writing Physics: the Figure, the Error Bar and the Defensible Claim (ages 23-24)

A result reaches other people as a figure that carries the claim, an uncertainty honest about both of its parts, and a sentence that says no more than the data supports. The method section exists so that someone else can repeat the work and disagree with it.

Ready when they can: Drafts a figure whose caption states the claim it supports; Reports a result with statistical and systematic uncertainties kept separate; Writes a method description detailed enough for another group to repeat.

https://lightmysky.com/learn/science/writing-physics-the-figure-the-error-bar-and-the-defensible-claim-mt_uUQ4gKXTN0

#### Testing a New Drug: Controls, Placebo and the Blind Trial (ages 15-16)

Deciding that a treatment works means ruling out that people would have got better anyway, or believed they had. The design that does this is a controlled trial, and each feature of it exists to close one specific way of being fooled.

Ready when they can: Explain what a placebo control rules out and what it does not; Say why a trial is blinded, and why double-blinding closes a gap that single-blinding leaves open; Describe the stages a candidate drug passes through before it is prescribed, and what each stage is testing for.

https://lightmysky.com/learn/science/testing-a-new-drug-controls-placebo-and-the-blind-trial-mt_If6qHIrOxT

#### Sampling Ecosystems with Quadrats and Transects (ages 15-16)

Estimate how many of a species live in an area by counting inside randomly placed quadrats and scaling up, or track how abundance changes along a transect. Covers random placement, the mean per quadrat, and what a bigger sample buys.

Ready when they can: Scales a mean count per quadrat up to a whole field and states the units of the estimate.; Explains why quadrat positions are chosen at random and what bias follows when they are not.; Chooses a transect over random quadrats when the question is about change across a gradient..

https://lightmysky.com/learn/science/sampling-ecosystems-with-quadrats-and-transects-mt_jI8rAOYdmb

#### Estimating Population Size by Mark, Release and Recapture (ages 15-16)

A quadrat cannot count animals that run away, so mobile populations are estimated from the proportion of marked individuals that turn up in a second sample. The estimate is only as good as its assumptions, and each one of them can be broken by a careless mark.

Ready when they can: Calculate a population estimate from the numbers marked, recaptured and marked-within-recaptured; State the assumptions the method rests on, including mixing, survival and no loss of marks; Explain how a mark that makes an animal easier for a predator to see biases the estimate, and in which direction.

https://lightmysky.com/learn/science/estimating-population-size-by-mark-release-and-recapture-mt_SrISE2trf9

#### Designing a Biological Experiment: Units, Controls and Randomisation (ages 22-23)

Before any measurement is taken, the design fixes what can be concluded: what the experimental unit is, what varies with it, and what is held fixed or randomised. This stop writes the design down while the data do not yet exist.

Ready when they can: Identify the experimental unit in a stated protocol and count it correctly; Choose blocking or randomisation for a stated nuisance factor and justify the choice; Name the control that rules out the alternative explanation a reviewer will raise first.

https://lightmysky.com/learn/science/designing-a-biological-experiment-units-controls-and-randomisation-mt_Hc6BAdlkLf

#### Pseudoreplication: When n Is Smaller Than It Looks (ages 22-23)

Counting wells, cells or sections as independent replicates inflates n and turns noise into a result. This stop separates technical from biological replication and matches the analysis to the level that was actually randomised.

Ready when they can: Given a protocol, state the true n and the level at which variation should be modelled; Explain why averaging technical replicates is usually the honest first step; Spot nesting in a published figure legend and say what analysis it demands.

https://lightmysky.com/learn/science/pseudoreplication-when-n-is-smaller-than-it-looks-mt_2gRWB6RTaI

#### Power and Effect Size, Decided Before the Data (ages 22-24)

Power depends on the effect size worth detecting, the variability and n, and it has to be settled beforehand rather than computed afterwards from what happened. This stop runs the calculation and treats the smallest useful effect as a scientific decision.

Ready when they can: Compute the sample size needed for a stated effect size, variability and power; Explain why power computed after the fact from the observed effect adds nothing; Argue why a significant result from an underpowered study tends to overstate the effect.

https://lightmysky.com/learn/science/power-and-effect-size-decided-before-the-data-mt_zYNmSWAJT8

#### Researcher Degrees of Freedom and the Pre-registered Analysis Plan (ages 22-24)

Every undeclared choice among exclusion rules, transformations, subgroups and stopping points widens the range of results a true null can produce. This stop writes an analysis plan that fixes those choices in advance.

Ready when they can: List the analysis decisions in a stated study that could have reasonably gone another way; Explain how looking at the data and deciding whether to continue raises the false positive rate; Write a short pre-registration covering hypothesis, exclusion rules and the primary analysis.

https://lightmysky.com/learn/science/researcher-degrees-of-freedom-and-the-pre-registered-analysis-plan-mt_UJgZQ2AADm

#### Reading a Primary Paper: The Claim, the Figure and the Missing Control (ages 22-24)

A paper's abstract states a claim that only one or two of its figures actually support. This stop finds the figure the claim rests on, checks what its controls exclude, and separates what was shown from what was inferred.

Ready when they can: State a paper's central claim in one sentence and name the figure that tests it; Identify a control that is absent and say which alternative explanation it would have excluded; Separate the results the data support from the conclusions the discussion asserts.

https://lightmysky.com/learn/science/reading-a-primary-paper-the-claim-the-figure-and-the-missing-control-mt_DZE7z5vu9X

#### Reproducibility in Practice: Data, Code and What Another Lab Can Rerun (ages 23-24)

A result that cannot be regenerated from raw data and a script is a claim rather than a method. This stop covers deposition, versioning, and the difference between reanalysing the same data and repeating the experiment.

Ready when they can: Package an analysis so a stranger can regenerate a stated figure from the raw data; Distinguish reproducing an analysis from replicating an experiment, and say what each tests; Choose an appropriate repository and metadata standard for a stated data type.

https://lightmysky.com/learn/science/reproducibility-in-practice-data-code-and-what-another-lab-can-rerun-mt_QuHuEyasFt

#### Ethics of Emerging Biotechnology: Editing, Enhancement and Biosecurity (ages 23-24)

Germline editing, gain-of-function work and cheap gene synthesis each pose a decision that no technical answer settles. This stop separates the empirical questions from the value questions and works through the review structures that already exist.

Ready when they can: Distinguish somatic from germline editing in terms of what each commits future people to; State the case for and the case against a stated gain-of-function experiment on its own terms; Explain what institutional review, dual-use policy and screening of synthesis orders each cover.

https://lightmysky.com/learn/science/ethics-of-emerging-biotechnology-editing-enhancement-and-biosecurity-mt_U5OY2wvimB

### The Human Body

https://lightmysky.com/learn/science/areas/the-human-body

#### Bones & Muscles (ages 5-7)

Know that the body has a skeleton made of bones inside it that gives the body its shape and protects important organs like the brain (skull) and heart (ribcage), and that muscles attached to bones allow the body to move

Ready when they can: State that bones give the body shape, support, and protection; Name at least three bones or bone groups (e.g. skull, ribcage, spine, leg bones); Explain that muscles pull on bones to make the body move.

https://lightmysky.com/learn/science/bones-and-muscles-mt_SdIWVjzopp

#### How Breathing Works (ages 5-7)

Know that we breathe air into our lungs through the nose and mouth, that our lungs take in oxygen from the air which our body needs to stay alive, and that we breathe out carbon dioxide as waste

Ready when they can: Trace the path of air: nose/mouth → windpipe → lungs; State that lungs take oxygen from the air, which the body needs; State that we breathe out carbon dioxide, which the body doesn't need.

https://lightmysky.com/learn/science/how-breathing-works-mt_tiPyEkm4cU

#### The Brain Controls the Body (ages 5-7)

Understand that the brain is the body’s control centre: it receives messages from the senses, thinks and makes decisions, and sends messages through nerves to tell muscles what to do

Ready when they can: State that the brain is inside the skull and controls the whole body; Describe the basic loop: senses send information to the brain, the brain decides what to do, and sends messages to muscles; Give an example (e.g. eyes see a ball coming, brain decides to catch it, nerves tell hands to move).

https://lightmysky.com/learn/science/the-brain-controls-the-body-mt_pJ5zsocdNx

#### The Five Senses (ages 5-7)

Explore the five senses in detail: sight uses eyes to detect light, hearing uses ears to detect sound, touch uses skin to feel pressure and temperature, taste uses the tongue to detect flavours, and smell uses the nose to detect odours

Ready when they can: Name all five senses and match each to the correct body part; Describe what each sense detects (e.g. eyes detect light, ears detect sound waves); Give an example of using each sense in everyday life (e.g. smelling food cooking, feeling hot water).

Needs first: Body Parts & Senses, The Brain Controls the Body.

https://lightmysky.com/learn/science/the-five-senses-mt_nwSWPTENmv

#### The Heart & Blood (ages 5-7)

Understand that the heart is a muscle that pumps blood around the body through tubes called blood vessels, and that we can feel our heartbeat by placing a hand on our chest or fingers on our wrist

Ready when they can: Locate their own heartbeat by touch (chest or pulse point); State that the heart pumps blood through the body continuously; Describe blood vessels as tubes that carry blood to every part of the body.

https://lightmysky.com/learn/science/the-heart-and-blood-mt_lp1eTsQen7

#### Basic Body Needs (ages 5-7)

Know that the body needs food for energy, water to stay hydrated, sleep to rest and grow, and exercise to keep muscles and the heart strong — and that these are basic needs every human body has

Ready when they can: List the four basic needs: food (energy), water (hydration), sleep (rest and growth), exercise (strength); Explain that food gives the body energy to move, think, and grow; Describe what happens if one need isn't met (e.g. feeling tired without sleep, thirsty without water).

Needs first: The Heart & Blood, How Breathing Works.

https://lightmysky.com/learn/science/basic-body-needs-mt_cxJRc15osy

#### Balanced Diet & Food Groups (ages 7-9)

Know the main food groups (carbohydrates, proteins, fats, vitamins, minerals, fibre, water) and understand that a balanced diet includes the right amounts from each group to keep the body healthy and provide energy, growth materials, and protection from illness

Ready when they can: Name at least five food groups and give an example food for each (e.g. carbohydrates = bread, protein = chicken); Explain what carbohydrates (energy), proteins (growth and repair), and fats (energy and warmth) do for the body; State that vitamins and minerals protect against illness and help the body work properly.

Needs first: Basic Body Needs, Animal Nutrition.

https://lightmysky.com/learn/science/balanced-diet-and-food-groups-mt_QhLAeAlHI0

#### Cells, Tissues & Organs (ages 7-9)

Understand that the body is organised in a hierarchy: tiny cells are the building blocks, groups of similar cells form tissues, tissues combine into organs (like the heart or stomach), and organs work together in organ systems (like the circulatory system)

Ready when they can: State that cells are the smallest building blocks of the body, too small to see without a microscope; Describe the hierarchy: cells → tissues → organs → organ systems; Give an example: muscle cells form muscle tissue, which forms the heart organ, which is part of the circulatory system.

Needs first: The Heart & Blood, The Brain Controls the Body, How Breathing Works.

https://lightmysky.com/learn/science/cells-tissues-and-organs-mt_C7FNeIDGc6

#### How the Eye Works (ages 7-9)

Describe how the eye works: light enters through the pupil, the lens focuses it onto the retina at the back of the eye, and the retina sends signals along the optic nerve to the brain, which interprets the image

Ready when they can: Name the main parts: pupil (lets light in), lens (focuses light), retina (detects light), optic nerve (sends signals to brain); Describe the sequence: light enters → lens focuses → retina detects → nerve signals brain → brain interprets image; Explain that the pupil gets bigger in dim light and smaller in bright light to control how much light enters.

Needs first: The Five Senses, The Brain Controls the Body.

https://lightmysky.com/learn/science/how-the-eye-works-mt_-gkJdxJUQT

#### Naming Major Bones (ages 7-9)

Identify major bones of the human skeleton by name (skull, spine/vertebrae, ribcage, pelvis, femur, humerus) and explain the skeleton’s three jobs: supporting the body’s shape, protecting organs, and enabling movement with muscles

Ready when they can: Name and locate at least six major bones or bone groups on a diagram or their own body; Explain the three functions: support (holds us upright), protection (skull protects brain, ribs protect heart/lungs), movement (bones work with muscles); State that not all animals have internal skeletons — some have shells or exoskeletons.

Needs first: Bones & Muscles.

https://lightmysky.com/learn/science/naming-major-bones-mt_OMmiuv9ZLH

#### How Muscles Move Bones (ages 7-9)

Understand that muscles work in pairs to move bones: when one muscle contracts (gets shorter and pulls), the opposite muscle relaxes, and that some muscles are voluntary (we choose to use them) while others like the heart are involuntary (they work automatically)

Ready when they can: Demonstrate or describe how biceps and triceps work as a pair to bend and straighten the arm; Explain the difference between voluntary muscles (we control them) and involuntary muscles (they work automatically); Name the heart and muscles of the digestive system as examples of involuntary muscles.

Needs first: Naming Major Bones, Bones & Muscles.

https://lightmysky.com/learn/science/how-muscles-move-bones-mt_6N-4TqCleR

#### The Digestive Journey (ages 7-9)

Trace the journey of food through the digestive system: food enters the mouth where teeth break it down and saliva begins digestion, travels down the oesophagus to the stomach, passes through the small intestine where nutrients are absorbed, and waste moves through the large intestine

Ready when they can: List the organs in order: mouth, oesophagus, stomach, small intestine, large intestine; Describe what happens at each stage (teeth chew, stomach churns with acid, small intestine absorbs nutrients); State that the small intestine is where most nutrients pass into the blood, and the large intestine removes water from waste.

Needs first: Basic Body Needs.

https://lightmysky.com/learn/science/the-digestive-journey-mt_JpQUM1129q

#### Types of Teeth (ages 7-9)

Identify the four types of human teeth (incisors for cutting, canines for tearing, premolars and molars for grinding) and understand that tooth shape is linked to function, just as in other animals — herbivores have flat teeth, carnivores have sharp teeth

Ready when they can: Name the four tooth types and describe each one's job: incisors cut, canines tear, premolars/molars grind; Compare human teeth to herbivore teeth (flat, for grinding plants) and carnivore teeth (sharp, for tearing meat); Explain that humans have all types because we are omnivores — we eat both plants and meat.

Needs first: The Digestive Journey, Herbivores, Carnivores & Omnivores.

https://lightmysky.com/learn/science/types-of-teeth-mt_I047mKeeaq

#### Growing Up & Puberty (ages 9-11)

Describe the stages of human development from birth to old age: baby, toddler, child, adolescent (puberty), young adult, middle-aged adult, elderly — understanding the physical changes that happen at each stage, especially during puberty

Ready when they can: Name and order at least six life stages from birth to old age; Describe key physical changes during puberty (growth spurts, body shape changes, development of adult features); Explain that puberty is triggered by hormones — chemical messengers released by glands.

Needs first: Basic Body Needs, Human Life Stages, Balanced Diet & Food Groups.

https://lightmysky.com/learn/science/growing-up-and-puberty-mt_pu2mmK27UA

#### Heart & Blood Circulation (ages 9-11)

Describe the circulatory system in detail: the heart has four chambers (two atria, two ventricles) that pump blood in a double loop — one to the lungs for oxygen and one to the rest of the body to deliver it — through arteries, veins, and tiny capillaries

Ready when they can: Name the four heart chambers and describe the double-loop pathway (heart → lungs → heart → body); Distinguish arteries (carry blood away from heart), veins (carry blood back to heart), and capillaries (tiny vessels where exchange happens); Name the components of blood: red blood cells (carry oxygen), white blood cells (fight infection), platelets (help clotting), plasma (liquid).

Needs first: Cells, Tissues & Organs, The Heart & Blood.

https://lightmysky.com/learn/science/heart-and-blood-circulation-mt_g_M4Vh_pK7

#### How the Lungs Work (ages 9-11)

Explain how the respiratory system works in detail: air travels through the nose/mouth, down the trachea, into bronchi and bronchioles, reaching tiny air sacs (alveoli) in the lungs where oxygen passes into the blood and carbon dioxide passes out

Ready when they can: Trace the air pathway: nose/mouth → trachea → bronchi → bronchioles → alveoli; Explain gas exchange in the alveoli: oxygen passes into blood capillaries, carbon dioxide passes out; Describe the mechanical process: the diaphragm contracts to pull air in and relaxes to push air out.

Needs first: Cells, Tissues & Organs, How Breathing Works.

https://lightmysky.com/learn/science/how-the-lungs-work-mt_zPDDJLAl-J

#### Circulation & Breathing Together (ages 9-11)

Understand how the circulatory and respiratory systems work together: the lungs oxygenate the blood, the heart pumps it around the body, cells use the oxygen and produce carbon dioxide waste, and the blood carries the waste back to the lungs to be breathed out

Ready when they can: Describe the cycle: lungs add oxygen to blood → heart pumps oxygenated blood to body → cells use oxygen → blood returns CO₂ to lungs; Explain why heart rate and breathing rate increase during exercise (muscles need more oxygen); Measure their own resting and post-exercise heart rate and explain the difference.

Needs first: Heart & Blood Circulation, How the Lungs Work.

https://lightmysky.com/learn/science/circulation-and-breathing-together-mt_QK-ZZb7UUN

#### The Immune System (ages 9-11)

Know that the body has an immune system that protects against illness: the skin acts as a barrier, white blood cells identify and destroy germs (bacteria and viruses), and vaccines train the immune system to recognise specific diseases before they cause illness

Ready when they can: Describe the skin as the body's first line of defence against germs; Explain that white blood cells detect and fight bacteria and viruses inside the body; Describe how vaccines work: they contain weakened or inactive germs that train the immune system to recognise the real disease.

Needs first: Cells, Tissues & Organs.

https://lightmysky.com/learn/science/the-immune-system-mt_4JpMXUIxeD

#### Healthy Lifestyle Choices (ages 9-11)

Understand how lifestyle choices affect the body’s health: a balanced diet, regular exercise, adequate sleep, and avoiding harmful substances (tobacco, alcohol, drugs) help body systems function well, while poor choices increase the risk of disease

Ready when they can: Explain how regular exercise strengthens the heart, lungs, and muscles; Describe how a poor diet high in sugar and fat can lead to obesity, tooth decay, and heart problems; State at least two harmful effects of smoking (damages lungs, increases heart disease risk) or alcohol (damages liver, affects brain).

Needs first: The Immune System, Balanced Diet & Food Groups, Circulation & Breathing Together.

https://lightmysky.com/learn/science/healthy-lifestyle-choices-mt_4k3HGahK2k

#### The Nervous System (ages 9-11)

Understand that the nervous system has two parts — the central nervous system (brain and spinal cord) and nerves that branch throughout the body — and that nerve signals travel at high speed to coordinate senses, thought, and movement

Ready when they can: Name the two parts of the nervous system: central (brain + spinal cord) and peripheral (nerves throughout the body); Describe the reflex arc: stimulus → sensory nerve → spinal cord/brain → motor nerve → muscle response; State that nerve signals travel extremely fast, which is why reflexes happen almost instantly.

Needs first: How the Eye Works, Senses, Brain & Responses, The Brain Controls the Body.

https://lightmysky.com/learn/science/the-nervous-system-mt_qzbgwaUQOA

#### Immunity & Vaccines (ages 11-13)

Distinguish innate (non-specific, immediate) from adaptive (specific, memory-forming) immunity; explain how B cells produce antibodies that recognise specific antigens, how T cells destroy infected cells, and why immunological memory makes vaccines work; and describe the gut microbiome as a community of trillions of microbes that significantly influences immune function

Ready when they can: Distinguishes innate immunity (rapid, non-specific barriers and inflammation) from adaptive immunity (slow, specific, memory-forming); Explains how B cells produce antibodies that bind to specific antigens on pathogens, targeting them for destruction; Explains immunological memory: after first exposure, memory B and T cells remain, making subsequent response faster and stronger — the basis of vaccine protection.

Needs first: The Immune System.

https://lightmysky.com/learn/science/immunity-and-vaccines-mt_LkOMijDvL7

#### Neurons & Brain Structure (ages 11-13)

Explain how neurons transmit signals as electrochemical impulses across synapses, describe how the brain is organised (lobes and functions, limbic system for emotion), and explain neuroplasticity — why learning and practice physically change brain structure — connecting to optical illusions as evidence that the brain constructs reality rather than passively recording it

Ready when they can: Describes the neuron-to-neuron signal pathway: electrical impulse travels along axon, neurotransmitter crosses the synapse, new impulse begins in the next neuron; Names the four lobes of the cerebral cortex (frontal, parietal, temporal, occipital) and gives one function for each; Explains neuroplasticity: repeated neural pathways become stronger and faster — this is the biological mechanism of learning and skill development.

Needs first: The Nervous System.

https://lightmysky.com/learn/science/neurons-and-brain-structure-mt_okUMpHsV-P

#### DNA & Genes (ages 12-14)

Describe the double helix structure of DNA (base pairs, complementarity), explain how genes are sections of DNA that code for proteins, introduce the central dogma (DNA → mRNA → protein) conceptually, and discuss the ethical implications of CRISPR gene editing — including potential benefits (genetic disease treatment) and concerns (germline editing, 'designer babies')

Ready when they can: Describes DNA as a double helix with four bases (A, T, C, G) where A pairs with T and C pairs with G; Explains that a gene is a section of DNA that codes for a specific protein, and that proteins carry out most of the body's functions; Describes CRISPR as a molecular tool that can cut and edit DNA sequences, and raises at least two distinct ethical considerations about its use in humans.

Needs first: Chromosomes, Genes & DNA.

https://lightmysky.com/learn/science/dna-and-genes-mt_0sELh0MYWb

#### How the Body Stays in Balance (ages 12-14)

Explain homeostasis as the process of maintaining a stable internal environment; describe the main feedback loop systems (negative feedback) using blood glucose regulation (insulin/glucagon) and body temperature as concrete examples; and connect the endocrine system (hormone-secreting glands) to the nervous system as two complementary communication systems with different speeds and durations

Ready when they can: Defines homeostasis and explains why maintaining a stable internal environment is essential for survival; Describes the blood glucose negative feedback loop: glucose rises → pancreas releases insulin → cells take up glucose → glucose falls → insulin release stops; Compares the nervous system (fast, electrical, short-duration signals) with the endocrine system (slower, chemical, longer-duration signals) and gives an example where each is more appropriate.

Needs first: Neurons & Brain Structure, Growing Up & Puberty.

https://lightmysky.com/learn/science/how-the-body-stays-in-balance-mt_J40cOn7VWn

#### Cancer & Stem Cells (ages 13-14)

Explain that cancer occurs when mutations in DNA disable normal cell-cycle controls, causing uncontrolled cell division and tumour formation; describe how stem cells differ from specialised cells and their potential for regenerative medicine; and evaluate the ethical debates around embryonic stem cell research and genetic testing

Ready when they can: Explains cancer as the result of DNA mutations that disable tumour suppressor genes or activate oncogenes, causing unchecked mitosis; Distinguishes stem cells (unspecialised, can differentiate) from specialised cells (fixed function) and explains why stem cells are medically valuable; Presents the embryonic stem cell debate with at least two specific scientific arguments in favour and two ethical objections against, without simply asserting one side is correct.

Needs first: DNA & Genes, Parts of Plant and Animal Cells.

https://lightmysky.com/learn/science/cancer-and-stem-cells-mt_roinupb_7L

#### The Reflex Arc and Synapses (ages 14-15)

A reflex runs receptor to sensory neurone to relay neurone to motor neurone to effector, with no decision from the conscious brain. Covers the synapse gap and why that gap is the slow step.

Ready when they can: Puts the parts of a reflex arc in order for a given stimulus and response.; Explains what crosses a synapse and why that step takes time.; Says why a reflex protects the body better than a decided response would..

https://lightmysky.com/learn/science/the-reflex-arc-and-synapses-mt_evlgCVxTnK

#### Hormones and Negative Feedback (ages 14-15)

A hormone travels in the blood, acts slowly and reaches every organ, which is the opposite trade-off from a nerve impulse. Negative feedback holds a quantity near a set point by acting against whichever way it moved.

Ready when they can: Compares nervous and hormonal control on speed, duration and how the message travels.; Names the gland that releases a given hormone and the organ that responds to it.; Traces one negative feedback loop and says what would happen if the loop were cut..

https://lightmysky.com/learn/science/hormones-and-negative-feedback-mt_OBa6BHmW29

#### Blood Glucose Control and Diabetes (ages 14-16)

Insulin and glucagon push blood glucose back towards its set point after a meal or a long gap without one. Type 1 and type 2 diabetes break the loop at different places, which is why the treatments differ.

Ready when they can: Says what the pancreas releases when glucose is high and when it is low, and what the liver does in each case.; Tells type 1 from type 2 by which part of the loop has failed.; Reads a glucose against time graph and marks where insulin was acting..

https://lightmysky.com/learn/science/blood-glucose-control-and-diabetes-mt_eOzNtiBvX2

#### Hormones in the Menstrual Cycle and Fertility (ages 14-16)

Four hormones run the monthly cycle: FSH and LH from the pituitary, oestrogen and progesterone from the ovaries. The same loop explains how hormonal contraception and fertility treatment work.

Ready when they can: Places each of the four hormones on a cycle diagram and states what it triggers.; Explains how keeping oestrogen high stops an egg being released.; Explains what fertility treatment adds and why it can lead to more than one embryo..

https://lightmysky.com/learn/science/hormones-in-the-menstrual-cycle-and-fertility-mt_DENo5Fbr1d

#### Blood Components and Blood Vessels (ages 15-16)

Plasma, red cells, white cells and platelets each carry a different job, and arteries, veins and capillaries are built for the pressures they meet. Explains why a red blood cell has no nucleus and why a capillary wall is one cell thick.

Ready when they can: Matches each blood component to what it transports or does.; Compares wall thickness, lumen size and valves across the three vessel types and ties each to the pressure it carries.; Explains one structural feature of a red blood cell in terms of carrying more oxygen..

https://lightmysky.com/learn/science/blood-components-and-blood-vessels-mt_aWZ2sGXGMn

#### Heart Rate, Stroke Volume and Cardiac Output (ages 15-16)

Cardiac output is stroke volume multiplied by heart rate, and breathing follows the same shape as tidal volume multiplied by breathing rate. Use both to compare a person at rest with the same person exercising.

Ready when they can: Calculates cardiac output from a stroke volume and a pulse rate, with units on the answer.; Rearranges the relation to find a missing quantity from the other two.; Says which quantity changes most during exercise and why that helps the working muscles..

https://lightmysky.com/learn/science/heart-rate-stroke-volume-and-cardiac-output-mt_mjrPFHgvfx

#### How Communicable Diseases Spread (ages 15-16)

Bacteria, viruses, fungi and protists spread through air, water, direct contact or a vector, and each route points at a different way to break the chain. Uses named human and plant diseases.

Ready when they can: Sorts named diseases by pathogen type and by route of spread.; Explains why a virus needs a host cell to reproduce while most bacteria do not.; Picks a control measure that matches a given route of transmission and says why it works..

https://lightmysky.com/learn/science/how-communicable-diseases-spread-mt_o__-bF814q

#### Non-Communicable Disease and What Counts as a Risk Factor (ages 15-16)

Diseases that nobody catches still have causes, and those causes are usually a raised probability rather than a certainty. Separating a correlation in a population from a demonstrated mechanism in a body is the core skill here.

Ready when they can: Explain what a risk factor is and why it does not guarantee the disease; Give a case where a mechanism is known and a case where only a correlation has been shown; Describe how uncontrolled cell division becomes a tumour and distinguish benign from malignant.

https://lightmysky.com/learn/science/non-communicable-disease-and-what-counts-as-a-risk-factor-mt_IciZ1CJn6h

#### The Brain: Regions and the Evidence for What They Do (ages 15-16)

The brain is not one organ doing one job, and the map of which region does what was built from damage, stimulation and scanning rather than from looking. Knowing how that evidence was gathered is what stops the map from being a set of labels to memorise.

Ready when they can: Name the major regions of the brain and state one function each is responsible for; Explain what a case of localised damage can and cannot show about a region's job; Say why treating the brain surgically is difficult, in terms of its structure rather than its importance.

https://lightmysky.com/learn/science/the-brain-regions-and-the-evidence-for-what-they-do-mt_BA_DGCDic8

#### The Eye as a Receptor Organ (ages 15-16)

The eye converts light into nerve impulses, and every part of it exists to serve that conversion: the lens to focus, the iris to control intensity, the retina to transduce. The common sight defects are all failures of focus, and each correction follows from where the image lands.

Ready when they can: Trace light from outside the eye to a nerve impulse, naming the structure responsible at each step; Explain accommodation as a change in lens shape driven by muscle; Say where the image forms in short and long sight, and which lens corrects each.

https://lightmysky.com/learn/science/the-eye-as-a-receptor-organ-mt_fslwsM3I7F

#### Vaccination and Antibiotic Resistance (ages 15-16)

A vaccine trains the immune system with a harmless form of a pathogen so the second response is fast enough to stop illness. Antibiotics kill bacteria and do nothing to viruses, and resistant strains spread when antibiotics are overused.

Ready when they can: Explains what a vaccine puts into the body and why illness does not follow.; Says why a high vaccination rate protects people who cannot be vaccinated themselves.; Explains resistance as selection among bacteria, not as a person becoming immune to the drug..

https://lightmysky.com/learn/science/vaccination-and-antibiotic-resistance-mt_XmDqQONako

#### The Resting Potential and the Action Potential (ages 16-18)

A neurone holds its inside negative by pumping sodium out and potassium in, and an impulse is that difference briefly reversing. Voltage-gated channels open in sequence and the membrane resets behind the impulse.

Ready when they can: Explains what maintains the resting potential and what it costs the cell.; Orders depolarisation, repolarisation and hyperpolarisation on a voltage trace.; Says which ion moves at each stage and through which kind of channel..

https://lightmysky.com/learn/science/the-resting-potential-and-the-action-potential-mt_0sh4w30ocz

#### The Specific Immune Response: Phagocytes, T Cells and B Cells (ages 16-17)

Beyond the general defences sits a response tailored to one antigen, built by cells that recognise a shape and then divide. Memory cells are why the second exposure is faster, and they are what a vaccine is actually for.

Ready when they can: Describe the sequence from phagocytosis and antigen presentation to antibody production; Distinguish the cell-mediated and humoral responses by which cell does what; Explain the shape of a secondary response curve in terms of memory cells.

https://lightmysky.com/learn/science/the-specific-immune-response-phagocytes-t-cells-and-b-cells-mt_hqI22Uey2k

#### Conduction Speed: Myelination and the Refractory Period (ages 17-18)

Myelin makes the impulse jump between gaps, so a myelinated axon conducts far faster than a bare one of the same width. The refractory period caps the frequency and keeps the impulse travelling one way.

Ready when they can: Explains why jumping between gaps is faster than conduction along a bare membrane.; Names two other features of an axon that change conduction speed.; Links the refractory period to both the direction and the maximum frequency of impulses..

https://lightmysky.com/learn/science/conduction-speed-myelination-and-the-refractory-period-mt_x3M0sv6oD6

#### Haemoglobin, the Dissociation Curve and the Bohr Shift (ages 17-18)

The oxygen dissociation curve is S-shaped because binding the first oxygen makes the next one easier. Carbon dioxide shifts the whole curve to the right, so tissue that is working hard gets unloaded first.

Ready when they can: Reads percentage saturation off the curve at a given partial pressure.; Explains the S shape in terms of what happens to haemoglobin after the first oxygen binds.; Predicts which way the curve moves in an active muscle and what that does for unloading..

https://lightmysky.com/learn/science/haemoglobin-the-dissociation-curve-and-the-bohr-shift-mt_MmYJArGxrE

#### Monoclonal Antibodies and What They Are Used For (ages 17-18)

One antibody-producing cell fused to a dividing one gives an unlimited supply of a single antibody, and that single specificity is the whole point. Pregnancy tests, diagnostic stains and targeted cancer drugs are three uses of the same trick.

Ready when they can: Outline how a monoclonal antibody is produced and why the fusion step is needed; Explain how a lateral flow test gives a visible line from an antibody binding event; Weigh a benefit of an antibody-based therapy against a known side effect.

https://lightmysky.com/learn/science/monoclonal-antibodies-and-what-they-are-used-for-mt_YfxZrdvIIo

#### Synaptic Transmission, Summation and Inhibition (ages 17-18)

Calcium entry makes vesicles release transmitter, which binds receptors on the next cell. Several small inputs can add up, and some synapses make the next cell harder to fire rather than easier.

Ready when they can: Orders the steps from an arriving impulse to a response in the postsynaptic membrane.; Distinguishes spatial from temporal summation with an example of each.; Explains how an inhibitory synapse acts on the postsynaptic membrane..

https://lightmysky.com/learn/science/synaptic-transmission-summation-and-inhibition-mt_0uM8xRV92B

#### The Cardiac Cycle and Pressure in the Heart (ages 17-18)

Valves open and shut because of pressure differences, not because of nerve signals, and a pressure trace shows it. Reading the trace explains the order of atrial and ventricular contraction.

Ready when they can: Identifies systole and diastole on a pressure against time trace.; Explains each valve opening or closing from the pressure either side of it.; Relates the trace to the volume of blood leaving the ventricle in one beat..

https://lightmysky.com/learn/science/the-cardiac-cycle-and-pressure-in-the-heart-mt_iOSVyoV3Pj

#### The Sliding Filament Model of Muscle Contraction (ages 17-18)

Calcium released inside a fibre uncovers binding sites, and myosin heads pull actin filaments past each other in a repeating cycle that spends ATP. The filaments do not shorten; their overlap grows.

Ready when they can: Explains what happens to each band of the sarcomere during contraction.; Orders the steps of the cross-bridge cycle and says where ATP is used.; Links calcium release to the uncovering of the myosin binding sites..

https://lightmysky.com/learn/science/the-sliding-filament-model-of-muscle-contraction-mt_BsB4s4HfD8

#### Tissue Fluid and Its Return to the Circulation (ages 17-18)

Hydrostatic pressure forces fluid out of a capillary at the arteriole end, and water potential pulls most of it back at the venule end. Whatever is left returns through the lymph vessels.

Ready when they can: Compares hydrostatic pressure and water potential at the two ends of a capillary.; Says what leaves the capillary and what stays in the blood.; Links a build-up of tissue fluid to a change in one of the two pressures..

https://lightmysky.com/learn/science/tissue-fluid-and-its-return-to-the-circulation-mt_0jw7uXpK3C

#### Ultrafiltration and Selective Reabsorption in the Nephron (ages 17-18)

The glomerulus filters blood by the same pressure argument as any capillary, only harder, and the tubule then takes back what the body needs. Filtration and reabsorption are separate steps with separate mechanisms.

Ready when they can: Explains why pressure in the glomerulus is high enough to force filtration.; Names what is filtered out of the blood and what is too large to pass.; Describes how glucose is recovered from the filtrate and why it normally never reaches the urine..

https://lightmysky.com/learn/science/ultrafiltration-and-selective-reabsorption-in-the-nephron-mt_vSKfoJN6zh

#### Osmoregulation and the Action of ADH (ages 17-18)

The water potential of blood is held steady by changing how much water the collecting duct takes back. ADH is the signal and the permeability of one tubule wall is the effector.

Ready when they can: Traces the loop from a fall in blood water potential through to a change in urine volume.; Explains what ADH does to the collecting duct rather than to the kidney as a whole.; Predicts what happens to urine concentration after a large drink of water..

https://lightmysky.com/learn/science/osmoregulation-and-the-action-of-adh-mt_Rz_MmL-Pa-

#### Equilibrium Potentials and What Sets the Resting Voltage (ages 18-19)

Each ion has a voltage at which its electrical pull balances its concentration gradient, and that value can be calculated from the two concentrations. The membrane sits near the equilibrium potential of whichever ion it is currently most permeable to.

Ready when they can: Calculates an equilibrium potential from inside and outside concentrations.; Predicts how the resting voltage shifts when external potassium is raised.; Explains why the resting membrane sits near the potassium value but not exactly at it..

https://lightmysky.com/learn/science/equilibrium-potentials-and-what-sets-the-resting-voltage-mt_mRT_5vDEO1

#### Channel Kinetics and the Ionic Basis of the Spike (ages 18-19)

The action potential comes from two channel populations with different speeds: sodium channels that open fast and then inactivate, and potassium channels that open late. Clamping the voltage and measuring the current is what separated those two currents.

Ready when they can: Assigns each phase of the spike to the channel population responsible.; Distinguishes inactivation from closing, and links inactivation to the refractory period.; Explains what holding the voltage fixed allows an experimenter to measure..

https://lightmysky.com/learn/science/channel-kinetics-and-the-ionic-basis-of-the-spike-mt_47-LDzgcKp

#### Cable Properties and Dendritic Integration (ages 18-20)

A voltage change spreads along a dendrite and fades with distance, at a rate set by membrane resistance and internal resistance. Inputs arriving close together in time and space add up, and only their sum at the trigger zone decides whether a spike is fired.

Ready when they can: Explains why a distant synapse contributes less than a nearby one of the same size.; Predicts the effect of a thicker axon or more myelin on how far a signal spreads.; Combines several inputs at the trigger zone rather than judging each on its own..

https://lightmysky.com/learn/science/cable-properties-and-dendritic-integration-mt_bbPl-eJUFF

#### Regional Anatomy of the Central Nervous System (ages 19-20)

The brain and spinal cord are organised into regions with distinct cell populations and connections, and the pathways between them run in predictable places. Knowing where a tract runs is what lets a clinician infer the site of damage from the pattern of loss.

Ready when they can: Name the major divisions of the brain and spinal cord and state what each contains; Trace one ascending and one descending pathway, including where each crosses the midline; Infer the likely site of a lesion from a described pattern of lost function.

https://lightmysky.com/learn/science/regional-anatomy-of-the-central-nervous-system-mt_S9f5cUS8NZ

#### Tissue Types and How a Body Is Organised (ages 18-19)

Every organ is built from four tissue types, and knowing which one you are looking at tells you what it can do: cover a surface, connect and support, contract, or signal. Reading a section under a microscope is a matter of matching structure to that short list.

Ready when they can: Identify the four primary tissue types from their structure and name a location for each; Explain why epithelium sits on a basement membrane and what that boundary does; Relate the composition of a connective tissue to the mechanical job it performs.

https://lightmysky.com/learn/science/tissue-types-and-how-a-body-is-organised-mt_dQ-glI4kdz

#### Bone, Cartilage and the Mechanics of a Joint (ages 19-20)

Bone is a living connective tissue that is constantly rebuilt in response to load, which is why it heals and why it thins when unloaded. A joint is then a mechanical problem: the shapes of the surfaces set what movements are possible, and the muscles that cross it set which ones happen.

Ready when they can: Explain bone remodelling in terms of the two cell types that build and remove matrix; Relate the structure of a named synovial joint to its permitted range of movement; Work out the force in a muscle from the geometry of the lever it acts on.

https://lightmysky.com/learn/science/bone-cartilage-and-the-mechanics-of-a-joint-mt_1_q3aL7E5D

#### From Photons to Spikes: the Retina (ages 19-20)

A photoreceptor works backwards from most sensory cells: light closes channels and the cell hyperpolarises. The retina then does real processing before anything leaves the eye, subtracting a centre from its surround so that what the optic nerve carries is contrast rather than brightness.

Ready when they can: Describe phototransduction from photon absorption to a change in membrane potential; Explain centre-surround organisation and what it discards; Relate the distribution of rods and cones to the difference between night and daylight vision.

https://lightmysky.com/learn/science/from-photons-to-spikes-the-retina-mt_kviN7WskmP

#### Transmitter Systems and Two Kinds of Receptor (ages 19-20)

A transmitter can open a channel directly or act through a receptor that starts an internal cascade, which makes one effect fast and brief and the other slow and lasting. The same transmitter can do both, depending on which receptor the target cell carries.

Ready when they can: Predicts the time course of a response from the receptor type involved.; Explains how one transmitter can excite one cell and inhibit another.; Names a transmitter system and the behaviour it is associated with, without treating the link as one to one..

https://lightmysky.com/learn/science/transmitter-systems-and-two-kinds-of-receptor-mt_yXaSbrBxua

#### Synaptic Plasticity and the Molecular Rules of Change (ages 19-21)

A synapse strengthens when its input arrives just before the target cell fires, and weakens when the timing is reversed. Calcium entry through receptors that need both transmitter and depolarisation is what detects the coincidence.

Ready when they can: Explains how one receptor type acts as a detector of two conditions at once.; Predicts strengthening or weakening from the order of firing.; Links a lasting change in strength to a change in receptor number or transmitter release..

https://lightmysky.com/learn/science/synaptic-plasticity-and-the-molecular-rules-of-change-mt_HldevO4Lzw

#### Pacemaker Potentials, Conduction and Reading an ECG (ages 19-20)

Heart cells that drift towards threshold on their own set the rhythm, and the wave they start spreads through the muscle by a fixed route with a deliberate delay. The trace recorded at the skin is the sum of those events, so each deflection can be named.

Ready when they can: Names each deflection of the trace and the electrical event behind it.; Explains why the delay at the atrioventricular node is useful rather than a flaw.; Reads a rate and a rhythm irregularity from a trace..

https://lightmysky.com/learn/science/pacemaker-potentials-conduction-and-reading-an-ecg-mt_D-WKFc7BZm

#### Preload, Afterload and the Frank-Starling Relationship (ages 19-21)

A heart that fills more stretches more and ejects more, which is how the two sides keep matched output without any signal between them. Output is set by filling, by the resistance the heart pumps against and by contractility.

Ready when they can: Calculates cardiac output from stroke volume and rate, and predicts the effect of a change in filling.; Separates a change in preload from a change in contractility on a stated curve.; Explains how the right and left sides stay matched without direct communication..

https://lightmysky.com/learn/science/preload-afterload-and-the-frank-starling-relationship-mt_WK8o6OPZ-O

#### Building a Visual Scene: Pathways, Maps and Receptive Fields (ages 20-21)

Beyond the retina the visual system is a set of maps in which neighbouring cells look at neighbouring parts of the world, and each cell responds best to a specific feature in its own small window. What a cell prefers gets more elaborate at each stage, from edges to objects.

Ready when they can: Define a receptive field and describe how one is measured; Trace the pathway from retina to primary visual cortex, including what the crossing achieves; Explain how selectivity for an oriented edge could be built from simpler inputs.

https://lightmysky.com/learn/science/building-a-visual-scene-pathways-maps-and-receptive-fields-mt_wOc4YpkdYL

#### Touch, Temperature and Pain (ages 20-21)

The body surface is mapped onto the cortex the way the retina is mapped, but the area given to a region reflects how finely it is sampled rather than how large it is. Pain is the case where the map breaks down, because what is felt depends on modulation on the way in as much as on the injury.

Ready when they can: Relate receptor type and adaptation rate to the kind of touch each one reports; Explain why the cortical body map is distorted and what sets the distortion; Describe one mechanism by which pain is turned up or down before it reaches the brain.

https://lightmysky.com/learn/science/touch-temperature-and-pain-mt_rnSuJA4-kj

#### Hearing and Balance: Frequency, Place and Head Motion (ages 20-21)

The cochlea sorts sound by frequency mechanically, so position along it stands for pitch before any neuron is involved. The same hair cell, placed in fluid-filled loops instead, reports how the head is turning, which is why one organ serves two senses.

Ready when they can: Explain the place code for frequency and what part of the cochlea does the sorting; Describe hair cell transduction and why it is fast enough to follow sound; Say how the semicircular canals and otolith organs report different kinds of head motion.

https://lightmysky.com/learn/science/hearing-and-balance-frequency-place-and-head-motion-mt_qzPAt9JMOZ

#### Motor Control: From Intention to Muscle (ages 21-22)

Movement is produced by a hierarchy: the cord holds reflex circuits and pattern generators, the brainstem handles posture, and the cortex specifies what to do rather than which muscle to use. Errors are corrected by loops through the cerebellum and basal ganglia, which is why damage there degrades movement without paralysing it.

Ready when they can: Distinguish the roles of spinal, brainstem and cortical levels in a single reaching movement; Explain what a motor unit is and how force is graded by recruitment; Contrast the movement disorder caused by cerebellar damage with the one caused by basal ganglia damage.

https://lightmysky.com/learn/science/motor-control-from-intention-to-muscle-mt_hrWOuRtPDl

#### Memory Systems: What Amnesia Separates (ages 21-22)

Memory is not one store: patients who cannot form new episodes still learn skills, and that dissociation is the main evidence that different structures do different jobs. The hippocampus is needed to acquire an episode but not to keep it forever, which is why consolidation is treated as a separate process.

Ready when they can: Distinguish declarative from non-declarative memory using evidence from a described case; Explain what systems consolidation claims and what evidence supports it; Relate a synaptic change to a behavioural memory without claiming they are the same thing.

https://lightmysky.com/learn/science/memory-systems-what-amnesia-separates-mt_oNFXpEHl8b

#### Acid-Base Balance: The Bicarbonate System and Compensation (ages 20-22)

Blood pH is held in a narrow range by a buffer whose two components are controlled separately: carbon dioxide by the lungs and bicarbonate by the kidneys. Because one is fast and the other slow, a disturbance in one can be partly offset by the other.

Ready when they can: Classifies a disturbance as respiratory or metabolic from pH, carbon dioxide and bicarbonate together.; Explains which organ compensates and roughly how quickly.; Says why a compensated result still shows the original disturbance..

https://lightmysky.com/learn/science/acid-base-balance-the-bicarbonate-system-and-compensation-mt_LFLgZre62C

#### Hormone Classes and Why Their Receptors Sit in Different Places (ages 20-21)

Water-soluble hormones cannot cross the membrane, so they bind receptors on the surface and act through cascades within seconds. Steroid and thyroid hormones cross, bind receptors inside and change transcription, which takes hours but lasts longer.

Ready when they can: Predicts the receptor location and response time from the chemistry of the hormone.; Explains why a steroid response outlasts a peptide response.; Links transport in the blood to whether the hormone dissolves in water..

https://lightmysky.com/learn/science/hormone-classes-and-why-their-receptors-sit-in-different-places-mt_GAg2xTiKVL

#### Hypothalamic and Pituitary Axes and Layered Feedback (ages 20-22)

Several hormone systems run through three levels, with each level releasing a hormone that drives the next and the final product suppressing both levels above it. That arrangement gives amplification going down and stability coming back.

Ready when they can: Traces one axis from the hypothalamus to the target gland and back through feedback.; Predicts hormone levels at all three levels when the target gland fails.; Explains why long-term treatment with the final hormone suppresses the axis above it..

https://lightmysky.com/learn/science/hypothalamic-and-pituitary-axes-and-layered-feedback-mt_tgRAAq3Poe

#### Lung Mechanics: Compliance, Surface Tension and the Work of Breathing (ages 20-21)

Filling the lungs means overcoming both the stretch of the tissue and the surface tension of the film lining each alveolus. Surfactant lowers that tension more in small alveoli than in large ones, which stops the small ones emptying into the big ones.

Ready when they can: Explains why surface tension would collapse small alveoli without surfactant.; Reads a pressure-volume loop as compliance and as work done.; Predicts the effect of stiffer lung tissue on the effort of breathing..

https://lightmysky.com/learn/science/lung-mechanics-compliance-surface-tension-and-the-work-of-breathing-mt_vNZEKuTjYQ

#### Resistance, Flow and the Regulation of Blood Pressure (ages 20-21)

Flow through a vessel depends steeply on its radius, so small changes in arteriole diameter make large changes in resistance. Pressure is held within range by fast reflexes that adjust rate, contractility and diameter, and by slower control of blood volume.

Ready when they can: Predicts the change in resistance when a vessel radius halves.; Traces the reflex from a stretch receptor to a corrected pressure.; Separates the fast neural correction from the slower volume correction by their time scales..

https://lightmysky.com/learn/science/resistance-flow-and-the-regulation-of-blood-pressure-mt_EvmGvDGNja

#### The Autonomic Nervous System and Its Two Outflows (ages 20-21)

A separate motor system runs the organs without conscious control, through two outflows that leave the cord at different levels and usually oppose each other. Because each outflow uses its own transmitters and receptors, most drugs that affect heart rate, pupils or gut motility act here.

Ready when they can: Contrast the sympathetic and parasympathetic outflows by origin, ganglion position and transmitter; Predict the effect on a named organ of blocking one receptor type; Explain an autonomic reflex as a loop with a sensor, an integrator and an effector.

https://lightmysky.com/learn/science/the-autonomic-nervous-system-and-its-two-outflows-mt_bnVgu4T4E9

#### Ventilation and Perfusion Matching, and the Control of Breathing (ages 20-22)

Gas exchange only works where air and blood arrive in the right ratio, and local vessel and airway responses steer both towards the regions that need them. Breathing rate is set mainly by carbon dioxide sensed as a change in pH, not by oxygen.

Ready when they can: Explains what happens to gas exchange when a region is ventilated but not perfused.; Names the main chemical stimulus for breathing rate and says why oxygen is the backup.; Predicts the ventilation response to a rise in blood carbon dioxide..

https://lightmysky.com/learn/science/ventilation-and-perfusion-matching-and-the-control-of-breathing-mt_O89KdcN_Vv

#### Adaptive Immunity: Antigen Presentation and T-Cell Selection (ages 21-22)

Cells display fragments of the proteins inside them on surface molecules, and T cells inspect those displays. Because the useful receptors are selected during development, the system reacts to what is foreign and normally ignores what is not.

Ready when they can: Distinguishes display of internal proteins from display of engulfed material by which T cell responds.; Explains how selection during development produces a repertoire that is useful and tolerant.; Says why a virus-infected cell can be killed while a healthy neighbour is not..

https://lightmysky.com/learn/science/adaptive-immunity-antigen-presentation-and-t-cell-selection-mt_8hTGqrnqGY

#### Antibody Diversity, Memory and What Tolerance Failure Costs (ages 21-22)

A limited set of gene segments is rearranged and mutated to give an enormous range of antibodies, and the cells that bind best are selected and kept. Memory explains why a second exposure is faster and stronger, and failures of tolerance explain autoimmunity and allergy.

Ready when they can: Explains how a small number of gene segments produces a very large receptor repertoire.; Compares the primary and secondary responses by speed, size and antibody quality.; Places one autoimmune and one allergic condition as specific failures rather than as too much immunity..

https://lightmysky.com/learn/science/antibody-diversity-memory-and-what-tolerance-failure-costs-mt_5YXKhiOqoA

#### Fuel Homeostasis and the Fed to Fasted Switch (ages 21-22)

After a meal insulin drives storage, and as fuel runs low glucagon and the counter-regulatory hormones release it again, with the liver switching direction between the two states. The switch is a pair of opposing signals acting on the same enzymes.

Ready when they can: Names what the liver, muscle and fat tissue each do in the fed and the fasted state.; Explains why two opposing hormones control the same enzymes rather than one hormone alone.; Traces the order in which fuel stores are used during a long fast..

https://lightmysky.com/learn/science/fuel-homeostasis-and-the-fed-to-fasted-switch-mt_zZrXwbWqw-

#### Innate Immunity: Pattern Recognition, Complement and Inflammation (ages 21-22)

The first response recognises molecular patterns shared by whole classes of microbe rather than any particular one, so it works within minutes without prior exposure. Complement proteins and the changes of inflammation both bring more defence to the site.

Ready when they can: Explains what a pattern receptor recognises and why that makes the response fast but general.; Links each sign of inflammation to a change in blood vessels or cell traffic.; Says what complement does once it is activated, beyond marking the target..

https://lightmysky.com/learn/science/innate-immunity-pattern-recognition-complement-and-inflammation-mt_3TcgoOGI0L

#### Sleep, Circadian Rhythms and the Clock in the Brain (ages 21-22)

A clock built from a gene loop inside single cells runs near a day, and light resets it through a dedicated pathway from the retina. Sleep itself is a sequence of states with distinct electrical signatures, and what is lost when it is disrupted is a way of testing what those states are for.

Ready when they can: Explain how a transcription and translation feedback loop produces a near-daily rhythm; Describe how light entrains the clock and why the pathway is separate from image-forming vision; Identify the sleep stages from their signatures and state what each has been linked to.

https://lightmysky.com/learn/science/sleep-circadian-rhythms-and-the-clock-in-the-brain-mt_cXx4SaLJUM

#### The Stress Response: Fast Nerves, Slow Hormones and the Cost of Staying On (ages 21-22)

A threat triggers a nerve-driven response in seconds and a hormone-driven one over minutes to hours, and the two do different jobs. The system is useful when it switches off, and much of its damage comes from staying on.

Ready when they can: Separates the fast and slow arms of the response by their signals and their time courses.; Explains what cortisol does to fuel availability and to the immune response.; Links long-running activation to a named cost rather than to stress in general..

https://lightmysky.com/learn/science/the-stress-response-fast-nerves-slow-hormones-and-the-cost-of-staying-on-mt_4ZxCU21ziH

#### Checkpoint Blockade: Taking a Brake Off a T Cell (ages 22-24)

Inhibitory receptors that normally limit T-cell responses are used by tumours to avoid killing, and antibodies against those receptors restore it in a minority of patients. This stop covers the mechanism, the markers that predict response, and the autoimmune cost.

Ready when they can: Explain how blocking CTLA-4 and blocking PD-1 act at different points of a T-cell response; Interpret mutational burden and antigen presentation status as predictors of response; Relate immune-related adverse events to the mechanism of the drug rather than to off-target effects.

https://lightmysky.com/learn/science/checkpoint-blockade-taking-a-brake-off-a-t-cell-mt_f9P4LlaBGb

#### Clinical Trials: Phases, Endpoints and Why Most Candidates Fail (ages 23-24)

Trial design decides what a result is allowed to claim: which patients, which comparator, which endpoint measured when. This stop reads a protocol and locates the point at which most candidates stop.

Ready when they can: State what each trial phase is designed to establish, and for which population; Distinguish a surrogate endpoint from a clinical one and say what each can support; Explain why efficacy failures cluster where they do and what that says about target choice.

https://lightmysky.com/learn/science/clinical-trials-phases-endpoints-and-why-most-candidates-fail-mt_xKBKzSYxLh

#### Engineered Cell Therapy: Receptor Design, Manufacture and Toxicity (ages 23-24)

A chimeric antigen receptor gives a patient's own T cells a new specificity that does not depend on antigen presentation. This stop follows the design choices through manufacture and into the toxicities they cause.

Ready when they can: Explain what each domain of a chimeric receptor contributes to the response it produces; State why solid tumours have proved harder targets than B-cell malignancies; Relate cytokine release syndrome and on-target off-tumour toxicity back to specific design decisions.

https://lightmysky.com/learn/science/engineered-cell-therapy-receptor-design-manufacture-and-toxicity-mt_e15TOnMMwL

### Genetics & Evolution

https://lightmysky.com/learn/science/areas/genetics-and-evolution

#### Meiosis and Why Gametes Are Haploid (ages 14-16)

Meiosis halves the chromosome number and makes four cells that are genetically different, so fertilisation puts the full set back. The contrast with mitosis is what explains why offspring vary and clones do not.

Ready when they can: States how many cells meiosis makes and how their chromosome number compares with the parent cell.; Explains what fertilisation restores, and why the number would otherwise double every generation.; Names the points in meiosis that make the four cells genetically different from each other..

https://lightmysky.com/learn/science/meiosis-and-why-gametes-are-haploid-mt_hvu0bczcfX

#### DNA Structure and Base Pairing (ages 15-16)

DNA is two strands of nucleotides wound into a double helix, with A always pairing to T and C to G. That pairing rule is what makes an exact copy possible before a cell divides.

Ready when they can: Names the three parts of a nucleotide and states the pairing rule between the bases.; Writes the complementary strand for a short given sequence.; Explains how base pairing lets one strand act as a template for its own copy..

https://lightmysky.com/learn/science/dna-structure-and-base-pairing-mt_PK4uNJeg_k

#### From Gene to Protein (ages 15-16)

A gene is a length of DNA whose base order fixes the amino acid order of one protein, read three bases at a time. Covers the messenger copy, the ribosome, and reading a codon table.

Ready when they can: Uses a codon table to turn a short base sequence into a run of amino acids.; Explains why the code is read in threes rather than singly or in pairs.; Says where in the cell each stage happens and why the message has to leave the nucleus..

https://lightmysky.com/learn/science/from-gene-to-protein-mt_PdNyzTl8Ye

#### Mutations and Their Effect on Proteins (ages 15-16)

A change to one base may change one amino acid, and a changed amino acid may change the shape the protein folds into. Explains why most mutations do nothing while a few change everything.

Ready when they can: Works out what a given single base change does to the amino acid sequence.; Explains why a mutation in an enzyme's active site matters more than one further along the chain.; Gives a reason why most mutations have no visible effect at all..

https://lightmysky.com/learn/science/mutations-and-their-effect-on-proteins-mt_dTOQH3vGSz

#### Punnett Squares and Monohybrid Ratios (ages 15-16)

Draw a Punnett square for a cross between two known genotypes and read off the expected ratio of offspring. Covers dominant and recessive alleles, homozygous and heterozygous, and genotype against phenotype.

Ready when they can: Completes a Punnett square for a monohybrid cross and states the phenotype ratio.; Uses the right term for a genotype with two identical alleles and for one with two different alleles.; Explains why a predicted 3 to 1 ratio rarely comes out exactly in a real litter..

https://lightmysky.com/learn/science/punnett-squares-and-monohybrid-ratios-mt_T4ZC45-77w

#### Sex Determination and Inherited Disorders (ages 15-16)

The X and Y chromosomes decide sex, which is why crossing XX with XY gives an even chance either way. The same squares, plus a family tree, give the probability that a child inherits a recessive disorder.

Ready when they can: Draws the cross that explains the roughly equal ratio of male to female births.; Reads a family tree and picks out a carrier.; Calculates the probability that two carriers have an affected child..

https://lightmysky.com/learn/science/sex-determination-and-inherited-disorders-mt_PJQnvtnO0D

#### Selective Breeding and Genetic Engineering (ages 15-16)

Selective breeding decides which individuals reproduce, generation after generation, while genetic engineering moves a gene from one organism straight into another. Compares what each can do, how long it takes, and the risks people raise.

Ready when they can: Describes the repeated steps of selective breeding and says why it takes generations.; Explains what inbreeding costs a population that has been bred for one trait.; States one benefit and one objection for a named engineered crop or bacterium..

https://lightmysky.com/learn/science/selective-breeding-and-genetic-engineering-mt_a3zTtiYrR2

#### Cloning: Cuttings, Tissue Culture and Adult Cell Cloning (ages 15-16)

A clone is an organism with the same genome as another, and plants have been making them without help for as long as there have been plants. Doing it from an adult animal cell is harder because the cell has to be persuaded to forget what it had become.

Ready when they can: Describe how a cutting and a tissue culture each produce clones, and say which one scales; Outline adult cell cloning as nuclear transfer into an enucleated egg; Give one reason cloning is useful and one risk that follows from a population having no genetic variation.

https://lightmysky.com/learn/science/cloning-cuttings-tissue-culture-and-adult-cell-cloning-mt_3NaPCGrZTg

#### Speciation and the Rate of Evolution (ages 15-16)

Two populations kept apart pile up different changes until they can no longer breed together and produce fertile offspring. Covers isolation, the evidence in DNA and fossils, and why the rate is not steady.

Ready when they can: Describes a sequence from one population to two species and names the isolating step.; Says what evidence would show that two similar-looking populations are now separate species.; Gives one reason why evolution can be fast in one period and slow in another..

https://lightmysky.com/learn/science/speciation-and-the-rate-of-evolution-mt_OdcdfeRyo1

#### Semi-conservative DNA Replication (ages 16-17)

Each new DNA molecule keeps one original strand and one newly built one. Helicase, DNA polymerase and the split into leading and lagging strands explain how base pairing gets copied.

Ready when they can: States what each new molecule inherits from the parent molecule.; Names the enzymes that unwind and that build, and says what each one needs.; Explains why one strand is built continuously and the other in fragments..

https://lightmysky.com/learn/science/semi-conservative-dna-replication-mt_wIcBfUw295

#### Taxonomy, the Three Domains and What a Species Name Encodes (ages 16-17)

A two-word species name places an organism inside a nested hierarchy, and every rank in that hierarchy is a claim about shared ancestry. The three-domain split was forced by molecular evidence that contradicted the older picture, which is why classification is treated as a hypothesis rather than a filing system.

Ready when they can: Place an organism in the taxonomic hierarchy and explain what each rank asserts; Explain why molecular data split the prokaryotes into two domains; Say what makes a classification wrong, and give the kind of evidence that would revise one.

https://lightmysky.com/learn/science/taxonomy-the-three-domains-and-what-a-species-name-encodes-mt_12ucjuHtHE

#### Transcription and RNA Splicing in Eukaryotes (ages 16-17)

RNA polymerase copies one strand into pre-mRNA, and introns are cut out before the message leaves the nucleus. Splicing is why one gene can give more than one protein.

Ready when they can: Says which DNA strand acts as the template and what the immediate product is.; Distinguishes introns from exons by what happens to each before translation.; Explains how alternative splicing lets one gene produce different proteins..

https://lightmysky.com/learn/science/transcription-and-rna-splicing-in-eukaryotes-mt_j2vc70vH5t

#### Translation at the Ribosome (ages 16-18)

The ribosome reads codons and tRNA brings the matching amino acid, turning a base sequence into an amino acid sequence. The code is degenerate, non-overlapping and read from a fixed start.

Ready when they can: Matches a codon to its anticodon and says what the tRNA carries.; Uses a codon table to build a short amino acid sequence from an mRNA sequence.; Explains what degeneracy means for a change in the third base of a codon..

https://lightmysky.com/learn/science/translation-at-the-ribosome-mt_1EdZzeqts1

#### Transcription Factors and Epigenetic Control (ages 17-18)

Transcription factors bind DNA and decide which genes are read, while methylation and histone changes decide which genes can be reached at all. Both are reversible and neither alters the base sequence.

Ready when they can: Explains how a transcription factor changes the rate at which a gene is transcribed.; Distinguishes a change in DNA methylation from a change in the DNA sequence.; Links a heritable change in expression to chromatin state rather than to mutation..

https://lightmysky.com/learn/science/transcription-factors-and-epigenetic-control-mt_nF4JJ_EDa4

#### Gene Mutations and Their Consequences (ages 17-18)

Substitutions, insertions and deletions change a gene in different ways, and only some of them change the protein. A frame shift does the most damage because every codon after it is misread.

Ready when they can: Classifies a mutation from the change in the base sequence.; Explains why a substitution is often silent while a single deletion rarely is.; Traces a frame shift through to the protein and says why the effect is so large..

https://lightmysky.com/learn/science/gene-mutations-and-their-consequences-mt_CDcaL6-iVp

#### Dihybrid Crosses and the 9:3:3:1 Ratio (ages 17-18)

Two gene pairs on different chromosomes assort independently, so a cross between two double heterozygotes gives four phenotypes in a 9:3:3:1 ratio. The grid is four by four and the ratio is a prediction, not a law.

Ready when they can: Sets out the four gamete types from a doubly heterozygous parent.; Completes a four by four grid and reads the phenotype ratio off it.; Names the stage of meiosis at which independent assortment happens..

https://lightmysky.com/learn/science/dihybrid-crosses-and-the-9-3-3-1-ratio-mt_9IlVo04Dbt

#### Testing Genetic Ratios with Chi-squared (ages 17-18)

Observed offspring counts never match a predicted ratio exactly, so chi-squared measures whether the gap is bigger than chance would give. The test hands back a decision, not a proof.

Ready when they can: Calculates expected counts from a predicted ratio and a total.; Works out the chi-squared value and compares it with the critical value at the right degrees of freedom.; States what accepting or rejecting the null hypothesis means for the cross..

https://lightmysky.com/learn/science/testing-genetic-ratios-with-chi-squared-mt_YCO6jijrNQ

#### The Hardy-Weinberg Principle and Allele Frequencies (ages 17-18)

In a population that meets a short list of conditions, allele and genotype frequencies stay put from one generation to the next. Departures from that prediction are how selection gets detected.

Ready when they can: Calculates allele frequencies from genotype counts and genotype counts from allele frequencies.; Lists the conditions the model assumes and names a real population that breaks one of them.; Explains why a change in the frequencies across generations counts as evidence of selection..

https://lightmysky.com/learn/science/the-hardy-weinberg-principle-and-allele-frequencies-mt_eJjwZ2qVAE

#### Recombinant DNA and Gene Transfer (ages 17-18)

Restriction enzymes cut DNA at named sequences, ligase joins the pieces, and a vector carries the gene into a host cell. Marker genes are how the few successful cells get found.

Ready when they can: Explains why sticky ends produced by the same restriction enzyme join.; Orders the steps from isolating a gene to a host cell expressing it.; Says what a marker gene is for and why most transformed cells fail..

https://lightmysky.com/learn/science/recombinant-dna-and-gene-transfer-mt_L9yncU_x2P

#### PCR, Electrophoresis and DNA Profiling (ages 17-18)

PCR copies a chosen stretch of DNA through repeated heating and cooling, and electrophoresis then sorts the fragments by length. A profile compares repeat lengths rather than reading whole genes.

Ready when they can: States what each temperature step in a PCR cycle does.; Explains why shorter fragments travel further through the gel.; Says which part of the genome a profile compares and why it differs between people..

https://lightmysky.com/learn/science/pcr-electrophoresis-and-dna-profiling-mt_Sv1jV0XnsX

#### Linkage, Recombination Frequency and Genetic Maps (ages 18-19)

Genes on the same chromosome are inherited together unless a crossover separates them, so the proportion of recombinant offspring measures how far apart they sit. Frequencies from several crosses can be assembled into a map order.

Ready when they can: Calculates recombination frequency from offspring counts and states it in map units.; Orders three genes from pairwise frequencies, and explains why the outer distance comes out short.; Recognises a frequency near fifty per cent as unlinked rather than as a very long distance..

https://lightmysky.com/learn/science/linkage-recombination-frequency-and-genetic-maps-mt_xBjZXt3TVn

#### Epistasis and Reading Pathway Order from Double Mutants (ages 18-19)

When one gene masks the effect of another, the offspring ratios change in ways that say which gene acts first. Combining two mutations in one organism is how the order of steps in a pathway is worked out.

Ready when they can: Reads a modified dihybrid ratio and names the interaction that produced it.; Infers which of two genes acts earlier in a pathway from the double mutant phenotype.; Separates epistasis from dominance rather than treating both as one gene overriding another..

https://lightmysky.com/learn/science/epistasis-and-reading-pathway-order-from-double-mutants-mt_eE2WRPyYPk

#### Quantitative Traits, Variance Components and Heritability (ages 18-20)

Traits governed by many genes vary continuously, and the observed variance can be split into genetic and environmental parts. Heritability is the share of variance that is genetic in one population and one environment, which is not the same as how much of the trait is inherited.

Ready when they can: Splits a stated total variance into its components and calculates heritability.; Explains why heritability changes when the environment changes, with the population unchanged.; Rejects the reading that a heritability of 0.6 means sixty per cent of an individual's trait comes from genes..

https://lightmysky.com/learn/science/quantitative-traits-variance-components-and-heritability-mt_orJhIlYnKM

#### Chromatin: Nucleosomes and Higher-Order Packing (ages 18-20)

Two metres of DNA fit in a nucleus by wrapping around histone cores and coiling those into thicker fibres. The packing is not just storage: how tightly a region is packed decides whether it can be read.

Ready when they can: Describes the levels of packing from bare DNA to a condensed chromosome with rough scale at each level.; Explains why histones bind DNA regardless of sequence, using the charge on each.; Links a tightly packed region to low transcription without claiming the genes are absent..

https://lightmysky.com/learn/science/chromatin-nucleosomes-and-higher-order-packing-mt_5q3Hsdqm9x

#### Selection Coefficients and Predicting Allele Frequency Change (ages 18-19)

Giving each genotype a relative fitness turns selection into arithmetic: the frequency after one generation follows from the frequencies before and the fitnesses. Working the change out generation by generation shows how slowly a rare recessive allele is removed.

Ready when they can: Calculates allele frequency after one generation from genotype frequencies and fitnesses.; Explains why selection against a recessive allele slows as the allele becomes rare.; Distinguishes relative fitness from survival or family size taken alone..

https://lightmysky.com/learn/science/selection-coefficients-and-predicting-allele-frequency-change-mt__JS2XJxOXV

#### Genetic Drift and Effective Population Size (ages 18-19)

Allele frequencies wander from generation to generation because gametes are a sample, and the smaller the population the wider that wandering. The effective size, which counts breeding individuals unevenly, is usually well below the number of individuals present.

Ready when they can: Explains drift as sampling error rather than as a force pushing in a direction.; Predicts the fate of a neutral allele in a small population over many generations.; Says why the effective size is smaller than the census size, with one cause named..

https://lightmysky.com/learn/science/genetic-drift-and-effective-population-size-mt_lbB1GbKv_t

#### Mutation, Gene Flow and the Balance That Holds Variation (ages 18-20)

Mutation makes new alleles slowly and migration moves existing ones between populations quickly, while selection and drift remove them. What is observed is the balance of those inputs and outputs rather than any of them alone.

Ready when they can: Explains why a harmful recessive allele persists at low frequency instead of disappearing.; Predicts what steady migration does to the difference between two populations.; Ranks mutation and migration by how fast each changes a frequency..

https://lightmysky.com/learn/science/mutation-gene-flow-and-the-balance-that-holds-variation-mt_A2UgDE0ORv

#### The Neutral Theory and Reading a Molecular Clock (ages 19-20)

Most substitutions between species change nothing about fitness, so they accumulate at a rate set by the mutation rate rather than by selection. That regularity is what lets sequence differences be read as elapsed time, once the clock is calibrated.

Ready when they can: Explains why neutral substitutions accumulate at a steady rate.; Estimates a divergence time from a difference count and a calibrated rate.; Says why the clock runs at different rates in different genes and in different lineages..

https://lightmysky.com/learn/science/the-neutral-theory-and-reading-a-molecular-clock-mt_yIidVpa703

#### Selection on Quantitative Traits and Predicting the Response (ages 19-20)

When selection acts on a continuous trait, the response over one generation is the strength of selection multiplied by the heritable share of variation. That single relation covers artificial breeding and natural selection alike.

Ready when they can: Predicts the mean of the next generation from a selection differential and a heritability.; Distinguishes directional, stabilising and disruptive selection by what happens to mean and spread.; Explains why the response stalls after many generations of the same selection..

https://lightmysky.com/learn/science/selection-on-quantitative-traits-and-predicting-the-response-mt_M-czTLDmfl

#### Speciation: Isolation, Hybrid Zones and Where the Boundary Blurs (ages 19-21)

Populations become separate species as barriers accumulate before and after mating, and those barriers can be geographic, behavioural or genetic. Hybrid zones show that the boundary is often partial, which is why one species definition does not fit every case.

Ready when they can: Sorts barriers into those acting before mating and those acting after, with an example of each.; Explains what a stable hybrid zone implies about the strength of the barriers.; Says why the interbreeding definition fails for asexual and for fossil organisms..

https://lightmysky.com/learn/science/speciation-isolation-hybrid-zones-and-where-the-boundary-blurs-mt_ngZxpFlwo1

#### Building a Phylogeny: Homology, Shared Derived Characters and Parsimony (ages 19-21)

A tree is built from characters that are shared because of common ancestry, not because of similar conditions, and only the derived states group taxa together. Parsimony picks the tree that needs the fewest changes to explain the data.

Ready when they can: Separates homology from convergence using a stated character and its distribution.; Counts the changes a candidate tree requires and compares two trees on that count.; Explains why shared ancestral states do not define a group..

https://lightmysky.com/learn/science/building-a-phylogeny-homology-shared-derived-characters-and-parsimony-mt_GFmiVZ8g-F

#### Homologous Recombination and Double-Strand Break Repair (ages 19-21)

A break across both strands is repaired by invading a matching sequence and copying from it, which is also how crossovers form in meiosis. The same mechanism is what makes targeted gene replacement possible.

Ready when they can: Traces a double-strand break through strand invasion to a repaired duplex.; Explains why this route needs a homologous partner and the alternative route does not.; Links the mechanism to the crossovers counted in a linkage map..

https://lightmysky.com/learn/science/homologous-recombination-and-double-strand-break-repair-mt_yWlwqAsXEf

#### Cancer as Clonal Evolution: Drivers, Passengers and Selection in a Tissue (ages 22-23)

A tumour is a cell population under selection inside a body, so population genetics applies to it directly. This stop separates driver from passenger mutations and reads a tumour's history out of its mutation data.

Ready when they can: Argue from recurrence and mutation frequency whether a gene is a plausible driver; Explain what subclonal structure in a sequenced tumour says about the order of events; Apply selection and drift arguments to a growing population of somatic cells.

https://lightmysky.com/learn/science/cancer-as-clonal-evolution-drivers-passengers-and-selection-in-a-tissue-mt_3qIJZwD0m5

#### Oncogenes and Tumour Suppressors: Why One Allele Is Sometimes Enough (ages 22-23)

Gain-of-function and loss-of-function lesions behave differently in a pedigree and in a tumour: a single altered allele can drive, while a suppressor usually needs both copies lost. This stop reads that difference out of inheritance patterns and tumour genotypes.

Ready when they can: Predict dominance or recessiveness from the mechanism of a stated mutation; Explain loss of heterozygosity and how it is detected in tumour sequence data; Use a familial cancer pedigree to argue which class a gene belongs to.

https://lightmysky.com/learn/science/oncogenes-and-tumour-suppressors-why-one-allele-is-sometimes-enough-mt_7WTgv1dLNx

#### Enhancers, Accessibility and Combinatorial Control (ages 19-21)

Sequences far from a gene raise its transcription by looping into contact with the promoter, and they only work when the chromatin there is open. Which genes a cell expresses is decided by which combination of factors is present, not by one master switch per gene.

Ready when they can: Explains how a sequence thousands of bases away affects a promoter.; Says why the same enhancer is active in one cell type and silent in another.; Predicts the expression pattern from a stated combination of available factors..

https://lightmysky.com/learn/science/enhancers-accessibility-and-combinatorial-control-mt_BTMCj6V6jD

#### Small RNAs and Silencing After Transcription (ages 20-21)

Short RNAs pair with a matching transcript and mark it for cutting or block its translation. A gene can therefore be fully transcribed and still produce almost no protein.

Ready when they can: Explains how base pairing gives the silencing its specificity.; Distinguishes cutting the transcript from blocking its translation by what happens to mRNA levels.; Predicts what a measurement of mRNA alone would miss in a silenced cell..

https://lightmysky.com/learn/science/small-rnas-and-silencing-after-transcription-mt_1AozDyS1Mn

#### Methylation, Histone Marks and Heritable Expression States (ages 20-22)

Chemical marks on DNA and on histone tails are copied when a cell divides, so a pattern of gene activity can be passed to daughter cells without any change in sequence. The marks are readable, writable and erasable, which is what makes them a control system.

Ready when they can: Explains how a methylation pattern survives replication.; Distinguishes an epigenetic change from a mutation by what is altered and what is not.; Gives one case where an environmental input leaves a lasting mark on expression..

https://lightmysky.com/learn/science/methylation-histone-marks-and-heritable-expression-states-mt_QIEjt77tjV

#### Sequencing Reads and How a Genome Is Assembled (ages 20-22)

Sequencing instruments produce many short reads rather than one long sequence, and a genome is rebuilt by finding where reads overlap. Coverage and read length decide which regions can be resolved and which stay ambiguous.

Ready when they can: Explains why repeated sequences are the hard part of assembly.; Says what coverage means and why more of it improves base accuracy.; Chooses between short and long reads for a stated purpose, with a reason..

https://lightmysky.com/learn/science/sequencing-reads-and-how-a-genome-is-assembled-mt_4mUJIUAZGd

#### Sequence Alignment and Reading a Search Result (ages 20-22)

Two sequences are compared by scoring matches, mismatches and gaps, and the best alignment is the one with the highest total score. A database search returns hits ranked by that score with a statistic saying how often such a match would appear by chance.

Ready when they can: Scores a short alignment by hand under a stated scheme, gaps included.; Reads a search result and separates a strong hit from a chance one using the reported statistic.; Explains why a short query returns weak statistics even for a perfect match..

https://lightmysky.com/learn/science/sequence-alignment-and-reading-a-search-result-mt_jNbEMFqgZ5

#### Distance and Likelihood Trees, and What Branch Support Means (ages 20-21)

Sequence-based trees are built either from pairwise distances or by asking which tree makes the observed data most probable under a model of change. Support values report how often a branch survives resampling, which is a statement about the data rather than about the truth of the branch.

Ready when they can: Explains what a model of sequence change adds beyond counting differences.; Reads a support value correctly as repeatability, not as probability of being right.; Identifies a poorly supported node in a published tree and says what would improve it..

https://lightmysky.com/learn/science/distance-and-likelihood-trees-and-what-branch-support-means-mt_mEO9PUEdh6

#### Using Trees: Ancestral States, Dates and Comparative Tests (ages 20-21)

Once a tree exists it becomes a tool: it reconstructs what an ancestor probably looked like, dates splits against fossils and corrects comparisons between species for shared ancestry. Species are not independent data points, which is the mistake the comparative method exists to avoid.

Ready when they can: Reconstructs a likely ancestral state from the distribution of states on a tree.; Explains why comparing species without a tree overstates the evidence.; Uses a fossil calibration to convert branch lengths into dates..

https://lightmysky.com/learn/science/using-trees-ancestral-states-dates-and-comparative-tests-mt_lEYWID9Ffs

#### Annotation, Orthologues and Comparative Genomics (ages 21-22)

An assembled genome is only useful once genes are located and their likely functions assigned, usually by similarity to genes already studied elsewhere. Comparing species shows which sequences have been conserved, which is a strong hint that they matter.

Ready when they can: Distinguishes genes related by speciation from genes related by duplication, and says why the difference matters for function.; Uses conservation across distant species as evidence of function, and states the limits of that argument.; Explains why an annotation transferred by similarity is a hypothesis rather than a result..

https://lightmysky.com/learn/science/annotation-orthologues-and-comparative-genomics-mt_eBRge2bLeC

#### Association Studies and What They Can and Cannot Show (ages 21-22)

Scanning many variants across many people finds positions where one allele is more common in affected individuals. The hit is usually a marker near the causal variant rather than the cause, and the effect of any one variant is normally small.

Ready when they can: Explains why a hit points to a region rather than to a gene.; Says why a strict significance threshold is needed when a million positions are tested.; Rejects the reading that an associated variant predicts an individual's outcome..

https://lightmysky.com/learn/science/association-studies-and-what-they-can-and-cannot-show-mt_IFFUFX3xrv

#### Measuring Genetic Variation: Heterozygosity and Population Structure (ages 21-22)

Variation within a population is summarised by how often individuals carry two different alleles, and variation between populations by how much of the total sits between rather than within groups. Those two numbers turn samples of sequence into a statement about how populations are connected.

Ready when they can: Calculates expected heterozygosity from allele frequencies.; Interprets a between-population index as gene flow or its absence.; Explains why a sample from two mixed populations looks short of heterozygotes..

https://lightmysky.com/learn/science/measuring-genetic-variation-heterozygosity-and-population-structure-mt_Prn7vgkyLl

#### Alignment Scoring: Substitution Matrices, Gap Penalties and Significance (ages 22-23)

An alignment is only as meaningful as the score that produced it. This stop derives substitution scores from observed substitution frequencies, sets gap penalties deliberately, and asks whether a score that good would arise by chance.

Ready when they can: Explain how a log-odds substitution matrix is built from aligned sequences of known relatedness; Choose a matrix and a gap penalty appropriate to a stated evolutionary distance; Interpret an E-value and say why it moves when the database grows.

https://lightmysky.com/learn/science/alignment-scoring-substitution-matrices-gap-penalties-and-significance-mt_k--A8iF5SC

#### Hidden Markov Models for Sequence: Profiles, States and Decoding (ages 22-23)

A profile hidden Markov model represents a whole family by position-specific emission and transition probabilities rather than by one representative sequence. This stop covers the decoding step that assigns states to a new sequence and what it buys.

Ready when they can: Describe the match, insert and delete states of a profile model and what each one emits; Explain what a single most probable path gives that per-position posteriors do not; Say why a profile search recovers remote homologues that a pairwise search misses.

https://lightmysky.com/learn/science/hidden-markov-models-for-sequence-profiles-states-and-decoding-mt_nk14IaZTcw

#### Models of Sequence Evolution and Maximum Likelihood Trees (ages 22-23)

Estimating a tree by likelihood needs an explicit model of how sites change: a rate matrix, an account of rate variation across sites, and a way to compare candidate models. This stop connects the model chosen to the tree that comes out.

Ready when they can: Compare Jukes-Cantor, HKY and the general time-reversible model by the parameters each adds; Explain what a gamma rate parameter corrects for and what goes wrong when it is left out; Interpret the likelihood of a tree given an alignment and a stated model.

https://lightmysky.com/learn/science/models-of-sequence-evolution-and-maximum-likelihood-trees-mt_Ujtg0xul9N

#### Bayesian Phylogenetics: Priors, Sampling and Judging Convergence (ages 22-24)

A Bayesian analysis returns a distribution over trees rather than a single tree, sampled by a Markov chain. This stop covers what the priors do to the answer and how to tell a converged chain from one that only looks settled.

Ready when they can: State what a posterior probability on a clade claims, and how it differs from a bootstrap proportion; Explain the effect of the tree prior and the clock prior on a dated analysis; Diagnose a chain from effective sample size, trace plots and agreement between independent runs.

https://lightmysky.com/learn/science/bayesian-phylogenetics-priors-sampling-and-judging-convergence-mt_7jWhYh1n5X

#### Phylogenomics: Gene Trees, Species Trees and Why They Disagree (ages 22-24)

Different genes give different trees for the same set of species, through incomplete lineage sorting, introgression, duplication and plain estimation error. This stop separates those causes and uses methods that expect the conflict instead of hiding it.

Ready when they can: Distinguish incomplete lineage sorting from introgression using tree topology counts and site patterns; Explain when concatenating genes is misleading and what a coalescent summary method does instead; Read a set of gene trees and locate the nodes where the conflict is real rather than noise.

https://lightmysky.com/learn/science/phylogenomics-gene-trees-species-trees-and-why-they-disagree-mt_rg7feIg1D4

#### Differential Expression from Counts: Dispersion, Fit and Shrinkage (ages 22-24)

Sequencing gives counts, not measurements, and counts carry a mean-variance relationship that a normal model gets wrong. This stop fits a count model, borrows information across genes to estimate dispersion, and reads the result honestly.

Ready when they can: Explain why read counts need a negative binomial rather than a normal or Poisson model; Say what library-size normalisation corrects and what composition effects it cannot fix; Interpret shrunken fold changes and explain why low-count genes move the most.

https://lightmysky.com/learn/science/differential-expression-from-counts-dispersion-fit-and-shrinkage-mt_nEV9547kSN

#### Testing Thousands of Genes at Once: False Discovery Rate and What q Means (ages 23-24)

With twenty thousand tests, a five percent error rate on each one is meaningless. This stop separates family-wise error control from false discovery rate control and reads a q-value for exactly what it claims.

Ready when they can: Contrast Bonferroni with a false discovery rate procedure applied to the same p-value list; State what a q-value of 0.05 asserts about a list of genes rather than about one gene; Explain how pre-filtering or an independent covariate changes the number of discoveries.

https://lightmysky.com/learn/science/testing-thousands-of-genes-at-once-false-discovery-rate-and-what-q-means-mt_mIQ27rphrC

#### From a Gene List to Biology: Enrichment Tests and Their Backgrounds (ages 23-24)

Enrichment analysis asks whether a gene list is unusually full of some annotated category, and the answer depends entirely on the background set chosen. This stop runs the test properly and names the biases that make it lie.

Ready when they can: Run and interpret an over-representation test against a stated, defensible background set; Explain how gene length and expression level bias enrichment results; Compare an over-representation test with a rank-based method on the same data.

https://lightmysky.com/learn/science/from-a-gene-list-to-biology-enrichment-tests-and-their-backgrounds-mt_M9eHEXq6iA

#### Gene Regulatory Networks: Motifs and What They Compute (ages 22-23)

A regulatory network is more than a list of activators and repressors: small recurring wiring patterns such as autoregulation, feed-forward loops and mutual repression each produce a characteristic response over time. This stop reads a network diagram as a computation rather than as a picture.

Ready when they can: Identify autoregulation, coherent and incoherent feed-forward loops, and mutual repression in a published network diagram; Predict the delay, pulse or persistence a given motif produces when its input switches on; Argue why the same motif turns up independently in bacteria, yeast and animal development.

https://lightmysky.com/learn/science/gene-regulatory-networks-motifs-and-what-they-compute-mt_QWMKReB10f

#### Stochastic Gene Expression: Bursting, Noise and Cell-to-Cell Variation (ages 22-23)

Transcription happens in bursts, so genetically identical cells in one flask hold different amounts of the same protein. This stop separates intrinsic from extrinsic noise and works out what each does to the distribution across a population.

Ready when they can: Distinguish intrinsic from extrinsic noise using the two-reporter experiment that separates them; Relate burst size and burst frequency to the mean and variance of protein number per cell; Argue when variation is a nuisance to be averaged away and when a cell uses it to pick a fate.

https://lightmysky.com/learn/science/stochastic-gene-expression-bursting-noise-and-cell-to-cell-variation-mt_YD6DOmrvng

#### Single-Cell RNA Sequencing: From Droplets to a Count Matrix (ages 22-23)

A single-cell protocol captures one cell per droplet, tags its transcripts with a cell barcode and a molecular identifier, and returns a sparse matrix of counts. This stop follows the sample through the bench steps that decide what that matrix can support.

Ready when they can: Trace a transcript from lysis through barcoding, amplification and sequencing to one entry in the count matrix; Explain what unique molecular identifiers correct for and what they leave uncorrected; Name the artefacts the protocol introduces: doublets, empty droplets, ambient RNA and dropout.

https://lightmysky.com/learn/science/single-cell-rna-sequencing-from-droplets-to-a-count-matrix-mt_QCoqY7w_De

#### Mapping Regulatory Elements: Accessibility, Occupancy and Contact (ages 22-24)

Three assay families answer three different questions about a piece of DNA: which regions are open, which protein sits there, and which distant regions touch it. This stop matches the question to the assay and to the controls its claim needs.

Ready when they can: Choose between an accessibility, an occupancy and a contact assay for a stated claim about an element; State the control that keeps each assay honest, including input and non-specific antibody controls; Read a genome browser track and say what it shows and what it does not show about function.

https://lightmysky.com/learn/science/mapping-regulatory-elements-accessibility-occupancy-and-contact-mt_W2YKGBADJ-

#### Single-Cell Analysis: Normalisation, Embedding and Naming Cell States (ages 23-24)

A count matrix becomes a cell atlas through normalisation, feature selection, a linear reduction, a neighbour graph and a clustering step, each with choices that move the answer. This stop makes the choices explicit and tests how much the conclusion rests on them.

Ready when they can: Justify a normalisation and feature-selection choice for a stated dataset; Explain what a two-dimensional embedding preserves and what it distorts; Assign an identity to a cluster from marker genes and state the evidence a label needs.

https://lightmysky.com/learn/science/single-cell-analysis-normalisation-embedding-and-naming-cell-states-mt_diYHLaLmij

#### Modelling a Biological System: Rate Equations, Parameters and Fit (ages 23-24)

A mechanistic model turns a pathway diagram into rate equations whose parameters have to be estimated from data and whose behaviour has to be checked against data held back. This stop asks what the data can identify before any conclusion is drawn from a fit.

Ready when they can: Write rate equations for a small pathway and state the units of every parameter; Distinguish a parameter the data can identify from one that only trades off against another; Use a sensitivity analysis to say which parameter the model's conclusion actually depends on.

https://lightmysky.com/learn/science/modelling-a-biological-system-rate-equations-parameters-and-fit-mt_Al6sNjUOW5

#### Genome Engineering: Cut Site, Repair Choice and Editing Outcome (ages 22-24)

The nuclease only makes a break; the cell decides the edit. This stop works out how guide design, the repair pathway available in that cell type and the donor template together determine which allele you end up with.

Ready when they can: Design a guide for a target site and predict the indel spectrum end joining will produce; Explain why homology-directed repair rates depend on cell cycle stage and on the donor design; Assess off-target risk from guide sequence and from the sensitivity of the assay used to measure it.

https://lightmysky.com/learn/science/genome-engineering-cut-site-repair-choice-and-editing-outcome-mt_3DqvkO4wdE

#### Base and Prime Editing: Changing a Letter Without Breaking Both Strands (ages 22-24)

Base editors tether a deaminase to a disabled nuclease and rewrite one letter inside a narrow window, while prime editors write from a template carried on the guide itself. This stop compares what each class can install and how each one goes wrong.

Ready when they can: State which base changes each editor class can and cannot make; Explain the editing window and why bystander edits appear next to the intended one; Compare the off-target profile of base editing, prime editing and a plain nuclease cut.

https://lightmysky.com/learn/science/base-and-prime-editing-changing-a-letter-without-breaking-both-strands-mt_roM4eWoWVn

#### Pooled Genetic Screens: Library Design, Selection and Reading a Hit List (ages 23-24)

A pooled screen turns a biological question into a counting problem: which guides are enriched or depleted after a selection. This stop covers library coverage, the choice of selection pressure, and how a real hit is told apart from a noisy guide.

Ready when they can: Work out the cell number a library of stated size needs for a stated coverage; Choose a positive or a negative selection design for a stated biological question; Judge a hit list using agreement between guides targeting the same gene, control guides and effect size.

https://lightmysky.com/learn/science/pooled-genetic-screens-library-design-selection-and-reading-a-hit-list-mt_0n-a7GfLOL

### Biochemistry & Molecular Biology

https://lightmysky.com/learn/science/areas/biochemistry-and-molecular-biology

#### Deriving the Michaelis-Menten Equation from the Steady State (ages 18-19)

Assuming the enzyme-substrate complex is formed and broken down at the same rate turns a scheme of four rate constants into one equation with two measurable constants. Seeing where each constant comes from explains why the Michaelis constant is not a binding constant.

Ready when they can: Derives the rate equation from the steady-state assumption and states where that assumption holds.; Explains the Michaelis constant in terms of the rate constants that make it up.; Says what the maximum rate depends on and why raising substrate further cannot pass it..

https://lightmysky.com/learn/science/deriving-the-michaelis-menten-equation-from-the-steady-state-mt_BFp0fwZ8_i

#### Double-Reciprocal Plots and Telling Inhibitor Types Apart (ages 18-19)

Plotting reciprocals turns a curve into a straight line whose intercepts give the two constants directly. Each inhibition type moves a different intercept, so the plot identifies the mechanism rather than just showing that the rate fell.

Ready when they can: Reads the maximum rate and the Michaelis constant from the intercepts of a straight-line plot.; Identifies competitive, uncompetitive and non-competitive inhibition from which intercept moves.; Explains why competitive inhibition can be overcome by more substrate and the others cannot..

https://lightmysky.com/learn/science/double-reciprocal-plots-and-telling-inhibitor-types-apart-mt_9y397ROu9X

#### How Enzymes Lower the Activation Barrier (ages 18-20)

Catalysis comes from binding the transition state more tightly than the substrate, helped by holding reactants together, straining bonds and moving protons at the right moment. The enzyme changes the path, never the position of the equilibrium.

Ready when they can: Names three catalytic strategies and matches each to what it does to the barrier.; Explains why tighter binding of the transition state, not of the substrate, is what speeds the reaction.; States that a catalyst leaves the equilibrium position unchanged and says why..

https://lightmysky.com/learn/science/how-enzymes-lower-the-activation-barrier-mt_uwB5TXF3Nb

#### Protein Folding, Chaperones and What Misfolding Costs (ages 18-19)

A chain of amino acids reaches its working shape by burying hydrophobic side chains and settling into the lowest free energy it can find. Chaperones keep partly folded chains apart while that happens, and a chain that ends up in the wrong shape is either recycled or aggregates.

Ready when they can: Explains folding as a search down a free-energy funnel rather than a fixed sequence of steps.; Says what a chaperone does and does not do: it prevents wrong contacts, it does not carry folding information.; Links an aggregation disease to the shape a chain took rather than to a missing protein..

https://lightmysky.com/learn/science/protein-folding-chaperones-and-what-misfolding-costs-mt_n9rlqjbaXK

#### Post-translational Modification and Protein Turnover (ages 18-19)

Most proteins are altered after they are made: phosphate groups, sugars, lipid tails and cleaved segments all change what a protein does. Tagging with ubiquitin sends it to the proteasome, so the amount of a protein is set by degradation as much as by synthesis.

Ready when they can: Names a modification and says what it changes: activity, location, binding partners or lifetime.; Explains why a cell with unchanged transcription can still change its protein levels.; Reads a half-life difference between two proteins as a statement about tagging and degradation..

https://lightmysky.com/learn/science/post-translational-modification-and-protein-turnover-mt_93cxQwxxkh

#### Allosteric Enzymes, Cooperativity and the Sigmoid Curve (ages 19-20)

Enzymes with several subunits can shift between a low-activity and a high-activity form, so binding at one site changes affinity at the others. The result is an S-shaped response that makes the enzyme act like a switch over a narrow concentration range.

Ready when they can: Explains why cooperativity produces a sigmoid curve instead of a hyperbolic one.; Predicts the effect of an allosteric activator and inhibitor on the position of that curve.; Links the switch-like response to control of a pathway rather than to faster catalysis..

https://lightmysky.com/learn/science/allosteric-enzymes-cooperativity-and-the-sigmoid-curve-mt_u8f5QLHq-g

#### Coenzymes, Cofactors and the Chemistry They Supply (ages 19-20)

Amino acid side chains cannot do every chemical job, so enzymes recruit metal ions and small organic molecules to carry electrons, groups or single carbons. Many of those helpers are what vitamins are for.

Ready when they can: Matches a coenzyme to the group or electrons it carries.; Explains what a metal ion contributes that a side chain cannot.; Links a vitamin deficiency to a specific reaction that stalls..

https://lightmysky.com/learn/science/coenzymes-cofactors-and-the-chemistry-they-supply-mt_CZ2ytn3SQr

#### Coupled Reactions and Why ATP Is the Cell's Currency (ages 19-21)

An unfavourable reaction proceeds when it shares an intermediate with a favourable one, so the two free energy changes add. ATP is used because its hydrolysis releases a useful amount, not the largest amount available.

Ready when they can: Adds free energy changes for a coupled pair and decides whether the pair proceeds.; Explains coupling through a shared intermediate rather than as energy being handed over.; Says why a compound with a much larger release is not a better currency..

https://lightmysky.com/learn/science/coupled-reactions-and-why-atp-is-the-cells-currency-mt_1yVJRArCow

#### Control Points in Glycolysis and the Committed Step (ages 19-21)

Only a few reactions in a pathway are far from equilibrium, and those are where regulation acts. In glycolysis the committed step responds to signals about how much energy the cell already has, which is why the pathway speeds up when demand rises.

Ready when they can: Identifies the irreversible steps of the pathway and explains why control sits there.; Predicts the flux response to a rise in the cell's energy charge.; Explains why regulating a near-equilibrium step would do little..

https://lightmysky.com/learn/science/control-points-in-glycolysis-and-the-committed-step-mt_2vAoKtnmoz

#### Replication Machinery: Origins, Forks and Telomeres (ages 19-20)

Replication starts at defined origins and runs in both directions, with one strand made continuously and the other in pieces. Because polymerase cannot start a chain or work backwards, linear chromosomes lose a little end sequence each round unless telomerase restores it.

Ready when they can: Explains the lagging strand as a consequence of the direction polymerase can work in.; Says why primers are needed and what removes them.; Links the end replication problem to telomere shortening and to what telomerase does about it..

https://lightmysky.com/learn/science/replication-machinery-origins-forks-and-telomeres-mt_v95MJWeV_B

#### DNA Damage and the Repair Pathways That Fix It (ages 19-20)

Bases are damaged constantly by chemistry inside the cell and by radiation outside it, and each kind of damage has a repair route matched to it. Proofreading and mismatch repair together cut the error rate of copying by orders of magnitude.

Ready when they can: Matches a damage type to a repair pathway and says what the pathway uses as its template.; Explains how mismatch repair knows which of the two strands carries the error.; Links a repair pathway failure to a raised mutation rate rather than to an immediate phenotype..

https://lightmysky.com/learn/science/dna-damage-and-the-repair-pathways-that-fix-it-mt_r0qipp0YRR

#### Transcription Initiation: Promoters, General Factors and Polymerase Recruitment (ages 19-21)

Eukaryotic polymerase does not find a promoter alone: general factors assemble on it first and position the enzyme at the start site. The rate of transcription is set mostly at this assembly step.

Ready when they can: Describes assembly at a promoter in order and says which step commits the enzyme.; Explains why initiation, rather than elongation, is the usual control point.; Contrasts the bacterial single-factor arrangement with the eukaryotic assembly..

https://lightmysky.com/learn/science/transcription-initiation-promoters-general-factors-and-polymerase-recruitment-mt_0Ky-pYgh0Y

#### Alternative Splicing and One Gene, Many Proteins (ages 20-21)

The spliceosome can include or skip particular exons, so one gene yields several related proteins depending on cell type and conditions. Which sites are used is set by regulatory proteins binding near them.

Ready when they can: Works out the possible mature transcripts from a stated exon arrangement.; Explains what decides which splice sites are used in a given cell.; Links a mutation at a splice site to a protein change without calling it a coding change..

https://lightmysky.com/learn/science/alternative-splicing-and-one-gene-many-proteins-mt_xei9v3IIsE

#### Gluconeogenesis and the Reciprocal Regulation of Opposing Pathways (ages 20-21)

Making glucose is not glycolysis run backwards: the three irreversible steps are bypassed by different enzymes, which is what allows separate control. Signals that activate one direction inhibit the other, so the cell avoids running both and wasting ATP.

Ready when they can: Names the steps that need bypass enzymes and says why reversal is impossible there.; Explains how one signal can activate one pathway and inhibit the opposite one.; Calculates the ATP cost of a futile cycle if both directions ran at once..

https://lightmysky.com/learn/science/gluconeogenesis-and-the-reciprocal-regulation-of-opposing-pathways-mt_D1MbKcb6Le

#### The Citric Acid Cycle as a Hub, and Refilling It (ages 20-21)

The cycle both oxidises acetyl groups and supplies carbon skeletons for biosynthesis, so intermediates are constantly withdrawn. Because it is a cycle, those withdrawals stop it unless separate reactions top the intermediates back up.

Ready when they can: Names two intermediates withdrawn for biosynthesis and what they become.; Explains why removing an intermediate slows the whole cycle.; Identifies a reaction that replenishes an intermediate and says when it is needed..

https://lightmysky.com/learn/science/the-citric-acid-cycle-as-a-hub-and-refilling-it-mt_BPPfI-vnab

#### Redox Potentials and the Proton-Motive Force (ages 20-21)

Electrons pass down a chain of carriers arranged in order of their standard potentials, and the energy released at three points is used to move protons out. The gradient stores that energy as both a concentration difference and a voltage.

Ready when they can: Orders carriers by potential and calculates the energy available for a stated electron transfer.; Separates the two components of the proton-motive force and says which dominates in mitochondria.; Predicts what an uncoupler does to electron flow and to ATP production..

https://lightmysky.com/learn/science/redox-potentials-and-the-proton-motive-force-mt_lU8kgepFRN

#### ATP Synthase as a Rotary Machine (ages 20-22)

Protons flowing back through the membrane turn a rotor, and that rotation changes the shape of three catalytic sites in turn so each binds, forms and releases ATP. The step that costs energy is releasing the product, not making the bond.

Ready when they can: Links proton flow to rotation and rotation to the cycle of site states.; Explains why release rather than bond formation is the energy-requiring step.; Predicts what happens when the enzyme runs in reverse..

https://lightmysky.com/learn/science/atp-synthase-as-a-rotary-machine-mt_PDe3f-FVfD

#### Fatty Acid Oxidation, Ketone Bodies and Choosing a Fuel (ages 20-22)

Fatty acids are shortened two carbons at a time, feeding acetyl groups into the cycle and reduced carriers into the chain, which is why fat yields more ATP per carbon than sugar. When carbohydrate runs low the liver converts some of that acetyl into ketone bodies the brain can use.

Ready when they can: Calculates the ATP yield of a stated fatty acid from the rounds it takes to break down.; Explains why fat cannot be converted to glucose in humans.; Links ketone body production to a shortage of cycle intermediates rather than to fat excess..

https://lightmysky.com/learn/science/fatty-acid-oxidation-ketone-bodies-and-choosing-a-fuel-mt_2GNrC-0ziR

#### Fluorescent Tagging and Reading a Live-Cell Image (ages 21-22)

Fusing a fluorescent protein to a gene lets a specific protein be watched in a living cell, and antibodies stained with dyes do the same job in fixed cells. Both methods report location and timing, and both can change the thing they measure.

Ready when they can: Chooses between a genetic tag and an antibody stain for a stated question, with a reason.; Reads a two-colour image as a claim about location, and says what it does not prove.; Names one way a tag changes the behaviour of the protein it labels..

https://lightmysky.com/learn/science/fluorescent-tagging-and-reading-a-live-cell-image-mt_J0toch-ZZ3

#### Fractionation, Blotting and Pulling Down a Binding Partner (ages 21-22)

Breaking cells open and spinning them at increasing speeds separates organelles by size and density, and a blot then asks whether a named protein is present in a fraction. Precipitating one protein with an antibody brings its partners with it, which is how binding is tested.

Ready when they can: Predicts which fraction an organelle appears in from a centrifugation scheme.; Reads a blot as presence, absence and rough amount, with a loading control taken into account.; Explains why a pull-down result can be a real partner or a shared third partner..

https://lightmysky.com/learn/science/fractionation-blotting-and-pulling-down-a-binding-partner-mt_MRfFQlBIPy

#### The Pentose Phosphate Pathway and Reducing Power for Biosynthesis (ages 21-22)

A branch off glycolysis produces the reduced carrier used for building molecules and for defending against oxidative damage, plus the five-carbon sugars needed for nucleotides. The cell adjusts the branch according to whether it needs reducing power, ribose or both.

Ready when they can: Distinguishes the carrier used for biosynthesis from the one that feeds the electron transport chain.; Explains what a rapidly dividing cell needs from this pathway.; Links a deficiency in the first enzyme to red cells being vulnerable to oxidative stress..

https://lightmysky.com/learn/science/the-pentose-phosphate-pathway-and-reducing-power-for-biosynthesis-mt_2p-JnaEaTO

#### Transamination, Ammonia and the Urea Cycle (ages 21-22)

Amino groups are moved onto keto acids rather than released, and only at the end is nitrogen freed as ammonia, which is toxic. The liver converts it into urea in a cycle that costs ATP, and the carbon skeletons left behind enter metabolism elsewhere.

Ready when they can: Traces an amino group from an amino acid to urea, naming what happens at each transfer.; Explains why the cell moves amino groups around instead of releasing ammonia immediately.; Says what becomes of the carbon skeleton after the amino group is removed..

https://lightmysky.com/learn/science/transamination-ammonia-and-the-urea-cycle-mt_MFu5uQKyFL

#### Flux Control and Following Atoms with Labelled Substrates (ages 21-22)

Control of a pathway is usually shared between several enzymes rather than held by one, and how much each holds can be measured. Feeding a substrate whose atoms are labelled and seeing where they appear is how the routes actually taken are established.

Ready when they can: Explains why calling one enzyme the rate-limiting step is usually an approximation.; Predicts where a label ends up given a stated pathway and starting position.; Uses a labelling result to choose between two proposed routes..

https://lightmysky.com/learn/science/flux-control-and-following-atoms-with-labelled-substrates-mt_PzhsDwD_aW

#### Proteomics: Mass Spectra, Quantification and Interaction Maps (ages 23-24)

Mass spectrometry identifies peptides from mass and fragmentation, and quantification turns spectra into abundances that can be compared between conditions. This stop covers what a proteome measurement misses and how an interaction map is built and misread.

Ready when they can: Describe how a peptide spectrum is matched to a sequence and what the false discovery rate there controls; Compare label-free and isotope-label quantification for a stated comparison; Explain why an affinity-purification interaction list needs both a control pull-down and a scoring step.

https://lightmysky.com/learn/science/proteomics-mass-spectra-quantification-and-interaction-maps-mt_a-8UHB2SFR

#### Target Validation and Lead Discovery: From a Biological Claim to a Molecule (ages 23-24)

A target is worth pursuing only if changing it changes disease and if a molecule can reach it. This stop covers genetic and chemical validation, screening for hits, and the properties a hit has to gain before it counts as a lead.

Ready when they can: Distinguish genetic validation of a target from chemical validation, and say what each leaves open; Explain what a screening hit has to survive before anyone calls it a lead; Relate potency, selectivity and exposure to whether a molecule can work in a body.

https://lightmysky.com/learn/science/target-validation-and-lead-discovery-from-a-biological-claim-to-a-molecule-mt_xHWq5Rg85r

### Microbiology

https://lightmysky.com/learn/science/areas/microbiology

#### Bacterial Cell Envelopes and What the Gram Stain Reveals (ages 18-19)

Bacteria differ in how their wall is built: a thick peptidoglycan layer outside the membrane, or a thin one sandwiched under a second outer membrane. The stain that separates the two works because those structures hold or release dye differently, which is why it predicts so much else.

Ready when they can: Explains the stain result from the wall structure rather than as a colour rule to remember.; Links the outer membrane to reduced entry of some antibiotics.; Predicts what happens to a cell whose peptidoglycan cannot be cross-linked..

https://lightmysky.com/learn/science/bacterial-cell-envelopes-and-what-the-gram-stain-reveals-mt_Q5zM0oO3Vu

#### Archaea: Different Membranes, Extreme Habitats, Separate Domain (ages 18-19)

Archaea build their membrane lipids with ether links and branched chains rather than ester links and straight chains, which holds up under heat, salt and acid. Their transcription and translation machinery is closer to ours than to that of bacteria, which is why they are a separate domain.

Ready when they can: Names two chemical differences in archaeal membranes and links each to stability.; Explains what evidence put archaea on a separate branch from bacteria.; Rejects the idea that archaea are bacteria that happen to live in hard places..

https://lightmysky.com/learn/science/archaea-different-membranes-extreme-habitats-separate-domain-mt_isKmuoGgAn

#### Microbial Growth: Generation Time, Growth Curves and Continuous Culture (ages 18-20)

A population that doubles at a fixed interval grows exponentially, so counts are handled on a log scale and generation time is read from the slope. A closed flask passes through lag, exponential, stationary and death phases, while a chemostat holds a culture in one phase by feeding it steadily.

Ready when they can: Calculates generation time from two counts and the time between them.; Explains why the exponential phase is a straight line only on a log axis.; Says what a chemostat controls that a closed flask cannot..

https://lightmysky.com/learn/science/microbial-growth-generation-time-growth-curves-and-continuous-culture-mt_ltzgjIBytk

#### Controlling Growth: What Sterile Means and How It Is Achieved (ages 18-20)

Heat, radiation, filtration and chemicals each kill or remove microbes by a particular mechanism, and each has organisms it handles badly. Killing follows a rate rather than an instant, so sterilisation is defined by how far the count is driven down.

Ready when they can: Chooses a control method for a stated material and organism, with a reason.; Explains why endospores set the standard for a sterilisation cycle.; Distinguishes killing from inhibiting by what happens after the agent is removed..

https://lightmysky.com/learn/science/controlling-growth-what-sterile-means-and-how-it-is-achieved-mt_j1kqpjUMzk

#### Metabolic Diversity: Choosing an Electron Donor and Acceptor (ages 19-20)

Microbes are classified by where they get carbon, where they get energy and what they pass electrons to at the end. The energy available depends on the gap between donor and acceptor, which is why oxygen respirers outgrow the alternatives when oxygen is present.

Ready when they can: Classifies an organism from its carbon source, energy source and terminal acceptor.; Ranks acceptors by the energy yield they allow and explains the ranking.; Predicts which metabolism dominates as a sediment loses oxygen with depth..

https://lightmysky.com/learn/science/metabolic-diversity-choosing-an-electron-donor-and-acceptor-mt__2yCr9OSIn

#### Virus Structure and Classification by Genome Type (ages 19-20)

A virus is a genome in a protein coat, sometimes wrapped in a membrane taken from a host. Grouping viruses by whether the genome is DNA or RNA, single or double stranded, and which way it reads predicts what has to happen first inside the cell.

Ready when they can: Works out the first step a virus must take from its genome type.; Explains why an envelope changes how a virus enters and how it survives outside.; Says why viruses are not counted as cells, using two specific criteria..

https://lightmysky.com/learn/science/virus-structure-and-classification-by-genome-type-mt_u2-ecQEwwn

#### Viral Life Cycles: Lysis, Lysogeny and Latency (ages 19-21)

A virus can replicate at once and burst the cell, or integrate and be copied quietly with the host genome until conditions change. The choice is a regulated decision, not an accident, and it explains why some infections recur years later.

Ready when they can: Traces both routes from entry to release, naming the point where they diverge.; Explains what conditions push an integrated virus back into replication.; Links latency to a recurring human infection rather than to a dormant organism..

https://lightmysky.com/learn/science/viral-life-cycles-lysis-lysogeny-and-latency-mt_OI8-dySb5A

#### Bacteriophages as Predators and as Laboratory Tools (ages 19-21)

Phages shape bacterial populations in the wild and were the system in which much of molecular genetics was first worked out. Their specificity for a host strain is what makes them useful for typing bacteria and for delivering genes.

Ready when they can: Explains what host range means and what determines it.; Reads a plaque assay as a count of infectious particles.; Gives one use of phages that depends on their narrow specificity..

https://lightmysky.com/learn/science/bacteriophages-as-predators-and-as-laboratory-tools-mt_vOnjSpXjrj

#### Operon Logic: Induction, Repression and Feedback on Transcription (ages 19-21)

Bacteria group related genes under one promoter and switch the whole set on or off with a repressor or activator that senses a small molecule. Whether the default is on or off depends on whether the pathway breaks something down or builds it.

Ready when they can: Predicts expression from the presence of a substrate or a product for a stated operon.; Explains why a catabolic operon is normally off and an anabolic one normally on.; Works out the phenotype of a mutation in the repressor or in its binding site..

https://lightmysky.com/learn/science/operon-logic-induction-repression-and-feedback-on-transcription-mt_yNvJjGMSJQ

#### Horizontal Gene Transfer: Uptake, Contact and Delivery (ages 20-21)

Bacteria acquire genes from other cells by taking up free DNA, by direct contact through a pilus, or by delivery inside a phage particle. Because transfer crosses species lines, a bacterial family tree drawn from one gene can disagree with one drawn from another.

Ready when they can: Distinguishes the three routes by what carries the DNA and what the recipient must do.; Designs a test that tells one route from another, such as separating cells with a filter.; Explains why transfer complicates a phylogeny built from a single gene..

https://lightmysky.com/learn/science/horizontal-gene-transfer-uptake-contact-and-delivery-mt_mrmn0_nQf7

#### Plasmids, Mobile Elements and How Resistance Spreads (ages 20-21)

Many resistance genes sit on plasmids and transposons that move between replicons and between cells, often several at once on one element. That is why resistance spreads faster than any single bacterial lineage could carry it.

Ready when they can: Explains why a plasmid can be gained and lost while the chromosome stays the same.; Links multiple resistances appearing together to one mobile element carrying several genes.; Predicts what happens to plasmid frequency when the selecting drug is withdrawn..

https://lightmysky.com/learn/science/plasmids-mobile-elements-and-how-resistance-spreads-mt_Vk0qOY64qv

#### CRISPR: A Bacterial Defence Turned into a Tool (ages 20-22)

Bacteria keep fragments of past invaders in an array and use transcripts of those fragments to guide a nuclease to matching sequences. Supplying a guide of our own choosing turns the same system into a way of cutting a chosen site in any genome.

Ready when they can: Explains how the array records past infections and how that record is used.; Says what decides where the nuclease cuts, and what stops it cutting the array itself.; Links the cut to a genome edit through the repair route the cell then uses..

https://lightmysky.com/learn/science/crispr-a-bacterial-defence-turned-into-a-tool-mt_0joPWRvOLw

#### Pathogenesis: Adhesion, Invasion and Virulence Factors (ages 20-22)

Causing disease takes a sequence of steps: reaching a surface, sticking to it, getting past defences and obtaining nutrients such as iron. Each step depends on specific molecules, and losing one of them can make a pathogen harmless.

Ready when they can: Orders the steps of an infection and names a factor used at each.; Explains why sticking to a particular tissue decides which disease results.; Predicts the effect of deleting one adhesion gene on the ability to infect..

https://lightmysky.com/learn/science/pathogenesis-adhesion-invasion-and-virulence-factors-mt_8SPj_E5foc

#### Exotoxins, Endotoxin and How Damage Is Actually Done (ages 20-22)

Some damage comes from secreted proteins with precise targets inside host cells, and some from a membrane component released when Gram-negative cells break up. The two differ in specificity, in potency and in whether heat destroys them.

Ready when they can: Separates a secreted protein toxin from endotoxin by source, specificity and heat stability.; Explains why an antibiotic that lyses cells can briefly make a patient worse.; Links a named toxin to the host process it disables..

https://lightmysky.com/learn/science/exotoxins-endotoxin-and-how-damage-is-actually-done-mt_RhMqBY_YhR

#### Antimicrobial Targets, Resistance Mechanisms and Selective Toxicity (ages 21-22)

A useful drug hits something the microbe has and we do not, such as the wall, the ribosome or a folate enzyme. Resistance arises by changing the target, destroying the drug, pumping it out or keeping it from entering, and the drug does not create those changes but selects for them.

Ready when they can: Matches a drug class to its target and explains what makes that target selective.; Names four resistance mechanisms and gives an example of each.; States why finishing a course and restricting use follow from selection rather than from tolerance..

https://lightmysky.com/learn/science/antimicrobial-targets-resistance-mechanisms-and-selective-toxicity-mt_fta5Ty8Liu

#### Epidemiology: Incidence, the Reproduction Number and Tracking an Outbreak (ages 21-22)

How fast a disease spreads is summarised by the average number of new cases one case produces, and that number falls as susceptible people run out or are protected. Incidence and prevalence answer different questions, and confusing them misreads an outbreak.

Ready when they can: Distinguishes incidence from prevalence with a case where they move in opposite directions.; Explains what a reproduction number above and below one implies for an outbreak.; Calculates the proportion that must be immune to hold the effective number below one..

https://lightmysky.com/learn/science/epidemiology-incidence-the-reproduction-number-and-tracking-an-outbreak-mt_f2tT08sEki

#### Applied Microbiology: Fermentation, Bioremediation and Host Microbiomes (ages 21-22)

Microbial metabolism is put to work to make foods and medicines, to break down pollutants and to keep host surfaces occupied by harmless residents. In each case the practical question is which conditions favour the organism we want over the ones we do not.

Ready when they can: Explains how conditions in a process are set to favour one metabolism over others.; Says what limits bioremediation for a given pollutant.; Describes one way a resident community protects its host without invoking immunity..

https://lightmysky.com/learn/science/applied-microbiology-fermentation-bioremediation-and-host-microbiomes-mt_WcfGvV_dD9

#### Synthetic Circuits: Switches, Oscillators and Why They Misbehave in Cells (ages 23-24)

A toggle switch and a ring oscillator are built from the same motifs found in natural networks, then fail in ways the design did not predict. This stop treats retroactivity, competition for shared resources and mutation as engineering constraints.

Ready when they can: Explain what makes a two-repressor toggle bistable and what sets its switching threshold; Predict how attaching a downstream module changes the behaviour of the module driving it; Give two reasons a working circuit stops working after many generations of growth.

https://lightmysky.com/learn/science/synthetic-circuits-switches-oscillators-and-why-they-misbehave-in-cells-mt_xRJGSHidqo

#### Metabolic Engineering: Redirecting Flux Through a Production Host (ages 23-24)

Making a host produce a chosen molecule means moving carbon and reducing power away from growth without killing the cell. This stop designs that trade using pathway balance, branch-point control and regulation that switches on at the right time.

Ready when they can: Balance a transplanted pathway for carbon, ATP and redox cofactors; Identify the branch point where flux leaks away and propose a change that redirects it; Explain why a growth-coupled or inducible design usually beats constant overexpression.

https://lightmysky.com/learn/science/metabolic-engineering-redirecting-flux-through-a-production-host-mt_fjz3EA-dDa

#### The Host Microbiome: Composition, Causation and Intervention (ages 23-24)

Sequencing a community gives composition, and composition on its own cannot say what causes what. This stop moves from a survey to a causal claim using gnotobiotic transfer, controlled intervention and a stated mechanism.

Ready when they can: Explain why compositional data need different treatment from ordinary abundance counts; Design a test that separates a microbiome cause from a microbiome consequence; Assess a probiotic or transplant claim against the evidence it would need to be true.

https://lightmysky.com/learn/science/the-host-microbiome-composition-causation-and-intervention-mt_-F8lNccQCU

### Ecology & Conservation

https://lightmysky.com/learn/science/areas/ecology-and-conservation

#### Optimal Foraging and the Currency of a Behavioural Decision (ages 20-21)

Foraging decisions can be modelled as maximising energy gained per unit of time, once handling time and travel time are counted. Predictions from that currency can be tested, and where they fail the failure usually names a cost the model left out.

Ready when they can: Predicts which prey types should be taken from their energy values and handling times.; Explains what a patch-leaving rule follows from when returns decline with time in the patch.; Names one cost, such as predation risk, that changes the prediction when included..

https://lightmysky.com/learn/science/optimal-foraging-and-the-currency-of-a-behavioural-decision-mt_9iNYB7d1Rh

#### Sexual Selection, Mate Choice and Parental Investment (ages 20-21)

When one sex invests more per offspring, that sex becomes the limiting resource and the other competes for access. Traits that lower survival can still spread if they raise mating success by more than they cost.

Ready when they can: Predicts which sex competes and which chooses from the investment each makes.; Explains how a costly ornament can be favoured despite lowering survival.; Uses a case where roles are reversed to test the argument rather than to break it..

https://lightmysky.com/learn/science/sexual-selection-mate-choice-and-parental-investment-mt_6oTPGFw_p5

#### Kin Selection, Relatedness and When Helping Pays (ages 20-22)

Helping a relative passes on shared alleles indirectly, so a costly act can spread when the benefit to the recipient, weighted by relatedness, exceeds the cost to the helper. Working out relatedness turns an argument about altruism into a calculation.

Ready when they can: Calculates relatedness between stated relatives and uses it in the inequality.; Explains why helping a full sibling can pay when helping an unrelated individual does not.; Separates kin selection from cooperation between unrelated individuals..

https://lightmysky.com/learn/science/kin-selection-relatedness-and-when-helping-pays-mt_scVf8G34WI

#### Life-History Trade-offs and How Reproduction Is Allocated (ages 20-22)

An organism cannot grow, survive and reproduce at full rate at once, so life histories are compromises: few large offspring or many small ones, early breeding or late. Where a species sits is predicted by how risky its environment is for juveniles and adults.

Ready when they can: Explains a trade-off in terms of a shared limited budget rather than as a preference.; Predicts the life history favoured when adult survival is unpredictable.; Reads a survivorship curve as a statement about where mortality falls..

https://lightmysky.com/learn/science/life-history-trade-offs-and-how-reproduction-is-allocated-mt_eGwlydfDWO

#### Competition, Niches and What Allows Coexistence (ages 20-22)

Two species using the same limiting resource cannot both persist unless something separates them, such as different resource use in space, in time or in what limits each one. Modelling competition shows that coexistence needs each species to limit itself more than it limits the other.

Ready when they can: States the coexistence condition in terms of self-limitation versus limitation of the other species.; Explains niche partitioning with an example and says what resource is being divided.; Predicts the outcome of a competition experiment from stated resource requirements..

https://lightmysky.com/learn/science/competition-niches-and-what-allows-coexistence-mt_VS9Yud3rCQ

#### Predation, Herbivory and Trophic Cascades (ages 21-22)

Predators and prey drive each other's numbers in cycles, and removing a top predator can change vegetation several links away. Whether a community is controlled from the top or the bottom is a question that field manipulation can answer.

Ready when they can: Explains the lag between predator and prey peaks in a cycle.; Traces a cascade through at least three links and names the direction of each effect.; Designs an observation or removal that separates top-down from bottom-up control..

https://lightmysky.com/learn/science/predation-herbivory-and-trophic-cascades-mt_T0jG4YImZp

#### Measuring Diversity: Richness, Evenness and Turnover Between Sites (ages 21-22)

Counting species is not enough, because two communities with the same number of species can differ in how evenly individuals are spread. Indices combine richness and evenness, and a separate measure compares which species differ between sites.

Ready when they can: Calculates a diversity index from abundance data and explains what evenness contributed.; Compares two communities with equal richness and different evenness.; Distinguishes diversity within a site from turnover between sites..

https://lightmysky.com/learn/science/measuring-diversity-richness-evenness-and-turnover-between-sites-mt_d_iIiIArWZ

#### Productivity, Nutrient Limitation and Ecosystem Stoichiometry (ages 21-22)

How much an ecosystem produces is usually set by whichever nutrient is scarcest relative to what organisms need, not by energy alone. Because tissues hold elements in fairly fixed ratios, adding one nutrient can shift what limits the system rather than raising production without end.

Ready when they can: Identifies the limiting nutrient from supply ratios and requirement ratios.; Predicts the effect of adding one nutrient, including a shift in what limits growth.; Links element ratios in tissue to the nutrients a decomposer releases..

https://lightmysky.com/learn/science/productivity-nutrient-limitation-and-ecosystem-stoichiometry-mt_QWdZj1G9iT

#### Biomes and What Draws Their Boundaries (ages 19-20)

Vegetation across the world falls into a modest number of types, and where each one occurs is predicted well by temperature and rainfall alone. The exceptions are as informative as the rule, because they point at fire, grazing or soil doing the work instead of climate.

Ready when they can: Place a biome on a temperature and precipitation plot and justify the position; Explain why unrelated plants in the same biome converge on the same growth form; Give a case where the biome present is not the one climate predicts, and name the cause.

https://lightmysky.com/learn/science/biomes-and-what-draws-their-boundaries-mt_LpO2gwRYHd

#### Biogeography: Why a Species Is Here and Not There (ages 20-21)

A species range is set by tolerance, by dispersal and by history, and the three explanations make different predictions. Island patterns, where richness tracks area and isolation, are the cleanest place to test them.

Ready when they can: Separate a range limit set by physiology from one set by dispersal or by a competitor; State the species-area relationship and use it to estimate loss from habitat reduction; Explain what the equilibrium theory of island biogeography predicts and what it leaves out.

https://lightmysky.com/learn/science/biogeography-why-a-species-is-here-and-not-there-mt_sRi0FPcK8r

#### Demography: Life Tables, Age Structure and What They Predict (ages 20-21)

A life table turns survival and reproduction at each age into a single growth rate, and the age structure of a population says whether that rate will hold. It is the tool behind fishery quotas, pension forecasts and every claim that a population is recovering.

Ready when they can: Build a life table from survival and fecundity data and compute the net reproductive rate; Read an age pyramid and predict how the population changes over the next generation; Explain why two populations with the same size can have very different futures.

https://lightmysky.com/learn/science/demography-life-tables-age-structure-and-what-they-predict-mt_raWfdLLACU

#### Conservation: Small Populations, Fragmentation and Reserve Design (ages 21-22)

Small populations face genetic and demographic risks that feed on each other, so viability analysis asks what size and connection a population needs to persist. Reserve design turns that into choices about area, edge and the corridors between patches.

Ready when they can: Names two risks specific to small populations and explains how they reinforce each other.; Explains why fragmenting a habitat costs more than the area removed.; Argues for a reserve layout using area, edge and connection rather than area alone..

https://lightmysky.com/learn/science/conservation-small-populations-fragmentation-and-reserve-design-mt_yOl2NGoLeb

#### Global Change Ecology: Ranges, Phenology and Regime Shifts (ages 21-22)

Warming moves species and shifts the timing of their life events, and because the shifts are not equal the partners in an interaction can pull apart. Some systems then change abruptly rather than gradually, which is why a slow forcing can produce a sudden result.

Ready when they can: Predict a range shift from a species' tolerance and explain why the shift may lag the climate; Explain a phenological mismatch and give a case where it damaged one partner; Describe what a regime shift is and why recovery is not simply the reverse of the change.

https://lightmysky.com/learn/science/global-change-ecology-ranges-phenology-and-regime-shifts-mt_tJ7XpAADMF

## Mathematics

860 topics, ages 4 to 24. https://lightmysky.com/learn/mathematics

### Counting & Cardinality

https://lightmysky.com/learn/mathematics/areas/counting-and-cardinality

#### One-to-one counting (ages 4-6)

One-to-one correspondence when counting objects: each object is paired with exactly one number name

Ready when they can: Point to or touch each object exactly once while saying number names; Do not skip objects or double-count when counting a set; Recognise an error when someone counts an object twice.

https://lightmysky.com/learn/mathematics/one-to-one-counting-mt_WcfaSfVT33

#### How Many in Total? (ages 4-6)

Cardinality principle: the last number said when counting a set tells how many objects are in the set, regardless of arrangement or order counted

Ready when they can: After counting a set, answer 'how many?' with the last number stated; Understand that rearranging objects does not change the count; Understand that counting in a different order gives the same total.

Needs first: One-to-one counting.

https://lightmysky.com/learn/mathematics/how-many-in-total-mt_dmNvjroCPT

#### One More Each Time (ages 4-6)

Each successive counting number represents a quantity that is one larger than the previous number

Ready when they can: Given a set of 5, know that adding one object makes 6; Explain that 8 is one more than 7; Given a number, identify one more and one less.

Needs first: How Many in Total?.

https://lightmysky.com/learn/mathematics/one-more-each-time-mt_sYpKWbq5ra

#### Representing numbers with objects (ages 4-6)

Represent numbers using objects, pictorial representations, and the number line

Ready when they can: Show a given number using counters, cubes, or fingers; Draw a pictorial representation of a quantity (e.g. tally marks, dots); Locate a number on a number line.

Needs first: How Many in Total?.

https://lightmysky.com/learn/mathematics/representing-numbers-with-objects-mt_pAcaehday5

#### Counting objects to 20 (ages 5-6)

Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)

Ready when they can: Accurately count up to 20 objects in a line; Count up to 10 scattered objects without losing track; Given a number 1–20, count out that many objects from a larger set.

Needs first: How Many in Total?, One-to-one counting.

https://lightmysky.com/learn/mathematics/counting-objects-to-20-mt_yqAL6O5i_v

#### Comparing groups: more or fewer (ages 4-6)

Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies

Ready when they can: Use one-to-one matching to compare two groups; State which group has more/fewer after counting both; Use the language 'equal to', 'more than', 'less than', 'fewer', 'most', 'least'.

Needs first: Counting objects to 20.

https://lightmysky.com/learn/mathematics/comparing-groups-more-or-fewer-mt__h7hvT4tEb

#### Rote counting to 100 (ages 5-6)

Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones

Ready when they can: Recite the number sequence 1–100 without skipping or repeating; Count backward from 20 to 0; Count forward starting from a number other than 1 (e.g. 'start at 23').

Needs first: One-to-one counting.

https://lightmysky.com/learn/mathematics/rote-counting-to-100-mt_M5PPDJStGm

#### Counting in 2s (ages 5-7)

Count in multiples of 2, 5, and 10 (skip counting)

Ready when they can: Count 2, 4, 6, 8 … up to at least 20; Count 5, 10, 15, 20 … up to at least 50; Count 10, 20, 30 … up to 100.

Needs first: Rote counting to 100.

https://lightmysky.com/learn/mathematics/counting-in-2s-mt_nvdpxAJTBG

#### Two written numerals between 1 and 10 (ages 5-6)

Compare two written numerals between 1 and 10 to determine which is greater or less

Ready when they can: Given two written numerals (e.g. 4 and 7), identify which is greater; Correctly use > and < or 'greater than' / 'less than' to compare single-digit numerals.

Needs first: Comparing groups: more or fewer.

https://lightmysky.com/learn/mathematics/two-written-numerals-between-1-and-10-mt__YRJ23GuIK

#### Counting forwards and backwards (ages 6-7)

Count forwards and backwards in steps of 3 from 0

Ready when they can: Count 3, 6, 9, 12, 15 … up to at least 30; Count backwards in 3s from 30; Identify the next number in a sequence of multiples of 3.

Needs first: Counting in 2s.

https://lightmysky.com/learn/mathematics/counting-forwards-and-backwards-mt_aHAM29nidj

#### Skip Counting (4s, 8s, 50s, 100s) (ages 7-8)

Count from 0 in multiples of 4, 8, 50, and 100

Ready when they can: Recite the multiples of 4 from 0 to at least 48; Recite the multiples of 8 from 0 to at least 96; Count in steps of 50 and 100 from 0 to 1000.

Needs first: Counting in 2s.

https://lightmysky.com/learn/mathematics/skip-counting-4s-8s-50s-100s-mt_IzQvs7k_sE

#### Counting in 6s (ages 8-9)

Count in multiples of 6, 7, 9, 25, and 1000

Ready when they can: Recite the multiples of 6 from 0 to at least 72; Recite the multiples of 7 from 0 to at least 84; Count in steps of 25 from 0 to 1000 and in steps of 1000 up to 10,000.

Needs first: Skip Counting (4s, 8s, 50s, 100s).

https://lightmysky.com/learn/mathematics/counting-in-6s-mt_7rJM8eWUfw

#### Counting forwards and backwards (age 6+) (ages 6-7)

Count forwards and backwards in tens from any number (not just multiples of 10)

Ready when they can: Count 7, 17, 27, 37 … from a non-multiple starting point; Count backwards in tens from 83; Explain the pattern of adding/subtracting 10.

Needs first: Counting in 2s, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/counting-forwards-and-backwards-age-6-mt_OkSJfrmFb_

#### Counting Within 1,000 (ages 7-8)

Count within 1000, including skip-counting by 5s, 10s, and 100s

Ready when they can: Count forwards and backwards within 1000 from any starting number; Skip-count by 5s from any multiple of 5 to 1000; Skip-count by 100s from any number (e.g. 150, 250, 350 …).

Needs first: Counting in 2s, The multiples of 100.

https://lightmysky.com/learn/mathematics/counting-within-1-000-mt_M2v1A9OEuM

### Addition & Subtraction

https://lightmysky.com/learn/mathematics/areas/addition-and-subtraction

#### Addition as combining or putting together two (ages 4-6)

Understand addition as combining or putting together two groups to find the total

Ready when they can: Model 'putting together' with physical objects and say the total; Act out an 'add to' situation (e.g. 3 children arrive, then 2 more join); Explain that addition means finding how many altogether.

Needs first: How Many in Total?.

https://lightmysky.com/learn/mathematics/addition-as-combining-or-putting-together-two-mt_OvyoRo47K-

#### Numbers up to 10 into pairs (ages 4-6)

Decompose numbers up to 10 into pairs in more than one way (part-part-whole)

Ready when they can: Show that 5 = 1 + 4, 5 = 2 + 3, 5 = 0 + 5 etc.; Use objects or drawings to find all pairs that make a given number; Record decompositions as equations.

Needs first: Addition as combining or putting together two.

https://lightmysky.com/learn/mathematics/numbers-up-to-10-into-pairs-mt_7XcCG43ZZW

#### Number bonds to 9 (ages 4-6)

Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)

Ready when they can: Given 7, respond '3' to make 10; Use a ten-frame to find the complement to 10; Record pairs that make 10 as equations (e.g. 6 + 4 = 10).

Needs first: Numbers up to 10 into pairs.

https://lightmysky.com/learn/mathematics/number-bonds-to-9-mt_e8CZ7E5qW7

#### Subtraction as taking away or separating (ages 4-6)

Understand subtraction as taking away or separating from a group to find how many remain

Ready when they can: Model 'taking away' with physical objects and say how many remain; Act out a 'take from' situation (e.g. 5 biscuits, eat 2, how many left?); Explain that subtraction means finding how many are left.

Needs first: How Many in Total?.

https://lightmysky.com/learn/mathematics/subtraction-as-taking-away-or-separating-mt_zuKAX6lcYR

#### Representing Addition and Subtraction (ages 4-6)

Represent addition and subtraction using objects, drawings, and mental images

Ready when they can: Use cubes or counters to show 3 + 2; Draw a picture to represent a subtraction situation; Use fingers to model an addition problem.

Needs first: Addition as combining or putting together two, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/representing-addition-and-subtraction-mt_PgsHGYJMH-

#### Addition and subtraction word problems (ages 4-6)

Solve addition and subtraction word problems within 10 using objects or drawings

Ready when they can: Solve 'There are 6 apples, 2 are eaten, how many left?' using counters; Solve 'add to' and 'take from' result-unknown problems; Solve 'put together/take apart' problems with total unknown.

Needs first: Representing Addition and Subtraction.

https://lightmysky.com/learn/mathematics/addition-and-subtraction-word-problems-mt_yJmvUCCym7

#### Fluent adding and subtracting within 5 (ages 5-6)

Fluently add and subtract within 5

Ready when they can: Answer 2 + 3 quickly without counting on fingers; Answer 5 – 2 from recall or with minimal counting; Complete a set of within-5 addition/subtraction facts accurately and quickly.

Needs first: Addition as combining or putting together two, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-5-mt_ghF3Vv6taM

#### Number bonds (ages 5-6)

Recall number bonds (addition and related subtraction facts) within 20

Ready when they can: Quickly recall that 8 + 5 = 13; Given 13 – 5, respond 8 using knowledge of related addition fact; Know all pairs of single-digit numbers that sum to numbers up to 20.

Needs first: Number bonds to 9, Fluent adding and subtracting within 5.

https://lightmysky.com/learn/mathematics/number-bonds-mt_s2mfRBoTal

#### Adding and subtracting (ages 5-6)

Add and subtract one-digit and two-digit numbers to 20, including zero

Ready when they can: Calculate 14 + 5 = 19; Calculate 17 – 3 = 14; Add or subtract 0 and explain the result stays the same.

Needs first: Number bonds.

https://lightmysky.com/learn/mathematics/adding-and-subtracting-mt_mr_Vk7FGzK

#### Early Word Problems (ages 5-7)

Solve one-step word problems involving addition and subtraction to 20, including missing-number problems

Ready when they can: Solve 'I have 12 sweets and eat 4, how many left?'; Solve missing number: 7 = [ ] – 9; Solve problems using concrete objects and pictorial representations.

Needs first: Adding and subtracting, Addition and subtraction word problems.

https://lightmysky.com/learn/mathematics/early-word-problems-mt_VAWV_l7J0D

#### Addition and subtraction strategies (ages 6-7)

Use counting on and counting back as strategies for addition and subtraction

Ready when they can: Add 8 + 3 by starting at 8 and counting on 3 (9, 10, 11); Subtract 12 − 3 by counting back 3 from 12 (11, 10, 9); Explain that counting on is a way to add.

Needs first: Addition as combining or putting together two, One More Each Time, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-mt_PpWSHA-0kv

#### Addition in any order (ages 6-7)

Understand and apply the commutative property of addition: addends can be added in any order

Ready when they can: Explain that 3 + 8 gives the same answer as 8 + 3; Use commutativity to choose the larger number to count on from; Demonstrate that subtraction is not commutative (5 − 3 ≠ 3 − 5).

Needs first: Addition as combining or putting together two.

https://lightmysky.com/learn/mathematics/addition-in-any-order-mt_QCgbiVrwnp

#### Finding a missing number in addition (ages 6-7)

Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)

Ready when they can: Solve 10 − 8 by thinking 'what do I add to 8 to make 10?'; Explain that subtraction can be thought of as a missing-addend problem; Use known addition facts to solve related subtraction problems.

Needs first: Addition as combining or putting together two, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/finding-a-missing-number-in-addition-mt_ezc2m_0dzN

#### Fluent adding and subtracting within 10 (ages 6-7)

Fluently add and subtract within 10

Ready when they can: Answer any addition fact within 10 quickly from memory; Answer any subtraction fact within 10 quickly from memory; Complete a timed set of within-10 facts with high accuracy.

Needs first: Number bonds to 9, Fluent adding and subtracting within 5.

https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-10-mt__we2TDqnJx

#### Addition and subtraction within 20 (ages 6-7)

Add and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts

Ready when they can: Solve 8 + 6 using making ten: 8 + 2 + 4 = 14; Solve 13 − 4 by decomposing: 13 − 3 − 1 = 9; Use a known fact (8 + 4 = 12) to derive 12 − 8 = 4.

Needs first: Fluent adding and subtracting within 10.

https://lightmysky.com/learn/mathematics/addition-and-subtraction-within-20-mt_m1W6nTQJ2b

#### Grouping numbers to add (ages 6-7)

Understand and apply the associative property of addition: when adding three numbers, any two can be added first

Ready when they can: Solve 2 + 6 + 4 by first adding 6 + 4 = 10, then 2 + 10 = 12; Explain that grouping addends differently gives the same total; Choose which two numbers to add first to make the calculation easier.

Needs first: Addition in any order.

https://lightmysky.com/learn/mathematics/grouping-numbers-to-add-mt_T76hKqXf0z

#### Adding Three Small Numbers (ages 6-7)

Add three one-digit numbers using strategies including looking for pairs that make 10

Ready when they can: Calculate 5 + 7 + 3 by first adding 7 + 3 = 10, then 5 + 10 = 15; Add any three single-digit numbers correctly; Identify useful pairs within three addends to make the calculation easier.

Needs first: Number bonds to 9, Grouping numbers to add.

https://lightmysky.com/learn/mathematics/adding-three-small-numbers-mt_Zx1xZM-RbX

#### Inverse: addition undoes subtraction (ages 6-7)

Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems

Ready when they can: Check 15 + 7 = 22 by calculating 22 − 7 = 15; Use the inverse to solve: □ + 9 = 14, so □ = 14 − 9 = 5; Explain that addition and subtraction 'undo' each other.

Needs first: Finding a missing number in addition.

https://lightmysky.com/learn/mathematics/inverse-addition-undoes-subtraction-mt_ehGS_uVSJv

#### Fluent adding and subtracting within 20 (ages 7-8)

Fluently add and subtract within 20 using mental strategies; know from memory all sums of two one-digit numbers

Ready when they can: Answer any single-digit addition fact within 3 seconds; Recall subtraction facts within 20 from memory (e.g. 15 − 8 = 7); Use known addition facts to derive related subtraction facts rapidly.

Needs first: Addition and subtraction within 20.

https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-20-mt__t4afSyZRm

#### Reading +, −, and = symbols (ages 5-6)

Read, write, and interpret the symbols +, −, and = in number sentences

Ready when they can: Read 3 + 2 = 5 aloud as 'three plus two equals five'; Write a number sentence to match a concrete addition situation; Interpret the = sign as 'is the same as' rather than just 'the answer is'.

Needs first: Reading and writing numbers to 20, Addition as combining or putting together two, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/reading-and-symbols-mt_8RmpkDxT9L

#### What the equals sign means (ages 6-7)

Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false

Ready when they can: Explain that 6 = 6 is true because both sides are the same; Determine that 4 + 1 = 5 + 2 is false; Understand that = does not mean 'the answer comes next' — it means balance.

Needs first: Reading +, −, and = symbols.

https://lightmysky.com/learn/mathematics/what-the-equals-sign-means-mt_oIzycTBeE4

#### Unknown in Addition & Subtraction (ages 6-7)

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers

Ready when they can: Solve 8 + ? = 11 and write 3; Solve 5 = □ − 3 and write 8; Solve 6 + 6 = □ and write 12.

Needs first: Inverse: addition undoes subtraction, What the equals sign means.

https://lightmysky.com/learn/mathematics/unknown-in-addition-and-subtraction-mt_3JgrHY221M

#### Subtracting multiples of 10 (ages 6-7)

Subtract multiples of 10 (10–90) from multiples of 10 using place value strategies

Ready when they can: Calculate 70 − 30 = 40; Use base-ten blocks to show 80 − 50 = 30; Explain that subtracting tens is like subtracting the tens digits.

Needs first: The multiples of 10, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/subtracting-multiples-of-10-mt_HJTuIGHvcR

#### Adding within 100 (ages 6-7)

Add within 100 using strategies based on place value, including adding a two-digit and one-digit number, and a two-digit and a multiple of 10

Ready when they can: Calculate 46 + 7 using place value (46 + 4 + 3 = 53); Calculate 38 + 40 = 78 using tens understanding; Relate the strategy to a written method and explain the reasoning.

Needs first: Addition and subtraction within 20, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/adding-within-100-mt_glPPG-kTQY

#### Fluent addition and subtraction (ages 6-7)

Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

Ready when they can: Rapidly recall 7 + 8 = 15 and 15 − 8 = 7; Use 6 + 4 = 10 to derive 60 + 40 = 100; Derive 35 + 5 = 40 from knowledge that 5 + 5 = 10.

Needs first: Addition and subtraction within 20, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/fluent-addition-and-subtraction-mt_3e_PQxwC12

#### Mental addition and subtraction (age 6+) (ages 6-7)

Add and subtract a two-digit number and ones mentally and using concrete/pictorial representations

Ready when they can: Calculate 36 + 7 = 43 using objects or mentally; Calculate 52 − 4 = 48 using a number line or mentally; Explain bridging through 10 when adding ones to a two-digit number.

Needs first: Adding and subtracting, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/mental-addition-and-subtraction-age-6-mt_AKAtWEwpcj

#### Fluent adding and subtracting within 100 (ages 7-8)

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

Ready when they can: Add two-digit numbers within 100 efficiently (e.g. 46 + 37 using place-value partitioning); Subtract two-digit numbers within 100 fluently (e.g. 83 − 25); Choose between strategies (decomposing, compensating, using known facts) based on the numbers involved.

Needs first: Adding within 100, Fluent adding and subtracting within 20.

https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-100-mt_cChv2j_-Da

#### Adding numbers (ages 7-8)

Add up to four two-digit numbers using strategies based on place value and properties of operations

Ready when they can: Add three or four two-digit numbers by grouping tens and ones; Look for pairs that make multiples of 10 to simplify addition; Explain the strategy used to combine multiple addends.

Needs first: Fluent adding and subtracting within 100, Adding Three Small Numbers.

https://lightmysky.com/learn/mathematics/adding-numbers-mt_TiQbi027PE

#### Two-Step Word Problems (ages 7-8)

Solve one- and two-step word problems within 100 using addition and subtraction, with unknowns in all positions

Ready when they can: Solve a two-step word problem involving adding to and taking from; Represent a word problem with an equation using a symbol for the unknown; Solve comparison problems (how many more/fewer) within 100.

Needs first: Fluent adding and subtracting within 100, Early Word Problems.

https://lightmysky.com/learn/mathematics/two-step-word-problems-mt_yTWxkzzoOZ

#### Adding and subtracting tens mentally (ages 6-7)

Add and subtract a two-digit number and tens mentally and using concrete/pictorial representations

Ready when they can: Calculate 45 + 30 = 75 mentally; Calculate 82 − 40 = 42 mentally; Explain that only the tens digit changes when adding/subtracting tens.

Needs first: 10 More or 10 Less, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/adding-and-subtracting-tens-mentally-mt_I5j1ZWo2cn

#### Adding two two-digit numbers (ages 6-7)

Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods

Ready when they can: Calculate 34 + 27 using base-ten blocks or column addition; Calculate 63 − 28 using a number line or partitioning; Explain a strategy for adding or subtracting two two-digit numbers.

Needs first: Mental addition and subtraction (age 6+), Adding and subtracting tens mentally.

https://lightmysky.com/learn/mathematics/adding-two-two-digit-numbers-mt_UQnAFPs83F

#### Mental and written addition and subtraction (ages 6-7)

Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures

Ready when they can: Solve a two-step problem: 'I had 35p, spent 12p, then found 5p. How much now?'; Choose an appropriate method (mental or written) for a given problem; Solve problems involving measures, e.g. 'a ribbon is 45cm, I cut off 18cm'.

Needs first: Adding two two-digit numbers, Early Word Problems.

https://lightmysky.com/learn/mathematics/mental-and-written-addition-and-subtraction-mt_wzAZ8qFDc4

#### Addition and subtraction strategies (age 7+) (ages 7-8)

Explain why addition and subtraction strategies work, using place value and the properties of operations

Ready when they can: Explain why adding tens and ones separately gives the correct total; Describe why a compensation strategy works (e.g. 'I added 1 too many, so I subtract 1'); Use place-value language to justify a written method step by step.

Needs first: The three digits of a three-digit number, Fluent adding and subtracting within 100, Addition and subtraction strategies.

https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-age-7-mt_zxST3MarI9

#### Addition and subtraction within 1000 (ages 7-8)

Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds

Ready when they can: Add two three-digit numbers using base-ten blocks or drawings, composing a ten or hundred when necessary; Subtract three-digit numbers, decomposing a ten or hundred when necessary; Relate the concrete/drawn strategy to a written method and explain why it works.

Needs first: The three digits of a three-digit number, Fluent adding and subtracting within 100.

https://lightmysky.com/learn/mathematics/addition-and-subtraction-within-1000-mt_ewmuMMPAzP

#### Adding and subtracting (age 7+) (ages 7-8)

Add and subtract numbers with up to three digits using formal written methods of columnar addition and subtraction

Ready when they can: Set out a columnar addition correctly with digits aligned by place value; Carry out columnar subtraction with exchange (borrowing) when needed; Check the answer using the inverse operation or estimation.

Needs first: Fluent adding and subtracting within 100, Addition and subtraction within 1000.

https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-7-mt_SrrsLiJkr3

#### Estimating by rounding (ages 7-9)

Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning

Ready when they can: Round numbers to the nearest 10 or 100 to estimate a sum or difference before calculating; Use addition to check a subtraction answer, or vice versa; Identify when a calculated answer is unreasonable based on the estimate; Round numbers to estimate a sum or difference before calculating; Use addition to check a subtraction answer and vice versa; Identify an unreasonable answer by comparing to the estimate.

Needs first: Inverse: addition undoes subtraction, Addition and subtraction within 1000.

https://lightmysky.com/learn/mathematics/estimating-by-rounding-mt_QaYfeVL-0C

#### Mental addition and subtraction (age 7+) (ages 7-8)

Mentally add and subtract a three-digit number and ones

Ready when they can: Calculate 345 + 7 mentally; Calculate 462 − 5 mentally; Explain that only the ones digit changes (unless bridging through a ten).

Needs first: The three digits of a three-digit number, Fluent adding and subtracting within 100, Mental and written addition and subtraction, Subtracting multiples of 10.

https://lightmysky.com/learn/mathematics/mental-addition-and-subtraction-age-7-mt_oDU_8zMZjp

#### Missing number problems (age 7+) (ages 7-8)

Solve addition and subtraction problems including missing-number problems, using number facts, place value, and more complex methods

Ready when they can: Solve a missing-number problem such as 245 + ? = 380; Choose an appropriate method (mental, written, or combination) based on the numbers; Solve multi-step problems combining addition and subtraction of three-digit numbers.

Needs first: Adding and subtracting (age 7+), Two-Step Word Problems.

https://lightmysky.com/learn/mathematics/missing-number-problems-age-7-mt_XuHmIn2xje

#### Fluent adding and subtracting within 1000 (ages 8-9)

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction

Ready when they can: Add two three-digit numbers fluently using an efficient method; Subtract three-digit numbers fluently, including with regrouping; Choose the most efficient strategy based on the numbers involved.

Needs first: Addition and subtraction within 1000, Adding and subtracting (age 7+), Adding numbers.

https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-1000-mt_HFRYjTb-Z5

#### Numbers on a number line (ages 7-8)

Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagram

Ready when they can: Place whole numbers on a number line with equally spaced points; Show an addition as a jump forward on the number line (e.g. 38 + 27 shown as jumps); Show a subtraction as a jump backward on the number line.

Needs first: Representing Numbers, Fluent adding and subtracting within 100.

https://lightmysky.com/learn/mathematics/numbers-on-a-number-line-mt_19j_5AuuQI

#### Mentally adding hundreds to 3-digit numbers (ages 7-8)

Mentally add and subtract a three-digit number and hundreds

Ready when they can: Calculate 345 + 200 mentally; Calculate 762 − 400 mentally; Explain that only the hundreds digit changes.

Needs first: The three digits of a three-digit number, 10 or 100 More or Less.

https://lightmysky.com/learn/mathematics/mentally-adding-hundreds-to-3-digit-numbers-mt_xPqczp7zPX

#### Mentally adding tens to 3-digit numbers (ages 7-8)

Mentally add and subtract a three-digit number and tens

Ready when they can: Calculate 345 + 40 mentally; Calculate 462 − 30 mentally; Explain that only the tens digit changes (unless bridging through a hundred).

Needs first: The three digits of a three-digit number, 10 or 100 More or Less.

https://lightmysky.com/learn/mathematics/mentally-adding-tens-to-3-digit-numbers-mt_aHQ9kNt3is

#### Adding and subtracting (age 8+) (ages 8-9)

Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction

Ready when they can: Set out and solve a columnar addition with up to four-digit numbers; Set out and solve a columnar subtraction with exchange across multiple columns; Check the answer using estimation or inverse operations.

Needs first: Place value of each digit, Adding and subtracting (age 7+).

https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-8-mt_mpS-JK_p_m

#### Two-step addition and subtraction problems (ages 8-9)

Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Ready when they can: Identify the two steps needed to solve a contextual problem; Choose between mental and written methods for each step based on the numbers; Explain why the chosen operations and methods are appropriate.

Needs first: Adding and subtracting (age 8+), Missing number problems (age 7+).

https://lightmysky.com/learn/mathematics/two-step-addition-and-subtraction-problems-mt_CDa5AVakLE

#### Fluent addition and subtraction (age 9+) (ages 9-10)

Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm

Ready when they can: Calculate 34,567 + 28,945 using columnar addition; Calculate 500,000 − 234,178 using columnar subtraction with multiple exchanges; Add three five-digit numbers in a single column layout.

Needs first: Adding and subtracting (age 8+), Fluent addition and subtraction.

https://lightmysky.com/learn/mathematics/fluent-addition-and-subtraction-age-9-mt_Yw1_4Nfsql

#### Two-Step Equations (ages 8-9)

Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity

Ready when they can: Solve a two-step problem that combines addition/subtraction with multiplication/division; Write an equation using a letter for the unknown (e.g. 3 × n + 5 = 26); Assess the reasonableness of the answer using estimation and mental computation.

Needs first: Fluent adding and subtracting within 1000, Rounding to 10, 100, 1000, Two-Step Word Problems.

https://lightmysky.com/learn/mathematics/two-step-equations-mt_anAe11HAEH

#### Mental addition and subtraction (age 9+) (ages 9-10)

Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts

Ready when they can: Mentally calculate 45,000 + 8,000; Mentally subtract 3,200 from 10,000 by counting up; Use near-doubles: 2,500 + 2,600 = 5,100.

Needs first: Mental addition and subtraction (age 7+), Place Value × 10 Pattern, Mentally adding hundreds to 3-digit numbers, Mentally adding tens to 3-digit numbers.

https://lightmysky.com/learn/mathematics/mental-addition-and-subtraction-age-9-mt_MWXPiaTnEu

#### Adding and subtracting (age 9+) (ages 9-10)

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Ready when they can: A school collects 12,450 bottles in Week 1 and 8,372 in Week 2; their target is 25,000 — how many more do they need?; Choose between mental and written methods for each step and explain why; Solve a three-step problem involving addition and subtraction of five-digit numbers.

Needs first: Two-step addition and subtraction problems, Mental addition and subtraction (age 9+), Fluent addition and subtraction (age 9+).

https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-9-mt_-F_Lv_apzH

#### Checking Answers by Rounding (ages 9-10)

Use rounding to check answers to calculations and determine appropriate levels of accuracy in context

Ready when they can: Check 47,832 + 23,156 ≈ 48,000 + 23,000 = 71,000 to verify the exact answer 70,988; Decide whether to round to the nearest 100 or 1,000 for a given estimation context; Identify that a calculated answer of 3,421 cannot be correct because the estimate gives approximately 50,000.

Needs first: Rounding Large Numbers, Estimating by rounding.

https://lightmysky.com/learn/mathematics/checking-answers-by-rounding-mt_G3sVFQNCme

#### Addition and subtraction strategies (age 10+) (ages 10-11)

Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning

Ready when they can: Correctly compute 3.45 + 2.78 and explain regrouping across decimal places; Use a number line or base-ten blocks to model 5.03 − 2.67; Explain why the standard algorithm works for decimal addition by connecting to place-value understanding.

Needs first: Reading and writing numbers (age 10+), Place Value × 10 and ÷ 10, Fluent addition and subtraction (age 9+).

https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-age-10-mt_JH_6RpNWjr

#### Adding and subtracting (age 10+) (ages 10-11)

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals

Ready when they can: Solve a two-step word problem involving addition and subtraction of numbers beyond 1,000,000; Choose between mental, written, and calculator methods for a multi-step problem and justify the choice; Interpret a real-life context to identify which addition/subtraction operations are needed across multiple steps.

Needs first: Adding and subtracting (age 9+), Reading and writing numbers to 10,000,000, Addition and subtraction strategies (age 10+).

https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-10-mt_M1tnXqmYbn

#### Positive and Negative Numbers (ages 11-13)

Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances

Ready when they can: Represent positive and negative numbers on a number line and explain what zero means in context; Add a positive or negative number to any integer using number line reasoning; Subtract a positive or negative number from any integer, understanding that subtracting a negative is equivalent to adding.

Needs first: Measuring temperature, Adding and subtracting (age 10+).

https://lightmysky.com/learn/mathematics/positive-and-negative-numbers-mt_9QzSnn8m80

#### Adding and Subtracting Negative Numbers (ages 12-13)

Add and subtract with negative integers, reading each move as a direction on the number line, and settle what subtracting a negative does.

Ready when they can: Work out sums like -7 + 3 and 4 - 9 without a calculator and say which way the answer lies from zero; Explain why subtracting a negative moves the same way as adding a positive, using a context such as debt or temperature; Order a mixed list of positive and negative numbers and find the distance between two of them.

https://lightmysky.com/learn/mathematics/adding-and-subtracting-negative-numbers-mt_qX7X7uMzsY

### Geometry

https://lightmysky.com/learn/mathematics/areas/geometry

#### 2-D shapes (ages 4-6)

Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)

Ready when they can: Name a triangle, circle, rectangle, and square when shown them; Identify a shape correctly regardless of its size or orientation; Pick out all the triangles from a mixed set of shapes.

https://lightmysky.com/learn/mathematics/2-d-shapes-mt_KJeEeTutJI

#### 3-D shapes (ages 4-6)

Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)

Ready when they can: Name a cube, sphere, cylinder, and cone when shown them; Identify 3-D shapes in the environment (e.g. a tin is a cylinder); Recognise a cuboid and a pyramid among a set of solid shapes.

https://lightmysky.com/learn/mathematics/3-d-shapes-mt_Qcp2d_kuta

#### Positional Language (ages 4-6)

Describe the position of objects using terms such as above, below, beside, in front of, behind, next to

Ready when they can: Describe a toy as being 'on top of' the table; Follow instructions like 'put the cube behind the box'; Use 'left' and 'right' in simple contexts.

https://lightmysky.com/learn/mathematics/positional-language-mt_qeZYF6HZ4o

#### 3-D shapes (age 5+) (ages 5-6)

Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes

Ready when they can: Count the sides and corners of a shape; Compare a triangle and a rectangle by number of sides; Describe a cube as having 'square faces' and 'corners'.

Needs first: 2-D shapes, 3-D shapes.

https://lightmysky.com/learn/mathematics/3-d-shapes-age-5-mt_yGv8doDAmp

#### Building & Drawing Shapes (ages 5-6)

Model shapes by building from components (e.g. sticks and clay balls) and by drawing

Ready when they can: Build a triangle from three sticks and three clay balls; Draw a recognisable rectangle; Construct a cube from straws and connectors.

Needs first: 3-D shapes (age 5+).

https://lightmysky.com/learn/mathematics/building-and-drawing-shapes-mt_2VR963szuk

#### Combining Simple Shapes (ages 5-6)

Compose simple shapes to form larger shapes (e.g. two triangles make a rectangle)

Ready when they can: Join two triangles to make a rectangle or larger triangle; Use pattern blocks to fill a hexagon outline; Create a picture or design by combining basic shapes.

Needs first: 2-D shapes, 3-D shapes (age 5+).

https://lightmysky.com/learn/mathematics/combining-simple-shapes-mt_XjwUlmxdCT

#### Flat vs Solid Shapes (ages 5-6)

Distinguish two-dimensional (flat) shapes from three-dimensional (solid) shapes

Ready when they can: Sort shapes into 'flat' and 'solid' groups; Explain that a circle is flat but a sphere is solid; Identify whether a given shape is 2-D or 3-D.

Needs first: 2-D shapes, 3-D shapes.

https://lightmysky.com/learn/mathematics/flat-vs-solid-shapes-mt_mnEVZNkX3p

#### 2-D faces on 3-D shapes (ages 6-7)

Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid)

Ready when they can: Point out a circular face on a cylinder or cone; Identify triangular faces on a pyramid; Recognise that the faces of 3-D shapes are 2-D shapes.

Needs first: Flat vs Solid Shapes.

https://lightmysky.com/learn/mathematics/2-d-faces-on-3-d-shapes-mt_UooUHC_V7U

#### Building with 3-D Shapes (ages 6-7)

Compose three-dimensional shapes (cubes, right rectangular prisms, right circular cones, right circular cylinders) and create composite shapes; build new shapes from component shapes

Ready when they can: Stack cubes and prisms to build towers or structures; Combine 3-D shapes to make a new solid (e.g. cone on top of cylinder); Describe a composite 3-D shape in terms of its component shapes.

Needs first: Building & Drawing Shapes, 3-D shapes.

https://lightmysky.com/learn/mathematics/building-with-3-d-shapes-mt_QNxFnxikCN

#### Composing Shapes (ages 6-7)

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape

Ready when they can: Combine two triangles to form a rectangle or larger triangle; Put together half-circles and quarter-circles to form circles or new shapes; Decompose a composite shape and describe which simpler shapes make it up.

Needs first: 2-D shapes, Combining Simple Shapes.

https://lightmysky.com/learn/mathematics/composing-shapes-mt_MqqR7VUoz1

#### Defining attributes of shapes (ages 6-7)

Distinguish defining attributes of shapes (e.g. triangles are closed and three-sided) from non-defining attributes (e.g. colour, orientation, overall size)

Ready when they can: Build and draw shapes that possess defining attributes; Identify that a shape remains a triangle regardless of its size, colour, or orientation; Explain why a given shape is or is not a particular type based on its defining properties.

Needs first: 2-D shapes, 3-D shapes (age 5+).

https://lightmysky.com/learn/mathematics/defining-attributes-of-shapes-mt_bfhng6mOuy

#### 2-D shapes (age 6+) (ages 6-7)

Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line

Ready when they can: Count the number of sides of a given 2-D shape; Identify whether a 2-D shape has a vertical line of symmetry; Use properties (number of sides, symmetry) to describe and distinguish between shapes.

Needs first: Defining attributes of shapes, 2-D shapes, 3-D shapes (age 5+).

https://lightmysky.com/learn/mathematics/2-d-shapes-age-6-mt_sBcRdUfAzV

#### Edges, vertices, and faces (ages 6-7)

Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces

Ready when they can: Count the edges, vertices, and faces of common 3-D shapes; Use the terms edge, vertex (vertices), and face correctly; Describe a 3-D shape by its properties (e.g. a cube has 6 faces, 12 edges, 8 vertices).

Needs first: 3-D shapes, 3-D shapes (age 5+).

https://lightmysky.com/learn/mathematics/edges-vertices-and-faces-mt_Mnodea7mG_

#### Patterns & Sequences (ages 6-7)

Order and arrange combinations of mathematical objects in patterns and sequences

Ready when they can: Continue a repeating pattern of shapes or colours; Describe the rule for a given sequence of objects; Create own patterns and sequences using mathematical objects.

Needs first: Rote counting to 100, Counting in 2s.

https://lightmysky.com/learn/mathematics/patterns-and-sequences-mt_WXW0hjNhph

#### Sorting 2-D and 3-D shapes (ages 6-7)

Compare and sort common 2-D and 3-D shapes and everyday objects by their properties

Ready when they can: Sort a collection of 2-D shapes by number of sides; Sort 3-D shapes by number of faces or whether faces are flat/curved; Explain criteria used to sort a group of shapes.

Needs first: Edges, vertices, and faces, 2-D shapes (age 6+).

https://lightmysky.com/learn/mathematics/sorting-2-d-and-3-d-shapes-mt_fEuoBYw6bU

#### 2-D shapes (age 7+) (ages 7-8)

Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

Ready when they can: Draw a triangle, rectangle, pentagon, or hexagon accurately; Construct a cube or cuboid from modelling materials (e.g. straws and connectors); Recognise a 3-D shape (e.g. a pyramid) when it is rotated or seen from a different angle.

Needs first: Edges, vertices, and faces, 2-D shapes (age 6+).

https://lightmysky.com/learn/mathematics/2-d-shapes-age-7-mt_vJUa62bxeR

#### Drawing shapes with given attributes (ages 7-8)

Recognise and draw shapes having specified attributes (e.g. a given number of angles or equal faces); identify triangles, quadrilaterals, pentagons, hexagons, and cubes

Ready when they can: Draw a shape with exactly 5 sides (pentagon); Identify all quadrilaterals in a set of mixed shapes; Name and draw a hexagon, explaining it has 6 sides and 6 angles.

Needs first: Defining attributes of shapes, 2-D shapes (age 6+).

https://lightmysky.com/learn/mathematics/drawing-shapes-with-given-attributes-mt_zuOGOGFAKb

#### Classifying quadrilaterals (ages 8-9)

Understand that shapes in different categories may share attributes defining a larger category; classify quadrilaterals (rhombuses, rectangles, squares) and draw examples of quadrilaterals not in those subcategories

Ready when they can: Explain that a square is a special rectangle and also a special rhombus; Sort shapes into a Venn diagram: quadrilaterals vs rectangles vs squares; Draw a quadrilateral that is not a rectangle, rhombus, or square.

Needs first: 2-D shapes (age 6+), Drawing shapes with given attributes.

https://lightmysky.com/learn/mathematics/classifying-quadrilaterals-mt_Xt1cRqaBOW

#### Nets of 3-D Shapes (ages 8-11)

Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net

Ready when they can: Draw the net of a cube, cuboid, or triangular prism and fold it mentally to identify which faces connect; Build a 3-D shape from its net and check that all faces, edges, and vertices match; Identify which of several given nets will fold into a specific 3-D shape and explain why the others won't.

Needs first: 2-D faces on 3-D shapes, Building with 3-D Shapes.

https://lightmysky.com/learn/mathematics/nets-of-3-d-shapes-mt_vnJEztczji

#### 3-D shapes (age 9+) (ages 9-10)

Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

Ready when they can: Identify a cuboid from its net; Name the 3-D shape shown in an isometric drawing; Match 2-D representations to the correct 3-D shape.

Needs first: 2-D shapes (age 7+), Nets of 3-D Shapes.

https://lightmysky.com/learn/mathematics/3-d-shapes-age-9-mt_wUSbRt3-qw

#### 3-D shapes (age 10+) (ages 10-11)

Recognise, describe, and build simple 3-D shapes, including making nets

Ready when they can: Identify which net will fold into a given 3-D shape; Construct the net of a triangular prism and fold it to verify; Describe a 3-D shape by naming its faces, edges, and vertices.

Needs first: Nets of 3-D Shapes, 3-D shapes (age 9+).

https://lightmysky.com/learn/mathematics/3-d-shapes-age-10-mt_REwgr0d_ss

#### 3-D shapes (age 11+) (ages 11-13)

Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections

Ready when they can: Count and describe the faces, edges, and vertices of a triangular prism and a square-based pyramid; Describe the 2-D cross-section produced by slicing a cylinder horizontally or a cone vertically; Use properties of 3-D shapes to determine whether a given net will fold into a specified solid.

Needs first: 3-D shapes (age 10+), 3-D shapes (age 9+).

https://lightmysky.com/learn/mathematics/3-d-shapes-age-11-mt_nRksLqt-iR

#### Turns & Directions (ages 5-6)

Describe movement and direction, including whole, half, quarter, and three-quarter turns

Ready when they can: Follow instructions to move forward, backward, turn left/right; Demonstrate a whole turn, half turn, and quarter turn with their body; Describe a route using directional language.

Needs first: What Is a Half?, Finding halves and quarters (age 5+), Positional Language.

https://lightmysky.com/learn/mathematics/turns-and-directions-mt_Y9XKzLrUAZ

#### Position, direction, and movement (ages 6-7)

Use mathematical vocabulary to describe position, direction, and movement, including straight lines and distinguishing rotation as a turn in terms of right angles (quarter, half, three-quarter turns, clockwise and anti-clockwise)

Ready when they can: Use terms such as clockwise, anti-clockwise, quarter turn, half turn, three-quarter turn; Describe a right angle as a quarter turn; Give and follow directions involving straight-line movement and turns.

Needs first: Positional Language, Turns & Directions, Telling Time: Hours and Half Hours.

https://lightmysky.com/learn/mathematics/position-direction-and-movement-mt_TdV9YGJEoY

#### Understanding angles (ages 7-8)

Recognise angles as a property of shape or a description of a turn

Ready when they can: Identify angles at the corners of 2-D shapes; Describe a turn (e.g. quarter turn, half turn) in terms of the angle made; Explain that an angle measures the amount of turn between two lines meeting at a point.

Needs first: 2-D shapes (age 6+), Position, direction, and movement.

https://lightmysky.com/learn/mathematics/understanding-angles-mt_8OAGVdeTJ_

#### Right Angles & Turns (ages 7-8)

Identify right angles; recognise that two right angles make a half-turn, three make three-quarters, and four make a complete turn

Ready when they can: Use a right-angle checker to identify right angles in shapes and the environment; Classify angles as right angles, less than a right angle, or greater than a right angle; Explain that 4 right angles make a full turn (360°).

Needs first: Understanding angles.

https://lightmysky.com/learn/mathematics/right-angles-and-turns-mt_MFfYcnv6Tv

#### Parallel and perpendicular lines (ages 7-8)

Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Ready when they can: Point out horizontal and vertical lines in shapes and real-world contexts; Identify a pair of parallel lines (lines that never meet and are always the same distance apart); Identify perpendicular lines (lines that meet at a right angle).

Needs first: Right Angles & Turns, Positional Language.

https://lightmysky.com/learn/mathematics/parallel-and-perpendicular-lines-mt_u23IGDxOpk

#### First Quadrant Coordinates (ages 8-9)

Describe positions on a 2-D grid as coordinates in the first quadrant

Ready when they can: Read the coordinates of a point on a grid as (3, 5); Explain that the first number is the horizontal distance and the second is the vertical distance; Identify the coordinates of all vertices of a shape plotted on a grid.

Needs first: Position, direction, and movement.

https://lightmysky.com/learn/mathematics/first-quadrant-coordinates-mt_jBQS-CicNn

#### Coordinates (age 8+) (ages 8-9)

Plot specified points on a coordinate grid and draw sides to complete a given polygon

Ready when they can: Plot points (1,1), (1,4), (5,4), (5,1) and join to make a rectangle; Given three vertices of a square, plot the fourth vertex; Complete a triangle by plotting the third vertex at given coordinates and drawing sides.

Needs first: First Quadrant Coordinates, Classifying quadrilaterals.

https://lightmysky.com/learn/mathematics/coordinates-age-8-mt_i5_HnoFOYw

#### Types of angles (ages 8-9)

Identify acute and obtuse angles; compare and order angles up to two right angles by size

Ready when they can: Classify given angles as acute, right, or obtuse; Order four angles from smallest to largest by visual comparison; Identify all acute and obtuse angles in a given triangle or quadrilateral.

Needs first: Right Angles & Turns.

https://lightmysky.com/learn/mathematics/types-of-angles-mt_h0CVtqI2xo

#### Lines, Rays & Angles (ages 9-10)

Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures

Ready when they can: Draw a pair of perpendicular lines and a pair of parallel lines; Identify all pairs of parallel sides in a trapezoid; Mark a right angle, an acute angle, and an obtuse angle in a given figure.

Needs first: Types of angles, Parallel and perpendicular lines.

https://lightmysky.com/learn/mathematics/lines-rays-and-angles-mt_QysgF57dxh

#### Classifying shapes by line properties (ages 9-10)

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category

Ready when they can: Sort a set of quadrilaterals into those with parallel sides and those without; Identify which triangles in a set are right triangles; Classify shapes that have both perpendicular and parallel sides.

Needs first: Lines, Rays & Angles, Classifying quadrilaterals, Sorting 2-D and 3-D shapes.

https://lightmysky.com/learn/mathematics/classifying-shapes-by-line-properties-mt_r8c43QB6wx

#### Transformations on a grid (ages 9-12)

Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

Ready when they can: Reflect a shape in a given mirror line on a grid and label the new coordinates; Translate a shape by a given number of squares horizontally and vertically and describe the movement; Rotate a shape 90° or 180° about a given centre on a grid and check the image is congruent to the original.

Needs first: First Quadrant Coordinates.

https://lightmysky.com/learn/mathematics/transformations-on-a-grid-mt_SH7QgFl8-v

#### Describing Movements (ages 8-9)

Describe movements between positions as translations of a given unit to the left/right and up/down

Ready when they can: Describe moving from (2,3) to (5,3) as 3 units to the right; Translate a shape 4 units right and 2 units up and state the new coordinates; Predict where a point will be after a given translation.

Needs first: First Quadrant Coordinates, Transformations on a grid.

https://lightmysky.com/learn/mathematics/describing-movements-mt_Uq5vYqboCR

#### Lines of symmetry in 2-D shapes (ages 8-10)

Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry

Ready when they can: Find all lines of symmetry in a rectangle, square, and equilateral triangle; Determine whether a given shape has a line of symmetry when rotated; Identify which shapes in a set have exactly one line of symmetry; Determine how many lines of symmetry a regular hexagon has; Draw all lines of symmetry for a given figure; Identify which figures from a set are not line-symmetric.

Needs first: 2-D shapes (age 6+), Transformations on a grid.

https://lightmysky.com/learn/mathematics/lines-of-symmetry-in-2-d-shapes-mt_hRZyKvz1KN

#### Lines of symmetry (ages 8-9)

Complete a simple symmetric figure with respect to a specific line of symmetry

Ready when they can: Given half a butterfly shape and a mirror line, complete the other half on a grid; Complete a symmetric pattern on squared paper with a vertical line of symmetry; Check a completed figure by folding along the mirror line.

Needs first: Lines of symmetry in 2-D shapes, Transformations on a grid.

https://lightmysky.com/learn/mathematics/lines-of-symmetry-mt_hR2Y7NhMSY

#### Reflection and Translation on a Grid (ages 9-10)

Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed

Ready when they can: Reflect a triangle in a vertical mirror line on a coordinate grid and state the new coordinates; Translate a shape 3 units right and 2 units up and describe the movement; Explain that a reflected/translated shape is congruent to the original.

Needs first: Lines of symmetry, Coordinates (age 8+), Transformations on a grid, Describing Movements.

https://lightmysky.com/learn/mathematics/reflection-and-translation-on-a-grid-mt_efOeaGFyGM

#### What Is an Angle? (ages 9-10)

Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes

Ready when they can: Identify the vertex and arms of an angle in a diagram; Find examples of angles in the classroom (e.g. open door, clock hands); Explain why two rays meeting at a point form an angle.

Needs first: Types of angles.

https://lightmysky.com/learn/mathematics/what-is-an-angle-mt_3S10OOGPqu

#### Degrees and turns (ages 9-10)

Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees

Ready when they can: Explain that a full turn is 360° and a right angle is 90°; Describe what 'one degree' means in terms of a fraction of a circle; State that an angle of 45° has turned through 45 one-degree angles.

Needs first: What Is an Angle?.

https://lightmysky.com/learn/mathematics/degrees-and-turns-mt_qUGMyMYn9m

#### Estimating Angles (ages 9-10)

Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size

Ready when they can: Estimate an angle as approximately 130° and classify it as obtuse; Identify a reflex angle in a diagram and estimate it as about 270°; Order four angles from smallest to largest by estimation before measuring.

Needs first: Degrees and turns.

https://lightmysky.com/learn/mathematics/estimating-angles-mt_YUJ5pwalqL

#### Geometric diagram conventions (ages 9-12)

Use and interpret standard geometric diagram conventions: mark right angles with a small square, equal lengths with single or double tick marks, and equal angles with arc marks; label angles in three-letter notation (∠ABC) and individual angles with a single letter or number; draw diagrams showing angles at a point, angles on a straight line, and angles inside polygons with these conventions; read diagrams with these marks to identify given information and find unknown values

Ready when they can: Mark a right angle with a small square symbol in a diagram and explain what it means; Use tick marks to show equal lengths in a shape and double tick marks for a second pair of equal sides; Read and interpret angle notation (e.g. angle ABC) and identify the angle being referred to in a diagram.

Needs first: What Is an Angle?, Right Angles & Turns, Degrees and turns.

https://lightmysky.com/learn/mathematics/geometric-diagram-conventions-mt_e4V6hvcuEJ

#### Angle Sum Rules (ages 9-10)

Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles

Ready when they can: State that two angles on a straight line add to 180°; Explain that four right angles at a point make 360°; Identify 270° as three right angles.

Needs first: Geometric diagram conventions, Degrees and turns.

https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L

#### Measuring angles (ages 9-10)

Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure

Ready when they can: Measure an angle with a protractor and read 47°; Draw an angle of 135° using a protractor; Identify which scale on the protractor to use for an obtuse angle.

Needs first: Geometric diagram conventions, Degrees and turns, Types of angles.

https://lightmysky.com/learn/mathematics/measuring-angles-mt_4MFUAsbx_6

#### Regular and irregular polygons (ages 9-10)

Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles

Ready when they can: Classify a set of polygons as regular or irregular; Explain that a regular pentagon has 5 equal sides and 5 equal angles; Identify that a rectangle is irregular (equal angles but not all equal sides) unless it is a square.

Needs first: Classifying quadrilaterals, Estimating Angles.

https://lightmysky.com/learn/mathematics/regular-and-irregular-polygons-mt_8H2kO4k2B9

#### 2-D shapes (age 10+) (ages 10-11)

Draw 2-D shapes using given dimensions and angles, using a ruler and protractor accurately

Ready when they can: Draw a triangle with sides 5 cm, 7 cm and an included angle of 60°; Construct a rectangle with given length and width using a ruler and set square; Draw a regular pentagon given the side length and interior angle.

Needs first: Measuring angles, Regular and irregular polygons.

https://lightmysky.com/learn/mathematics/2-d-shapes-age-10-mt_hdrMoiTgqu

#### Classifying shapes by properties (ages 10-11)

Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties

Ready when they can: Explain why all squares are rectangles but not all rectangles are squares; Place quadrilaterals in a hierarchy diagram showing subset relationships; Identify properties shared by all parallelograms and explain why rhombuses and rectangles are special cases.

Needs first: Regular and irregular polygons, Classifying shapes by line properties.

https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh

#### Angles in triangles (age 10+) (ages 10-11)

Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties

Ready when they can: Find a missing angle in a triangle given two angles (using angle sum = 180°); Calculate a missing angle in a quadrilateral (angle sum = 360°); Calculate the interior angle of a regular hexagon from the angle sum formula.

Needs first: Geometric diagram conventions, Classifying shapes by properties, Angle Sum Rules.

https://lightmysky.com/learn/mathematics/angles-in-triangles-age-10-mt_cdMlC7EpTJ

#### Parts of a circle (ages 10-11)

Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius

Ready when they can: Label the radius, diameter, and circumference on a circle diagram; Calculate the diameter given a radius of 4.5 cm (diameter = 9 cm); Explain the relationship between radius and diameter in their own words.

Needs first: Classifying shapes by line properties.

https://lightmysky.com/learn/mathematics/parts-of-a-circle-mt_xq3YHZ2zeR

#### The coordinate plane and ordered pairs (ages 10-11)

Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin

Ready when they can: Identify the x-axis, y-axis, and origin on a coordinate grid; Explain that (3, 5) means go 3 along the x-axis and 5 up the y-axis; Distinguish (2, 4) from (4, 2) by explaining each coordinate's meaning.

Needs first: Lines, Rays & Angles.

https://lightmysky.com/learn/mathematics/the-coordinate-plane-and-ordered-pairs-mt_oDlduFnemk

#### Plotting points in the first quadrant (ages 10-11)

Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context

Ready when they can: Plot the point (4, 7) accurately on a first-quadrant grid; Graph a set of data pairs (e.g. time vs distance) as points on the coordinate plane; Read coordinates of a plotted point and explain what they represent in a given scenario.

Needs first: The coordinate plane and ordered pairs.

https://lightmysky.com/learn/mathematics/plotting-points-in-the-first-quadrant-mt_snlqRCiA1R

#### Accurate drawing and scale diagrams (ages 11-13)

Draw and measure line segments and angles accurately using ruler and protractor, and interpret scale drawings to extract real measurements

Ready when they can: Draw a triangle accurately given two sides and the included angle (SAS); Measure angles in a geometric figure to the nearest degree using a protractor; Read a scale drawing to determine actual lengths, explaining the scale used.

Needs first: Measuring angles, 2-D shapes (age 10+).

https://lightmysky.com/learn/mathematics/accurate-drawing-and-scale-diagrams-mt_Jf8xcX4UTq

#### Geometric terms and notation (ages 11-13)

Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons

Ready when they can: Use correct notation for line segments (AB), angles (∠ABC), and parallel lines (AB ∥ CD); Sketch a regular hexagon and describe its rotational and reflective symmetry; Identify and label perpendicular and parallel lines in a given figure using standard symbols.

Needs first: Regular and irregular polygons, Classifying shapes by properties.

https://lightmysky.com/learn/mathematics/geometric-terms-and-notation-mt_WtIFJSCQIT

#### Properties of triangles and quadrilaterals (ages 11-13)

Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

Ready when they can: List and verify properties of a parallelogram (opposite sides parallel/equal, opposite angles equal, diagonals bisect each other); Explain why a square is a special case of both a rectangle and a rhombus; Derive the relationship between the radius, diameter, and circumference of a circle.

Needs first: Geometric terms and notation.

https://lightmysky.com/learn/mathematics/properties-of-triangles-and-quadrilaterals-mt_DNYQLahbfa

#### Ruler and compass constructions (ages 12-14)

Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle

Ready when they can: Construct the perpendicular bisector of a line segment using compasses and a straight edge; Construct an angle bisector and verify by measuring both halves; Construct a perpendicular from a point to a line using compasses only.

Needs first: Accurate drawing and scale diagrams.

https://lightmysky.com/learn/mathematics/ruler-and-compass-constructions-mt_ZrsqGVG-Wt

#### Triangle congruence criteria (ages 12-14)

Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent

Ready when they can: State which congruence criterion (SSS, SAS, ASA, or RHS) applies to a given pair of triangles; Use the notation △ABC ≅ △DEF and match corresponding sides and angles; Determine whether given measurements produce a unique triangle, more than one, or none.

Needs first: Accurate drawing and scale diagrams, Geometric terms and notation.

https://lightmysky.com/learn/mathematics/triangle-congruence-criteria-mt_167X6Ax8P7

#### Properties of rectangles (ages 9-10)

Use the properties of rectangles to deduce related facts and find missing lengths and angles

Ready when they can: Given one side of a rectangle is 8 cm and the perimeter is 28 cm, find the other side; Explain that all angles in a rectangle are 90°; Find a missing side of a rectangle given its area and one side length.

Needs first: Area and perimeter of rectangles, Classifying quadrilaterals.

https://lightmysky.com/learn/mathematics/properties-of-rectangles-mt_KFKUR_gBg_

#### Angles that add up on a diagram (ages 9-10)

Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown

Ready when they can: Two angles on a straight line are 65° and x°; find x = 115°; An angle is decomposed into 35° and 40°; state the whole angle is 75°; Solve: angles at a point are 120°, 90°, and x°; find x = 150°.

Needs first: Measuring angles, Geometric diagram conventions, Angle Sum Rules, Two-Step Equations.

https://lightmysky.com/learn/mathematics/angles-that-add-up-on-a-diagram-mt_89riIKwGYp

#### Understanding angles (age 10+) (ages 10-11)

Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties

Ready when they can: Find a missing angle at a point given the other angles (total 360°); Use the straight-line property (angles sum to 180°) to find an unknown angle; Identify vertically opposite angles and use the property that they are equal to find unknowns.

Needs first: Angles that add up on a diagram, Angle Sum Rules, Properties of rectangles.

https://lightmysky.com/learn/mathematics/understanding-angles-age-10-mt_QDTO3GAgcq

#### Understanding angles (age 11+) (ages 11-13)

Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems

Ready when they can: Find a missing angle using the fact that angles on a straight line sum to 180°; Use vertically opposite angles are equal to set up and solve an equation for an unknown; Combine multiple angle facts in a single diagram to find several missing angles step by step.

Needs first: Angle Sum Rules, Understanding angles (age 10+).

https://lightmysky.com/learn/mathematics/understanding-angles-age-11-mt_tedML_iu4Y

#### Angles with parallel lines (ages 12-14)

Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

Ready when they can: Identify alternate, corresponding, and co-interior angle pairs in a diagram with parallel lines; Explain why alternate angles are equal using the concept of translation along the transversal; Find missing angles in a parallel-line diagram using a combination of angle relationships.

Needs first: Understanding angles (age 11+).

https://lightmysky.com/learn/mathematics/angles-with-parallel-lines-mt_H_pNJ3ZI_S

#### Coordinates (age 10+) (ages 10-11)

Describe positions on the full coordinate grid (all four quadrants); use coordinates with negative values

Ready when they can: Plot points with negative coordinates such as (−3, 4) and (2, −5) on a four-quadrant grid; Identify the quadrant in which a given point lies; Describe the position of a shape using coordinates in all four quadrants.

Needs first: Coordinates (age 8+), Measuring temperature, Transformations on a grid, Plotting points in the first quadrant.

https://lightmysky.com/learn/mathematics/coordinates-age-10-mt_R4AY0LKxfl

#### Translating and reflecting shapes (ages 10-11)

Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes

Ready when they can: Translate a triangle 3 units right and 2 units down on a coordinate grid and state the new coordinates; Reflect a shape in the x-axis and list the coordinates of the reflected vertices; Explain how translation changes coordinates (add/subtract) while reflection changes the sign of one coordinate.

Needs first: Reflection and Translation on a Grid, Coordinates (age 10+).

https://lightmysky.com/learn/mathematics/translating-and-reflecting-shapes-mt_lxaM6iVpdr

#### Area and volume formulae (ages 11-14)

Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning

Ready when they can: Calculate the area of a trapezium using A = ½(a + b) × h and explain why the formula works; Find the volume of a triangular prism by calculating cross-sectional area × length; Derive the formula for the volume of a cylinder as π × r² × h by reasoning from the prism formula.

Needs first: Area and perimeter of rectangles, Area of Triangles & Parallelograms, Volume of cuboids.

https://lightmysky.com/learn/mathematics/area-and-volume-formulae-mt_tAJH5BrpOx

#### Surface Area of Solids (ages 11-13)

Find the surface area of prisms and pyramids by unfolding them into nets of rectangles and triangles, working out each face's area and summing them; apply this to practical problems like wrapping boxes or painting walls

Ready when they can: Draw or identify the net of a cuboid, prism, or pyramid and label the dimensions of each face; Calculate the area of every face and add them to find the total surface area (e.g., a 3 cm × 4 cm × 5 cm box); Solve a practical surface-area problem (e.g., how much card is needed to build a model, with the right units).

Needs first: Nets of 3-D Shapes, Area of Triangles & Parallelograms, 3-D shapes (age 11+).

https://lightmysky.com/learn/mathematics/surface-area-of-solids-mt_hdhmurUndc

#### Circles: Circumference & Area (ages 12-14)

Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

Ready when they can: Calculate the circumference and area of a circle given its radius or diameter; Find the perimeter or area of a composite shape made from rectangles and semicircles; Explain the relationship between π, diameter, and circumference informally.

Needs first: Area and volume formulae, Parts of a circle, Perimeter (age 10+).

https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_

#### Volume and Surface Area of Prisms and Cylinders (ages 14-15)

Find the volume of any prism as base area times length, and its surface area as the two ends plus the wrapped rectangle, including the cylinder.

Ready when they can: Compute the volume of a triangular prism and of a cylinder from the base area and length; Find the surface area of a cylinder by separating the two circles from the curved rectangle; Work backwards from a stated volume to a missing radius or length, keeping units cubed and squared straight.

https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh

#### Bearings and Scale Drawings (ages 14-15)

Describe a direction as a three-figure bearing measured clockwise from north, and use a scale drawing to move between a plan and real distances.

Ready when they can: Measure and write a bearing as three figures, including bearings past 180 degrees; Find the back bearing of a stated direction and justify the calculation; Construct a scale drawing from bearings and distances, then read a real distance off it.

https://lightmysky.com/learn/mathematics/bearings-and-scale-drawings-mt_9q32jC0Fk_

#### Angle sums in triangles and polygons (ages 11-14)

Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons

Ready when they can: Calculate a missing angle in a triangle by subtracting the known angles from 180°; Find the sum of interior angles in a hexagon by dividing it into triangles; Calculate each interior and exterior angle of a regular polygon given the number of sides.

Needs first: Angles in triangles (age 10+), Algebraic Notation, Understanding angles (age 11+).

https://lightmysky.com/learn/mathematics/angle-sums-in-triangles-and-polygons-mt_J03RFlVdas

#### Coordinate Transformations (ages 11-14)

Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

Ready when they can: Reflect a shape in a given mirror line (including diagonal lines) and state the coordinates of the image; Rotate a shape about a given centre by 90° or 180° and describe the result; Translate a shape by a given vector and verify that lengths and angles are preserved.

Needs first: Coordinates (age 11+), Translating and reflecting shapes.

https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY

#### Similarity and enlargement (ages 12-14)

Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids

Ready when they can: Enlarge a shape by a given scale factor from a specified centre of enlargement; Determine the scale factor between two similar shapes by comparing corresponding sides; Explain why corresponding angles in similar shapes are equal while sides are in proportion.

Needs first: Scale and similar shapes, Coordinate Transformations, Ratio Notation.

https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B

#### Pythagoras' Theorem (ages 13-14)

Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts

Ready when they can: Calculate the hypotenuse of a right-angled triangle given the two shorter sides; Find a shorter side given the hypotenuse and the other short side; Use Pythagoras’ Theorem to find the distance between two points on a coordinate grid.

Needs first: Simple formulae, Angle sums in triangles and polygons, Integer powers and roots, First Quadrant Coordinates.

https://lightmysky.com/learn/mathematics/pythagoras-theorem-mt_1VmTUxBrNd

#### Trigonometry basics (ages 13-15)

Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem

Ready when they can: Identify which trigonometric ratio to use (SOH CAH TOA) based on the known and unknown sides; Calculate an unknown side using sin, cos, or tan and a known angle; Find an unknown angle using the inverse trigonometric function (e.g. tan⁻¹).

Needs first: Pythagoras' Theorem, Simple formulae, Ruler and compass constructions, Using a Calculator Well.

https://lightmysky.com/learn/mathematics/trigonometry-basics-mt_KB_Czd7RQH

#### Similar Triangles and Proving Similarity (ages 14-15)

Decide whether two triangles are similar from equal angles or matching side ratios, set the reason out in one line, and use the scale factor to find a missing length.

Ready when they can: Show two triangles are similar by naming the pairs of equal angles; Match corresponding vertices before writing any ratio; Find a missing side using the scale factor between matching sides.

https://lightmysky.com/learn/mathematics/similar-triangles-and-proving-similarity-mt_NPRVlr4lrs

#### Similar Shapes: Area and Volume Scale Factors (ages 14-15)

Use the fact that areas scale by the square of the length scale factor and volumes by its cube, and work the relationship in both directions.

Ready when they can: Find the area of an enlarged shape from the length scale factor; Work back to the length scale factor from a ratio of volumes; Explain why doubling every length of a solid multiplies its volume by eight.

https://lightmysky.com/learn/mathematics/similar-shapes-area-and-volume-scale-factors-mt_v37c_AeLQa

#### Congruent Triangles and the Congruence Conditions (ages 14-15)

Use SSS, SAS, ASA and RHS to decide whether two triangles are congruent, and write the decision as a short reasoned argument.

Ready when they can: Pick the condition that the information in the diagram matches; Explain why two sides and a non-included angle is not enough; Use a congruence argument to justify that two lengths in a diagram are equal.

https://lightmysky.com/learn/mathematics/congruent-triangles-and-the-congruence-conditions-mt_it8t7mY71J

#### Volume and Surface Area of Cones, Spheres and Pyramids (ages 15-16)

Apply the standard formulae for pyramids, cones and spheres, and find a slant height when only the perpendicular height is given.

Ready when they can: Use the one-third factor for a pyramid or cone and say which height the formula wants; Find a cone's slant height from its radius and perpendicular height before computing curved surface area; Handle a composite solid such as a hemisphere on a cylinder by adding volumes and adjusting which faces are exposed.

https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-cones-spheres-and-pyramids-mt_s4K5YMBSzG

#### Exact Values of Sine, Cosine and Tangent (ages 15-16)

Know and use the exact values of sin, cos and tan for 0, 30, 45, 60 and 90 degrees, taken from a halved equilateral triangle and a half square.

Ready when they can: Recall sin 30, cos 60 and tan 45 without a calculator; Derive the 30 and 60 degree values from an equilateral triangle cut in half; Leave an answer in surd form instead of rounding it.

https://lightmysky.com/learn/mathematics/exact-values-of-sine-cosine-and-tangent-mt_SNJEbXYOrR

#### The Sine Rule (ages 15-16)

Use a/sin A = b/sin B in triangles with no right angle to find a missing side or angle, and check whether an obtuse second answer also fits.

Ready when they can: Pair each side with the angle opposite it before substituting; Find a missing angle and test whether the obtuse partner also works; Choose the sine rule when a side and its opposite angle are both known.

https://lightmysky.com/learn/mathematics/the-sine-rule-mt_cTt_-9KZho

#### The Cosine Rule (ages 15-16)

Use a² = b² + c² - 2bc cos A when the sine rule does not apply: three sides given, or two sides with the angle between them.

Ready when they can: Find the third side from two sides and the included angle; Rearrange the rule to find an angle from three known sides; Recognise Pythagoras as the case where the angle is 90 degrees.

https://lightmysky.com/learn/mathematics/the-cosine-rule-mt_yy73gK5CEP

#### Triangle Area with Half ab sin C (ages 15-16)

Find the area of any triangle from two sides and the angle between them, and run the same rule backwards to find an angle from a known area.

Ready when they can: Use the two sides either side of the given angle, not any two sides; Find an angle when the area and two sides are known; Split a quadrilateral into two triangles to find its area.

https://lightmysky.com/learn/mathematics/triangle-area-with-half-ab-sin-c-mt_PiwizT4D2b

#### Pythagoras and Trigonometry in Three Dimensions (ages 15-16)

Find lengths and angles inside cuboids, prisms and pyramids by picking a right-angled triangle out of the solid and solving it on its own.

Ready when they can: Find the long diagonal of a cuboid with two uses of Pythagoras; Redraw the chosen triangle flat before calculating anything; Find the angle between an edge and the base of a pyramid.

https://lightmysky.com/learn/mathematics/pythagoras-and-trigonometry-in-three-dimensions-mt_7yKxYqQHB2

#### Choosing a Triangle Method (ages 15-16)

Decide from what a question gives you which tool a triangle needs: Pythagoras, right-angle ratios, the sine rule or the cosine rule.

Ready when they can: Sort triangle questions by what is given before calculating anything; Say why the chosen rule is the only one that fits the given information; Spot a diagram that has to be split into two triangles solved in order.

https://lightmysky.com/learn/mathematics/choosing-a-triangle-method-mt_nubZzZjVvn

#### Arc Length, Sector Area and Segments (ages 15-16)

Find arc lengths and sector areas as fractions of a whole circle, and find a segment by subtracting a triangle from its sector.

Ready when they can: Work out an arc length as the angle over 360 of the circumference; Find a sector area and leave it in terms of pi when asked; Find a segment area by subtracting the triangle from the sector.

https://lightmysky.com/learn/mathematics/arc-length-sector-area-and-segments-mt_z9LIwmfKYJ

#### Bearing Problems with the Sine and Cosine Rules (ages 15-16)

Turn a journey described by bearings into a triangle, then solve it with the sine or cosine rule instead of drawing it to scale.

Ready when they can: Draw the triangle a two-leg journey makes and mark the angle each bearing contributes; Choose the sine or cosine rule from what the sketch gives, then compute the return distance; Convert a computed angle back into a three-figure bearing for the answer.

https://lightmysky.com/learn/mathematics/bearing-problems-with-the-sine-and-cosine-rules-mt_YQFdU4aiFP

#### Circle Theorems: Angles at the Centre and in a Semicircle (ages 15-16)

Use the fact that the angle at the centre is twice the angle at the circumference on the same arc, and that the angle in a semicircle is a right angle.

Ready when they can: Find a missing angle from the centre and circumference relationship; Recognise the semicircle result as the case where the centre angle is 180 degrees; Name the theorem as the reason for each step of the working.

https://lightmysky.com/learn/mathematics/circle-theorems-angles-at-the-centre-and-in-a-semicircle-mt_kOwb61sfUR

#### Circle Theorems: Cyclic Quadrilaterals and the Same Segment (ages 15-16)

Use the equal angles subtended by the same arc, and the opposite angles of a cyclic quadrilateral adding to 180 degrees.

Ready when they can: Find equal angles standing on the same arc in a busy diagram; Use opposite angles of a cyclic quadrilateral to find a missing angle; Give the theorem name with each step rather than the answer alone.

https://lightmysky.com/learn/mathematics/circle-theorems-cyclic-quadrilaterals-and-the-same-segment-mt_11GlmkiqB1

#### Tangents, Radii and the Alternate Segment Theorem (ages 15-16)

Use the right angle between a tangent and the radius at the point of contact, the equal tangents from an outside point, and the alternate segment theorem.

Ready when they can: Mark the right angle where a tangent meets the radius and use it; Use the two equal tangents from an external point to find a length; Apply the alternate segment theorem to find an angle in a triangle inside the circle.

https://lightmysky.com/learn/mathematics/tangents-radii-and-the-alternate-segment-theorem-mt_Y-Xf0BOb1C

#### Constructions and Loci (ages 15-16)

Construct perpendicular bisectors, angle bisectors and perpendiculars with compasses, and shade the region that fits a set of distance conditions.

Ready when they can: Construct a perpendicular bisector and an angle bisector, leaving the arcs visible; Describe the locus of points a fixed distance from a line segment; Shade the region that satisfies two conditions at once.

https://lightmysky.com/learn/mathematics/constructions-and-loci-mt_yqoXwrKaW3

#### Vectors: Notation, Addition and Scalar Multiples (ages 15-16)

Write vectors as columns or as bold letters, add and subtract them along a route, and multiply by a scalar to change length or reverse direction.

Ready when they can: Add two column vectors and draw the result on a grid; Write a route around a shape as a sum of named vectors; Say what -2a does to the length and the direction of a.

https://lightmysky.com/learn/mathematics/vectors-notation-addition-and-scalar-multiples-mt_NkqmrL7pLe

#### Proving Geometry Facts with Vectors (ages 15-16)

Show that one vector expression is a multiple of another, and use that to prove lines are parallel or that three points lie on a straight line.

Ready when they can: Write a route in terms of the two given vectors before comparing anything; Argue that one vector is a multiple of another, so the lines are parallel; Use a shared point plus parallel vectors to show three points are in a line.

https://lightmysky.com/learn/mathematics/proving-geometry-facts-with-vectors-mt_A00MA7Ecgf

#### Radian Measure and Sectors (ages 16-17)

Measure an angle by the arc it cuts on a circle of radius 1, so a full turn is 2π. In radians the arc length is rθ and the sector area is ½r²θ, with no fraction of 360 to carry.

Ready when they can: Convert between degrees and radians for 30°, 45°, 60° and 180°; Find an arc length and a sector area with the angle given in radians; State sin, cos and tan of π/6, π/4 and π/3 exactly.

https://lightmysky.com/learn/mathematics/radian-measure-and-sectors-mt_SvAYAu6mQ4

#### Vectors in Three Dimensions (ages 19-20)

Extend position, addition and scalar multiples to space, with distance and the standard unit vectors. Everything later in the spine is written in this notation.

Ready when they can: Write a vector in component form and find its magnitude in space; Find the distance between two points and the midpoint of the segment; Express a vector as a combination of i, j and k.

https://lightmysky.com/learn/mathematics/vectors-in-three-dimensions-mt_o97GclnNC-

#### The Unit Circle and the Graphs of Sine, Cosine and Tangent (ages 16-17)

Define sine and cosine as the coordinates of a point travelling round the unit circle, which extends them beyond a right angle and explains the period, symmetry and repeated values of their graphs.

Ready when they can: Sketch y = sin x from 0 to 2π and mark where it repeats; Use the circle to explain why sin(π - x) = sin x; State the period and amplitude of y = 2 sin 3x and say why tan has asymptotes.

https://lightmysky.com/learn/mathematics/the-unit-circle-and-the-graphs-of-sine-cosine-and-tangent-mt_VJaimevi3-

#### The Pythagorean and Quotient Identities (ages 16-17)

sin²θ + cos²θ = 1 is Pythagoras on the unit circle, and tan θ = sin θ / cos θ is a ratio of coordinates. Use both to simplify expressions and to prove further identities.

Ready when they can: Derive sin²θ + cos²θ = 1 from the radius of the unit circle; Simplify (1 - cos²θ) / sin θ to a single function; Prove a given identity by working on one side until it matches the other.

https://lightmysky.com/learn/mathematics/the-pythagorean-and-quotient-identities-mt_NXBq37vxQh

#### Solving Trigonometric Equations in a Given Interval (ages 16-17)

Find every solution inside a stated interval, using the graph or the circle to get the solutions the calculator does not show, and adjusting the interval first when the angle is 2x or x + 30°.

Ready when they can: Solve sin x = 0.5 for 0 ≤ x ≤ 2π and give both solutions; Stretch the interval before solving an equation written in 2x; Use an identity to reduce an equation to a single trigonometric function first.

https://lightmysky.com/learn/mathematics/solving-trigonometric-equations-in-a-given-interval-mt_74_jiK2xXA

#### Compound Angle Formulae (ages 16-17)

Expand sin(A ± B), cos(A ± B) and tan(A ± B), and use them for exact values of angles built from known ones and for equations mixing two angles.

Ready when they can: Find an exact value for cos 15° by writing it as cos(45° - 30°); Expand sin(x + π/4) and simplify the constants; Solve an equation after expanding its compound angle.

https://lightmysky.com/learn/mathematics/compound-angle-formulae-mt_ANDmX8exwg

#### Double Angle Formulae (ages 16-17)

Set B = A in the compound angle formulae to get sin 2A, cos 2A and tan 2A, and pick between the three forms of cos 2A to remove either a squared term or a doubled angle.

Ready when they can: Derive sin 2A by writing it as sin(A + A); Choose the form of cos 2A that clears a sin²x from an equation; Solve an equation containing both sin 2x and sin x.

https://lightmysky.com/learn/mathematics/double-angle-formulae-mt_AC9MmZ_fam

#### Combining a Sine and a Cosine into a Single Wave (ages 16-17)

Write a sin x + b cos x as R sin(x + α), so two waves become one with a single amplitude and shift. Maximum and minimum values, and the x where they happen, then read off directly.

Ready when they can: Write 3 sin x + 4 cos x in the form R sin(x + α); State the maximum value of that expression and the x where it occurs; Solve an equation by rewriting the left side as a single wave.

https://lightmysky.com/learn/mathematics/combining-a-sine-and-a-cosine-into-a-single-wave-mt_IwQkNDRWyq

#### Parametric Equations of Curves (ages 16-17)

Describe a curve by giving x and y separately in terms of a parameter, plot it from a table of parameter values, and convert to Cartesian form by eliminating the parameter.

Ready when they can: Plot the curve x = 2t, y = t² for a range of t values; Eliminate t to get the Cartesian equation of that curve; Use sin²t + cos²t = 1 to show x = 3 cos t, y = 3 sin t is a circle.

https://lightmysky.com/learn/mathematics/parametric-equations-of-curves-mt_7NC7SCeU2P

#### Small Angle Approximations (ages 17-18)

Near zero, and only in radians, the sine of an angle is the angle, the tangent of it is the angle too, and the cosine drops off as one minus half the square. These are the approximations that turn an equation nobody can solve into one anybody can, and knowing when they stop being safe is half the point.

Ready when they can: States the three approximations, insists on radians, and says what goes wrong in degrees; Reads the approximations off the graphs of sine, cosine and tangent near the origin; Uses an approximation to simplify an expression, then checks the size of the error it introduced at a stated angle.

https://lightmysky.com/learn/mathematics/small-angle-approximations-mt_fIsZes5Os3

#### Forms of the Equation of a Straight Line (ages 16-17)

Move between y = mx + c, y - y₁ = m(x - x₁) and ax + by + c = 0, and produce the equation of a line from a point and a gradient or from two points.

Ready when they can: Find the equation of the line through (2, 5) and (6, 13); Rewrite 3x + 4y - 12 = 0 in gradient-intercept form and state its gradient; Find where a given line meets each axis.

Needs first: Sketching a Curve from Its Factorised Form, Plotting Linear Graphs.

https://lightmysky.com/learn/mathematics/forms-of-the-equation-of-a-straight-line-mt_dhIIxdFwcp

#### Parallel and Perpendicular Lines in Coordinates (ages 16-17)

Use equal gradients for parallel lines and a gradient product of -1 for perpendicular ones, and apply both to find missing lines, midpoints and distances.

Ready when they can: Find the line through (1, 4) perpendicular to y = 2x - 3; Show that two given lines are parallel and never meet; Find the perpendicular bisector of the segment joining two points.

Needs first: Forms of the Equation of a Straight Line, Pythagoras' Theorem.

https://lightmysky.com/learn/mathematics/parallel-and-perpendicular-lines-in-coordinates-mt_xNEmm139Ka

#### The Equation of a Circle (ages 16-17)

Read a circle's centre and radius from (x - a)² + (y - b)² = r², and recover them from an expanded equation by completing the square in both variables.

Ready when they can: Write the equation of the circle with centre (3, -1) and radius 5; Find the centre and radius of x² + y² - 6x + 4y - 12 = 0; Decide whether a given point is inside, on, or outside a circle.

Needs first: Parallel and Perpendicular Lines in Coordinates, Completing the Square.

https://lightmysky.com/learn/mathematics/the-equation-of-a-circle-mt_YARqmi_ioe

#### Lines Meeting Circles: Tangents and Chords (ages 16-17)

Find where a line cuts a circle by substitution, use the discriminant to tell a tangent from a chord or a miss, and use the right angle between a tangent and the radius.

Ready when they can: Find the two intersection points of a line and a circle by substituting; Show a line is a tangent by getting a discriminant of zero; Find the tangent at a given point on a circle using the radius gradient.

Needs first: The Equation of a Circle, The Discriminant and the Number of Roots.

https://lightmysky.com/learn/mathematics/lines-meeting-circles-tangents-and-chords-mt_ELA4IzIVdv

#### Conic Sections: Ellipse, Parabola and Hyperbola (ages 17-18)

Meet the three curves a plane cuts from a cone, in both their locus definitions and their standard equations, and read foci and axes off the equation.

Ready when they can: Match each standard equation to its curve and identify centre, axes and foci; State the distance property that defines an ellipse, a parabola and a hyperbola; Recognise a conic from a shifted equation by completing the square in both variables.

https://lightmysky.com/learn/mathematics/conic-sections-ellipse-parabola-and-hyperbola-mt_V4YSI3a_Eu

#### Polar Coordinates and Polar Curves (ages 17-18)

Locate a point by distance and angle instead of two displacements, convert between the two systems, and sketch curves that are simpler in polar form.

Ready when they can: Convert a point and an equation between Cartesian and polar form; Sketch a circle, a spiral and a rose curve from a polar equation by tracking the radius as the angle turns; Say which shapes gain from polar form and which lose, with a reason.

https://lightmysky.com/learn/mathematics/polar-coordinates-and-polar-curves-mt_R5QMUJvA1v

#### The Dot Product: Angles and Projections (ages 19-20)

One product of two vectors returns a number that encodes the angle between them. It tests perpendicularity, projects one vector onto another and computes work.

Ready when they can: Find the angle between two vectors from their dot product; Decide perpendicularity from a dot product of zero; Resolve a vector into components parallel and perpendicular to another.

https://lightmysky.com/learn/mathematics/the-dot-product-angles-and-projections-mt_yFBcyE4sFw

#### The Cross Product and Oriented Area (ages 19-20)

The other product of two vectors returns a vector perpendicular to both, whose length is the area of the parallelogram they span and whose direction records the orientation.

Ready when they can: Compute a cross product and check it is perpendicular to both inputs; Use the magnitude to find the area of a triangle in space; Show that swapping the order reverses the result.

https://lightmysky.com/learn/mathematics/the-cross-product-and-oriented-area-mt_QEBM_Ms-SK

#### Lines and Planes in Space (ages 19-20)

Write lines and planes in vector, parametric and Cartesian form, and answer distance and intersection questions with dot and cross products.

Ready when they can: Convert a plane between its normal form and its parametric form; Find the distance from a point to a line and to a plane; Decide whether two lines meet, are parallel, or are skew, and find the angle where relevant.

https://lightmysky.com/learn/mathematics/lines-and-planes-in-space-mt_kIX5ak1GRv

#### Arc Length and Curvature of a Space Curve (ages 20-21)

Reparametrise a curve by arc length and measure how fast its direction turns, separating the path from the speed along it.

Ready when they can: Compute the arc length of a space curve and reparametrise a simple one by it; Compute curvature and interpret it as the reciprocal of the radius of the best-fitting circle; Split an acceleration into tangential and normal components and say what each means physically.

https://lightmysky.com/learn/mathematics/arc-length-and-curvature-of-a-space-curve-mt_8mXYE8bVG1

### Measurement

https://lightmysky.com/learn/mathematics/areas/measurement

#### Comparing durations (ages 4-6)

Use comparative language for time: quicker, slower, earlier, later

Ready when they can: Compare two events and say which was quicker/slower; Use 'earlier' and 'later' correctly to describe daily events; Solve practical problems like 'Who finished first?'.

https://lightmysky.com/learn/mathematics/comparing-durations-mt_TcG90kS8nu

#### Measurable Attributes of Objects (ages 4-6)

Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)

Ready when they can: Identify that a pencil has length and can be measured; Describe multiple attributes of one object (e.g. a bottle has height, weight, and capacity); Use words like 'long', 'heavy', 'full' to describe objects.

https://lightmysky.com/learn/mathematics/measurable-attributes-of-objects-mt_NtJYlJdUe9

#### Comparing Capacity (ages 4-6)

Compare and describe capacity and volume using language such as full, empty, more than, less than, half full

Ready when they can: Compare two containers and say which holds more/less; Use 'half full' and 'quarter full' to describe a container; Solve practical problems like 'Which cup has more water?'.

Needs first: Measurable Attributes of Objects.

https://lightmysky.com/learn/mathematics/comparing-capacity-mt_zkFbMLpu3U

#### Comparing Lengths & Heights (ages 4-6)

Compare two objects directly by length or height and describe the difference using language such as long, short, tall, longer, shorter, taller, double, half

Ready when they can: Stand two children back-to-back and say who is taller/shorter; Directly compare the heights of two towers and describe one as taller; Use 'longer' and 'shorter' to compare two ribbons placed side by side.

Needs first: Measurable Attributes of Objects.

https://lightmysky.com/learn/mathematics/comparing-lengths-and-heights-mt_uhuxX8sg9f

#### Measuring mass and weight (age 4+) (ages 4-6)

Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter than

Ready when they can: Heft two objects and say which is heavier/lighter; Use a simple balance to compare the weight of two objects; Describe one object as 'heavier than' another.

Needs first: Measurable Attributes of Objects.

https://lightmysky.com/learn/mathematics/measuring-mass-and-weight-age-4-mt_-P1kdZhHbL

#### Ordering Events in Time (ages 4-6)

Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening

Ready when they can: Order three daily events using 'first', 'next', 'last'; Use 'yesterday', 'today', 'tomorrow' correctly; Describe an event as happening in the 'morning' or 'afternoon'.

https://lightmysky.com/learn/mathematics/ordering-events-in-time-mt_-vvVxpOHG2

#### Capacity and volume (ages 5-6)

Measure and begin to record capacity and volume using non-standard and standard units

Ready when they can: Measure capacity by counting how many cups fill a container; Begin to use litres as a unit of capacity; Record capacity measurements with a number and unit.

Needs first: Comparing Capacity.

https://lightmysky.com/learn/mathematics/capacity-and-volume-mt_4lp_b5Pzik

#### Days, Weeks, Months & Years (ages 5-6)

Recognise and use language relating to dates, including days of the week, weeks, months, and years

Ready when they can: Name the seven days of the week in order; Name the twelve months of the year in order; Understand that a year is made up of months and weeks.

Needs first: Ordering Events in Time.

https://lightmysky.com/learn/mathematics/days-weeks-months-and-years-mt_bj1YCgNWUx

#### Measuring length and height (age 5+) (ages 5-6)

Measure and begin to record lengths and heights using non-standard and standard units

Ready when they can: Measure the length of a table using cubes and record the result; Begin to use a ruler to measure in centimetres; Record a measurement as a number with a unit.

Needs first: Comparing Lengths & Heights.

https://lightmysky.com/learn/mathematics/measuring-length-and-height-age-5-mt_KaF0SQvaiu

#### Measuring mass and weight (ages 5-6)

Measure and begin to record mass/weight using non-standard and standard units

Ready when they can: Use a balance to compare masses of two objects; Measure mass using non-standard units (e.g. 'this book weighs 5 cubes'); Begin to read a simple scale for mass.

Needs first: Measuring mass and weight (age 4+).

https://lightmysky.com/learn/mathematics/measuring-mass-and-weight-mt_zd0YkB3xNj

#### Telling time to the minute (ages 5-6)

Measure and begin to record time in hours, minutes, and seconds

Ready when they can: Use a sand timer or stopwatch to time an activity; Begin to understand that 1 minute = 60 seconds; Record a duration in simple terms (e.g. 'it took about 2 minutes').

Needs first: Comparing durations.

https://lightmysky.com/learn/mathematics/telling-time-to-the-minute-mt__N55B7u7HD

#### Choosing measurement units (ages 6-7)

Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit

Ready when they can: Measure the length of a table in centimetres using a ruler; Weigh an object in grams using a scale; Measure the capacity of a container in millilitres using a measuring jug.

Needs first: Capacity and volume, Measuring length and height (age 5+), Measuring mass and weight.

https://lightmysky.com/learn/mathematics/choosing-measurement-units-mt_DOe893F6gN

#### Measuring length (ages 6-7)

Order three objects by length and compare the lengths of two objects indirectly using a third object

Ready when they can: Put three ribbons in order from shortest to longest; Use a piece of string to compare the heights of two objects that cannot be placed side by side; Explain that if A is longer than B and B is longer than C, then A is longer than C.

Needs first: Comparing Lengths & Heights.

https://lightmysky.com/learn/mathematics/measuring-length-mt_skYly2Qm01

#### Measuring length (age 6+) (ages 6-7)

Measure the length of an object using same-size length units laid end to end with no gaps or overlaps

Ready when they can: Measure a book by laying paper clips end to end and counting them; Understand that the length measurement is the number of units that span the object; Avoid gaps and overlaps when placing units.

Needs first: Measuring length and height (age 5+), Measuring length.

https://lightmysky.com/learn/mathematics/measuring-length-age-6-mt_cqSf213hSa

#### Number of minutes in an hour (ages 6-7)

Know the number of minutes in an hour and the number of hours in a day

Ready when they can: State that there are 60 minutes in an hour; State that there are 24 hours in a day; Use these facts to solve simple time problems.

Needs first: Telling time to the minute.

https://lightmysky.com/learn/mathematics/number-of-minutes-in-an-hour-mt_2XDGT5tei1

#### Sequence intervals of time (ages 6-7)

Compare and sequence intervals of time

Ready when they can: Order three events by how long they took; Compare the duration of two activities (e.g. 'the race took longer than the walk'); Sequence intervals on a timeline.

Needs first: Telling time to the minute.

https://lightmysky.com/learn/mathematics/sequence-intervals-of-time-mt_6XCURuNwPw

#### Measuring length (age 7+) (ages 7-8)

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes

Ready when they can: Choose the most appropriate tool for measuring a given object; Align the zero mark of a ruler with the end of the object and read the measurement; Measure lengths in inches, feet, centimetres, and metres using the correct tool.

Needs first: Measuring length (age 6+), Choosing measurement units.

https://lightmysky.com/learn/mathematics/measuring-length-age-7-mt_e4x3l2JeLI

#### Comparing lengths by measuring (ages 7-8)

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit

Ready when they can: Measure two objects and calculate the difference in length; Express the difference using the correct unit (e.g. '7 cm longer'); Solve a comparison problem: 'How much taller is the bookshelf than the desk?'.

Needs first: Measuring length (age 7+), Measuring length.

https://lightmysky.com/learn/mathematics/comparing-lengths-by-measuring-mt_xWg0lI_gG4

#### Estimating Lengths (ages 7-8)

Estimate lengths using units of inches, feet, centimetres, and metres

Ready when they can: Estimate the length of a classroom object before measuring it; Use a known reference (e.g. width of a finger ≈ 1 cm) to make reasonable estimates; Check estimates by measuring and evaluate how close they were.

Needs first: Measuring length (age 7+).

https://lightmysky.com/learn/mathematics/estimating-lengths-mt_OzRZ89GrQW

#### Measuring with different units (ages 7-8)

Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen

Ready when they can: Measure a desk in both centimetres and inches and compare the two numbers; Explain that measuring with a smaller unit gives a larger number; Predict whether a measurement in centimetres will be greater or less than in inches.

Needs first: Measuring length (age 7+).

https://lightmysky.com/learn/mathematics/measuring-with-different-units-mt_jHv4BgRK8B

#### Time Units and Calendar Facts (ages 7-8)

Know the number of seconds in a minute and the number of days in each month, year, and leap year

Ready when they can: State that there are 60 seconds in a minute; Name the months and state the number of days in each; Explain that a leap year has 366 days and occurs every 4 years.

Needs first: Number of minutes in an hour.

https://lightmysky.com/learn/mathematics/time-units-and-calendar-facts-mt_EXlmTURK_o

#### Understanding Area (ages 8-9)

Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlaps

Ready when they can: Identify a unit square and state its area is 1 square unit; Explain why a figure covered by 12 unit squares has area 12 square units; Distinguish between area and perimeter as different measurements.

Needs first: Measuring length (age 7+).

https://lightmysky.com/learn/mathematics/understanding-area-mt_6xNmQLzuqm

#### Area (age 8+) (ages 8-9)

Measure areas by counting unit squares (square cm, square m, square in, square ft)

Ready when they can: Count unit squares to find the area of an L-shaped figure; Measure the area of a book cover using square-centimetre tiles; Compare areas of two shapes by counting their unit squares.

Needs first: Understanding Area.

https://lightmysky.com/learn/mathematics/area-age-8-mt_y1n0Zwhoca

#### Area by Tiling (ages 8-9)

Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths

Ready when they can: Tile a 4×6 rectangle and count 24 squares, then verify 4×6=24; Explain why the number of rows times the number in each row gives the area; Draw a rectangle on squared paper, tile it, and write the multiplication.

Needs first: Area (age 8+), Composing Shapes, Rows & Columns in Rectangles.

https://lightmysky.com/learn/mathematics/area-by-tiling-mt_Jvvh5P06NV

#### Rectangle area by multiplying (ages 8-9)

Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas

Ready when they can: Calculate the area of a 7 cm × 9 cm rectangle as 63 cm²; Draw a rectangle with area 36 square units and label its side lengths; Solve: A garden is 8 m by 5 m — what is its area?.

Needs first: Area by Tiling.

https://lightmysky.com/learn/mathematics/rectangle-area-by-multiplying-mt_GzcJEVkNRn

#### Area and the distributive property (ages 8-9)

Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property

Ready when they can: Tile a 3×(4+2) rectangle and show it decomposes into 3×4 and 3×2; Use an area model to compute 6×13 as 6×10 + 6×3; Draw an area model showing 5×(7+3) = 5×7 + 5×3.

Needs first: Rectangle area by multiplying.

https://lightmysky.com/learn/mathematics/area-and-the-distributive-property-mt_AQo4u7O4sM

#### Area of compound shapes (ages 8-9)

Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas

Ready when they can: Decompose an L-shape into two rectangles, find each area, and add them; Find the area of a floor plan shaped like a T by splitting into rectangles; Solve: A room is L-shaped (3m×5m plus 2m×4m) — what is the total area?.

Needs first: Rectangle area by multiplying.

https://lightmysky.com/learn/mathematics/area-of-compound-shapes-mt_eMtV6tBSJm

#### Measuring & Plotting Lengths (ages 7-8)

Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot

Ready when they can: Measure the lengths of several objects and record the data; Create a line plot with a horizontal scale marked in whole-number units; Interpret a line plot to answer questions about the data.

Needs first: Interpreting categorical data, Measuring length (age 7+).

https://lightmysky.com/learn/mathematics/measuring-and-plotting-lengths-mt_mayItsxMUu

#### Coin Values (ages 5-6)

Recognise and know the value of different coins and notes

Ready when they can: Identify 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2 coins; Know that a £2 coin is worth more than a 50p coin; Recognise £5 and £10 notes.

Needs first: Reading and writing numbers to 20.

https://lightmysky.com/learn/mathematics/coin-values-mt_cPZwlUk8Nd

#### Telling Time: Hours and Half Hours (ages 5-6)

Tell the time to the hour and half past the hour, and draw clock hands to show these times

Ready when they can: Read an analogue clock showing 3 o'clock; Read an analogue clock showing half past 7; Draw the hour and minute hands on a blank clock face to show a given o'clock or half-past time.

Needs first: Reading and writing numbers to 20, What Is a Half?, Telling time to the minute.

https://lightmysky.com/learn/mathematics/telling-time-hours-and-half-hours-mt_0XxyaQLRhn

#### Pounds & Pence Notation (ages 6-7)

Recognise and use symbols for pounds (£) and pence (p) and combine amounts to make a particular value

Ready when they can: Write £1.50 or 150p correctly; Combine coins to make a given total, e.g. 50p + 20p + 5p = 75p; Read prices written with £ and p symbols.

Needs first: Coin Values.

https://lightmysky.com/learn/mathematics/pounds-and-pence-notation-mt_pbuhUQJjtt

#### Adding money and giving change (ages 6-7)

Find different combinations of coins that equal the same amount of money

Ready when they can: Show that 50p can be made with 2×20p + 1×10p, or 5×10p, or 1×50p; Systematically find multiple coin combinations for a given total; Explain why different coin sets give the same total.

Needs first: Addition as combining or putting together two, Pounds & Pence Notation.

https://lightmysky.com/learn/mathematics/adding-money-and-giving-change-mt_AF2BeFQwfX

#### Money Addition & Subtraction (ages 6-7)

Solve simple money problems involving addition and subtraction, including giving change

Ready when they can: Calculate the total cost of two items priced in pence; Work out change from 50p after buying an item costing 35p; Solve 'How much more money do I need?' problems.

Needs first: Adding money and giving change, Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/money-addition-and-subtraction-mt_6J1wmCWf41

#### Telling Time: Minutes (ages 6-7)

Tell and write the time to five minutes, including quarter past and quarter to, and draw clock hands to show these times

Ready when they can: Read an analogue clock showing 3:25; Write 'quarter past 9' or '9:15'; Draw clock hands to show twenty to four.

Needs first: Telling Time: Hours and Half Hours, Counting in 2s.

https://lightmysky.com/learn/mathematics/telling-time-minutes-mt_HNOPGJYiRK

#### Giving Change (ages 7-8)

Add and subtract amounts of money to give change, using both £ and p in practical contexts

Ready when they can: Calculate the total cost of two or three items priced in pounds and pence; Work out the change from £5 or £10; Record money calculations using £ and p notation correctly (e.g. £3.47).

Needs first: Money Addition & Subtraction, Pounds & Pence Notation.

https://lightmysky.com/learn/mathematics/giving-change-mt_6_O6THdEDK

#### Telling time to the minute (age 7+) (ages 7-8)

Tell and write time from analogue and digital clocks to the nearest five minutes, using a.m., p.m., and 12-hour and 24-hour notation

Ready when they can: Read the time to five minutes on an analogue clock face; Write the time using digital notation (e.g. 3:25); Distinguish between a.m. and p.m. and relate to daily events.

Needs first: Telling Time: Minutes.

https://lightmysky.com/learn/mathematics/telling-time-to-the-minute-age-7-mt_4m8BimI4G5

#### Estimating and reading time (ages 7-8)

Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours

Ready when they can: Read an analogue clock to the nearest minute; Estimate how long an activity takes in minutes or seconds; Compare two durations and determine which is longer.

Needs first: Telling time to the minute (age 7+), Sequence intervals of time.

https://lightmysky.com/learn/mathematics/estimating-and-reading-time-mt_3XJkeIn6J6

#### Comparing Time Durations (ages 7-8)

Compare durations of events and calculate the time taken by particular events or tasks

Ready when they can: Calculate how long an activity lasted given start and end times; Compare the duration of two events and identify which was longer; Solve a problem such as 'The lesson starts at 10:15 and ends at 11:00. How long is it?'.

Needs first: Estimating and reading time, Time Units and Calendar Facts.

https://lightmysky.com/learn/mathematics/comparing-time-durations-mt_4emC463IyW

#### 12-hour and 24-hour time (ages 8-9)

Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks

Ready when they can: Convert 3:45 pm to 15:45 in 24-hour time; Read 19:30 and state the 12-hour equivalent as 7:30 pm; Match a set of 12-hour and 24-hour times.

Needs first: Telling time to the minute (age 7+).

https://lightmysky.com/learn/mathematics/12-hour-and-24-hour-time-mt_WfrE_4r-kY

#### Telling time to the minute (age 8+) (ages 8-9)

Tell and write time to the nearest minute using analogue and digital clocks

Ready when they can: Read 7:43 from an analogue clock face; Write 11:06 on a digital display given a clock with hands; Match analogue and digital times to the nearest minute.

Needs first: Telling time to the minute (age 7+).

https://lightmysky.com/learn/mathematics/telling-time-to-the-minute-age-8-mt_UNzojLkNdm

#### Elapsed time problems (ages 8-9)

Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line

Ready when they can: A film starts at 2:15 and lasts 47 minutes — when does it end?; Calculate how many minutes between 9:20 and 10:05; Use a number line to show the elapsed time between two events.

Needs first: Comparing Time Durations, Telling time to the minute (age 8+).

https://lightmysky.com/learn/mathematics/elapsed-time-problems-mt_IL86kadLSS

#### Length word problems within 100 (ages 7-8)

Solve word problems involving lengths within 100, using addition and subtraction with drawings and equations

Ready when they can: Solve 'The rope is 45 cm long. I cut off 18 cm. How long is it now?'; Draw a diagram (e.g. a ruler drawing) to represent a length word problem; Write an equation with a symbol for the unknown to represent the problem.

Needs first: Fluent adding and subtracting within 100, Comparing lengths by measuring.

https://lightmysky.com/learn/mathematics/length-word-problems-within-100-mt_DLcEzmmj2r

#### Money problems with coins and notes (ages 7-8)

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately

Ready when they can: Determine the total value of a collection of coins; Solve a word problem about making change with US currency; Use $ and ¢ symbols correctly in answers.

Needs first: Fluent adding and subtracting within 100.

https://lightmysky.com/learn/mathematics/money-problems-with-coins-and-notes-mt_3tz3Otap5j

#### Measuring to the nearest half and quarter inch (ages 8-9)

Generate measurement data by measuring lengths to the nearest half and quarter inch; display the data on a line plot with a scale marked in whole numbers, halves, and quarters

Ready when they can: Measure five objects to the nearest 1/4 inch; Create a line plot showing the lengths of classmates' pencils in half-inches; Read a line plot and answer questions about the data.

Needs first: Measuring & Plotting Lengths, Fractions of a whole, Money problems with coins and notes.

https://lightmysky.com/learn/mathematics/measuring-to-the-nearest-half-and-quarter-inch-mt_ghK1mnEstc

#### Measurement Line Plots (ages 9-10)

Make a line plot to display measurement data in fractions of a unit (1/2, 1/4, 1/8); solve problems involving addition and subtraction of fractions using line plot data

Ready when they can: Create a line plot of seed growth measurements in 1/8-inch increments; Use a line plot to find the difference between the longest and shortest specimens; Calculate the total length of all items in a line plot by adding the fractional measurements.

Needs first: Measuring to the nearest half and quarter inch, Fraction Addition Concepts.

https://lightmysky.com/learn/mathematics/measurement-line-plots-mt_42QD6nYjiZ

#### Comparing and ordering measurements (ages 6-7)

Compare and order lengths, mass, and capacity and record results using >, <, and =

Ready when they can: Measure two objects and write 45cm > 32cm; Order three containers by capacity after measuring each; Use = when two measurements are the same.

Needs first: Choosing measurement units, Comparing and ordering numbers.

https://lightmysky.com/learn/mathematics/comparing-and-ordering-measurements-mt_BFJ-ch_8QU

#### Calculating with measurements (ages 7-8)

Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units

Ready when they can: Measure a length in centimetres and millimetres; Weigh an object using grams and kilograms; Add two measurements in the same unit (e.g. 250 ml + 400 ml = 650 ml).

Needs first: Comparing and ordering measurements, Choosing measurement units.

https://lightmysky.com/learn/mathematics/calculating-with-measurements-mt_6oxQPNLHNv

#### Measuring Perimeters (ages 7-8)

Measure the perimeter of simple 2-D shapes

Ready when they can: Measure each side of a rectangle and add the lengths to find the perimeter; Calculate the perimeter of a regular shape given the side length; Explain that perimeter is the total distance around a shape.

Needs first: Calculating with measurements, 2-D shapes (age 6+).

https://lightmysky.com/learn/mathematics/measuring-perimeters-mt_wE7-Gs9ENL

#### Converting measurement units (ages 8-9)

Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day)

Ready when they can: Convert 3 km to 3000 m; State 2 hours = 120 minutes; Convert 5 weeks to 35 days.

Needs first: Calculating with measurements, Time Units and Calendar Facts, Measuring with different units.

https://lightmysky.com/learn/mathematics/converting-measurement-units-mt_d8al9JcajP

#### Estimating and comparing money (ages 8-9)

Estimate, compare, and calculate different measures including money in pounds and pence

Ready when they can: Estimate the length of the classroom in metres; Compare 1.5 kg and 1200 g and identify which is heavier; Calculate the total cost of 3 items at £2.45, £1.30, and £0.75.

Needs first: Giving Change, Calculating with measurements.

https://lightmysky.com/learn/mathematics/estimating-and-comparing-money-mt_mFJ-2ZF6Tk

#### Measuring Liquids & Masses (ages 8-9)

Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume

Ready when they can: Estimate the mass of a textbook in grams or kilograms; Read a scale to measure liquid volume in litres; Solve: 3 bags weigh 250 g each — what is the total mass?.

Needs first: Calculating with measurements.

https://lightmysky.com/learn/mathematics/measuring-liquids-and-masses-mt_-af65bxfdp

#### Perimeters of polygons (ages 8-9)

Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa)

Ready when they can: Calculate the perimeter of a rectangle with sides 8 cm and 5 cm; Find the missing side of a pentagon with perimeter 30 cm and four known sides; Draw two rectangles both with perimeter 24 cm but different areas.

Needs first: Rectangle area by multiplying, Measuring Perimeters.

https://lightmysky.com/learn/mathematics/perimeters-of-polygons-mt_WtcFrxGOgw

#### Area and perimeter of rectangles (ages 9-10)

Apply the area formula (l × w) and perimeter formula (2l + 2w) for rectangles including squares in real-world and mathematical problems; calculate and compare areas using standard units (cm², m²) and estimate areas of irregular shapes

Ready when they can: Find the width of a room given area = 48 m² and length = 8 m; Calculate the area of a square with side 7.5 cm; Estimate the area of an irregular pond drawn on a cm² grid.

Needs first: Rectangle area by multiplying, Perimeters of polygons.

https://lightmysky.com/learn/mathematics/area-and-perimeter-of-rectangles-mt_eiB3-6pu6a

#### Estimating volume (ages 9-10)

Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water

Ready when they can: Build a cuboid from 1 cm³ blocks and state its volume; Estimate how many cm³ blocks would fill a given box; Estimate the capacity of a jug by comparing to known litre measures.

Needs first: Area (age 8+), Measuring Liquids & Masses, Estimating Lengths.

https://lightmysky.com/learn/mathematics/estimating-volume-mt_NSC3LT_-ch

#### Perimeter of Compound Shapes (ages 9-10)

Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

Ready when they can: Find the perimeter of an L-shaped figure by identifying all side lengths; Calculate the perimeter of a composite shape where some sides must be deduced; Draw a composite rectilinear shape with a perimeter of 40 cm.

Needs first: Area of compound shapes, Perimeters of polygons.

https://lightmysky.com/learn/mathematics/perimeter-of-compound-shapes-mt_n0AlyLQwC9

#### Telling time to the minute (age 9+) (ages 9-10)

Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)

Ready when they can: Convert 3 hours 25 minutes to 205 minutes; A programme lasts 150 seconds — express in minutes and seconds; How many days are in 8 weeks and 3 days?.

Needs first: Converting measurement units, Elapsed time problems, 12-hour and 24-hour time.

https://lightmysky.com/learn/mathematics/telling-time-to-the-minute-age-9-mt_2yas4Unc8o

#### Perimeter (age 10+) (ages 10-11)

Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically

Ready when they can: Draw two rectangles with area 24 cm² but different perimeters; Find two shapes with perimeter 20 cm but different areas; Explain why a long thin rectangle and a square can have the same area but different perimeters.

Needs first: Area and perimeter of rectangles, Perimeter of Compound Shapes.

https://lightmysky.com/learn/mathematics/perimeter-age-10-mt_MJZA90uc6H

#### Volume with unit cubes (ages 10-11)

Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units

Ready when they can: Explain what 'volume' means for a 3D shape and how it differs from area; Identify a unit cube and explain that it represents one cubic unit of volume; Determine the volume of a small solid by counting the unit cubes that fill it.

Needs first: Estimating volume.

https://lightmysky.com/learn/mathematics/volume-with-unit-cubes-mt_IuHa5UI5od

#### Counting Unit Cubes (ages 10-11)

Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units

Ready when they can: Count unit cubes in a 3D diagram to determine volume in cm³; Measure the volume of a small container by filling it with centimetre cubes; Express a measured volume using the correct cubic unit notation.

Needs first: Volume with unit cubes.

https://lightmysky.com/learn/mathematics/counting-unit-cubes-mt_d7XktBQPxm

#### Volume of cuboids (ages 10-11)

Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)

Ready when they can: Use V = l × w × h to find the volume of a cuboid 4 cm × 3 cm × 5 cm = 60 cm³; Explain why packing a prism with unit cubes gives the same result as multiplying edge lengths; Compare volumes of two cuboids and identify which has greater capacity.

Needs first: Counting Unit Cubes, Long multiplication (age 10+).

https://lightmysky.com/learn/mathematics/volume-of-cuboids-mt_nTL-owFJTF

#### Converting measurement units (age 9+) (ages 9-10)

Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables

Ready when they can: Convert 3.5 km to 3,500 m; Complete a conversion table for cm and mm: (1,10), (2,20), (3,30)...; Express 2 kg 350 g as 2,350 g.

Needs first: Converting measurement units, Multiplying and dividing.

https://lightmysky.com/learn/mathematics/converting-measurement-units-age-9-mt_Zks8xyInSG

#### Measure word problems with fractions and decimals (ages 9-10)

Solve word problems involving distances, time intervals, liquid volumes, masses, and money using the four operations with fractions or decimals; represent with diagrams including number lines

Ready when they can: A 2.5 kg bag of flour is split equally into 4 portions — what does each weigh?; A journey takes 1 hr 45 min; what time do you arrive if you leave at 09:20?; Three ribbons of 0.75 m, 1.2 m, and 0.95 m — what is the total length?.

Needs first: Estimating and comparing money, Decimals for Tenths & Hundredths, Converting measurement units (age 9+).

https://lightmysky.com/learn/mathematics/measure-word-problems-with-fractions-and-decimals-mt_5HV4mbgSGH

#### Metric & Imperial Conversion (ages 9-10)

Understand and use approximate equivalences between metric units and common imperial units (inches, pounds, pints)

Ready when they can: State that 1 inch ≈ 2.5 cm and use this to estimate length in inches; Know that 1 kg ≈ 2.2 pounds and estimate a person's weight in pounds; Convert approximately between litres and pints (1 litre ≈ 1.75 pints).

Needs first: Converting measurement units (age 9+).

https://lightmysky.com/learn/mathematics/metric-and-imperial-conversion-mt_p6MhZJYYPN

#### Volume as additive (ages 10-11)

Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms

Ready when they can: Decompose an L-shaped solid into two cuboids and calculate total volume; Solve a real-world problem requiring the volume of a composite figure (e.g. a step-shaped structure); Explain why splitting a composite solid into rectangular prisms allows calculation of total volume.

Needs first: Addition and subtraction strategies (age 10+), Volume of cuboids.

https://lightmysky.com/learn/mathematics/volume-as-additive-mt_5TBUFnCy5-

#### Converting units with decimal notation (ages 10-11)

Convert among different-sized standard measurement units within a given system (e.g. 5 cm to 0.05 m) using decimal notation to up to three decimal places; convert between smaller and larger units of length, mass, volume, and time

Ready when they can: Convert 3,250 g to 3.25 kg using decimal notation; Convert 0.45 km to 450 m; Explain the relationship between mm, cm, m, and km using powers of 10.

Needs first: Multiplying and dividing (age 10+), Converting measurement units (age 9+).

https://lightmysky.com/learn/mathematics/converting-units-with-decimal-notation-mt_2VpdPjvewx

#### Measurement Conversions (ages 10-11)

Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts

Ready when they can: Solve: 'A recipe uses 0.75 kg of flour. How many grams are needed for 3 batches?'; Compare 2.5 litres and 2,450 ml by converting to the same unit; Solve a multi-step problem involving time, distance, and unit conversion.

Needs first: Converting units with decimal notation, Measure word problems with fractions and decimals.

https://lightmysky.com/learn/mathematics/measurement-conversions-mt_SqhXQhAEUf

#### Miles & Kilometres (ages 10-11)

Convert between miles and kilometres using the approximate relationship (5 miles ≈ 8 km)

Ready when they can: Convert 40 miles to approximately 64 km; Explain why the conversion factor between miles and km is approximately 1.6; Use the miles↔km relationship to compare a 10 km race with a 6-mile run.

Needs first: Metric & Imperial Conversion, Multiplying decimals by whole numbers.

https://lightmysky.com/learn/mathematics/miles-and-kilometres-mt_3tPI0HqqcN

#### Area of Triangles & Parallelograms (ages 10-11)

Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)

Ready when they can: Calculate the area of a parallelogram with base 8 cm and height 5 cm; Calculate the area of a triangle with base 12 cm and height 7 cm; Explain why the area of a triangle is half the area of a related parallelogram.

Needs first: Multiplying fractions (age 10+), Area and perimeter of rectangles, Using Simple Formulae, Classifying shapes by properties.

https://lightmysky.com/learn/mathematics/area-of-triangles-and-parallelograms-mt_ML5t7n2-U8

### Multiplication & Division

https://lightmysky.com/learn/mathematics/areas/multiplication-and-division

#### Division as equal sharing (ages 4-6)

Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)

Ready when they can: Share 10 counters equally between 2 plates; Group 12 objects into sets of 3 and count 4 groups; Use concrete objects to solve 'How many groups of 2 in 8?'.

Needs first: Subtraction as taking away or separating.

https://lightmysky.com/learn/mathematics/division-as-equal-sharing-mt_LpSuPgL31x

#### Multiplication as repeated addition (ages 5-6)

Understand multiplication as repeated addition and grouping equal sets

Ready when they can: Explain that 3 groups of 2 is the same as 2 + 2 + 2; Use objects to make equal groups and count the total; Recognise an array as showing equal rows.

Needs first: Counting in 2s, Addition as combining or putting together two.

https://lightmysky.com/learn/mathematics/multiplication-as-repeated-addition-mt_PZ909yPrEC

#### Arrays for multiplication (ages 5-6)

Use arrays to represent multiplication and division situations

Ready when they can: Build an array of 3 rows of 4 objects to show 3 × 4; Read an array and state the total; Use an array to solve a simple division problem (e.g. 12 objects in rows of 4 → 3 rows).

Needs first: Division as equal sharing, Multiplication as repeated addition.

https://lightmysky.com/learn/mathematics/arrays-for-multiplication-mt_GRWwTDZ3wD

#### Commutative Multiplication (ages 6-7)

Understand and apply the commutative property of multiplication and recognise that division is not commutative

Ready when they can: Explain that 3 × 5 = 5 × 3 and show this with an array rotated; Use commutativity to choose the easier calculation; Demonstrate that 12 ÷ 3 ≠ 3 ÷ 12.

Needs first: Arrays for multiplication, Multiplication as repeated addition.

https://lightmysky.com/learn/mathematics/commutative-multiplication-mt_C9ZfT-4cgn

#### Odd and even numbers (ages 6-7)

Recognise odd and even numbers

Ready when they can: Identify whether a given number is odd or even; Explain that even numbers can be divided into 2 equal groups; Spot the pattern: even numbers end in 0, 2, 4, 6, or 8.

Needs first: Division as equal sharing, Counting in 2s.

https://lightmysky.com/learn/mathematics/odd-and-even-numbers-mt_0u4KLbvBa1

#### Times tables (ages 6-7)

Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables

Ready when they can: Quickly answer 5 × 3 = 15 from memory; Quickly answer 20 ÷ 5 = 4 from memory; Recite the 2, 5, and 10 times tables fluently.

Needs first: Counting in 2s, Multiplication as repeated addition.

https://lightmysky.com/learn/mathematics/times-tables-mt_HhuSDxwDNM

#### Multiplication as repeated addition (age 6+) (ages 6-7)

Solve problems involving multiplication and division using arrays, repeated addition, mental methods, and known facts

Ready when they can: Solve 'There are 5 bags with 2 apples in each. How many apples?' using repeated addition or known fact; Solve 'Share 15 sweets equally among 3 children' using grouping; Draw an array to solve a multiplication problem in context.

Needs first: Arrays for multiplication, Times tables.

https://lightmysky.com/learn/mathematics/multiplication-as-repeated-addition-age-6-mt_wh3UqnWsa7

#### Arrays for multiplication (age 7+) (ages 7-8)

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and 5 columns; write an equation to express the total as a sum of equal addends

Ready when they can: Count objects in a 3×4 array and write 4 + 4 + 4 = 12; Explain that each row has the same number of objects so the total can be found by repeated addition; Draw a rectangular array to model a given repeated-addition equation.

Needs first: Arrays for multiplication, Multiplication as repeated addition.

https://lightmysky.com/learn/mathematics/arrays-for-multiplication-age-7-mt_B1zj1RwQ3a

#### Rows & Columns in Rectangles (ages 7-8)

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them

Ready when they can: Divide a rectangle into equal rows and columns of unit squares; Count the total number of squares using repeated addition or skip counting; Relate the rows-and-columns structure to a rectangular array.

Needs first: Arrays for multiplication (age 7+).

https://lightmysky.com/learn/mathematics/rows-and-columns-in-rectangles-mt_UTnDKQkVX5

#### Times tables (age 7+) (ages 7-8)

Recall and use multiplication and division facts for the 3, 4, and 8 multiplication tables

Ready when they can: Recall 3 × 1 through 3 × 12 and corresponding division facts; Recall 4 × 1 through 4 × 12 and corresponding division facts; Recall 8 × 1 through 8 × 12 and corresponding division facts.

Needs first: Times tables, Skip Counting (4s, 8s, 50s, 100s).

https://lightmysky.com/learn/mathematics/times-tables-age-7-mt_wQ89AEXhz3

#### All times tables to 12×12 (ages 8-9)

Recall multiplication and division facts for multiplication tables up to 12 × 12

Ready when they can: Recall any fact from the 1–12 times tables rapidly; Recall the corresponding division fact for any multiplication fact; Use known facts to check or derive answers in calculations.

Needs first: Counting in 6s, Times tables (age 7+).

https://lightmysky.com/learn/mathematics/all-times-tables-to-12-12-mt_K5jM7vlVhA

#### What Division Means (ages 8-9)

Interpret whole-number quotients (e.g. 56 ÷ 8 as the number of objects in each share or the number of equal groups)

Ready when they can: Explain that 56 ÷ 8 can mean sharing 56 into 8 equal groups or making groups of 8; Draw a picture to represent a division expression; Match a division expression to a word problem involving equal sharing or grouping.

Needs first: Division as equal sharing.

https://lightmysky.com/learn/mathematics/what-division-means-mt_iNdrM2-oJf

#### What Multiplication Means (ages 8-9)

Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)

Ready when they can: Explain that 4 × 6 means 4 groups of 6 objects; Draw a picture or array to represent a multiplication expression; Match a multiplication expression to a word problem involving equal groups.

Needs first: Arrays for multiplication (age 7+), Multiplication as repeated addition.

https://lightmysky.com/learn/mathematics/what-multiplication-means-mt_gtTl3R5buH

#### Division as Unknown Factor (ages 8-9)

Understand division as an unknown-factor problem (e.g. find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)

Ready when they can: Explain that 32 ÷ 8 = ? is the same as 8 × ? = 32; Use a known multiplication fact to find a division answer; Describe the relationship between multiplication and division as inverse operations.

Needs first: What Multiplication Means, What Division Means.

https://lightmysky.com/learn/mathematics/division-as-unknown-factor-mt_GDG9_SZmsO

#### Fluent multiplication and division facts (ages 8-9)

Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division

Ready when they can: Answer any single-digit multiplication fact within 3 seconds; Answer any related division fact within 3 seconds; Use known facts to derive unknown facts (e.g. 9 × 7 from 10 × 7 − 7).

Needs first: Division as Unknown Factor, Times tables (age 7+).

https://lightmysky.com/learn/mathematics/fluent-multiplication-and-division-facts-mt_WX30dzi4dt

#### Multiplication and Division Word Problems (ages 8-9)

Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities

Ready when they can: Solve an equal-groups word problem using multiplication; Solve a measurement division problem (e.g. 'How many 4-cm pieces from a 28-cm ribbon?'); Solve an array/area word problem using multiplication.

Needs first: What Multiplication Means, What Division Means.

https://lightmysky.com/learn/mathematics/multiplication-and-division-word-problems-mt_Zdv-b-iW5K

#### Properties of Operations (ages 8-9)

Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide

Ready when they can: Use commutativity: if 6 × 4 = 24 then 4 × 6 = 24; Use the distributive property: 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56; Use associativity to multiply three numbers: 2 × 3 × 5 = 6 × 5 = 30.

Needs first: Commutative Multiplication, What Multiplication Means.

https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR

#### Factor Pairs & Commutativity (ages 8-9)

Recognise and use factor pairs and commutativity in mental calculations

Ready when they can: List all factor pairs of a given number (e.g. 24: 1×24, 2×12, 3×8, 4×6); Use commutativity to reorder a multiplication for easier mental calculation; Explain what a factor pair is and how commutativity helps.

Needs first: All times tables to 12×12, Properties of Operations.

https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX

#### Patterns in Times Tables (ages 8-9)

Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations

Ready when they can: Notice that all products of 5 end in 0 or 5 and explain why; Observe that the sum of two even numbers is always even; Identify a pattern in the multiplication table and explain it using commutativity or the distributive property.

Needs first: Properties of Operations, Fluent multiplication and division facts.

https://lightmysky.com/learn/mathematics/patterns-in-times-tables-mt_w6MxaaoMXZ

#### Unknown in Multiplication & Division (ages 8-9)

Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42)

Ready when they can: Find the missing factor in 7 × ? = 63; Find the missing dividend in ? ÷ 5 = 9; Explain the strategy used (e.g. using the related multiplication fact).

Needs first: Division as Unknown Factor.

https://lightmysky.com/learn/mathematics/unknown-in-multiplication-and-division-mt_xZvDCYA5Ae

#### Factors, multiples, and primes (ages 9-11)

Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems

Ready when they can: List all factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6); State the first five multiples of 7; Find the common factors of 24 and 36; Find all common factors of 36 and 48; Identify the first three common multiples of 6 and 8; Determine whether a given number (e.g. 97) is prime and justify the reasoning.

Needs first: Factor Pairs & Commutativity.

https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU

#### Generating a pattern from a rule (ages 9-10)

Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

Ready when they can: Given 'start at 1, add 3', generate terms and notice they alternate odd/even; Given a shape pattern, predict the next three terms and describe the rule; Explain why starting at 2 and adding 4 always gives even numbers.

Needs first: Patterns in Times Tables.

https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy

#### Multiplicative Comparison as an Equation (ages 9-10)

Interpret a multiplication equation as a comparison (e.g. 35 = 5 × 7 means 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons as equations

Ready when they can: Explain that '4 times as many' means multiply by 4; Write an equation for: Sarah has 3 times as many stickers as Tom, who has 8 stickers; Distinguish multiplicative comparison from additive comparison in word problems.

Needs first: What Multiplication Means.

https://lightmysky.com/learn/mathematics/multiplicative-comparison-as-an-equation-mt_U4cIBXVug4

#### Multiplicative Comparison Word Problems (ages 9-10)

Solve word problems involving multiplicative comparison using drawings and equations with a symbol for the unknown number

Ready when they can: A blue ribbon is 3 times as long as a red ribbon of 7 cm — how long is the blue ribbon?; 36 is 4 times a number — what is the number?; Explain why 'Sam has 5 more' is additive but 'Sam has 5 times as many' is multiplicative.

Needs first: Multiplicative Comparison as an Equation, Multiplication and Division Word Problems.

https://lightmysky.com/learn/mathematics/multiplicative-comparison-word-problems-mt_6-j1NO2ZUH

#### Short division (ages 9-10)

Divide numbers up to four digits by a one-digit number using short division (and place-value/array strategies); interpret remainders appropriately for the context

Ready when they can: Calculate 4,932 ÷ 6 using short division; Solve 125 ÷ 8 and interpret: 15 remainder 5 means 15 full bags with 5 left over; Use the multiplication–division relationship to check a division answer.

Needs first: Division as Unknown Factor, Fluent multiplication and division facts.

https://lightmysky.com/learn/mathematics/short-division-mt_MCu_SNg_OW

#### Square and cube numbers (ages 9-10)

Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

Ready when they can: Identify 49 as 7² and explain that 7 × 7 = 49; Calculate 4³ = 64 and explain it means 4 × 4 × 4; List the first ten square numbers.

Needs first: All times tables to 12×12.

https://lightmysky.com/learn/mathematics/square-and-cube-numbers-mt_gxCIASSezX

#### Factors, multiples, and primes (age 9+) (ages 9-10)

Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes

Ready when they can: Is 156 a multiple of 6? Explain how you know; Find two square numbers that add to make 100; Use factor pairs to simplify 24 × 25 as 6 × (4 × 25) = 6 × 100 = 600.

Needs first: Factors, multiples, and primes, Square and cube numbers.

https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-age-9-mt_0Wg5F97osg

#### Scaling by fractions and simple rates (ages 9-10)

Solve problems involving scaling by simple fractions and problems involving simple rates

Ready when they can: A recipe for 4 people needs 200 g of flour — how much for 6 people?; If 3 kg costs £12, how much does 5 kg cost?; Scale a shape by a factor of 1/2 and find the new dimensions.

Needs first: Fractions of amounts (harder), Multiplicative Comparison Word Problems.

https://lightmysky.com/learn/mathematics/scaling-by-fractions-and-simple-rates-mt_ZOJ6EbdPOb

#### Reading ×, ÷, and = Symbols (ages 6-7)

Read, write, and interpret the symbols ×, ÷, and = in multiplication and division number sentences

Ready when they can: Read 3 × 4 = 12 aloud as 'three times four equals twelve'; Write a multiplication sentence to match an array; Read 12 ÷ 3 = 4 aloud correctly.

Needs first: Reading +, −, and = symbols, Division as equal sharing, Multiplication as repeated addition.

https://lightmysky.com/learn/mathematics/reading-and-symbols-mt_zOWwLxa77y

#### Prime numbers (ages 9-10)

Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19

Ready when they can: Explain that a prime number has exactly two factors: 1 and itself; Determine whether 51 is prime or composite and justify the answer; List all prime numbers up to 19 from memory.

Needs first: Factors, multiples, and primes, Odd or Even.

https://lightmysky.com/learn/mathematics/prime-numbers-mt_y1XCVsIelg

#### Factors, multiples, and primes (age 11+) (ages 11-12)

Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property

Ready when they can: Express any integer as a product of its prime factors using index notation; Find the HCF and LCM of two numbers using prime factorisation; Apply the unique factorisation theorem to explain why every number has exactly one set of prime factors.

Needs first: Factors, multiples, and primes, Factors, multiples, and primes (age 9+), Prime numbers.

https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-age-11-mt_xhoOWnhtHq

#### Written Multiplication & Division (ages 7-8)

Write and calculate mathematical statements for multiplication and division using known tables, including two-digit × one-digit, using mental and progressing to formal written methods

Ready when they can: Calculate 23 × 4 using partitioning (20 × 4 + 3 × 4); Calculate 96 ÷ 8 using known table facts; Begin to use a formal written layout for short multiplication.

Needs first: The three digits of a three-digit number, Times tables (age 7+), Reading ×, ÷, and = Symbols.

https://lightmysky.com/learn/mathematics/written-multiplication-and-division-mt_DyGBW3ZHh3

#### Multi-Step Multiply & Divide (ages 7-8)

Solve problems involving multiplication and division, including scaling problems and correspondence problems where n objects are connected to m objects

Ready when they can: Solve a scaling problem (e.g. 'the ribbon is 3 times as long'); Solve a correspondence problem (e.g. '4 shirts and 3 trousers — how many outfits?'); Solve a missing-number multiplication or division problem.

Needs first: Written Multiplication & Division, Multiplication as repeated addition (age 6+).

https://lightmysky.com/learn/mathematics/multi-step-multiply-and-divide-mt_EmR5n58jZt

#### Multiplying by Tens (ages 8-9)

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations

Ready when they can: Calculate 7 × 30 = 210 by reasoning 7 × 3 tens = 21 tens = 210; Explain why multiplying by a multiple of 10 adds a zero to the product; Use this skill to estimate products of larger numbers.

Needs first: The three digits of a three-digit number, Fluent multiplication and division facts.

https://lightmysky.com/learn/mathematics/multiplying-by-tens-mt_isojCL9yy-

#### Written Multiplication (ages 8-9)

Multiply two-digit and three-digit numbers by a one-digit number using formal written layout

Ready when they can: Set out and solve 47 × 6 using short multiplication; Set out and solve 234 × 5 using short multiplication with carrying; Check the answer using estimation (e.g. 234 × 5 ≈ 200 × 5 = 1000).

Needs first: Written Multiplication & Division, All times tables to 12×12.

https://lightmysky.com/learn/mathematics/written-multiplication-mt_18fK9sQdIz

#### Multiply & Add Problems (ages 8-9)

Solve problems involving multiplying and adding, including using the distributive law, integer scaling problems, and harder correspondence problems

Ready when they can: Use the distributive law to solve 14 × 6 as 10 × 6 + 4 × 6; Solve a scaling problem (e.g. 'A tower is 3 times as tall as a 15 m building'); Solve a correspondence problem (e.g. '3 types of bread, 4 types of filling — how many different sandwiches?').

Needs first: Written Multiplication, Multi-Step Multiply & Divide, Properties of Operations.

https://lightmysky.com/learn/mathematics/multiply-and-add-problems-mt_AR-K72OIIO

#### Long multiplication (ages 9-10)

Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models

Ready when they can: Calculate 2,347 × 6 using formal written layout; Calculate 34 × 27 using long multiplication; Draw an area model for 45 × 23 and connect to the written method.

Needs first: Written Multiplication, Area and the distributive property, Multiplying by Tens.

https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8

#### Division with remainders (ages 9-10)

Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation

Ready when they can: 52 children go on a trip in minibuses holding 9 each — how many minibuses are needed? (interpret remainder); A shop sells packs of 6 pencils for £1.50 each — how much do 5 packs cost?; Represent a two-step problem with an equation using n for the unknown.

Needs first: Multiply & Add Problems, Short division, Long multiplication.

https://lightmysky.com/learn/mathematics/division-with-remainders-mt_p-nbe0w_lf

#### Long multiplication (age 10+) (ages 10-11)

Fluently multiply multi-digit whole numbers (up to 4 digits by 2 digits) using the formal written method of long multiplication

Ready when they can: Correctly compute 2,463 × 37 using long multiplication; Explain each partial product in a long multiplication and why they are added; Multiply a four-digit number by a two-digit number without procedural errors.

Needs first: Long multiplication.

https://lightmysky.com/learn/mathematics/long-multiplication-age-10-mt_XLP1IM3Qbb

#### Brackets in Expressions (ages 10-11)

Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols

Ready when they can: Evaluate 3 × (4 + 5) by computing inside the parentheses first; Evaluate {2 × [3 + (7 − 1)]} with nested grouping symbols; Insert parentheses into an expression to make it equal a target value.

Needs first: Division with remainders, Long multiplication (age 10+).

https://lightmysky.com/learn/mathematics/brackets-in-expressions-mt_8jFSnXxqQD

#### Division with remainders (age 10+) (ages 10-11)

Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate

Ready when they can: Compute 4,752 ÷ 13 using long division and express the remainder as a fraction; Decide whether to round up or down a division remainder in a real-life context (e.g. buses needed); Explain each step of the long division algorithm for a 4-digit ÷ 2-digit calculation.

Needs first: Short division, Long multiplication (age 10+).

https://lightmysky.com/learn/mathematics/division-with-remainders-age-10-mt_WsM4EmdOLe

#### Dividing by two-digit numbers (ages 10-11)

Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context

Ready when they can: Use short division to compute 3,648 ÷ 16 efficiently; Explain when short division is more appropriate than long division; Interpret a remainder as a decimal or fraction in a measurement context.

Needs first: Short division, Division with remainders (age 10+).

https://lightmysky.com/learn/mathematics/dividing-by-two-digit-numbers-mt_FvEq4heNBx

#### Order of operations (ages 10-11)

Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations

Ready when they can: Explain why 8 + 2 × 5 = 18 (not 50) by referencing multiplication before addition; Evaluate a multi-step expression like 12 ÷ 3 + 4 × 2 correctly as 12; State the correct order: brackets, then orders/exponents, then multiplication/division (L→R), then addition/subtraction (L→R).

Needs first: Brackets in Expressions.

https://lightmysky.com/learn/mathematics/order-of-operations-mt_jHgRQ4hR0g

#### Multi-step problems: choosing operations (ages 10-11)

Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts

Ready when they can: Solve a three-step word problem involving a mix of all four operations; Explain why particular operations were chosen for each step of a multi-step problem; Identify and correct an error in a multi-step solution that used the wrong operation.

Needs first: Order of operations, Division with remainders, Division with remainders (age 10+).

https://lightmysky.com/learn/mathematics/multi-step-problems-choosing-operations-mt_RXnyhCRYXA

#### Writing Number Sentences (ages 10-11)

Write simple numerical expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g. recognise that 3 × (18932 + 921) is three times as large as 18932 + 921)

Ready when they can: Write an expression for 'add 8 and 7, then multiply by 2' using parentheses; Explain what 4 × (365 − 12) represents without computing it; Compare two expressions and determine which is larger without evaluating.

Needs first: Brackets in Expressions.

https://lightmysky.com/learn/mathematics/writing-number-sentences-mt_4WaKWECpcv

#### Order of operations with powers and roots (ages 11-12)

Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions

Ready when they can: Evaluate expressions involving brackets, indices, and all four operations in the correct order; Explain why the order of operations is necessary to avoid ambiguity; Use the reciprocal of a number and understand that a number multiplied by its reciprocal gives 1.

Needs first: Order of operations.

https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU

#### Using inverse operations (ages 11-12)

Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations

Ready when they can: Use addition and subtraction as inverse operations to check and solve problems; Use multiplication and division as inverse operations to check and solve problems; Recognise that squaring and square-rooting are inverse operations.

Needs first: Order of operations, Multi-step problems: choosing operations.

https://lightmysky.com/learn/mathematics/using-inverse-operations-mt_VUQNveSYjQ

#### Mental multiplication and division (ages 8-9)

Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers

Ready when they can: Calculate 40 × 6 = 240 mentally using place value; Explain why any number × 0 = 0 and any number × 1 = the number itself; Multiply three numbers mentally by choosing a useful pair first (e.g. 2 × 7 × 5 = 2 × 5 × 7 = 70).

Needs first: Place value of each digit, All times tables to 12×12.

https://lightmysky.com/learn/mathematics/mental-multiplication-and-division-mt_pjfmCMMPjO

#### Mental multiplication and division (age 9+) (ages 9-10)

Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments

Ready when they can: Calculate 40 × 60 mentally by using 4 × 6 = 24 then appending zeros; Derive 7 × 15 by calculating 7 × 10 + 7 × 5; Calculate 360 ÷ 9 mentally using 36 ÷ 9 = 4.

Needs first: Mental multiplication and division.

https://lightmysky.com/learn/mathematics/mental-multiplication-and-division-age-9-mt_8A3pZNOp7Z

#### Multiplying and dividing (ages 9-10)

Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000

Ready when they can: Calculate 3.45 × 100 = 345; Calculate 72 ÷ 1000 = 0.072; Explain that multiplying by 10 shifts each digit one place to the left.

Needs first: Dividing by 10 and 100, Place Value × 10 Pattern.

https://lightmysky.com/learn/mathematics/multiplying-and-dividing-mt_LlMl2PbaZe

#### Mental calculation strategies (ages 10-11)

Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts

Ready when they can: Mentally compute 45 × 8 by partitioning into 40 × 8 + 5 × 8; Use known facts to derive 6.5 × 4 mentally; Solve a multi-operation mental calculation such as 250 × 3 + 500 and explain the strategy used.

Needs first: Mental addition and subtraction (age 9+), Long multiplication (age 10+), Mental multiplication and division (age 9+).

https://lightmysky.com/learn/mathematics/mental-calculation-strategies-mt_vmW2cb5c7A

#### Sign Rules for Multiplication (ages 11-13)

Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient

Ready when they can: Apply the sign rules when multiplying two integers (positive × negative, negative × negative); Apply the sign rules when dividing two integers; Solve multi-step real-world problems involving all four operations with positive and negative rational numbers.

Needs first: Positive and Negative Numbers.

https://lightmysky.com/learn/mathematics/sign-rules-for-multiplication-mt_rxInpOQ74w

#### Multiplying and dividing (age 10+) (ages 10-11)

Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart

Ready when they can: Compute 3.456 × 100 = 345.6 correctly; Compute 45.2 ÷ 1000 = 0.0452 correctly; Explain why multiplying by 10 shifts each digit one place to the left.

Needs first: Multiplying and dividing, Reading Decimal Places.

https://lightmysky.com/learn/mathematics/multiplying-and-dividing-age-10-mt_wPgpMJ0-PA

#### Division with Decimals (ages 10-11)

Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers

Ready when they can: Compute 14.76 ÷ 4 using a written method to get 3.69; Explain how to continue long division past the decimal point to obtain a decimal quotient; Solve a context problem that requires dividing a decimal amount equally (e.g. sharing £18.60 among 5 people).

Needs first: Multiplying and dividing (age 10+), Division with remainders (age 10+), Pounds & Pence Notation, Dividing by two-digit numbers.

https://lightmysky.com/learn/mathematics/division-with-decimals-mt_lU-2aTRB9f

#### Multiplying decimals by whole numbers (ages 10-11)

Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)

Ready when they can: Correctly compute 4.56 × 7 using a written method; Use place-value reasoning to explain why 3.2 × 5 = 16.0; Model a decimal multiplication using an area diagram or expanded form.

Needs first: Multiplying and dividing (age 10+), Long multiplication (age 10+).

https://lightmysky.com/learn/mathematics/multiplying-decimals-by-whole-numbers-mt_SoDP1fSQEB

#### Estimation to check answers to calculations (ages 10-11)

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Ready when they can: Estimate 487 × 23 by rounding to 500 × 20 and use this to check a calculated answer; Determine whether an exact answer or an estimate is more appropriate in a given context; Spot an unreasonable answer by comparing with a quick mental estimate.

Needs first: Rounding to a required degree of accuracy, Checking Answers by Rounding.

https://lightmysky.com/learn/mathematics/estimation-to-check-answers-to-calculations-mt_ilPrU0cbtT

#### Rounding Answers (ages 10-11)

Solve problems which require answers to be rounded to specified degrees of accuracy

Ready when they can: Compute a division and round the result to one decimal place as specified; Determine the appropriate degree of accuracy for a measurement context (e.g. round to nearest penny); Solve a problem where an unrounded decimal answer must be interpreted in context (e.g. whole containers needed).

Needs first: Rounding to a required degree of accuracy, Estimation to check answers to calculations, Division with Decimals.

https://lightmysky.com/learn/mathematics/rounding-answers-mt_QU5R7Aajy9

### Fractions

https://lightmysky.com/learn/mathematics/areas/fractions

#### What Is a Half? (ages 5-6)

Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity

Ready when they can: Fold a shape into two equal parts and identify each as 'a half'; Find half of 8 objects by sharing into 2 equal groups; Identify whether a shape has been divided into halves or not (equal vs unequal parts).

Needs first: Division as equal sharing.

https://lightmysky.com/learn/mathematics/what-is-a-half-mt_-hTTat0mBR

#### Finding halves and quarters (age 5+) (ages 5-6)

Recognise, find, and name a quarter as one of four equal parts of an object, shape, or quantity

Ready when they can: Fold a shape into four equal parts and identify each as 'a quarter'; Find a quarter of 12 objects by sharing into 4 equal groups; Identify whether a shape has been divided into quarters (four equal parts).

Needs first: What Is a Half?.

https://lightmysky.com/learn/mathematics/finding-halves-and-quarters-age-5-mt_g3W0mdADVu

#### Fraction Notation (ages 6-9)

Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole

Ready when they can: Point to and name the numerator and denominator in any given fraction and explain what each tells you; Correctly classify fractions as unit, proper, improper, or mixed number with an example of each; Explain in own words why 2/4 and 1/2 are equivalent fractions.

https://lightmysky.com/learn/mathematics/fraction-notation-mt_vKcxX6iNOA

#### Fractions of amounts (ages 6-7)

Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity

Ready when they can: Find 1/3 of 12 objects by sharing into 3 equal groups; Shade 3/4 of a rectangle that has been divided into 4 equal parts; Identify 1/4 of a length on a number line or ruler.

Needs first: Finding halves and quarters (age 5+), Division as equal sharing, Fraction Notation.

https://lightmysky.com/learn/mathematics/fractions-of-amounts-mt_cFltwUQi-d

#### Halves & Quarters of Shapes (ages 6-7)

Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters

Ready when they can: Divide a circle into two equal halves; Divide a rectangle into four equal quarters; Describe the whole as 'two halves' or 'four quarters'.

Needs first: Finding halves and quarters (age 5+), 2-D shapes.

https://lightmysky.com/learn/mathematics/halves-and-quarters-of-shapes-mt_xACS3rWWDp

#### Decomposing a shape into more equal shares (ages 6-7)

Understand that decomposing a shape into more equal shares creates smaller shares

Ready when they can: Explain that a quarter of a pizza is smaller than a half of the same pizza; Demonstrate that fourths are smaller pieces than halves; Compare the size of halves and quarters of the same shape.

Needs first: Halves & Quarters of Shapes.

https://lightmysky.com/learn/mathematics/decomposing-a-shape-into-more-equal-shares-mt_hyvHv2BCwb

#### Splitting shapes into equal parts (age 7+) (ages 7-8)

Partition circles and rectangles into two, three, or four equal shares; describe shares as halves, thirds, and fourths; recognise that equal shares of identical wholes need not have the same shape

Ready when they can: Partition a circle into 3 equal parts and label each 'a third'; Partition a rectangle into 4 equal shares in more than one way; Explain that two different-looking shares can still be equal in size.

Needs first: Decomposing a shape into more equal shares, Halves & Quarters of Shapes.

https://lightmysky.com/learn/mathematics/splitting-shapes-into-equal-parts-age-7-mt_Xp-rj46S2w

#### Tenths (ages 7-8)

Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10

Ready when they can: Count: one tenth, two tenths, three tenths … up to ten tenths (one whole); Show that dividing a shape into 10 equal parts gives tenths; Explain that 3 ÷ 10 = 3/10.

Needs first: Fractions of amounts, Counting in 2s.

https://lightmysky.com/learn/mathematics/tenths-mt_YzM5goBctT

#### Fractions on a number line (ages 7-8)

Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line

Ready when they can: Place 1/2, 1/4, 3/4 on a number line from 0 to 1; Identify that 1/3 lies between 0 and 1/2 on the number line; Understand that a fraction is a single number, not just 'part of a shape'.

Needs first: Fractions of amounts, Tenths.

https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-mt_Kr3IyA6m-O

#### Comparing fractions (ages 7-8)

Compare and order unit fractions, and fractions with the same denominator

Ready when they can: Order 1/2, 1/3, 1/4, 1/5 from largest to smallest; Explain that a larger denominator means smaller unit fractions; Compare 2/5 and 4/5 and explain that 4/5 is larger because it has more fifths.

Needs first: Decomposing a shape into more equal shares, Fractions on a number line.

https://lightmysky.com/learn/mathematics/comparing-fractions-mt_IfEgu0X449

#### Simple Fraction Sums (ages 7-8)

Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

Ready when they can: Calculate 2/5 + 2/5 = 4/5; Calculate 6/8 − 3/8 = 3/8; Explain that when denominators are the same, you add/subtract the numerators.

Needs first: Fractions on a number line, Addition as combining or putting together two.

https://lightmysky.com/learn/mathematics/simple-fraction-sums-mt_a1FdAsRKOF

#### Unit fractions (ages 7-8)

Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Ready when they can: Find 1/4 of 12 objects by dividing into 4 equal groups; Find 3/4 of 12 objects; Write the fraction of a set that is shaded or selected.

Needs first: Fractions of amounts, Division as equal sharing.

https://lightmysky.com/learn/mathematics/unit-fractions-mt_k2WE0-22-4

#### Comparing fractions (age 7+) (ages 7-8)

Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison

Ready when they can: Solve a word problem requiring finding a fraction of a quantity; Solve a problem that requires comparing or ordering fractions; Choose and apply appropriate fraction knowledge to a multi-step problem.

Needs first: Simple Fraction Sums, Comparing fractions, Unit fractions.

https://lightmysky.com/learn/mathematics/comparing-fractions-age-7-mt_SsLWS_APM7

#### Adding Fractions (Same Denominator) (ages 8-9)

Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)

Ready when they can: Calculate 3/5 + 4/5 = 7/5 and explain it equals 1 2/5; Subtract 2/6 from 5/6; Solve addition problems where the sum exceeds the whole: 7/8 + 3/8.

Needs first: Simple Fraction Sums.

https://lightmysky.com/learn/mathematics/adding-fractions-same-denominator-mt_CBHwluE6Lp

#### Decimal & Percent Notation (ages 8-11)

Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value

Ready when they can: Read and write decimal numbers correctly, identifying the value of each digit (ones, tenths, hundredths); Use the % symbol correctly and explain that per cent means 'out of 100'; Convert between simple fractions, decimals, and percentages (e.g. 1/2 = 0.5 = 50%) and explain why they are equal.

Needs first: Tenths, Fraction Notation.

https://lightmysky.com/learn/mathematics/decimal-and-percent-notation-mt_W17Kbwm0-u

#### Fractions of a whole (ages 8-9)

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b

Ready when they can: Given a shape divided into 5 equal parts, identify one shaded part as 1/5; Explain that 3/4 means 3 parts each of size 1/4; Draw a model showing 2/6 as 2 pieces of a whole cut into 6.

Needs first: Fractions of amounts, Fraction Notation, Splitting shapes into equal parts (age 7+).

https://lightmysky.com/learn/mathematics/fractions-of-a-whole-mt_ndGqFPWyen

#### Comparing fractions (age 8+) (ages 8-9)

Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols

Ready when they can: Compare 3/8 and 3/4: same numerator, larger denominator means smaller pieces so 3/8 < 3/4; Compare 5/6 and 2/6: same denominator so 5/6 > 2/6; Justify a comparison using a visual model and explain why both fractions must refer to the same whole.

Needs first: Comparing fractions, Fractions of a whole, Comparing fractions (age 7+).

https://lightmysky.com/learn/mathematics/comparing-fractions-age-8-mt_HnKbuCliNS

#### Fractions as parts of shapes (ages 8-9)

Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole

Ready when they can: Partition a rectangle into 6 equal-area parts and label each 1/6; Show two different ways to partition a square into 4 equal parts; Given a pre-partitioned shape, write the unit fraction for one part.

Needs first: Fractions of a whole, Splitting shapes into equal parts (age 7+).

https://lightmysky.com/learn/mathematics/fractions-as-parts-of-shapes-mt_idbKDrf9qZ

#### Fractions of a whole (age 8+) (ages 8-9)

Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6)

Ready when they can: Write 5 as 5/1 and explain why; Locate 4/4 and 1 at the same point on a number line; Identify which fractions from a list equal a whole number: 6/3, 8/4, 5/2.

Needs first: Fractions of a whole.

https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-8-mt_AYzE1EAvI0

#### Fractions of amounts (harder) (ages 8-9)

Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number

Ready when they can: Find 3/5 of 20; Calculate 2/3 of 18 and explain the two-step process (divide then multiply); Solve: A bag has 24 sweets, 3/8 are red — how many red sweets?.

Needs first: Adding Fractions (Same Denominator), Unit fractions.

https://lightmysky.com/learn/mathematics/fractions-of-amounts-harder-mt_3y7xKP9MjU

#### Fractions on a number line (age 8+) (ages 8-9)

Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b

Ready when they can: Partition a 0-to-1 number line into 4 equal parts and mark 1/4; Explain that each part on the line has size 1/b; Locate 1/3 and 1/6 on separate number lines; Locate 3/4 on a number line by counting three 1/4-jumps from 0; Place 5/6 on a number line and explain the process; Identify a fraction shown by a point on a pre-partitioned number line.

Needs first: Fractions on a number line, Fractions of a whole.

https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-age-8-mt_NoB20kVa4w

#### Tenths (age 8+) (ages 8-9)

Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10

Ready when they can: Count from 3/100 to 12/100 in hundredths; Explain that 1/10 ÷ 10 = 1/100; Place several hundredths on a number line between 0 and 1/10.

Needs first: Tenths.

https://lightmysky.com/learn/mathematics/tenths-age-8-mt_doX1BhmFgk

#### Decimal equivalents of tenths and hundredths (ages 8-9)

Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)

Ready when they can: Write 7/10 as 0.7 and vice versa; Convert 45/100 to 0.45; Place 0.3 and 3/10 at the same point on a number line.

Needs first: Tenths (age 8+), Decimal & Percent Notation.

https://lightmysky.com/learn/mathematics/decimal-equivalents-of-tenths-and-hundredths-mt_TqDq6jyOmL

#### Decimal place value (ages 8-9)

Round decimals with one decimal place to the nearest whole number

Ready when they can: Round 3.7 to 4 and 3.2 to 3; Place 6.5 on a number line between 6 and 7 and decide it rounds to 7; Round a set of one-decimal-place numbers and explain the rounding rule.

Needs first: Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/decimal-place-value-mt_Fl7b8q9pI1

#### Decimal place value (age 8+) (ages 8-9)

Compare numbers with the same number of decimal places up to two decimal places

Ready when they can: Order 0.45, 0.54, 0.39 from smallest to largest; Compare 3.72 and 3.27 using place-value reasoning; Place three two-decimal-place numbers on a number line in order.

Needs first: Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/decimal-place-value-age-8-mt_IegHBHERVa

#### Decimals and fractions (ages 8-9)

Solve simple measure and money problems involving fractions and decimals to two decimal places

Ready when they can: Calculate 1/4 of £3.20; A rope is 2.5 m long; how much is left after cutting 0.75 m?; Find 3/10 of 1 kg and express the answer in grams and as a decimal of a kg.

Needs first: Fractions of amounts (harder), Adding Fractions (Same Denominator), Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/decimals-and-fractions-mt_wB-GBDkoNr

#### Dividing by 10 and 100 (ages 8-9)

Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits as ones, tenths, and hundredths

Ready when they can: Calculate 37 ÷ 10 = 3.7 and identify 3 as ones and 7 as tenths; Calculate 4 ÷ 100 = 0.04 and identify 4 as hundredths; Explain that dividing by 10 shifts each digit one place to the right.

Needs first: Tenths (age 8+), Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/dividing-by-10-and-100-mt_kDMKJ5Ztt6

#### Decimal place value (age 9+) (ages 9-10)

Round decimals with two decimal places to the nearest whole number and to one decimal place

Ready when they can: Round 3.47 to the nearest whole number (3) and to 1 d.p. (3.5); Round 12.95 to 1 d.p. (13.0) and explain the boundary case; Estimate 4.83 + 2.17 by rounding each to the nearest whole number.

Needs first: Decimal place value.

https://lightmysky.com/learn/mathematics/decimal-place-value-age-9-mt_Ii1hV4V5ql

#### Understanding fractions (age 9+) (ages 9-10)

Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)

Ready when they can: Express 5/8 as a sum of five copies of 1/8; Show on a number line how 4/3 is built by iterating 1/3 four times; Explain why 7/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4.

Needs first: Fractions of a whole.

https://lightmysky.com/learn/mathematics/understanding-fractions-age-9-mt_09sySPqM9Z

#### Fraction Addition Concepts (ages 9-10)

Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way

Ready when they can: Show that 3/8 = 1/8 + 1/8 + 1/8 and also 3/8 = 1/8 + 2/8; Write two different decompositions of 5/6; Use a visual model to justify a decomposition of 2 1/8 into whole-number and fraction parts.

Needs first: Understanding fractions (age 9+), Adding Fractions (Same Denominator).

https://lightmysky.com/learn/mathematics/fraction-addition-concepts-mt_VgOePicFYK

#### Mixed numbers and improper fractions (ages 9-10)

Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)

Ready when they can: Convert 11/4 to 2 3/4; Convert 3 2/5 to 17/5; Write 6/5 + 4/5 = 10/5 = 2 as both improper fraction and whole number.

Needs first: Understanding fractions (age 9+), Fractions of a whole (age 8+), Fraction Notation.

https://lightmysky.com/learn/mathematics/mixed-numbers-and-improper-fractions-mt_o_p-3tCxiM

#### Adding and subtracting mixed numbers (ages 9-10)

Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations

Ready when they can: Calculate 2 3/5 + 1 4/5 and express as a mixed number; Subtract 3 1/4 from 5 3/4; Solve 4 2/6 − 1 5/6 by regrouping the whole number.

Needs first: Mixed numbers and improper fractions, Fraction Addition Concepts.

https://lightmysky.com/learn/mathematics/adding-and-subtracting-mixed-numbers-mt_70qDTI14td

#### Multiplying fractions (ages 9-10)

Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)

Ready when they can: Calculate 4 × 3/8 using repeated addition or the rule n × a/b = (n×a)/b; Multiply 2 1/3 × 3 and express as a mixed number; Use a visual model to show why 5 × 1/4 = 5/4.

Needs first: Understanding fractions (age 9+).

https://lightmysky.com/learn/mathematics/multiplying-fractions-mt_TgHxujL81r

#### Fractions of a whole (age 9+) (ages 9-10)

Solve word problems involving multiplication of a fraction by a whole number using visual models and equations

Ready when they can: Each person eats 3/8 of a pizza and there are 5 people — how many pizzas are needed?; A ribbon is cut into pieces of 2/3 metre; how long are 4 pieces altogether?; Between what two whole numbers does 6 × 3/4 lie?.

Needs first: Multiplying fractions.

https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-9-mt_HJA2Oz-Zh1

#### Word problems adding and subtracting fractions (ages 9-10)

Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations

Ready when they can: A jug contains 3/4 litre of juice; 2/4 litre is poured out — how much remains?; Two pieces of ribbon are 2 3/8 and 1 5/8 inches — what is their total length?; Draw a fraction model to represent and solve a fraction word problem.

Needs first: Adding and subtracting mixed numbers.

https://lightmysky.com/learn/mathematics/word-problems-adding-and-subtracting-fractions-mt_ZLqYE7la4Z

#### Writing simple fractions (ages 6-7)

Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2

Ready when they can: Write 1/2 of 10 = 5; Explain that 2/4 is the same as 1/2 using a diagram; Calculate simple unit fractions of quantities and write the result.

Needs first: Reading +, −, and = symbols, Fractions of amounts.

https://lightmysky.com/learn/mathematics/writing-simple-fractions-mt_MyGblah2yY

#### Equivalent fractions (ages 7-8)

Recognise and show, using diagrams, equivalent fractions with small denominators

Ready when they can: Show that 1/2 = 2/4 using a diagram of equal parts; Use a fraction wall or bar model to find equivalent fractions; Explain why two fractions are equivalent by comparing the shaded areas.

Needs first: Fractions on a number line, Writing simple fractions.

https://lightmysky.com/learn/mathematics/equivalent-fractions-mt_FbDKeLfBCo

#### Equivalent fractions on a number line (ages 8-9)

Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams

Ready when they can: Use fraction strips to show 1/2 = 2/4 = 3/6; Verify on a number line that 2/3 and 4/6 land on the same point; Identify at least three fractions equivalent to 1/2 using diagrams.

Needs first: Equivalent fractions, Fractions on a number line (age 8+).

https://lightmysky.com/learn/mathematics/equivalent-fractions-on-a-number-line-mt_Ep7TDFuYUa

#### Equivalent fractions (age 8+) (ages 8-9)

Generate simple equivalent fractions and explain why they are equivalent using visual fraction models

Ready when they can: Given 1/3, generate 2/6 as equivalent and show with area model; Simplify 4/8 to 1/2 and justify with a fraction strip; Complete equivalence chains: 1/4 = ?/8 = ?/12.

Needs first: Equivalent fractions on a number line.

https://lightmysky.com/learn/mathematics/equivalent-fractions-age-8-mt_FP-mjXaq3B

#### Fraction-Decimal Equivalents (ages 8-9)

Recognise and write decimal equivalents of 1/4, 1/2, and 3/4

Ready when they can: State that 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75; Match fractions to decimals in a sorting activity; Explain why 1/4 = 25/100 = 0.25 using a hundredths grid.

Needs first: Equivalent fractions on a number line, Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/fraction-decimal-equivalents-mt_DRlbMok2lT

#### Equivalent fractions (age 9+) (ages 9-10)

Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths

Ready when they can: Use a fraction strip to show 2/3 = 4/6 = 6/9; Explain that multiplying numerator and denominator by the same number gives an equivalent fraction because the size of the whole is unchanged; Generate three fractions equivalent to 3/5 and verify with diagrams.

Needs first: Equivalent fractions on a number line, Equivalent fractions (age 8+).

https://lightmysky.com/learn/mathematics/equivalent-fractions-age-9-mt_ebPelt-qAl

#### Adding fractions (different denominators) (ages 9-10)

Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator

Ready when they can: Calculate 1/3 + 1/6 by converting to sixths: 2/6 + 1/6 = 3/6 = 1/2; Calculate 3/4 − 1/8 by converting to eighths; Add 2/5 + 3/10 and simplify the answer.

Needs first: Equivalent fractions (age 9+), Fraction Addition Concepts.

https://lightmysky.com/learn/mathematics/adding-fractions-different-denominators-mt_-V7EnqU7gG

#### Comparing fractions (age 9+) (ages 9-10)

Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models

Ready when they can: Compare 3/8 and 5/12 by finding a common denominator of 24; Order 2/3, 3/5, and 7/10 from smallest to largest; Use the benchmark 1/2 to decide that 5/8 > 3/7.

Needs first: Equivalent fractions (age 9+), Comparing fractions (age 8+).

https://lightmysky.com/learn/mathematics/comparing-fractions-age-9-mt_SXbZ3bC9z7

#### Converting tenths to hundredths (ages 9-10)

Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)

Ready when they can: Rewrite 7/10 as 70/100; Calculate 3/10 + 4/100 = 34/100; Explain why 5/10 = 50/100 using a hundredths grid.

Needs first: Tenths (age 8+), Equivalent fractions (age 9+), Adding Fractions (Same Denominator).

https://lightmysky.com/learn/mathematics/converting-tenths-to-hundredths-mt_NaqEP8xDhZ

#### Decimals for Tenths & Hundredths (ages 9-10)

Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)

Ready when they can: Rewrite 0.62 as 62/100; Write 3/10 as 0.3 and locate on a number line; Read 0.07 and express as 7/100.

Needs first: Converting tenths to hundredths, Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/decimals-for-tenths-and-hundredths-mt_Vi4Vo5xs_g

#### Understanding Percentages (ages 9-10)

Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal

Ready when they can: Write 35% as 35/100 and as 0.35; Shade 40% of a 10×10 grid and write the fraction 40/100; Explain that 100% means the whole, 50% means half.

Needs first: Decimals for Tenths & Hundredths, Decimal & Percent Notation.

https://lightmysky.com/learn/mathematics/understanding-percentages-mt_ZM9mhHsyYZ

#### Percentage and decimal equivalents (ages 9-10)

Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25

Ready when they can: State that 1/5 = 20% = 0.2 and use this to find 20% of 60; Convert 3/4 to 75% and to 0.75; A shop offers 25% off a £40 item — what is the sale price?.

Needs first: Fraction-Decimal Equivalents, Understanding Percentages.

https://lightmysky.com/learn/mathematics/percentage-and-decimal-equivalents-mt_4ubP_RMg9o

#### Simplifying Fractions (ages 10-11)

Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator

Ready when they can: Simplify 18/24 to 3/4 by identifying the HCF of 18 and 24; Express 2/3 and 5/8 with a common denominator of 24; Explain why dividing numerator and denominator by a common factor produces an equivalent fraction.

Needs first: Equivalent fractions (age 9+), Factors, multiples, and primes, Fraction Notation.

https://lightmysky.com/learn/mathematics/simplifying-fractions-mt_b7T-CjOYUR

#### Adding Fractions (Unlike Denominators) (ages 10-11)

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator

Ready when they can: Compute 2/3 + 5/4 by converting to twelfths: 8/12 + 15/12 = 23/12; Subtract 1 3/5 from 3 1/4 using a common denominator; Explain the strategy of finding a common denominator and verify using a visual model.

Needs first: Simplifying Fractions, Mixed numbers and improper fractions, Adding fractions (different denominators).

https://lightmysky.com/learn/mathematics/adding-fractions-unlike-denominators-mt_14T5yPXUq_

#### Comparing fractions (age 10+) (ages 10-11)

Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks

Ready when they can: Order 3/4, 7/8, 5/6, and 11/12 from smallest to largest; Compare 7/5 and 4/3 using common denominators; Place improper fractions and mixed numbers on a number line in correct order.

Needs first: Simplifying Fractions, Comparing fractions (age 9+).

https://lightmysky.com/learn/mathematics/comparing-fractions-age-10-mt_PL9VkDwXfh

#### Fraction Word Problems (ages 10-11)

Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness

Ready when they can: Solve: 'Tara ate 2/5 of a pizza and Sam ate 1/3. How much did they eat together?'; Recognise that 2/5 + 1/2 ≠ 3/7 because 3/7 < 1/2 but the sum should exceed 1/2; Estimate a fraction sum using benchmarks (0, 1/2, 1) before computing exactly.

Needs first: Adding Fractions (Unlike Denominators), Word problems adding and subtracting fractions.

https://lightmysky.com/learn/mathematics/fraction-word-problems-mt_e7filQgayF

#### Multiplying fractions (age 10+) (ages 10-11)

Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form

Ready when they can: Compute (2/3) × (4/5) = 8/15 and show with an area model; Use a visual model to demonstrate (2/3) × 4 = 8/3 = 2 2/3; Simplify the product 3/4 × 2/3 = 6/12 = 1/2.

Needs first: Simplifying Fractions, Multiplying fractions.

https://lightmysky.com/learn/mathematics/multiplying-fractions-age-10-mt_AabJisinfi

#### Area with Fractions (ages 10-11)

Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths

Ready when they can: Tile a 2/3 × 3/4 rectangle with 1/12 squares and count to find area = 6/12 = 1/2; Explain why the number of unit-fraction tiles equals the product of the two fractions; Calculate the area of a rectangle with sides 1 1/2 and 2/3 using fraction multiplication.

Needs first: Multiplying fractions (age 10+), Area and perimeter of rectangles, Fractions as parts of shapes.

https://lightmysky.com/learn/mathematics/area-with-fractions-mt_gx6KQK5-Kx

#### Multiplication as scaling (ages 10-11)

Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1

Ready when they can: Predict without calculating whether 3/4 × 7 is greater or less than 7; Explain why multiplying by 5/3 makes a number larger and multiplying by 2/5 makes it smaller; Relate multiplying a/b by n/n = 1 to the principle of fraction equivalence.

Needs first: Multiplying fractions (age 10+), Equivalent fractions (age 9+), Area with Fractions.

https://lightmysky.com/learn/mathematics/multiplication-as-scaling-mt_VKW8lOcFaw

#### Real-world fraction multiplication (ages 10-11)

Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations

Ready when they can: Solve: 'A recipe needs 2 1/3 cups of flour; you want to make 1 1/2 batches. How much flour?'; Draw a fraction model to represent and solve a multiplication word problem; Check the reasonableness of a fraction product in context using estimation.

Needs first: Multiplying fractions (age 10+), Area with Fractions, Multiplication as scaling.

https://lightmysky.com/learn/mathematics/real-world-fraction-multiplication-mt_lvaSGHwvQ5

#### Fractions of a whole (age 10+) (ages 10-11)

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers

Ready when they can: Explain that 3/4 means 3 ÷ 4 and verify by showing 3/4 × 4 = 3; Solve: '9 people share a 50-pound sack equally — how many pounds each?' and express the answer as 5 5/9; Use a visual model to show that sharing 3 wholes among 4 people gives each person 3/4.

Needs first: Multiplying fractions, Division with remainders (age 10+).

https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-10-mt_4Km38F4L-6

#### Decimals and fractions (age 10+) (ages 10-11)

Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts

Ready when they can: Convert 3/8 to 0.375 by dividing 3 ÷ 8; State that 1/5 = 0.2 = 20% from memory; Use fraction–decimal–percentage equivalences to compare 30%, 1/3, and 0.35 and put them in order.

Needs first: Fractions of a whole (age 10+), Percentage and decimal equivalents, Decimal & Percent Notation, Understanding Percentages, Decimals and fractions.

https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi

#### Dividing fractions (unit fractions) (ages 10-11)

Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result

Ready when they can: Compute (1/3) ÷ 4 = 1/12 and explain using a visual model of splitting 1/3 into 4 equal parts; Create a story context for (1/6) ÷ 3 and solve it; Verify (1/3) ÷ 4 = 1/12 by showing (1/12) × 4 = 1/3.

Needs first: Fractions of a whole (age 10+), Multiplying fractions (age 10+).

https://lightmysky.com/learn/mathematics/dividing-fractions-unit-fractions-mt_ifPDOYvUqm

#### Dividing by Fractions (ages 10-11)

Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend

Ready when they can: Compute 4 ÷ (1/5) = 20 and explain: 'How many fifths fit in 4 wholes?'; Create a story context for 6 ÷ (1/4) and solve it; Verify 4 ÷ (1/5) = 20 by showing 20 × (1/5) = 4.

Needs first: Fractions of a whole (age 10+), Multiplying fractions (age 10+), Dividing fractions (unit fractions).

https://lightmysky.com/learn/mathematics/dividing-by-fractions-mt_1PAWhRhpdg

#### Dividing unit fractions and whole numbers (ages 10-11)

Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations

Ready when they can: Solve: '3 people share 1/2 lb of chocolate equally — how much each?' (1/6 lb); Solve: 'How many 1/3-cup servings in 2 cups of raisins?' (6 servings); Create a story context for a given unit-fraction division expression.

Needs first: Dividing by Fractions, Fractions of a whole (age 9+), Dividing fractions (unit fractions).

https://lightmysky.com/learn/mathematics/dividing-unit-fractions-and-whole-numbers-mt_rCMdwG-YOE

#### Mixed & Improper Fractions (ages 11-13)

Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Ready when they can: Add, subtract, multiply, and divide with positive and negative integers; Apply formal written methods to calculations with decimals of any size; Perform all four operations with proper fractions, improper fractions, and mixed numbers.

Needs first: Adding Fractions (Unlike Denominators), Dividing fractions (unit fractions), Comparing fractions (age 10+).

https://lightmysky.com/learn/mathematics/mixed-and-improper-fractions-mt_gNUE4B3vuk

#### Decimals and fractions (age 11+) (ages 11-13)

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms

Ready when they can: Convert any terminating decimal to a fraction in simplest form; Convert any fraction with a denominator whose prime factors are only 2 and 5 to a terminating decimal; Explain why some fractions produce terminating decimals and others do not.

Needs first: Decimals and fractions (age 10+), Mixed & Improper Fractions.

https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ

#### Tenths (age 9+) (ages 9-10)

Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)

Ready when they can: Write 0.025 as 25/1000; Explain that 1 tenth = 100 thousandths; Place 0.345 on a number line between 0.34 and 0.35.

Needs first: Decimals for Tenths & Hundredths, Using Mathematical Structure.

https://lightmysky.com/learn/mathematics/tenths-age-9-mt_kdWoAel3Zl

#### Comparing Decimals (ages 9-10)

Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <

Ready when they can: Compare 0.45 and 0.405 and explain which is greater; Order 3.142, 3.14, 3.2 from smallest to largest; Justify that 0.7 = 0.70 = 0.700 using place-value reasoning.

Needs first: Decimal place value (age 8+), Tenths (age 9+).

https://lightmysky.com/learn/mathematics/comparing-decimals-mt_933BohS9BH

#### Decimals to three places (ages 9-10)

Solve problems involving numbers with up to three decimal places

Ready when they can: Calculate the total of three measurements: 1.234 m + 0.567 m + 2.199 m; A bottle holds 1.5 litres; 0.375 l is poured out — how much remains?; Find two numbers with 3 d.p. that add to make 1.

Needs first: Comparing Decimals, Decimal place value (age 9+).

https://lightmysky.com/learn/mathematics/decimals-to-three-places-mt_sA2OvTiech

#### Multiplying fractions (age 11+) (ages 11-12)

Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)

Ready when they can: Calculate a fraction of a given amount by multiplying; Calculate a percentage of a given amount by converting to a decimal and multiplying; Use the operator interpretation to solve multi-step problems involving discounts, taxes, and portions.

Needs first: Percentages as Fractions, Real-world fraction multiplication.

https://lightmysky.com/learn/mathematics/multiplying-fractions-age-11-mt_J339bO7qLe

#### Dividing fractions (ages 11-12)

Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions

Ready when they can: Divide a fraction by a fraction using the reciprocal method; Use visual fraction models to represent and explain fraction division; Create story contexts for fraction division problems and solve them.

Needs first: Multiplying fractions (age 10+), Dividing fractions (unit fractions), Multiplying fractions (age 11+), Dividing unit fractions and whole numbers.

https://lightmysky.com/learn/mathematics/dividing-fractions-mt_9Y96vxG_LH

### Data & Statistics

https://lightmysky.com/learn/mathematics/areas/data-and-statistics

#### Sorting into categories (ages 5-6)

Classify objects into given categories, count the number in each category, and sort the categories by count

Ready when they can: Sort a set of shapes by colour and count how many in each group; Sort objects by size (big/small) and state how many in each category; Identify which category has the most/fewest after sorting and counting.

Needs first: Comparing groups: more or fewer, Counting objects to 20.

https://lightmysky.com/learn/mathematics/sorting-into-categories-mt_xppl18avyY

#### Data collection and display vocabulary (ages 6-9)

Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data

Ready when they can: Correctly label the axes of a bar chart including a title, axis labels, and scale; Distinguish between discrete data (counted) and continuous data (measured) with an example of each; Use 'tally', 'frequency', and 'pictogram' correctly when describing how to record and display data.

https://lightmysky.com/learn/mathematics/data-collection-and-display-vocabulary-mt_u5HkSxZECM

#### Sorting Data into Categories (ages 6-8)

Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity

Ready when they can: Sort a set of objects into 2-3 given categories and count each group; Create a simple table or list showing category names and counts; Order categories from most to fewest or fewest to most.

Needs first: How Many in Total?, Data collection and display vocabulary, Sorting into categories.

https://lightmysky.com/learn/mathematics/sorting-data-into-categories-mt_ylXdiVRAYv

#### Interpreting categorical data (ages 6-8)

Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another

Ready when they can: Answer 'how many?' for each category in a data set; Calculate the total number of data points across all categories; Compare two categories using 'how many more/fewer' language.

Needs first: Asking Questions, Sorting Data into Categories.

https://lightmysky.com/learn/mathematics/interpreting-categorical-data-mt_1VSfm9yiLn

#### Pictograms and tally charts (ages 6-8)

Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

Ready when they can: Read a pictogram where each symbol represents one item; Construct a tally chart from collected data; Draw a block diagram to represent data from a survey.

Needs first: Data collection and display vocabulary, Sorting into categories, Sorting Data into Categories.

https://lightmysky.com/learn/mathematics/pictograms-and-tally-charts-mt_c29FaCTNsx

#### Picture & Bar Graphs (ages 7-8)

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph

Ready when they can: Draw a picture graph with a symbol representing one unit for each data point; Draw a bar graph with labelled axes and a single-unit scale; Use a bar graph to answer comparison questions (e.g. 'How many more votes did cats get than dogs?').

Needs first: Sorting Data into Categories.

https://lightmysky.com/learn/mathematics/picture-and-bar-graphs-mt_VhBH8wrFC6

#### Scaled picture graphs and bar graphs (ages 8-9)

Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables

Ready when they can: Draw a bar graph where each square represents 5 pets; From a scaled pictogram, answer: how many more children chose football than tennis?; Solve a two-step problem: how many votes in total for the top two choices?.

Needs first: Pictograms and tally charts, Picture & Bar Graphs.

https://lightmysky.com/learn/mathematics/scaled-picture-graphs-and-bar-graphs-mt_r8XnXwRA6g

#### Bar graphs (ages 8-9)

Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

Ready when they can: Read a time graph showing temperature changes over a day; Present data about plant growth over weeks as a time graph; Explain the difference between a bar chart (discrete) and a time graph (continuous).

Needs first: Scaled picture graphs and bar graphs, Data collection and display vocabulary.

https://lightmysky.com/learn/mathematics/bar-graphs-mt_ChjMU2GDJa

#### Reading and Comparing Bar Graphs (ages 9-10)

Solve comparison, sum, and difference problems using information presented in a bar graph

Ready when they can: Read a line graph of temperature over a week and identify the warmest day; Find the difference in rainfall between two months from a line graph; Explain what a rising/falling line means on a time-series graph.

Needs first: Bar graphs.

https://lightmysky.com/learn/mathematics/reading-and-comparing-bar-graphs-mt_H6LlpWgEYS

#### Statistical Analysis Vocabulary (ages 9-11)

Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes

Ready when they can: Correctly define and calculate the mean, median, mode, and range of a small data set; Use 'outlier' correctly to identify a value that doesn't fit the pattern, and explain its effect on the mean; Use 'correlation' correctly when describing the relationship shown in a scatter graph.

Needs first: Bar graphs.

https://lightmysky.com/learn/mathematics/statistical-analysis-vocabulary-mt_fmm-P17Vka

#### Statistical Questions (ages 11-13)

Tell a statistical question from one with a single fixed answer: a statistical question anticipates variability ('How tall are the students in my class?' rather than 'How tall am I?') and is answered by collecting many values

Ready when they can: Sort questions into statistical and non-statistical, explaining that the statistical ones expect varied answers; Rewrite a fixed-answer question as a statistical one (e.g., turn 'How old is my teacher?' into 'How old are the teachers at my school?'); Pose a statistical question about their class and describe what data they would collect to answer it.

Needs first: Reading and Comparing Bar Graphs.

https://lightmysky.com/learn/mathematics/statistical-questions-mt_4Ax4JPXJWD

#### Line plots with fractions of a unit (ages 10-11)

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally)

Ready when they can: Create a line plot showing lengths measured to the nearest 1/8 inch; Use the line plot to find the total of all measurements by adding fractions; Solve: 'If the total liquid were redistributed equally among all beakers, how much would each have?'.

Needs first: Adding Fractions (Unlike Denominators), Measurement Line Plots.

https://lightmysky.com/learn/mathematics/line-plots-with-fractions-of-a-unit-mt_IHipFGTFEY

#### Reading tables (ages 9-10)

Complete, read, and interpret information in tables, including timetables

Ready when they can: Read a bus timetable to find the departure time for a particular stop; Complete a two-way table from given data about favourite sports by gender; Calculate how long a train journey takes using a timetable.

Needs first: Telling time to the minute (age 9+), Scaled picture graphs and bar graphs.

https://lightmysky.com/learn/mathematics/reading-tables-mt_Cqm8iy48UI

#### Two-Way Tables (ages 12-14)

Construct and read two-way tables that sort the same people by two categories at once (e.g., year group against preferred sport); use row and column totals and relative frequencies to judge whether the two categories are associated

Ready when they can: Build a two-way table from raw data on two categories collected from the same people; Read off joint and total frequencies (e.g., how many students both walk to school and pack their lunch); Compare row or column relative frequencies to say whether two things seem linked (e.g., do pet owners do more sport?).

Needs first: Reading tables, Fractions, Decimals & Percentages, Statistical Questions.

https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3

#### Calculating the Mean (ages 10-11)

Calculate and interpret the mean as an average of a data set

Ready when they can: Calculate the mean of five test scores: 72, 85, 90, 68, 95; Explain what the mean represents and how it differs from individual data values; Find a missing data value given the mean and all other values.

Needs first: Statistical Analysis Vocabulary, Addition and subtraction strategies (age 10+), Division with Decimals.

https://lightmysky.com/learn/mathematics/calculating-the-mean-mt_Cg8VPguS_V

#### Line graphs (age 10+) (ages 10-11)

Interpret and construct pie charts and line graphs; use these to solve problems

Ready when they can: Read values from a line graph showing temperature over a day and identify trends; Construct a pie chart from given data by calculating sector angles; Use a pie chart to determine the actual quantity represented by each sector given the total.

Needs first: Measuring angles, Reading and Comparing Bar Graphs, Angle Sum Rules, Calculating Percentages, Data collection and display vocabulary.

https://lightmysky.com/learn/mathematics/line-graphs-age-10-mt_bESTSBB0wK

#### Frequency tables, bar charts and pie charts (ages 11-13)

Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type

Ready when they can: Construct a grouped frequency table from raw continuous data, choosing appropriate class intervals; Draw a pie chart by calculating the angle for each category; Interpret a bar chart comparing two data sets and draw a conclusion about the difference.

Needs first: Line graphs (age 10+), Reading tables, Statistical Analysis Vocabulary, Percentages (age 12+).

https://lightmysky.com/learn/mathematics/frequency-tables-bar-charts-and-pie-charts-mt_eKJG-0eC6D

#### Comparing measurements (ages 11-13)

Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

Ready when they can: Calculate mean, median, and mode for a data set and explain when each is most appropriate; Find the range of a data set and explain how an outlier affects the mean versus the median; Compare two data sets using their averages and ranges to draw conclusions.

Needs first: Calculating the Mean, Frequency tables, bar charts and pie charts, Statistical Analysis Vocabulary, Line plots with fractions of a unit.

https://lightmysky.com/learn/mathematics/comparing-measurements-mt_XSXnTQoQ4l

#### Scatter Graphs & Correlation (ages 13-14)

Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions

Ready when they can: Plot bivariate data on a scatter graph and describe the type of correlation observed; Draw a line of best fit by eye and use it to estimate a value within the data range; Explain what positive, negative, and no correlation mean in the context of real data (e.g., temperature vs. ice-cream sales).

Needs first: Statistical Analysis Vocabulary, Coordinates (age 11+), Linear Function Graphs, Comparing measurements.

https://lightmysky.com/learn/mathematics/scatter-graphs-and-correlation-mt_8atyuvPUZc

#### Scatter Graphs (ages 13-14)

Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate

Ready when they can: Plot 10 data points on a scatter graph with correct axis labels and a consistent scale; Draw a line of best fit by eye, ensuring roughly equal numbers of points above and below; Use the line of best fit to estimate a y-value for a given x-value within the data range.

Needs first: Scatter Graphs & Correlation.

https://lightmysky.com/learn/mathematics/scatter-graphs-mt_BdAeZJUOir

#### Populations, Samples and Bias (ages 14-15)

Tell a population from a sample, judge whether a way of collecting data is fair, and say how a biased sample bends the conclusion.

Ready when they can: Name the population that a survey is trying to describe; Point out the bias in a method such as asking only people leaving a gym; Say what has to be true for a sample to count as random.

Needs first: Scatter Graphs.

https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt

#### Stratified Sampling (ages 14-15)

Work out how many to take from each group so that a sample matches the proportions in the population, and round the results sensibly.

Ready when they can: Work out each group's share of the population before sampling; Calculate how many to sample from one group for a stated sample size; Say why the numbers may need adjusting after rounding.

Needs first: Populations, Samples and Bias, Ratio Notation and Relationships.

https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609

#### Averages from Frequency Tables (ages 14-15)

Find the mean, median, mode and range from a frequency table by working with the counts instead of listing every value.

Ready when they can: Multiply value by frequency and divide by the total to get the mean; Find the median position from the running total of frequencies; Read the mode straight off the largest frequency.

Needs first: Stratified Sampling, Calculating the Mean.

https://lightmysky.com/learn/mathematics/averages-from-frequency-tables-mt_5WF_Rhdb1X

#### Estimating the Mean from Grouped Data (ages 14-15)

Estimate a mean from grouped data using class midpoints, say why the answer is only an estimate, and identify the modal class and the class holding the median.

Ready when they can: Use the midpoint of each class as the value standing for that class; Explain why the result is an estimate rather than the true mean; Identify the modal class and the class that contains the median.

Needs first: Averages from Frequency Tables.

https://lightmysky.com/learn/mathematics/estimating-the-mean-from-grouped-data-mt_3PHP7NLZAw

#### Quartiles and the Interquartile Range (ages 15-16)

Find the median, the quartiles and the interquartile range of a data set, and use the interquartile range to compare how spread out two sets are.

Ready when they can: Find the lower and upper quartile positions in an ordered list; Work out the interquartile range and say what it measures; Explain why the interquartile range survives one extreme value better than the range.

Needs first: Estimating the Mean from Grouped Data.

https://lightmysky.com/learn/mathematics/quartiles-and-the-interquartile-range-mt_vN10d1I9dA

#### Box Plots and Comparing Distributions (ages 15-16)

Draw a box plot from a five-figure summary, and compare two distributions by their medians and their spread in words about the situation.

Ready when they can: Draw a box plot from minimum, quartiles, median and maximum; Compare two box plots in a sentence about the context, not only the numbers; Spot a skewed distribution from where the median sits inside the box.

Needs first: Quartiles and the Interquartile Range.

https://lightmysky.com/learn/mathematics/box-plots-and-comparing-distributions-mt_G_SnfEllzQ

#### Cumulative Frequency Curves (ages 15-16)

Build a cumulative frequency table from grouped data, plot the curve at the upper bound of each class, and read off the median, the quartiles and how many lie above a value.

Ready when they can: Plot cumulative totals against the upper bound of each class; Read the median and quartiles from the curve using the total frequency; Estimate how many values sit above a stated amount.

https://lightmysky.com/learn/mathematics/cumulative-frequency-curves-mt_5U70qgbnST

#### Histograms and Frequency Density (ages 15-16)

Draw and read histograms where the classes have different widths, using frequency density so that area, not height, shows the frequency.

Ready when they can: Work out frequency density as frequency divided by class width; Find the frequency in part of a class by using area; Say why a bar chart with unequal classes misleads the reader.

https://lightmysky.com/learn/mathematics/histograms-and-frequency-density-mt_0QAOgzD-Qw

#### Lines of Best Fit: Prediction and Its Limits (ages 15-16)

Use a line of best fit to predict inside the range of the data, say why predicting far outside it is unsafe, and separate correlation from cause.

Ready when they can: Predict a value from the line and state the range the prediction is valid over; Explain what can go wrong when the line is extended past the data; Give an example of two correlated quantities with no causal link.

https://lightmysky.com/learn/mathematics/lines-of-best-fit-prediction-and-its-limits-mt_CnYCx1a0j5

#### Sampling Methods and Their Trade-offs (ages 16-17)

Compare simple random, systematic, stratified, quota and opportunity sampling by what each costs to run and what bias each risks, and describe the sampling frame a method needs.

Ready when they can: Describe how to take a systematic sample and what could go wrong with it; Choose a method for a stated population and defend the choice; Say what a census gives that no sample can.

https://lightmysky.com/learn/mathematics/sampling-methods-and-their-trade-offs-mt_aSsRQvnKa6

#### Standard Deviation and Variance (ages 16-17)

Measure spread by how far the values sit from the mean on average, using squared deviations so that distances on both sides count. Compare data sets by mean and standard deviation together.

Ready when they can: Calculate the standard deviation of a small data set by hand; Compute it from Σx and Σx² for a frequency table; Compare two sets with the same mean but different spreads.

https://lightmysky.com/learn/mathematics/standard-deviation-and-variance-mt_eNpow5tIX2

#### Sampling Distributions and the Central Limit Theorem (ages 17-18)

The mean of a sample is itself a random variable. Across repeated samples it centres on the population mean with a spread of σ divided by the square root of n, and its shape approaches a normal one as n grows.

Ready when they can: Describe how the spread of sample means changes as the sample gets bigger; Use the σ over root n result for a stated sample size; Explain why a mean from a large sample is more trustworthy than one from a small sample.

https://lightmysky.com/learn/mathematics/sampling-distributions-and-the-central-limit-theorem-mt_nugaEeUSii

#### Setting Up a Hypothesis Test (ages 17-18)

State a null and an alternative hypothesis about a population, fix a significance level before looking at the data, and decide in advance what result would count as surprising enough to reject the null.

Ready when they can: Write null and alternative hypotheses for a stated claim; Decide whether the test is one-tailed or two-tailed and say why; Describe a Type I error in the words of the question.

https://lightmysky.com/learn/mathematics/setting-up-a-hypothesis-test-mt_JmpLNHK0Nf

#### Testing a Binomial Proportion (ages 17-18)

Test a claim about a proportion by finding the probability of a result at least as extreme under the null model, comparing it with the significance level, and writing the conclusion in the words of the situation.

Ready when they can: Calculate the probability of the observed count or anything more extreme; Compare that probability with a 5 percent level and state the decision; Find the critical region for a stated test and sample size.

https://lightmysky.com/learn/mathematics/testing-a-binomial-proportion-mt_ZJ8MTLYYKE

#### Correlation and the Product-Moment Coefficient (ages 17-18)

Summarise the strength and direction of a linear relationship in one number between -1 and 1, judge it against a critical value for the sample size, and keep it apart from any claim about cause.

Ready when they can: Describe what values of r near 0, 1 and -1 look like on a scatter plot; Test a value of r against a critical value for the sample size; Give a case where two correlated quantities share an outside cause.

https://lightmysky.com/learn/mathematics/correlation-and-the-product-moment-coefficient-mt_Rs_Z0P7ELJ

#### The Regression Line and Making Predictions (ages 17-18)

Fit the least-squares line through the data, read its gradient and intercept in the units of the problem, and predict only inside the range the data covers.

Ready when they can: Interpret the gradient of a fitted line in the units of the situation; Predict a value for an x inside the range of the data; Explain why a prediction well outside that range is not supported.

https://lightmysky.com/learn/mathematics/the-regression-line-and-making-predictions-mt_tsjctRmkyE

#### The Law of Large Numbers and the Central Limit Theorem (ages 19-20)

Averages settle on the population mean as samples grow, and their distribution approaches a normal one whatever the population looked like. The two results are what makes inference possible at all.

Ready when they can: State both results with their conditions and say what each claims; Apply the theorem to a skewed population and check the sample size; Separate the claim about the average from the claim about a single observation.

https://lightmysky.com/learn/mathematics/the-law-of-large-numbers-and-the-central-limit-theorem-mt_NknG3L5rQp

#### Point Estimation: Bias, Variance and Consistency (ages 20-21)

An estimator is a random variable computed from a sample. Judge it by whether it is centred on the truth, how much it varies, and whether it settles down as the sample grows.

Ready when they can: Show that the sample mean is unbiased for the population mean; Explain the n - 1 divisor in the sample variance; Compare two estimators on bias and variance together.

https://lightmysky.com/learn/mathematics/point-estimation-bias-variance-and-consistency-mt_I374r2UU_i

#### Maximum Likelihood Estimation (ages 20-21)

Write the probability of the observed data as a function of the unknown parameter and choose the parameter that makes the data most likely. Logs turn the product into a sum you can differentiate.

Ready when they can: Write a likelihood for a sample from a stated model; Maximise the log-likelihood and verify it is a maximum; Derive the estimator for a binomial proportion or an exponential rate.

https://lightmysky.com/learn/mathematics/maximum-likelihood-estimation-mt_ZRTrcy7-KV

#### Confidence Intervals for Means and Proportions (ages 20-21)

Turn the sampling distribution around to produce an interval and a stated coverage. The t-distribution replaces the normal when the population standard deviation is estimated.

Ready when they can: Construct an interval for a mean with the t-distribution; Construct an interval for a proportion and check the conditions; State what the confidence level does and does not say about one interval.

https://lightmysky.com/learn/mathematics/confidence-intervals-for-means-and-proportions-mt_Pg2fPDW1sn

#### Hypothesis Tests for a Mean with the t-Distribution (ages 20-21)

Test a claim about a mean when the population spread is unknown: a t statistic, degrees of freedom, and a p-value read as the probability of data at least this extreme if the claim held.

Ready when they can: Carry out a one-sample t-test and state the conclusion in context; Choose between one-tailed and two-tailed alternatives before seeing the data; State what a p-value is and what it is not.

https://lightmysky.com/learn/mathematics/hypothesis-tests-for-a-mean-with-the-t-distribution-mt_ig2o39hAwh

#### Errors, Power and the Design of a Test (ages 20-21)

Two ways to be wrong, and a trade-off between them. Power is the chance of detecting a real effect, and it is decided at design time by the sample size.

Ready when they can: Describe a type I and a type II error in the context of a study; Explain how sample size and effect size change power; Say why a nonsignificant result is not evidence of no effect.

https://lightmysky.com/learn/mathematics/errors-power-and-the-design-of-a-test-mt_D7ZXbvSD0l

#### Comparing Two Populations (ages 21-22)

Two means or two proportions, with the paired design treated separately because pairing removes a source of variation rather than adding a group.

Ready when they can: Choose between independent samples and a paired design for a stated study; Run a two-sample test and interpret the interval for the difference; Say what pairing buys and what it costs.

https://lightmysky.com/learn/mathematics/comparing-two-populations-mt_v34rZkMfqr

#### Chi-Square Tests for Categorical Data (ages 21-22)

Compare observed counts with the counts a model predicts. The same statistic serves goodness of fit, independence and homogeneity, with the degrees of freedom telling them apart.

Ready when they can: Compute expected counts and the statistic for a contingency table; State the degrees of freedom for each of the three tests; Check the expected-count condition before trusting the result.

https://lightmysky.com/learn/mathematics/chi-square-tests-for-categorical-data-mt_yxc87pzaXX

#### One-Way Analysis of Variance (ages 21-22)

Compare several group means at once by splitting the total variation into a between-groups and a within-groups part. The F ratio asks whether the split is more lopsided than chance allows.

Ready when they can: Partition the total sum of squares into its two parts; Interpret an F ratio and its two degrees of freedom; Explain why running many pairwise t-tests inflates the error rate.

https://lightmysky.com/learn/mathematics/one-way-analysis-of-variance-mt_WYGK3Ktnqz

#### Simple Linear Regression and Inference on the Slope (ages 21-22)

State regression as a model with an error term, estimate its slope by least squares, then test and bound that slope. Residual plots are the check on whether the model was reasonable.

Ready when they can: Write the model with its error assumptions; Test whether a slope differs from zero and give an interval for it; Read a residual plot for curvature and changing spread.

https://lightmysky.com/learn/mathematics/simple-linear-regression-and-inference-on-the-slope-mt_W2huNTKsMj

#### Multiple Regression and Model Diagnostics (ages 21-22)

Several predictors at once, where a coefficient reads as the effect of one variable with the others held fixed. Correlated predictors, influential points and overfitting are the standing hazards.

Ready when they can: Interpret a coefficient with the other predictors held fixed; Spot collinearity and say what it does to the coefficients; Compare models without letting the fit statistic decide on its own.

https://lightmysky.com/learn/mathematics/multiple-regression-and-model-diagnostics-mt_TUx1tDF0jv

#### How a Chart Can Mislead (ages 11-13)

The same numbers can be drawn to argue opposite things. A vertical axis that does not start at zero, a broken scale, unequal category widths, a 3-D effect, or a picture whose area grows faster than its height all change what a reader sees without changing a single value.

Ready when they can: Redraw a bar chart with a truncated axis so it starts at zero, and describe what changed in the impression it gives; Spot three features of a published chart that make a difference look larger than it is; Explain why doubling the height of a pictogram symbol more than doubles the area a reader perceives.

https://lightmysky.com/learn/mathematics/how-a-chart-can-mislead-mt_z7yMoRWipf

#### Who Was Asked: Samples and the People Left Out (ages 14-15)

A statistic is about the people who answered, not the people you care about. Covers the difference between a population and a sample, why the method of asking decides who is missing, and how a poll of a self-selected group can be precisely wrong.

Ready when they can: State the population a given claim is really about, given how the data was collected; Name two ways of choosing a sample that leave out a predictable group, and say who is missing in each; Explain why a larger self-selected sample does not fix a biased one.

https://lightmysky.com/learn/mathematics/who-was-asked-samples-and-the-people-left-out-mt_NQju6n-CKb

### Mathematical Thinking

https://lightmysky.com/learn/mathematics/areas/mathematical-thinking

#### Early Maths Vocabulary (ages 5-6)

Use mathematical words carefully when counting, comparing, and describing shapes and positions

Ready when they can: Use 'more than', 'fewer than', and 'the same as' correctly when comparing groups; Name shapes correctly and describe their features using words like 'sides' and 'corners'; Use positional words (above, below, next to) precisely to describe where objects are.

Needs first: Comparing groups: more or fewer, Positional Language, Basic Nouns & Verbs.

https://lightmysky.com/learn/mathematics/early-maths-vocabulary-mt_lMz9nAs7VO

#### Finding efficient methods (ages 5-6)

Notice when a calculation or pattern repeats and use this to count more efficiently or predict results

Ready when they can: Notice that skip counting by 2s follows a repeating odd/even pattern; Recognise that adding 1 to any number always gives the next counting number; Use a repeated pattern (e.g. +10 on a hundred chart always moves down one row) to predict answers.

Needs first: Counting in 2s, One More Each Time.

https://lightmysky.com/learn/mathematics/finding-efficient-methods-mt_RFeVlw0QvX

#### Hands-On Problem Solving (ages 5-6)

Select and use familiar tools (concrete objects, fingers, ten frames) to help solve a mathematical problem

Ready when they can: Choose cubes, counters, or fingers to help solve an addition or subtraction problem; Use a ten frame to organise objects for counting or comparing; Explain why a particular tool (e.g. cubes rather than fingers) was chosen for a given problem.

Needs first: Counting objects to 20.

https://lightmysky.com/learn/mathematics/hands-on-problem-solving-mt_20WfHhnL39

#### Making Sense of Problems (ages 5-6)

Make sense of a problem by identifying what is being asked, choosing concrete objects or pictures to represent the situation, and explaining a pathway to the solution

Ready when they can: When given a word problem within 10, explain what the problem is asking before attempting to solve; Choose objects, fingers, or drawings to represent a problem situation; After finding an answer, check it makes sense (e.g. re-count objects to verify a total).

Needs first: Checking Your Own Work, How Many in Total?, Listening to Texts Read Aloud, Addition as combining or putting together two, Persisting When It's Hard.

https://lightmysky.com/learn/mathematics/making-sense-of-problems-mt_WkKkb7W9Qd

#### Real-World to Maths Connections (ages 5-6)

Move between a real-world situation and a mathematical representation using concrete objects, drawings, diagrams, tables, number sentences, or bar models

Ready when they can: Given a story about combining groups, represent it with counters or cubes and find the total; Given a set of objects, tell a simple addition or subtraction story to match; Connect a physical action (putting together, taking away) to the matching operation.

Needs first: Representing Addition and Subtraction, Addition and subtraction word problems.

https://lightmysky.com/learn/mathematics/real-world-to-maths-connections-mt_IM1G_7QzTa

#### Showing Your Working (ages 5-6)

Show and tell how a mathematical answer was found using objects, drawings, and spoken words

Ready when they can: Use objects or drawings to demonstrate how an addition or subtraction was solved; Respond to 'how do you know?' by pointing to objects or a drawing and describing what was done; Listen to a peer's explanation and say whether they agree or disagree.

Needs first: Numbers up to 10 into pairs, Number bonds to 9, Listening and responding.

https://lightmysky.com/learn/mathematics/showing-your-working-mt_nyK25mNOeR

#### Using objects to model real problems (ages 5-6)

Use objects, drawings, or simple number sentences to represent a real-world situation (early mathematical modelling)

Ready when they can: Draw a picture or use objects to represent a simple real-world situation involving counting or comparing; Write or dictate a number sentence to describe a real-world situation (e.g. 'I had 5 apples and ate 2'); Use the model to answer a question about the situation.

Needs first: Sorting into categories, Addition and subtraction word problems.

https://lightmysky.com/learn/mathematics/using-objects-to-model-real-problems-mt_fLOkq-HfPB

#### Guided Multi-Step Problem Solving (ages 6-7)

With teacher guidance, make sense of multi-step and more complex problems by planning a pathway to the solution, identifying relevant information, and choosing appropriate operations

Ready when they can: When given a word problem within 20 or 100, identify the known information and what needs to be found; Try a strategy (drawing, number line, known fact) and switch approach if the first attempt stalls; Check the reasonableness of an answer using estimation or a different method.

Needs first: Feeling of not understanding, Addition and subtraction within 20, Planning a Task, Early Word Problems, Making Sense of Problems.

https://lightmysky.com/learn/mathematics/guided-multi-step-problem-solving-mt_O_UOTiMvT_

#### Connecting maths to real life (ages 6-7)

Represent real-world problems with number sentences, bar models, or diagrams, and interpret the mathematical result back in context

Ready when they can: Choose and write an appropriate number sentence for a measurement or money word problem; Draw a bar model or diagram to represent a two-step or comparison problem; Interpret the numerical answer in context (e.g. '15 cm means the ribbon is 15 centimetres long').

Needs first: Interpreting categorical data, Unknown in Addition & Subtraction, Using objects to model real problems.

https://lightmysky.com/learn/mathematics/connecting-maths-to-real-life-mt_f67qGDhyfi

#### Connecting Representations (ages 6-7)

Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)

Ready when they can: Write a number sentence (e.g. 14 + 5 = 19) to match a word problem and explain the connection; Draw a bar model or part-whole diagram to represent a problem, then solve using the diagram; Translate between a concrete model and a symbolic equation, describing what each number represents.

Needs first: Reading +, −, and = symbols, Inverse: addition undoes subtraction, Real-World to Maths Connections.

https://lightmysky.com/learn/mathematics/connecting-representations-mt_EBYGhd8X3x

#### Explaining Mathematical Reasoning (ages 6-7)

With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words

Ready when they can: Explain a solution strategy using a drawing or number sentence (e.g. 'I made ten first, then added the rest'); Justify why an answer is correct by showing an alternative method that gives the same result; Identify and explain an error in a worked example or a peer's solution.

Needs first: Showing Your Working, What the equals sign means, Addition in any order.

https://lightmysky.com/learn/mathematics/explaining-mathematical-reasoning-mt_kJ5wYzO8qC

#### Spotting mathematical patterns (ages 5-6)

Notice simple patterns and structures: spot that changing order doesn't change the total, and recognise how numbers relate to each other

Ready when they can: Notice that 3 + 2 gives the same answer as 2 + 3 (early commutativity); Recognise that teen numbers are 'ten and some more' (e.g. 14 is 10 and 4); Spot a pattern in a sequence of objects or numbers and predict what comes next.

Needs first: Addition as combining or putting together two, The teen numbers.

https://lightmysky.com/learn/mathematics/spotting-mathematical-patterns-mt_uG2mjHFOlO

#### Choosing a tool or representation (ages 6-7)

Select and use appropriate tools and representations (number lines, hundred squares, rulers, part-whole models) to support problem-solving

Ready when they can: Choose a number line or hundred square to support adding or subtracting two-digit numbers; Select a ruler when a problem requires measuring length; Explain why one representation (e.g. a number line vs cubes) is more helpful for a particular problem.

Needs first: Hands-On Problem Solving, Measuring length (age 6+), Adding within 100.

https://lightmysky.com/learn/mathematics/choosing-a-tool-or-representation-mt_zMEvtigoM3

#### Using structure to calculate efficiently (ages 6-7)

Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently

Ready when they can: Use the commutative property deliberately (e.g. reorder 3 + 9 as 9 + 3 to count on from the larger number); Use place-value structure to add or subtract tens (e.g. 47 + 10 = 57 because only the tens digit changes); Recognise structural similarities between shapes (e.g. rectangles and squares both have 4 sides and 4 right angles).

Needs first: Addition in any order, The two digits of a two-digit number, Spotting mathematical patterns.

https://lightmysky.com/learn/mathematics/using-structure-to-calculate-efficiently-mt_DW2D1c0fKx

#### Working with money (ages 7-8)

Model real-world problems involving measurement, money, and time by choosing appropriate representations and interpreting results in context

Ready when they can: Choose whether to use a bar model, number line, or equation for a measurement problem; Model a multi-step money problem with equations and interpret the final answer as change or total cost; Create a line plot from measurement data and use it to answer questions about the real-world situation.

Needs first: Length word problems within 100, Connecting maths to real life, Measuring & Plotting Lengths.

https://lightmysky.com/learn/mathematics/working-with-money-mt_iQYPw8bMfN

#### Generalising Patterns (ages 6-7)

Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts

Ready when they can: Use a known doubles fact to derive a near-doubles answer (e.g. 6 + 7 = 6 + 6 + 1 = 13); Notice that subtracting 10 from any two-digit number always reduces the tens digit by 1; Describe a rule for a pattern and use it to extend or predict (e.g. 'each time we add 5, the ones digit alternates between 0 and 5').

Needs first: 10 More or 10 Less, Addition and subtraction within 20, Finding efficient methods.

https://lightmysky.com/learn/mathematics/generalising-patterns-mt_fZTn0W_iZR

#### Extending Table Patterns (ages 7-8)

Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences

Ready when they can: Notice that all multiples of 4 are even and use this to check answers; Derive 8 × 7 from 8 × 5 + 8 × 2 by spotting the pattern; Describe a rule for a growing pattern (e.g. 'add 50 each time') and use it to predict the next terms.

Needs first: Generalising Patterns, Skip Counting (4s, 8s, 50s, 100s), Times tables (age 7+).

https://lightmysky.com/learn/mathematics/extending-table-patterns-mt_2jbUekyTu4

#### Generalising from repeated reasoning (ages 8-9)

Recognise and use repeated reasoning to generalise: extend patterns in times tables and equivalent fractions, derive unknown facts from known facts efficiently, describe general rules

Ready when they can: Notice that all fractions equivalent to 1/2 have a numerator that is half the denominator; Use the pattern 3×4=12, 3×40=120, 3×400=1200 and explain the generalisation; Derive 8×7 from 8×5=40 plus 8×2=16 and describe the strategy as a general approach.

Needs first: Extending Table Patterns, Equivalent fractions on a number line, Rectangle area by multiplying, Describing Rules & Patterns.

https://lightmysky.com/learn/mathematics/generalising-from-repeated-reasoning-mt_aivrWs6jrS

#### Reasoning with Equivalences (ages 9-10)

Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms

Ready when they can: Notice that multiplying any number by 25 can be done by multiplying by 100 then dividing by 4, and explain why; Describe the general rule for a sequence and predict the 20th term; Generalise: to find 10% divide by 10, to find 5% halve 10%, and use this to find 35% of any number.

Needs first: Generating a pattern from a rule, Generalising from repeated reasoning, Equivalent fractions (age 9+), Describing Rules & Patterns.

https://lightmysky.com/learn/mathematics/reasoning-with-equivalences-mt_jCy07DyBNU

#### Precise Maths Communication (ages 6-7)

Communicate with mathematical precision: use correct vocabulary, specify units, and use symbols accurately

Ready when they can: Use the = sign correctly to mean 'is the same as' rather than 'the answer is'; Include units when giving a measurement answer (e.g. '12 cm' not just '12'); Use precise terms such as 'edge', 'vertex', 'face' when describing 3-D shapes, and 'greater than', 'less than' when comparing numbers.

Needs first: Early Maths Vocabulary, What the equals sign means, Comparing and ordering numbers.

https://lightmysky.com/learn/mathematics/precise-maths-communication-mt_TMoHjMhRS2

#### Precision in mathematical language and notation (ages 7-8)

Communicate with mathematical precision: use correct place-value and fraction vocabulary, specify units in measurement answers, and use notation accurately

Ready when they can: Consistently specify units in measurement answers (e.g. '35 cm' not '35'); Use fraction vocabulary precisely (numerator, denominator, equivalent); Write equations with correct notation including £/p, >, <, = and fraction symbols.

Needs first: Calculating with measurements, Simple Fraction Sums, Grammar Terms: Clauses and Conjunctions, Precise Maths Communication.

https://lightmysky.com/learn/mathematics/precision-in-mathematical-language-and-notation-mt_HY8Yycu_rz

#### Mathematical Precision (ages 8-9)

Communicate with mathematical precision: use correct fraction/decimal vocabulary, name angle types accurately, specify units in measurement and money, and use notation (=, <, >, ÷, ×) correctly

Ready when they can: Distinguish between 'three fourths' and 'three quarters' and use both correctly; State an answer in the correct unit: '63 square centimetres' not just '63'; Write 15:45 in 24-hour notation and explain the distinction from 3:45 pm.

Needs first: Types of angles, Precision in mathematical language and notation, Area (age 8+).

https://lightmysky.com/learn/mathematics/mathematical-precision-mt_mywsN77hGZ

#### Modelling with multiplication and fractions (ages 8-9)

Model real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical results in context

Ready when they can: Model a tiling/area problem with an array and write the corresponding multiplication; Represent a recipe-scaling problem as a fraction calculation and interpret the answer in grams; Use a bar model to set up a unit conversion problem (metres to centimetres).

Needs first: Converting measurement units, Rectangle area by multiplying, Working with money.

https://lightmysky.com/learn/mathematics/modelling-with-multiplication-and-fractions-mt_K3R0yaHVcx

#### Precise Maths Vocabulary (ages 9-10)

Communicate with mathematical precision: use correct vocabulary for primes, factors, multiples, angle types, and polygon regularity; specify units including cm², m³, °; use notation for squares/cubes and percentages accurately

Ready when they can: Distinguish 'factor' from 'multiple' in a written explanation; Write an area answer as 48 cm² (not just 48) and a volume estimate as approximately 60 cm³; Use 5² notation correctly and read it as 'five squared'.

Needs first: Regular and irregular polygons, Square and cube numbers, Mathematical Precision.

https://lightmysky.com/learn/mathematics/precise-maths-vocabulary-mt_xfwv0M83mJ

#### Real-World Maths Modelling (ages 9-10)

Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context

Ready when they can: Model a recipe-scaling problem with multiplication and fractions, then interpret the answer in grams; Represent a room-carpet problem by drawing a scale diagram and applying the area formula; Use a percentage bar model to find a sale price and explain the answer in £.

Needs first: Area and perimeter of rectangles, Modelling with multiplication and fractions, Scaling by fractions and simple rates.

https://lightmysky.com/learn/mathematics/real-world-maths-modelling-mt_8xVHooT4aI

#### Choosing the right strategy (ages 7-8)

Select and use appropriate tools and representations strategically, including choosing between mental methods, jottings, formal algorithms, and calculators for arithmetic with multi-digit numbers, decimals, and fractions

Ready when they can: Choose a mental method for 345 + 200 but a written method for 345 + 278; Select a ruler vs a metre stick based on the object being measured; Decide when a number line is more useful than base-ten blocks for a given problem.

Needs first: Measuring length (age 7+), Adding and subtracting (age 7+), Choosing a tool or representation.

https://lightmysky.com/learn/mathematics/choosing-the-right-strategy-mt_mQcWGh02no

#### Justifying mathematical reasoning (ages 7-8)

Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work

Ready when they can: Explain step by step why a columnar addition method gives the correct answer; Find and explain an error in a worked example (e.g. incorrect regrouping); Construct a simple argument for why a general statement is true (e.g. 'adding two even numbers always gives an even number').

Needs first: Describing Aloud, Teaching It Back, Explaining Mathematical Reasoning, Adding and subtracting (age 7+), Addition and subtraction strategies (age 7+).

https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-mt_pyMD_SIiYO

#### Multi-Step Problem Solving (ages 7-8)

With teacher support, make sense of multi-step problems involving larger numbers or mixed operations by breaking them into parts, choosing strategies, and checking answers for reasonableness — children at this stage are developing the habit with guidance; independent strategy evaluation comes later

Ready when they can: Break a two-step word problem within 1000 into sub-problems and solve each part; Estimate an answer before calculating to set a reasonableness benchmark; Check an answer using a different method or inverse operation and revise if needed.

Needs first: Trying a New Approach, Building sentences, Guided Multi-Step Problem Solving, Estimating by rounding, Missing number problems (age 7+).

https://lightmysky.com/learn/mathematics/multi-step-problem-solving-mt_RKeheOL9uo

#### Using place-value structure to calculate (ages 7-8)

Look for and use mathematical structure: apply place-value patterns to three-digit operations, use multiplication/division relationships, and exploit shape properties to classify

Ready when they can: Use the structure of place value to explain why adding hundreds only changes the hundreds digit; Use commutativity and the relationship between multiplication and division to derive unknown facts; Classify shapes by their structural properties (number of sides, right angles, parallel lines).

Needs first: The three digits of a three-digit number, Using structure to calculate efficiently, Parallel and perpendicular lines, Spotting Patterns, Patterns & Sequences.

https://lightmysky.com/learn/mathematics/using-place-value-structure-to-calculate-mt_FAXjFkgG6X

#### Choosing mathematical tools (ages 8-9)

Select and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking; select fraction models suited to the task

Ready when they can: Decide to use mental multiplication for 25×4 but a written method for 167×3; Choose fraction strips rather than a number line to compare 3/8 and 1/4; Use a ruler and squared paper to verify area by counting squares after calculating l×w.

Needs first: Equivalent fractions on a number line, Elapsed time problems, Choosing the right strategy.

https://lightmysky.com/learn/mathematics/choosing-mathematical-tools-mt_d-WZC2OyMB

#### Justifying mathematical reasoning (age 8+) (ages 8-9)

Construct and present multi-step mathematical arguments; critique the reasoning of others and explain clearly why a method works or fails

Ready when they can: Explain why 1/3 > 1/5 using the idea that more parts means smaller pieces; Find and explain an error in a peer's column subtraction with exchanges; Present a chain of reasoning: since 6×8=48 and 6×2=12, then 6×10=60 so 6×8=60−12=48.

Needs first: Equivalent fractions (age 8+), Comparing fractions (age 8+), Justifying mathematical reasoning, Understanding Why.

https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-age-8-mt_a3dov8CZkq

#### Multi-Step Problem Solving (age 8+) (ages 8-9)

Make sense of multi-step problems involving four operations, fractions, and area/volume by identifying sub-steps, choosing a strategy, and monitoring progress

Ready when they can: Break a two-step word problem into parts and explain a plan before calculating; Choose between drawing a diagram or writing equations for a perimeter problem; Check a fraction-of-quantity answer by estimating: 3/5 of 20 must be more than half of 20.

Needs first: Fractions of amounts (harder), Multi-Step Problem Solving, Analysing Your Own Errors, Perimeters of polygons.

https://lightmysky.com/learn/mathematics/multi-step-problem-solving-age-8-mt_SmghasIvbT

#### Using Mathematical Structure (ages 8-9)

Look for and use mathematical structure: exploit place-value patterns for ×10/×100, use the distributive property to break apart multiplications, apply fraction equivalence to compare and compute, use shape properties to classify quadrilaterals

Ready when they can: Decompose 7×13 into 7×10 + 7×3 using the distributive property; Explain why multiplying by 10 shifts digits one place left using place-value structure; Use the fact that a square is a special rectangle to reason about quadrilateral properties.

Needs first: Using place-value structure to calculate, Dividing by 10 and 100, Spotting Patterns, Classifying quadrilaterals.

https://lightmysky.com/learn/mathematics/using-mathematical-structure-mt__Itf4aQZUj

#### Choosing representations strategically (ages 9-10)

Select and use tools and representations strategically: choose between mental methods, formal written methods, protractors, fraction strips, and diagrams based on the demands of the problem

Ready when they can: Choose mental multiplication for 25 × 40 but long multiplication for 347 × 26; Select a protractor to verify an estimated angle rather than relying on visual inspection alone; Choose a common-denominator approach vs. benchmark comparison for ordering fractions, and explain why.

Needs first: Measuring angles, Choosing mathematical tools, Adding fractions (different denominators).

https://lightmysky.com/learn/mathematics/choosing-representations-strategically-mt_IwEOCN6bL1

#### Complex Multi-Step Problems (ages 9-10)

Make sense of complex multi-step problems involving large numbers, fractions, decimals, and percentages by analysing what is known and unknown, planning multi-step strategies, and evaluating reasonableness through estimation and inverse operations

Ready when they can: Break a three-step problem involving unit conversion and multiplication into sub-problems and solve systematically; Estimate 4,832 × 7 as roughly 5,000 × 7 = 35,000 to check a calculated answer of 33,824; Identify that a percentage answer over 100% doesn't make sense in context.

Needs first: Percentage and decimal equivalents, Division with remainders, Choosing a Strategy, Multi-Step Problem Solving (age 8+).

https://lightmysky.com/learn/mathematics/complex-multi-step-problems-mt_GpltXPoaoc

#### Fractions, Decimals & Percentages (ages 9-10)

Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically

Ready when they can: Use the structure 25 × 16 = 25 × 4 × 4 = 100 × 4 = 400 by exploiting factor pairs; Recognise that 0.75 = 3/4 = 75% and use whichever form is most efficient for the problem; Use the fact that angles on a straight line sum to 180° as a structural tool to find missing angles.

Needs first: Factors, multiples, and primes, Using Mathematical Structure, Angle Sum Rules, Spotting Patterns.

https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ

#### Advanced Multi-Step Problems (ages 10-11)

Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations

Ready when they can: Break down a three-step ratio problem into sub-problems and plan a solution pathway; Identify which quantities are known/unknown in an algebraic word problem and set up equations; Use estimation to check whether a decimal division answer is reasonable before finalising.

Needs first: Finding Knowledge Gaps, Unequal sharing and grouping, Complex Multi-Step Problems, Multi-step problems: choosing operations.

https://lightmysky.com/learn/mathematics/advanced-multi-step-problems-mt_FieL-vVTI_

#### Choosing Maths Tools (ages 10-11)

Select and use tools and representations strategically: choose between mental methods, formal written methods, algebraic approaches, coordinate grids, and technology based on the demands of the problem

Ready when they can: Explain why long division is more appropriate than mental methods for 4,752 ÷ 13; Choose a coordinate grid approach to verify a translation rather than computing from a description alone; Select a formula-based approach rather than counting cubes to find volume efficiently.

Needs first: Choosing representations strategically, Plotting points in the first quadrant, Division with remainders (age 10+).

https://lightmysky.com/learn/mathematics/choosing-maths-tools-mt_ZJC7JnnPCu

#### Real-World Mathematical Modelling (ages 10-11)

Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations

Ready when they can: Choose a bar model or double number line to represent a ratio problem and solve it; Model a volume problem with a labelled diagram, apply the formula, and interpret the result in context; Determine whether a measurement answer should be rounded and to what degree of accuracy.

Needs first: Scale and similar shapes, Real-World Maths Modelling, Volume of cuboids.

https://lightmysky.com/learn/mathematics/real-world-mathematical-modelling-mt_yqZiX6vS7D

#### Using structure in shapes and expressions (ages 10-11)

Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently

Ready when they can: Use the property that all rectangles are parallelograms to deduce missing angle facts; Recognise that 3 × (n + 5) = 3n + 15 by applying distributive structure; Use the equivalence 1/8 = 0.125 = 12.5% flexibly to solve a comparison problem.

Needs first: Decimals and fractions (age 10+), Fractions, Decimals & Percentages, Classifying shapes by properties, Spotting Patterns.

https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh

#### Moving between situations, diagrams and equations (ages 7-8)

Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents

Ready when they can: Write an equation with three-digit numbers to match a measurement or money word problem; Draw a bar model to represent a fraction problem and use it to solve; Explain how a number line diagram relates to the quantities in a word problem.

Needs first: Numbers on a number line, Connecting Representations, Fractions on a number line, Writing simple fractions.

https://lightmysky.com/learn/mathematics/moving-between-situations-diagrams-and-equations-mt_dXq9VWm31W

#### Moving between diagrams and equations with fractions (ages 8-9)

Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows

Ready when they can: Represent a sharing problem as both a fraction diagram and a division equation; Explain how a bar model for 4 × 23 connects to the area model and the written method; Translate a decimal on a number line into a fraction and explain the equivalence.

Needs first: Area and the distributive property, Moving between situations, diagrams and equations, Decimal equivalents of tenths and hundredths.

https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ

#### Moving between bar models, number lines and equations (ages 9-10)

Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connections between representations

Ready when they can: Represent a scaling problem as both a bar model and a multiplication equation; Show how 0.35, 35/100, and 35% all represent the same quantity on a hundredths grid; Translate a line-graph reading into a subtraction equation to find the difference.

Needs first: Moving between diagrams and equations with fractions, Long multiplication, Understanding Percentages, Reading and Comparing Bar Graphs.

https://lightmysky.com/learn/mathematics/moving-between-bar-models-number-lines-and-equations-mt_CUmjcE7W6c

#### Building and critiquing a mathematical argument (ages 9-10)

Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods

Ready when they can: Prove that 3/4 > 2/3 using a common denominator argument and a visual model; Find and explain an error in a long multiplication where a partial product was misaligned; Present a chain of reasoning to show that angles in a triangle sum to 180° by tearing and arranging.

Needs first: Angles that add up on a diagram, Justifying mathematical reasoning (age 8+), Comparing fractions (age 9+), Analysing Your Own Errors.

https://lightmysky.com/learn/mathematics/building-and-critiquing-a-mathematical-argument-mt_2ESZh70NyS

#### Constructing mathematical arguments (ages 10-11)

Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches

Ready when they can: Prove that a given angle must be 60° by chaining angle facts in a logical sequence; Find and explain the error in a peer's fraction division calculation; Construct a counter-example to disprove a false conjecture (e.g. 'multiplying always makes bigger').

Needs first: Building and critiquing a mathematical argument, Angles in triangles (age 10+), Multiplication as scaling.

https://lightmysky.com/learn/mathematics/constructing-mathematical-arguments-mt_j5YqQnN6xe

#### Using a Calculator Well (ages 11-14)

Use a calculator to get accurate answers and interpret them sensibly: key in multi-step calculations respecting the order of operations, use brackets and memory, round the display appropriately, and sanity-check results by estimating first

Ready when they can: Key a multi-step calculation using brackets so the calculator performs operations in the intended order; Interpret the display in context (e.g., read 4.5 as £4.50, or 3.5 hours as 3 hours 30 minutes); Estimate the answer before calculating and re-check the keying when the calculator result is wildly different.

Needs first: Using structure in shapes and expressions, Volume of cuboids, Choosing Maths Tools, Advanced Multi-Step Problems, Mental calculation strategies.

https://lightmysky.com/learn/mathematics/using-a-calculator-well-mt_FZE80D2jS_

#### Generalising with repeated reasoning (ages 10-11)

Recognise and use repeated reasoning to generalise: describe algebraic rules for nth terms, use properties of operations to simplify, and verify generalisations with specific cases

Ready when they can: Explain that the interior angle sum of an n-sided polygon is (n−2) × 180° based on the pattern for triangles, quadrilaterals, pentagons; Predict the 20th term of a linear sequence by identifying and applying the general rule; Generalise that dividing by n always gives a denominator of n in the fraction, for any whole numbers.

Needs first: Angles in triangles (age 10+), Describing Rules & Patterns, Linear number sequences, Reasoning with Equivalences.

https://lightmysky.com/learn/mathematics/generalising-with-repeated-reasoning-mt_iyovKgZC1q

#### Moving between representations of a relationship (ages 10-11)

Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations

Ready when they can: Translate a word problem into an equation, with a bar or symbol standing for the unknown and also represent it on a bar model; Plot data from a table onto a coordinate grid and interpret the relationship; Explain how a pie chart, a fraction, and a percentage all represent the same proportion.

Needs first: Line graphs (age 10+), Moving between bar models, number lines and equations, Number Pattern Relationships.

https://lightmysky.com/learn/mathematics/moving-between-representations-of-a-relationship-mt_9KmVWCuh5_

#### Advanced Maths Vocabulary (ages 10-11)

Communicate with mathematical precision: use correct vocabulary for ratio, proportion, algebra, volume, coordinate geometry, and circle parts; specify units including cm³, m³, and miles/km; use notation for algebraic expressions and order of operations accurately

Ready when they can: Use 'radius', 'diameter', and 'circumference' correctly when describing a circle; Distinguish between an expression, an equation, and a formula in mathematical writing; Specify units correctly when presenting volume calculations (e.g. 60 cm³ not just 60).

Needs first: Choosing Formal Vocabulary, Writing Algebraic Equations, Precise Maths Vocabulary, Parts of a circle.

https://lightmysky.com/learn/mathematics/advanced-maths-vocabulary-mt_3rTIyJDw7-

#### From Examples to a General Argument (ages 12-13)

Move from checking a pattern on a few cases to an argument that covers every case, using a letter to stand for any number.

Ready when they can: Say why testing five cases does not settle a claim about all numbers; Turn a spotted pattern into a statement with a letter in it and check the statement against a fresh case; Write a short argument for a claim such as the sum of two even numbers being even.

https://lightmysky.com/learn/mathematics/from-examples-to-a-general-argument-mt_vm7cigeRtg

#### Finding a Counterexample (ages 13-14)

Disprove a claim by producing one case where it fails, and see why a single case is enough to sink a general statement.

Ready when they can: Produce a counterexample to a plausible claim such as every odd number being prime; Explain the asymmetry: one case disproves, no number of cases proves; Decide, for a given claim, whether to hunt for a counterexample or attempt an argument.

https://lightmysky.com/learn/mathematics/finding-a-counterexample-mt_EoLyw6eP87

#### Choosing a Model and Naming What It Ignores (ages 14-15)

Set up a mathematical model for a real situation, state the assumptions it rests on, and say which of them would break the answer if they were wrong.

Ready when they can: Turn a described situation into a formula or graph and list the assumptions made; Identify which assumption the answer is most sensitive to; Judge whether a model's answer is usable, and say what would have to change to trust it further.

https://lightmysky.com/learn/mathematics/choosing-a-model-and-naming-what-it-ignores-mt_UtK9aauJ6e

#### Algebraic Proof with Odd, Even and Consecutive Numbers (ages 15-16)

Prove a general claim about integers by naming them algebraically, expanding, and showing the required factor is always there.

Ready when they can: Write any even number, any odd number and consecutive integers in terms of n; Prove that the product of two consecutive integers is even, showing the factor explicitly; Say why an algebraic argument settles a claim that no number of tested cases can.

https://lightmysky.com/learn/mathematics/algebraic-proof-with-odd-even-and-consecutive-numbers-mt_p9bajOC17q

#### Proof by Deduction and Exhaustion (ages 17-18)

Argue from what is given to what is claimed with every step justified, and settle a claim about a small finite set by checking every case in it.

Ready when they can: Prove that the sum of two odd numbers is even by writing each as 2n + 1; Prove a claim about the integers 1 to 5 by checking each case; Explain why three worked examples do not prove a general statement.

https://lightmysky.com/learn/mathematics/proof-by-deduction-and-exhaustion-mt_QNWvbkg04f

#### Proof by Contradiction and Counterexample (ages 17-18)

Kill a general claim with a single counterexample, and prove one by assuming the opposite and following it until something impossible appears.

Ready when they can: Disprove 'every prime number is odd' with one example; Prove that √2 cannot be written as a fraction; State clearly what is being assumed at the start of a contradiction proof.

https://lightmysky.com/learn/mathematics/proof-by-contradiction-and-counterexample-mt_pbFTv4v6k8

#### Statements, Quantifiers and Negation (ages 18-19)

Read mathematical statements as objects: connectives, the two quantifiers, and the order they appear in. Negating a quantified statement correctly is the skill everything else rests on.

Ready when they can: Negate a statement with two quantifiers and read the result aloud; Show that swapping the order of two quantifiers changes the claim; Distinguish a conditional from its converse and its contrapositive.

https://lightmysky.com/learn/mathematics/statements-quantifiers-and-negation-mt_S5NvyPxEZ_

#### Sets, Functions and Relations in the Language of Proof (ages 18-19)

Set operations, images and preimages, and what injective, surjective and bijective actually require. Proofs at this level are mostly element-chasing arguments in this language.

Ready when they can: Prove a set identity by double inclusion; Prove a given function is injective or produce a counterexample; Distinguish the image of a set from the preimage of a set.

https://lightmysky.com/learn/mathematics/sets-functions-and-relations-in-the-language-of-proof-mt_XAcHX_3DVz

#### Proof by Induction and Strong Induction (ages 18-19)

Prove a statement for every natural number by settling a base case and showing each case forces the next. Strong induction assumes all earlier cases when one predecessor is not enough.

Ready when they can: Prove a summation formula by induction with the inductive step written out; Use strong induction where the previous case alone is insufficient; Diagnose a flawed induction that skips the base case.

https://lightmysky.com/learn/mathematics/proof-by-induction-and-strong-induction-mt_7lvC02JBOC

#### Equivalence Relations and Partitions (ages 18-19)

A relation that is reflexive, symmetric and transitive cuts a set into classes with no overlap. Modular arithmetic, quotient constructions and much of later algebra are this one idea.

Ready when they can: Verify the three properties for a proposed relation; Describe the classes of congruence modulo n; Show that equivalence classes either coincide or are disjoint.

https://lightmysky.com/learn/mathematics/equivalence-relations-and-partitions-mt_wgEupYwEUF

#### Countable and Uncountable Sets (ages 18-19)

Compare infinite sets by pairing their elements. The rationals pair with the naturals; the reals do not, and the diagonal argument shows why.

Ready when they can: Build an explicit bijection showing a set is countable; Present the diagonal argument for the reals; Explain why a proper subset can pair with the whole set only for infinite sets.

https://lightmysky.com/learn/mathematics/countable-and-uncountable-sets-mt_VTHPloNBbJ

#### Reading a Mathematics Paper (ages 22-23)

A paper is written in logical order and read in a different one. The workable route is the statement first, then an example, then the proof, with the machinery left until it is actually needed.

Ready when they can: Extract the main theorem and its hypotheses before reading any proof; Separate the definitions a paper assumes from the ones it introduces; Say what a given lemma is doing for the main argument.

https://lightmysky.com/learn/mathematics/reading-a-mathematics-paper-mt_pTF-HzLWE6

#### Writing a Proof Someone Else Can Check (ages 22-23)

A written proof is a claim about what a reader can verify, not a record of how it was found. Announced structure, named hypotheses and explicit quantifiers are what make it checkable.

Ready when they can: Write a proof whose structure is announced in the first line; Name the hypothesis at the step where it is used, not in a preamble; Rewrite an argument that hides a quantifier so the order is explicit.

https://lightmysky.com/learn/mathematics/writing-a-proof-someone-else-can-check-mt_nZ-zMzj18N

#### Definitions as Design Decisions (ages 22-24)

A definition is chosen rather than discovered, and the choice decides which theorems become provable. Comparing two candidate definitions of one idea is the fastest way to see what a definition costs.

Ready when they can: Compare two definitions of one idea and say what each one makes easy; Show that a theorem fails under a slightly weaker definition; Explain a definition's edge cases and why they are included or ruled out.

https://lightmysky.com/learn/mathematics/definitions-as-design-decisions-mt_b6ip8eP0-d

#### Counterexamples and Testing a Conjecture (ages 22-24)

Before proving a statement, spend real effort trying to break it. A counterexample settles the question outright, and a failed attempt usually shows which hypothesis the proof will need.

Ready when they can: Construct a counterexample to a plausible but false statement; Turn a failed counterexample into the hypothesis the theorem was missing; Test a conjecture on the smallest cases and the most awkward ones first.

https://lightmysky.com/learn/mathematics/counterexamples-and-testing-a-conjecture-mt_SjA4jqNkaM

#### Open Problems as a Genre (ages 23-24)

An open problem is a question stated precisely enough to be attacked and known to have resisted attack. Reading a few shows what makes a question worth asking and what a partial result looks like.

Ready when they can: State an open problem precisely and say what a solution would have to produce; Describe a known partial result and the gap it leaves; Explain why a vague question is not yet a problem.

https://lightmysky.com/learn/mathematics/open-problems-as-a-genre-mt_qBWcaUWG9J

### Ratio & Proportion

https://lightmysky.com/learn/mathematics/areas/ratio-and-proportion

#### Ratio and proportion vocabulary (ages 9-11)

Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole)

Ready when they can: Explain the difference between a 'ratio' and a 'proportion' using a concrete example like mixing paint; Use 'per cent' correctly and convert between fractions, decimals, and percentages in context; Define 'scale factor' and use it to describe how a shape has been enlarged or reduced.

Needs first: Understanding Percentages.

https://lightmysky.com/learn/mathematics/ratio-and-proportion-vocabulary-mt_ESgc4YBw-a

#### Bar Models for Ratios (ages 9-12)

Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer

Ready when they can: Draw a bar model to represent a ratio problem — e.g. sharing £20 in the ratio 3:2 by drawing 5 equal blocks; Use a bar model to solve a proportion problem and explain each step; Compare bar models with other representations (tables, double number lines) and explain when each is most useful.

Needs first: Modelling with multiplication and fractions.

https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU

#### Ratio Problems (ages 10-11)

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

Ready when they can: If the ratio of red to blue beads is 3:5 and there are 15 blue beads, find the number of red beads; Use multiplication facts to find the missing value: 'For every 2 apples there are 5 oranges; if there are 20 oranges, how many apples?'; Explain the multiplicative relationship between two quantities in a ratio context.

Needs first: Multiplying fractions (age 10+), Bar Models for Ratios, Ratio and proportion vocabulary, Multiplicative Comparison as an Equation.

https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL

#### Scale and similar shapes (ages 10-11)

Solve problems involving similar shapes where the scale factor is known or can be found

Ready when they can: Find the missing side of a similar rectangle given a scale factor of 3; Determine the scale factor between two similar triangles from given side lengths; Use a scale factor to enlarge or reduce a shape and verify that all sides are in the same ratio.

Needs first: Area and perimeter of rectangles, Bar Models for Ratios, Ratio and proportion vocabulary, Ratio Problems, Classifying shapes by properties.

https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW

#### Unequal sharing and grouping (ages 10-11)

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Ready when they can: Share 40 sweets between two children in the ratio 3:5; Solve: 'Tom gets twice as many as Sam and Sam gets three times as many as Jo. If there are 30 altogether, how many does each get?'; Use fraction knowledge to explain why sharing in ratio 2:3 means one person gets 2/5 of the total.

Needs first: Simplifying Fractions, Bar Models for Ratios, Ratio Problems.

https://lightmysky.com/learn/mathematics/unequal-sharing-and-grouping-mt_FnUJMXPUZX

#### Proportion Graphs (ages 11-14)

Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed

Ready when they can: Plot pairs of proportional values on a coordinate grid and draw the straight line through the origin; Explain why a directly proportional relationship always passes through (0,0); Read a proportion graph to find an unknown value — e.g. 'If 3 kg costs £6, how much does 5 kg cost?'.

Needs first: Coordinates (age 10+).

https://lightmysky.com/learn/mathematics/proportion-graphs-mt_FspV_imUGK

#### Calculating Percentages (ages 10-11)

Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison

Ready when they can: Calculate 15% of 360 by finding 10% and 5% and combining; Compare two discounts given as percentages of different original prices; Explain a strategy for finding any percentage of an amount using known percentage facts.

Needs first: Decimals and fractions (age 10+), Bar Models for Ratios, Ratio and proportion vocabulary, Multiplying decimals by whole numbers.

https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ

#### Proportional Reasoning Vocabulary (ages 11-14)

Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts

Ready when they can: Distinguish between 'direct proportion' and 'inverse proportion' with real-world examples; Use 'rate', 'speed', and 'density' correctly and explain what units they are measured in; Calculate using compound measures — e.g. work out the speed of a car that travels 120 miles in 2 hours.

Needs first: Advanced Maths Vocabulary.

https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-

#### One Quantity as a Fraction (ages 11-12)

Express one quantity as a fraction of another where the result may be less than 1 or greater than 1, and interpret the meaning in context

Ready when they can: Express 45 minutes as a fraction of 2 hours (= 3/8); Express a larger quantity as a fraction of a smaller one and explain why the result exceeds 1; Simplify the resulting fraction and interpret its meaning in the original context.

Needs first: Adding Fractions (Unlike Denominators), Decimals and fractions (age 10+), Proportional Reasoning Vocabulary, Fraction Word Problems.

https://lightmysky.com/learn/mathematics/one-quantity-as-a-fraction-mt_xAf2bu9wYK

#### Percentages as Fractions (ages 11-13)

Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%

Ready when they can: Convert fluently between percentages, fractions, and decimals; Express one quantity as a percentage of another; Calculate percentage increases and decreases and interpret percentages greater than 100%.

Needs first: Proportional Reasoning Vocabulary, Calculating Percentages, Moving between representations of a relationship.

https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ

#### Ratio Notation (ages 11-12)

Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations

Ready when they can: Write a ratio from a word problem and simplify it (e.g. 12:8 = 3:2); Convert a ratio to equivalent fractions of a whole (e.g. 3:2 means 3/5 and 2/5); Simplify ratios involving decimals or fractions by finding a common multiplier.

Needs first: Proportional Reasoning Vocabulary, Factors, multiples, and primes, Unequal sharing and grouping, Proportion Graphs.

https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It

#### Dividing Quantities by Ratio (ages 11-13)

Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole

Ready when they can: Share £60 between two people in the ratio 2:3 by finding the value of one part; Express the result of sharing 24 sweets as 10 and 14 in ratio form as 5:7; Solve problems involving three-part ratios (e.g. divide 180 in the ratio 1:2:3).

Needs first: Proportional Reasoning Vocabulary, Bar Models for Ratios, Ratio Notation.

https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z

#### Unit Conversions (ages 11-12)

Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate

Ready when they can: Convert between area units such as cm² and m² using the square of the linear scale factor; Perform multi-step conversions (e.g. convert 2.5 hours to seconds via minutes); Convert volume units such as cm³ to litres and explain the relationship.

Needs first: Converting units with decimal notation, Proportional Reasoning Vocabulary, Measurement Conversions, Miles & Kilometres.

https://lightmysky.com/learn/mathematics/unit-conversions-mt_tpT9brpI6D

#### Scale drawings and maps (ages 11-13)

Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa

Ready when they can: Calculate a real-life distance from a map measurement using a given scale (e.g. 1:25,000); Draw a scale diagram of a room using a chosen scale factor; Convert between map distance and actual distance in problems involving different units.

Needs first: Scale and similar shapes, Proportional Reasoning Vocabulary, Proportion Graphs, Unit Conversions.

https://lightmysky.com/learn/mathematics/scale-drawings-and-maps-mt_1badik7iKJ

#### Percentages (age 12+) (ages 12-14)

Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest

Ready when they can: Calculate a 15% increase on £240 using a decimal multiplier (× 1.15); Find the original price before a 20% discount resulted in a sale price of £64; Calculate simple interest on £500 at 3% per annum for 4 years.

Needs first: Proportional Reasoning Vocabulary, Calculating Percentages.

https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x

#### Compound Interest and Repeated Percentage Change (ages 14-15)

Applying a percentage change again and again multiplies rather than adds, so the multiplier raised to a power gives the answer in one step. The same calculation covers savings growing, a debt growing, and a value depreciating.

Ready when they can: Turn a percentage rise or fall into a multiplier and use a power of it for n periods; Show that a 10% rise followed by a 10% fall does not return to the starting value, and say why; Compare the total repaid on a debt at simple and at compound interest over the same term.

https://lightmysky.com/learn/mathematics/compound-interest-and-repeated-percentage-change-mt_2vJz9VKle_

#### Ratio Notation and Relationships (ages 12-14)

Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios

Ready when they can: Explain why 'for every 2 red beads there are 5 blue beads' can be written as 2:5 or as 2/5 of the blue count; Identify the multiplicative relationship in a table of values (e.g. y is always 3 times x); Connect the ratio a:b to the fraction a/b and to the linear function y = (a/b)x.

Needs first: Proportional Reasoning Vocabulary, Proportion Graphs, Linear Function Graphs, One Quantity as a Fraction, Ratio Notation.

https://lightmysky.com/learn/mathematics/ratio-notation-and-relationships-mt_yK51ZnKA8m

#### Proportion (ages 12-14)

Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations

Ready when they can: Identify whether a real-world relationship is direct or inverse proportion and justify the choice; Set up and solve a direct-proportion equation (e.g. if 4 pens cost £6, find the cost of 10); Sketch graphs showing direct proportion (straight line through origin) and inverse proportion (curve).

Needs first: Proportional Reasoning Vocabulary, Proportion Graphs, Dividing Quantities by Ratio, Linear Function Graphs, Ratio Notation and Relationships.

https://lightmysky.com/learn/mathematics/proportion-mt_5mIcmKRCgA

#### Compound Units (ages 11-14)

Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

Ready when they can: Calculate average speed given distance and time, converting between km/h and m/s if needed; Compare unit prices of two products sold in different quantities to find the better deal; Use the density formula to find mass, volume, or density given the other two values.

Needs first: Simple formulae, Proportion, Proportional Reasoning Vocabulary, Proportion Graphs, Unit Conversions.

https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5

#### Ratio Problems: Sharing, Changing and Combining (ages 14-15)

Solve ratio problems where a total is shared, one part is known, a ratio changes, or two ratios have to be joined through the quantity they share.

Ready when they can: Find the total from one known part of a ratio; Combine a : b and b : c into a : b : c through the shared term; Work out the new ratio after a stated change to one part.

https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv

#### Direct Proportion as a Formula (ages 14-15)

Write y = kx for two quantities in direct proportion, find k from one pair of values, and use the formula to predict others.

Ready when they can: Find the constant of proportionality from one given pair; Use the formula in both directions, from x to y and back; Recognise direct proportion from a straight line through the origin.

https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz

#### Inverse Proportion (ages 14-15)

Use y = k/x when one quantity falls as the other rises, find k from a given pair, and recognise the curve it produces.

Ready when they can: Tell direct from inverse proportion in a word problem; Find k and use it, for example with workers and the time a job takes; Describe the shape of an inverse proportion graph.

https://lightmysky.com/learn/mathematics/inverse-proportion-mt_ZbbN2x6tcL

#### Percentage Change with Multipliers (ages 15-16)

Use one multiplier for an increase or a decrease, chain multipliers for repeated changes, and divide by the multiplier to find the original amount.

Ready when they can: Write a 15 percent rise as a multiplier of 1.15; Find the original price from a sale price and the discount; Explain why a 20 percent rise then a 20 percent fall does not return to the start.

https://lightmysky.com/learn/mathematics/percentage-change-with-multipliers-mt_uqclfF4OBR

#### Compound Growth and Decay (ages 15-16)

Apply a repeated percentage change as a multiplier raised to a power, for savings, depreciation and populations, and find how many steps it takes to pass a target.

Ready when they can: Use the multiplier to the power n for n years of growth; Tell compound growth from simple interest in a word problem; Find by trial how many years pass before a value drops below a target.

https://lightmysky.com/learn/mathematics/compound-growth-and-decay-mt_xf5FQ2sugf

### Number Representation & Place Value

https://lightmysky.com/learn/mathematics/areas/number-representation-and-place-value

#### Reading and writing numbers to 20 (ages 5-6)

Read and write numerals from 0 to 20

Ready when they can: Read any numeral 0–20 when shown it; Write numerals 0–20 legibly from dictation; Represent a number of objects with the correct written numeral.

Needs first: How Many in Total?, Writing digits 0-9.

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-20-mt_fR0UtsSREU

#### Number Words to Twenty (ages 5-6)

Read and write number words from one to twenty

Ready when they can: Read the word 'twelve' and identify it as 12; Write the word form of a given number 1–20; Match numeral cards to number word cards.

Needs first: Reading and writing numbers to 20, Blending Sounds to Read Words, Reading High-Frequency Words by Sight.

https://lightmysky.com/learn/mathematics/number-words-to-twenty-mt_9IzhGUZ30z

#### Reading and writing numbers to 100 (ages 5-6)

Read and write numerals from 0 to 100

Ready when they can: Read two-digit numerals up to 100 correctly; Write any number 0–100 as a numeral from dictation.

Needs first: Reading and writing numbers to 20, Rote counting to 100.

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-100-mt_x8TshvbbQT

#### The teen numbers (ages 5-7)

Understand that the teen numbers (11–19) are composed of ten ones and some further ones (early place value)

Ready when they can: Compose 14 as a group of ten and four ones using objects; Decompose 17 into 10 + 7 and record as an equation; Explain that 13 is 'one ten and three ones'.

Needs first: Reading and writing numbers to 20.

https://lightmysky.com/learn/mathematics/the-teen-numbers-mt_xmmgAzxe5j

#### A Ten Is Ten Ones (ages 6-7)

Understand that 10 can be thought of as a bundle of ten ones — called a 'ten'

Ready when they can: Group 10 single cubes into one rod of 10 and explains why; Explain that 10 ones is the same as 1 ten; Exchange 10 ones for a single tens block.

Needs first: The teen numbers.

https://lightmysky.com/learn/mathematics/a-ten-is-ten-ones-mt_r0VXbfAmsH

#### Number Words to 100 (ages 6-7)

Read and write numbers to at least 100 in words

Ready when they can: Read 'fifty-seven' and write the numeral 57; Write 'eighty-three' when shown the numeral 83; Read and write all decade words (twenty, thirty … ninety) correctly.

Needs first: Number Words to Twenty, Reading and writing numbers to 100.

https://lightmysky.com/learn/mathematics/number-words-to-100-mt_76SPWvdI7r

#### Reading and writing numbers to 120 (ages 6-7)

Count to 120 starting at any number less than 120; read and write numerals to 120

Ready when they can: Count from 47 to 120 without errors; Read the numeral 108 correctly; Write the numeral for one hundred and fifteen.

Needs first: Reading and writing numbers to 100.

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-120-mt_XV0B4kWwqL

#### The multiples of 10 (ages 6-7)

Understand that the multiples of 10 (10, 20, 30 … 90) represent one to nine tens and 0 ones

Ready when they can: Explain that 30 means 3 tens and 0 ones; Represent 50 using 5 tens rods and no unit cubes; Match decade numbers to their tens representation.

Needs first: Counting in 2s, A Ten Is Ten Ones.

https://lightmysky.com/learn/mathematics/the-multiples-of-10-mt_zfy1gOEewd

#### The two digits of a two-digit number (ages 6-7)

Understand that the two digits of a two-digit number represent amounts of tens and ones

Ready when they can: Explain that in 47, the 4 represents 4 tens (40) and the 7 represents 7 ones; Use base-ten blocks to show a two-digit number as tens and ones; Identify the tens digit and ones digit in any two-digit number.

Needs first: A Ten Is Ten Ones, The teen numbers.

https://lightmysky.com/learn/mathematics/the-two-digits-of-a-two-digit-number-mt_THl9GLxwoL

#### 10 More or 10 Less (ages 6-7)

Mentally find 10 more or 10 less than a given two-digit number without counting

Ready when they can: Given 56, quickly say 66 is 10 more and 46 is 10 less; Explain that adding 10 increases the tens digit by 1; Answer '10 more than 73' without using fingers or counting on.

Needs first: One More Each Time, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/10-more-or-10-less-mt_kw7xmp68rU

#### Comparing and ordering numbers (ages 6-7)

Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding

Ready when they can: Correctly place > or < between 34 and 43; Order a set of two-digit numbers from smallest to largest; Explain a comparison by referring to the tens digit first, then ones.

Needs first: The two digits of a two-digit number, Two written numerals between 1 and 10.

https://lightmysky.com/learn/mathematics/comparing-and-ordering-numbers-mt_U0waNfD8PB

#### Place value understanding and number facts (ages 6-7)

Use place value understanding and number facts to solve problems

Ready when they can: Use knowledge that 34 = 30 + 4 to help add 34 + 20 = 54; Solve 'I think of a number, add 10, and get 45. What was my number?'; Apply partitioning to solve a problem in an unfamiliar context.

Needs first: Number bonds, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/place-value-understanding-and-number-facts-mt_kJGCjnuelW

#### A Hundred Is Ten Tens (ages 7-8)

Understand that 100 can be thought of as a bundle of ten tens — called a 'hundred'

Ready when they can: Explain that 10 groups of 10 ones make 100; Bundle ten tens sticks into one hundred and describe what happened; Represent 100 using base-ten blocks showing 10 tens.

Needs first: A Ten Is Ten Ones, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/a-hundred-is-ten-tens-mt_8gy7uxRlF6

#### Odd or Even (ages 7-8)

Determine whether a group of objects (up to 20) has an odd or even number of members

Ready when they can: Pair objects and determine whether there is one left over (odd) or not (even); Count a group by 2s to determine if the total is even; Write an equation to express an even number as a sum of two equal addends (e.g. 8 = 4 + 4).

Needs first: Counting in 2s, Addition as combining or putting together two, Odd and even numbers.

https://lightmysky.com/learn/mathematics/odd-or-even-mt_hniI4E-OCE

#### The multiples of 100 (ages 7-8)

Understand that the multiples of 100 (100–900) each represent a number of hundreds with 0 tens and 0 ones

Ready when they can: Identify that 300 means 3 hundreds, 0 tens, 0 ones; Place multiples of 100 on a number line to 1000; Read and write multiples of 100 and explain their place-value structure.

Needs first: A Hundred Is Ten Tens.

https://lightmysky.com/learn/mathematics/the-multiples-of-100-mt_R2ccrI-nKD

#### The three digits of a three-digit number (ages 7-8)

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones

Ready when they can: State the value of each digit in a three-digit number (e.g. in 362, the 3 represents 3 hundreds); Partition a three-digit number into hundreds, tens, and ones (e.g. 485 = 400 + 80 + 5); Explain why 706 has 7 hundreds, 0 tens, and 6 ones.

Needs first: A Hundred Is Ten Tens.

https://lightmysky.com/learn/mathematics/the-three-digits-of-a-three-digit-number-mt_aPBzD28_mT

#### Representing Numbers (ages 6-8)

Identify, represent, and estimate numbers using different representations including the number line

Ready when they can: Place a two-digit number on a 0–100 number line in approximately the right position; Estimate 'about how many' objects are in a set of 30–50 without counting; Represent the same number using base-ten blocks, a number line, and a drawing; Represent a three-digit number using base-ten blocks, a number line, or a place-value chart; Estimate where a number falls on a 0–1000 number line; Match a base-ten representation to the correct numeral.

Needs first: The three digits of a three-digit number, Representing numbers with objects, The two digits of a two-digit number.

https://lightmysky.com/learn/mathematics/representing-numbers-mt_9L3NQqgqRd

#### 10 or 100 More or Less (ages 7-8)

Find 10 or 100 more or less than a given number up to 1000

Ready when they can: Given a three-digit number, state what is 10 more and 10 less; Given a three-digit number, state what is 100 more and 100 less; Explain the strategy using place-value understanding (e.g. only the tens/hundreds digit changes).

Needs first: The three digits of a three-digit number, 10 More or 10 Less.

https://lightmysky.com/learn/mathematics/10-or-100-more-or-less-mt_izien3ZX51

#### Ordering Numbers to 1000 (ages 7-8)

Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding

Ready when they can: Compare two three-digit numbers by examining hundreds first, then tens, then ones; Use >, =, and < correctly to record comparisons of three-digit numbers; Order a set of numbers up to 1000 from smallest to largest.

Needs first: The three digits of a three-digit number, Comparing and ordering numbers.

https://lightmysky.com/learn/mathematics/ordering-numbers-to-1000-mt_AQcVRBddko

#### Place Value to 1000 (ages 7-8)

Solve number problems and practical problems involving place value of numbers up to 1000

Ready when they can: Solve a problem that requires identifying how many hundreds, tens, or ones are in a number; Apply place-value knowledge to a practical context (e.g. counting money in pounds); Explain the strategy used to solve a place-value problem.

Needs first: The three digits of a three-digit number, 10 or 100 More or Less, Place value understanding and number facts.

https://lightmysky.com/learn/mathematics/place-value-to-1000-mt_98c2qwEF7Q

#### Reading and writing numbers to 1000 (ages 7-8)

Read and write numbers to 1000 in numerals, number names, and expanded form

Ready when they can: Read a three-digit numeral aloud correctly; Write a three-digit number in words (e.g. 'three hundred and forty-two'); Write a number in expanded form (e.g. 600 + 30 + 7).

Needs first: Number Words to 100, The three digits of a three-digit number, Reading and writing numbers to 120.

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-1000-mt_VFsuftfvYM

#### Negative Numbers (ages 8-9)

Count backwards through zero to include negative numbers

Ready when they can: Count backwards from 5 through zero: 5, 4, 3, 2, 1, 0, −1, −2 …; Place negative numbers on a number line; Understand that negative numbers are less than zero and use them in context (e.g. temperature).

Needs first: Counting Within 1,000.

https://lightmysky.com/learn/mathematics/negative-numbers-mt_vXRzMbiPff

#### Place value of each digit (ages 8-9)

Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

Ready when they can: State the value of each digit in a four-digit number (e.g. in 7,345 the 7 represents 7 thousands); Partition a four-digit number into thousands, hundreds, tens, and ones; Compose a four-digit number from given place-value parts (e.g. 3000 + 400 + 50 + 2 = 3,452).

Needs first: The three digits of a three-digit number.

https://lightmysky.com/learn/mathematics/place-value-of-each-digit-mt_jY7uf0Cb7o

#### 1000 More or Less (ages 8-9)

Find 1000 more or less than a given number

Ready when they can: Given 4,562, state that 1000 more is 5,562 and 1000 less is 3,562; Explain using place value that only the thousands digit changes; Apply this skill to numbers beyond 10,000.

Needs first: 10 or 100 More or Less, Place value of each digit.

https://lightmysky.com/learn/mathematics/1000-more-or-less-mt_9XVFje6Tyr

#### Numbers to 10,000 (ages 8-9)

Identify, represent, and estimate numbers up to 10,000 using different representations

Ready when they can: Represent a four-digit number on a place-value chart or with base-ten materials; Estimate where a number falls on a 0–10,000 number line; Match different representations of the same number (e.g. expanded form, place-value counters, numeral).

Needs first: Representing Numbers, Place value of each digit, Place Value to 1000.

https://lightmysky.com/learn/mathematics/numbers-to-10-000-mt_lC_Q5mSL_I

#### Comparing Large Numbers (ages 8-9)

Order and compare numbers beyond 1000

Ready when they can: Compare two four-digit numbers using >, <, and = by examining digits from the highest place value; Order a set of numbers up to 10,000 from smallest to largest; Justify the ordering using place-value reasoning.

Needs first: Ordering Numbers to 1000, Numbers to 10,000.

https://lightmysky.com/learn/mathematics/comparing-large-numbers-mt_MHaiUd2FLA

#### Roman numerals to 100 (ages 8-9)

Read Roman numerals to 100 (I to C) and understand that the numeral system changed over time to include zero and place value

Ready when they can: Read and write Roman numerals I, V, X, L, C and combinations up to 100; Convert between Roman numerals and Hindu-Arabic numerals (e.g. XLIV = 44); Explain that Roman numerals have no zero and no place-value system.

Needs first: Place value of each digit.

https://lightmysky.com/learn/mathematics/roman-numerals-to-100-mt_MewIRdzpzz

#### Rounding to 10, 100, 1000 (ages 8-9)

Round any number to the nearest 10, 100, or 1000

Ready when they can: Round 4,367 to the nearest 10 (4,370), 100 (4,400), and 1000 (4,000); Explain the rounding rule using a number line (which multiple is closer); Apply rounding to estimate calculations.

Needs first: Ordering Numbers to 1000, Place value of each digit, Estimating by rounding.

https://lightmysky.com/learn/mathematics/rounding-to-10-100-1000-mt_NLSfvB9vUl

#### Place Value Problem-Solving (ages 8-9)

Solve number and practical problems involving place value with increasingly large positive numbers

Ready when they can: Solve a problem requiring rounding, comparing, or ordering numbers beyond 1000; Apply place-value knowledge in a practical context (e.g. population figures, distances); Explain the strategy used, referencing place-value understanding.

Needs first: Place value of each digit, Rounding to 10, 100, 1000.

https://lightmysky.com/learn/mathematics/place-value-problem-solving-mt__sMrmOv3bx

#### Place Value × 10 Pattern (ages 9-10)

Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10)

Ready when they can: Explain that the 3 in 3,000 is ten times the 3 in 300; Complete: 700 ÷ 70 = __ and explain using place-value reasoning; State how many times greater the value of the 5 in 50,000 is than the 5 in 5,000.

Needs first: Place Value Problem-Solving.

https://lightmysky.com/learn/mathematics/place-value-10-pattern-mt_QqG6IdmTSE

#### Counting forwards and backwards (age 9+) (ages 9-10)

Count forwards and backwards in steps of powers of 10 (10, 100, 1000, 10,000, 100,000) for any given number up to 1,000,000

Ready when they can: Count on in 10,000s from 462,000; Count back in 100,000s from 800,000; Identify the next three terms: 375,000; 475,000; 575,000; ....

Needs first: 1000 More or Less, Place Value × 10 Pattern, Counting forwards and backwards, Counting forwards and backwards (age 6+).

https://lightmysky.com/learn/mathematics/counting-forwards-and-backwards-age-9-mt_tAtMET4EIU

#### Negative numbers in context (ages 9-10)

Interpret negative numbers in context (temperature, sea level, bank balance); count forwards and backwards with positive and negative whole numbers, including through zero

Ready when they can: Place –3, –1, 0, 2, 5 on a number line; The temperature is –4°C and rises by 7 degrees — what is the new temperature?; Count backwards from 3 in ones: 3, 2, 1, 0, –1, –2.

Needs first: Negative Numbers, Counting forwards and backwards (age 9+).

https://lightmysky.com/learn/mathematics/negative-numbers-in-context-mt_1KkvzwYxbR

#### Reading and writing numbers (age 9+) (ages 9-10)

Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding

Ready when they can: Write 403,072 in words and in expanded form; Compare 548,301 and 543,801 using < and explain the reasoning; Order four six-digit numbers from smallest to largest.

Needs first: Comparing Large Numbers, Place Value × 10 Pattern, Reading and writing numbers to 1000.

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-age-9-mt_JwP9QFv6gQ

#### Roman numerals to 1000 (ages 9-10)

Read Roman numerals to 1000 (M) and recognise years written in Roman numerals

Ready when they can: Read MCMXCIX as 1999; Write 2024 in Roman numerals (MMXXIV); Explain the subtractive principle: IV = 4 not IIII.

Needs first: Roman numerals to 100.

https://lightmysky.com/learn/mathematics/roman-numerals-to-1000-mt_To9HdLy8vq

#### Rounding Large Numbers (ages 9-10)

Round any whole number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000, or 100,000 using place-value understanding

Ready when they can: Round 456,782 to the nearest 10,000 (460,000); Round 950,500 to the nearest 100,000 and explain the boundary case; Use rounding to estimate the sum of 387,412 + 214,560.

Needs first: Rounding to 10, 100, 1000, Place Value × 10 Pattern.

https://lightmysky.com/learn/mathematics/rounding-large-numbers-mt_5NwqN6pf_A

#### Working with Large Numbers (ages 9-10)

Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000

Ready when they can: What is the largest six-digit number with digits summing to 15?; A stadium holds 67,450 people. Round to the nearest thousand for a news report; Order the populations of five cities and find the difference between the largest and smallest.

Needs first: Rounding Large Numbers, Reading and writing numbers (age 9+).

https://lightmysky.com/learn/mathematics/working-with-large-numbers-mt_xMt1TLTs--

#### Measuring temperature (ages 10-11)

Use negative numbers in context (temperature, finance, sea level); calculate intervals across zero

Ready when they can: The temperature falls from 3°C to −5°C — what is the drop? (8 degrees); Calculate the difference between a bank balance of −£120 and £350; Order −7, −3, 0, 2, 5 on a number line and find the interval from −7 to 5.

Needs first: Negative numbers in context.

https://lightmysky.com/learn/mathematics/measuring-temperature-mt_RVK655t391

#### Place Value × 10 and ÷ 10 (ages 10-11)

Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left

Ready when they can: Explain that the 4 in 0.04 is 1/10 of the 4 in 0.4; State that a digit moving one place left is ×10 and one place right is ÷10; Compare the value of the 6 in 6,000 and in 0.006.

Needs first: Tenths (age 9+), Place Value × 10 Pattern.

https://lightmysky.com/learn/mathematics/place-value-10-and-10-mt_EDgw64OmfA

#### Patterns with Powers of Ten (ages 10-11)

Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)

Ready when they can: Write 10⁴ = 10,000 and explain the exponent means four factors of 10; Explain why 3.4 × 10² = 340 by describing the decimal shift; Predict 2.56 × 10³ without calculating and explain the pattern.

Needs first: Place Value × 10 and ÷ 10, Multiplying and dividing.

https://lightmysky.com/learn/mathematics/patterns-with-powers-of-ten-mt_HLUqHJ9Y7n

#### Reading and writing numbers (age 10+) (ages 10-11)

Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning

Ready when they can: Write 347.392 in expanded form: 3×100 + 4×10 + 7×1 + 3×(1/10) + 9×(1/100) + 2×(1/1000); Compare 0.372 and 0.38 using place-value reasoning; Write 'five and sixty-two thousandths' as 5.062.

Needs first: Comparing Decimals, Place Value × 10 and ÷ 10, Tenths (age 9+), Reading and writing numbers (age 9+).

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-age-10-mt_Ac7oMWhyPw

#### Reading and writing numbers to 10,000,000 (ages 10-11)

Read, write, order, and compare numbers up to 10,000,000 and determine the value of each digit

Ready when they can: Write 4,302,561 in words; Order four seven-digit numbers from smallest to largest; State the value of the 7 in 7,045,200 as seven million.

Needs first: Place Value × 10 and ÷ 10, Reading and writing numbers (age 9+).

https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-10-000-000-mt_Gag_h98jWP

#### Reading Decimal Places (ages 10-11)

Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)

Ready when they can: State the value of each digit in 2.635 (2 ones, 6 tenths, 3 hundredths, 5 thousandths); Explain the relationship between adjacent decimal places (each place is ten times smaller); Write a number given digit values (e.g. 4 ones, 0 tenths, 7 hundredths, 3 thousandths = 4.073).

Needs first: Reading and writing numbers (age 10+).

https://lightmysky.com/learn/mathematics/reading-decimal-places-mt_lNGpnILM5C

#### Rounding to a required degree of accuracy (ages 10-11)

Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy

Ready when they can: Round 3.4567 to 2 decimal places (3.46); Round 7,654,321 to the nearest 100,000 (7,700,000); Use rounding to estimate 4.83 × 2.17 ≈ 5 × 2 = 10.

Needs first: Rounding Large Numbers, Reading and writing numbers (age 10+), Decimals to three places.

https://lightmysky.com/learn/mathematics/rounding-to-a-required-degree-of-accuracy-mt__casygEB85

#### Numbers to Ten Million (ages 10-11)

Solve number and practical problems involving reading, writing, ordering, comparing, rounding, and negative numbers up to 10,000,000

Ready when they can: A country's population is 8,274,500 — round to the nearest million for a headline; Order the depths of three ocean trenches given in metres including negative values; Estimate the total attendance at three events by rounding each to the nearest 100,000.

Needs first: Rounding to a required degree of accuracy, Reading and writing numbers to 10,000,000, Measuring temperature, Working with Large Numbers.

https://lightmysky.com/learn/mathematics/numbers-to-ten-million-mt_XNmGwNggdU

#### Absolute value as distance from zero (ages 11-12)

Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements

Ready when they can: Define absolute value as distance from zero on a number line; Calculate the absolute value of positive and negative rational numbers; Distinguish between comparing absolute values and comparing signed numbers in real-world contexts.

Needs first: Positive and Negative Numbers.

https://lightmysky.com/learn/mathematics/absolute-value-as-distance-from-zero-mt_RWUY7_IXvw

#### Decimal place value (age 11+) (ages 11-13)

Round numbers and measures to an appropriate degree of accuracy including to a specified number of decimal places or significant figures

Ready when they can: Round numbers to a given number of decimal places; Round numbers to a given number of significant figures; Choose an appropriate degree of accuracy for a given context.

Needs first: Rounding to a required degree of accuracy.

https://lightmysky.com/learn/mathematics/decimal-place-value-age-11-mt_U9sme87C32

#### Integer powers and roots (ages 11-14)

Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations

Ready when they can: Calculate squares, cubes, and higher integer powers of whole numbers; Find square roots and cube roots of perfect squares and perfect cubes; Recognise key powers (powers of 2 up to 2¹⁰, powers of 3 up to 3⁵, etc.) and distinguish exact roots from approximations.

Needs first: Order of operations with powers and roots.

https://lightmysky.com/learn/mathematics/integer-powers-and-roots-mt_hCVPYlF-7Y

#### Place value for decimals, measures and integers (ages 11-12)

Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line

Ready when they can: Identify the value of any digit in numbers of any size including decimals; Place positive and negative integers, decimals, and fractions on a number line; Use place value to compare and order numbers across the full number system.

Needs first: Reading and writing numbers to 10,000,000.

https://lightmysky.com/learn/mathematics/place-value-for-decimals-measures-and-integers-mt_PsylzZ9lHW

#### Fractions on a number line (age 11+) (ages 11-12)

Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations

Ready when they can: Order a mixed set of positive and negative integers, decimals, and fractions; Use the symbols =, ≠, <, >, ≤, ≥ correctly in mathematical statements; Compare numbers presented in different forms such as 0.75 and 3/4.

Needs first: Positive and Negative Numbers, Place value for decimals, measures and integers.

https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-age-11-mt_uDJY0X0hgo

#### Bounds and error in rounded values (ages 12-14)

Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values

Ready when they can: Estimate the answer to a calculation by rounding all values appropriately; Calculate upper and lower bounds of a rounded measurement; Express error intervals using inequality notation.

Needs first: Decimal place value (age 11+), Rounding Answers.

https://lightmysky.com/learn/mathematics/bounds-and-error-in-rounded-values-mt_VVn1IXjkzn

#### Powers of Ten Notation (ages 12-14)

Interpret and compare numbers in standard form A × 10ⁿ where 1 ≤ A < 10 and n is an integer; convert between ordinary numbers and standard form

Ready when they can: Convert large and small numbers into standard form A × 10ⁿ; Convert numbers from standard form back to ordinary notation; Compare and order numbers given in standard form.

Needs first: Integer powers and roots, Numbers to Ten Million.

https://lightmysky.com/learn/mathematics/powers-of-ten-notation-mt_bO-njVOige

#### Number Sets & Infinity (ages 13-14)

Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers

Ready when they can: Explain that rational numbers can be written as a fraction of two integers and have terminating or repeating decimals; Give examples of irrational numbers and explain why their decimal expansions neither terminate nor repeat; Appreciate that between any two numbers there are infinitely many other numbers.

Needs first: Integer powers and roots, Decimals and fractions (age 11+).

https://lightmysky.com/learn/mathematics/number-sets-and-infinity-mt_b4lbTOJYwI

#### Recurring Decimals as Exact Fractions (ages 14-15)

A decimal that repeats forever is still an exact fraction, and multiplying by a power of ten before subtracting is what pins it down. This is the step that makes the claim about rational numbers repeating into something a learner can act on rather than believe.

Ready when they can: Converts a recurring decimal such as 0.4545... to a fraction by subtracting a shifted copy of it; Handles a decimal with a non-recurring part before the repeat, such as 0.16333...; States which fractions give terminating decimals and which recur, from the prime factors of the denominator.

https://lightmysky.com/learn/mathematics/recurring-decimals-as-exact-fractions-mt_Mb-sXIZDWd

#### Zero and Negative Indices (ages 14-15)

Extend the index laws so that any non-zero number to the power 0 is 1 and a negative index means the reciprocal.

Ready when they can: Rewrite an expression with negative indices in fraction form; Explain why x⁰ = 1 by dividing two equal powers; Combine the multiplication, division and power laws in one expression.

https://lightmysky.com/learn/mathematics/zero-and-negative-indices-mt_jAtXBSVqkj

#### Fractional Indices and Roots (ages 15-16)

Read x^(1/n) as the nth root and x^(m/n) as a root and a power together, and move between root form and index form.

Ready when they can: Work out 27^(1/3) and 16^(3/4) without a calculator; Rewrite a root as a fractional index and back again; Handle a negative fractional index in one calculation.

https://lightmysky.com/learn/mathematics/fractional-indices-and-roots-mt_fdK-nbQcBu

#### Surds: Simplifying and Rationalising (ages 15-16)

Simplify surds by taking out square factors, add and multiply them, and clear a surd from the bottom of a fraction.

Ready when they can: Simplify √50 to 5√2 by finding the largest square factor; Expand a bracket containing surds and collect like terms; Rationalise a denominator such as 6/√2.

https://lightmysky.com/learn/mathematics/surds-simplifying-and-rationalising-mt_cqr0crUUXS

#### Standard Form (ages 15-16)

Write very large and very small numbers as a number between 1 and 10 times a power of ten, and calculate with them by hand and on a calculator.

Ready when they can: Convert between ordinary numbers and standard form in both directions; Multiply and divide in standard form using the index laws; Correct an answer such as 34 × 10⁵ that is not yet in standard form.

https://lightmysky.com/learn/mathematics/standard-form-mt_GbZZ2xjBTt

#### Upper and Lower Bounds (ages 15-16)

Give the upper and lower bounds of a rounded measurement and write the error interval, using the half-unit rule for the accuracy stated.

Ready when they can: State the bounds of a length given as 12.4 cm to 1 decimal place; Write an error interval with the correct strict and inclusive signs; Say what a mass rounded to the nearest 10 g could really be.

https://lightmysky.com/learn/mathematics/upper-and-lower-bounds-mt_HaoOqujpRU

#### Calculating with Bounds in Compound Measures (ages 15-16)

Combine bounds in a calculation by picking the values that give the greatest and least results, including for speed, density and other compound measures.

Ready when they can: Pick which bounds give the greatest result of a division; Find the range of possible speeds from a bounded distance and time; Give a final answer to an accuracy the bounds actually support.

https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf

### Algebra

https://lightmysky.com/learn/mathematics/areas/algebra

#### Linear number sequences (ages 10-11)

Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule

Ready when they can: Continue the sequence 2.5, 4.0, 5.5, ... and state the rule as 'add 1.5'; Generate terms of a sequence that crosses zero (e.g. 3, 1, −1, −3, ...); Describe the term-to-term rule for a given linear sequence and predict the 10th term.

Needs first: Generating a pattern from a rule, Measuring temperature.

https://lightmysky.com/learn/mathematics/linear-number-sequences-mt_hBZwbst0ow

#### Number Pattern Relationships (ages 10-11)

Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane

Ready when they can: Generate sequences starting at 0 with rules 'add 3' and 'add 6'; observe terms in one are twice the other; Form ordered pairs from corresponding terms and plot them on a coordinate grid; Explain informally why the relationship between the two sequences holds.

Needs first: Generating a pattern from a rule, Ratio Problems, Coordinates (age 8+).

https://lightmysky.com/learn/mathematics/number-pattern-relationships-mt_fxPtngwUfz

#### Systematic Listing (ages 10-11)

Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)

Ready when they can: List all possible meal combinations from 3 starters and 4 mains; Organise combinations into a systematic table to ensure none are missed; Explain why the total number of combinations equals the product of the options in each category.

Needs first: Long multiplication (age 10+).

https://lightmysky.com/learn/mathematics/systematic-listing-mt_gu0NPDvlhY

#### Using Simple Formulae (ages 10-11)

Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))

Ready when they can: Substitute values into P = 2(l + w) to find the perimeter of a rectangle; Use the formula for area of a triangle (A = 1/2 × b × h) given base and height values; Interpret a formula expressed in words and use it to compute an output.

Needs first: Writing Number Sentences, Order of operations.

https://lightmysky.com/learn/mathematics/using-simple-formulae-mt_Jvg8X0N5u0

#### Writing Algebraic Equations (ages 10-11)

Express missing number problems algebraically using letters for unknowns; translate word problems into equations

Ready when they can: Write 'I think of a number, double it, and add 5 to get 17' as 2n + 5 = 17; Solve a one-step equation such as 3x = 24 and explain the reasoning; Express a word problem as an algebraic equation and find the unknown value.

Needs first: Writing Number Sentences, Order of operations, Unknown in Multiplication & Division.

https://lightmysky.com/learn/mathematics/writing-algebraic-equations-mt_i9rJbuFO3p

#### Equations with Two Unknowns (ages 10-11)

Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)

Ready when they can: List all whole-number pairs (a, b) where a + b = 12 with a, b > 0; Find three pairs that satisfy 2x + y = 20; Explain systematically how to generate all integer solutions to a two-variable equation within a given range.

Needs first: Writing Algebraic Equations.

https://lightmysky.com/learn/mathematics/equations-with-two-unknowns-mt_YFS7JFk64p

#### Algebraic Notation (ages 11-12)

Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently

Ready when they can: Read and interpret expressions using standard algebraic conventions for multiplication, division, and powers; Write algebraic expressions from word descriptions using correct notation; Understand that juxtaposition means multiplication and that a/b means a divided by b.

Needs first: Writing Algebraic Equations, Using Simple Formulae.

https://lightmysky.com/learn/mathematics/algebraic-notation-mt_KwdjWEmMNo

#### Coordinates (age 11+) (ages 11-12)

Plot and read coordinates in all four quadrants of the Cartesian plane, using positive and negative x- and y-values to describe positions precisely

Ready when they can: Plot points with negative coordinates accurately in all four quadrants; Identify the quadrant a point belongs to from its coordinate signs; Read coordinates from a graph including fractional and negative values.

Needs first: Coordinates (age 10+), Fractions on a number line (age 11+).

https://lightmysky.com/learn/mathematics/coordinates-age-11-mt_hVpGOEz2kG

#### Expressions & Equations Vocabulary (ages 11-12)

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)

Ready when they can: Define and distinguish between expression, equation, and inequality; Identify terms, coefficients, and factors in algebraic expressions; Use the vocabulary of algebra precisely in mathematical discussions.

Needs first: Algebraic Notation, Advanced Maths Vocabulary.

https://lightmysky.com/learn/mathematics/expressions-and-equations-vocabulary-mt_g_fkAqmz72

#### Collecting Like Terms (ages 11-12)

Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence

Ready when they can: Identify like terms in an algebraic expression; Combine like terms involving positive and negative coefficients; Simplify expressions involving multiple variables and constant terms.

Needs first: Expressions & Equations Vocabulary.

https://lightmysky.com/learn/mathematics/collecting-like-terms-mt_nNNVrLqPW3

#### Expanding Single Brackets (ages 11-13)

Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers

Ready when they can: Multiply a single positive term over a bracket to expand the expression; Multiply a negative term over a bracket, correctly handling signs; Combine expanding brackets with collecting like terms to simplify fully.

Needs first: Collecting Like Terms.

https://lightmysky.com/learn/mathematics/expanding-single-brackets-mt_FX4a2Q8XXN

#### Substituting into Formulae (ages 11-12)

Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations

Ready when they can: Substitute positive and negative values into algebraic expressions and evaluate; Substitute values into formulae involving multiple operations and powers; Use correct order of operations when evaluating expressions after substitution.

Needs first: Algebraic Notation.

https://lightmysky.com/learn/mathematics/substituting-into-formulae-mt_vHzVa3SURC

#### Generating Sequences (ages 11-14)

Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither

Ready when they can: Continue a sequence given a term-to-term rule involving addition, subtraction, or multiplication; Generate the first five terms from a position-to-term formula such as 3n − 2; Classify sequences as arithmetic (constant difference), geometric (constant ratio), or other.

Needs first: Linear number sequences, Substituting into Formulae.

https://lightmysky.com/learn/mathematics/generating-sequences-mt_yXO7lQ9Yn7

#### Solving Linear Equations (ages 11-14)

Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

Ready when they can: Solve one-step and two-step linear equations in one variable; Solve equations requiring expansion of brackets and collection of like terms; Solve equations with the unknown on both sides and with fractional or negative coefficients.

Needs first: Expanding Single Brackets, Writing Algebraic Equations, Substituting into Formulae, Using inverse operations.

https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO

#### Algebraic Transformations (ages 11-13)

Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations

Ready when they can: Translate a word problem or real-world situation into an algebraic expression or formula; Construct a table of values from an algebraic rule; Plot the corresponding graph and interpret it in the context of the problem.

Needs first: Algebraic Notation, Solving Linear Equations.

https://lightmysky.com/learn/mathematics/algebraic-transformations-mt_z5iwdZyeDr

#### Inequalities and their solution sets (ages 11-14)

Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

Ready when they can: Write an inequality from a worded constraint (e.g., 'must be at least 12' → x ≥ 12); Represent the solution set of an inequality on a number line with open or closed circles; Solve a one-step or two-step inequality such as 3x + 1 < 10.

Needs first: Solving Linear Equations, Fractions on a number line (age 11+).

https://lightmysky.com/learn/mathematics/inequalities-and-their-solution-sets-mt_i2F1nWxJjv

#### Factorising Expressions (ages 12-13)

Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

Ready when they can: Identify the highest common factor of all terms in an expression; Write the factorised form as a product of the HCF and a bracket; Check factorisation by expanding the brackets back out.

Needs first: Expanding Single Brackets, Sign Rules for Multiplication.

https://lightmysky.com/learn/mathematics/factorising-expressions-mt_uESbzWCZIq

#### Laws of Exponents (ages 12-14)

Apply the rules of integer exponents to write equivalent expressions: multiply powers by adding indices, divide by subtracting, raise a power to a power by multiplying, and interpret zero and negative exponents (3² × 3⁻⁵ = 3⁻³ = 1/27)

Ready when they can: Simplify products and quotients of powers with the same base (e.g., 5³ × 5⁴ = 5⁷, 2⁸ ÷ 2³ = 2⁵); Evaluate expressions with zero and negative exponents (e.g., 7⁰ = 1, 2⁻³ = 1/8); Spot and correct a common exponent error, such as claiming 3² × 3³ = 9⁵.

Needs first: Integer powers and roots, Patterns with Powers of Ten.

https://lightmysky.com/learn/mathematics/laws-of-exponents-mt_UjNba32kkz

#### Linear Function Graphs (ages 12-14)

Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context

Ready when they can: Explain that changing m in y = mx + c alters the steepness and direction of the line; Identify the y-intercept of a line from its equation and from its graph; Determine whether a given equation will produce a straight line or a curve.

Needs first: Coordinates (age 11+), Substituting into Formulae, Algebraic Transformations.

https://lightmysky.com/learn/mathematics/linear-function-graphs-mt_WBdHkc2HTf

#### Nth-Term Rules (ages 12-14)

Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence

Ready when they can: Derive the nth-term rule for an arithmetic sequence such as 3, 7, 11, 15, … as 4n − 1; Use an nth-term formula to find the 50th or 100th term without listing all preceding terms; Determine whether a given number (e.g., 99) is a term in a specified arithmetic sequence.

Needs first: Solving Linear Equations, Generating Sequences, Generalising with repeated reasoning.

https://lightmysky.com/learn/mathematics/nth-term-rules-mt_HRKzwEQJgO

#### Simple formulae (ages 12-14)

Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable

Ready when they can: Identify the subject of a given formula; Use inverse operations to rearrange a formula to make a different variable the subject; Rearrange formulae involving multiple steps including fractions and powers.

Needs first: Solving Linear Equations, Substituting into Formulae, Using inverse operations, Real-World Mathematical Modelling.

https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU

#### Plotting Linear Graphs (ages 12-14)

Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line

Ready when they can: Generate a table of (x, y) values for a linear equation and plot the points accurately; Rearrange an equation such as 2x + 3y = 12 into the form y = mx + c; Calculate the gradient between two coordinate points using rise over run.

Needs first: Simple formulae, Linear Function Graphs.

https://lightmysky.com/learn/mathematics/plotting-linear-graphs-mt_-3udyo6VyB

#### Expanding Double Brackets (ages 13-14)

Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms

Ready when they can: Expand the product of two binomials using a systematic method (grid or FOIL); Collect like terms after expansion to simplify the result; Expand products involving negative terms correctly.

Needs first: Expanding Single Brackets.

https://lightmysky.com/learn/mathematics/expanding-double-brackets-mt_KhS7K1Mgrw

#### Quadratic Graphs (ages 13-14)

Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions

Ready when they can: Explain why x² produces a U-shaped curve rather than a straight line; Plot a simple quadratic such as y = x² − 4 from a table of values; Read approximate solutions from a quadratic graph (e.g., where y = 0).

Needs first: Plotting Linear Graphs.

https://lightmysky.com/learn/mathematics/quadratic-graphs-mt_GZuoYaDdWd

#### Reading solutions from a graph (ages 13-14)

Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts

Ready when they can: Read off an approximate y-value for a given x from a plotted curve; Find approximate solutions to an equation by identifying where a graph crosses the x-axis or another line; Interpret a real-world graph (e.g., distance–time) to answer contextual questions.

Needs first: Plotting Linear Graphs, Quadratic Graphs.

https://lightmysky.com/learn/mathematics/reading-solutions-from-a-graph-mt_Yw27nweoTj

#### Simultaneous Equations (ages 13-14)

Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations

Ready when they can: Explain that the intersection of two lines represents values satisfying both equations; Find the approximate solution to a pair of simultaneous equations by reading a graph; Verify a proposed solution by substituting into both equations.

Needs first: Plotting Linear Graphs, Solving Linear Equations, Equations with Two Unknowns.

https://lightmysky.com/learn/mathematics/simultaneous-equations-mt_mqgu72aCMz

#### Factorising Quadratics into Two Brackets (ages 14-15)

Undo the expansion of two brackets for quadratics of the form x² + bx + c by finding the number pair that multiplies to c and adds to b. Check every answer by expanding it back.

Ready when they can: Factorise x² + 7x + 12 by finding the pair that multiplies to 12 and adds to 7; Choose signs correctly for a quadratic with a negative constant, such as x² - 2x - 15; Check a factorisation by expanding the brackets back to the original quadratic.

Needs first: Expanding Double Brackets, Factorising Expressions.

https://lightmysky.com/learn/mathematics/factorising-quadratics-into-two-brackets-mt_3QXgmWKfoA

#### Difference of Two Squares and Perfect Square Trinomials (ages 14-15)

Recognise the two quadratics that factorise on sight: a² - b² splitting into (a + b)(a - b), and a perfect square trinomial folding back into one bracket squared.

Ready when they can: Factorise x² - 49 and 9x² - 25 as a difference of two squares; Spot that x² + 10x + 25 is (x + 5)² from the halved middle coefficient; Use the difference of two squares to work out 51 × 49 mentally.

Needs first: Factorising Quadratics into Two Brackets.

https://lightmysky.com/learn/mathematics/difference-of-two-squares-and-perfect-square-trinomials-mt_GSpsHuserT

#### Factorising Quadratics with a Leading Coefficient (ages 14-15)

Factorise quadratics such as 6x² + 11x + 3, where the x² coefficient is not 1, by splitting the middle term and grouping.

Ready when they can: Split the middle term of 6x² + 11x + 3 using the pair that multiplies to 18 and adds to 11; Factorise by grouping once the middle term has been split; Take out a common factor first when the whole quadratic shares one, as in 2x² + 10x + 12.

Needs first: Difference of Two Squares and Perfect Square Trinomials.

https://lightmysky.com/learn/mathematics/factorising-quadratics-with-a-leading-coefficient-mt_IdKGCzbH07

#### Solving Quadratic Equations by Factorising (ages 14-15)

Rearrange a quadratic equation so one side is zero, factorise it, then use the fact that a product is zero only when one factor is zero to read off both solutions.

Ready when they can: Rearrange x² + 5x = 14 into x² + 5x - 14 = 0 before factorising; Apply the zero product rule to get both solutions from (x - 2)(x + 7) = 0; Reject a solution that cannot fit the context, such as a negative length.

Needs first: Factorising Quadratics with a Leading Coefficient.

https://lightmysky.com/learn/mathematics/solving-quadratic-equations-by-factorising-mt_tg_sqRzDjU

#### Simplifying Algebraic Fractions (ages 14-15)

Factorise the top and the bottom of an algebraic fraction, cancel the common bracket, and state the values of x the fraction cannot take.

Ready when they can: Simplify (x² - 9)/(x² + 7x + 12) by factorising both parts; Cancel whole factors only, never single terms inside a sum; State the excluded values that would make the denominator zero.

Needs first: Solving Quadratic Equations by Factorising, Dividing fractions.

https://lightmysky.com/learn/mathematics/simplifying-algebraic-fractions-mt_scDNSoz3eW

#### Geometric Sequences and Common Ratios (ages 15-16)

Recognise a sequence built by multiplying by the same number each time, find the common ratio and the nth term rule, and link it to growth and decay.

Ready when they can: Find the common ratio by dividing consecutive terms; Write the nth term as a first term times r to a power; Continue a decaying sequence with a ratio between 0 and 1.

https://lightmysky.com/learn/mathematics/geometric-sequences-and-common-ratios-mt_NDnbJm2hTY

#### Rearranging Formulae When the Subject Appears Twice (ages 15-16)

Change the subject of a formula where the new subject shows up more than once: clear any fraction, collect those terms on one side, factorise the subject out, then divide.

Ready when they can: Multiply through to clear a fraction before collecting terms; Gather every term containing the new subject on one side; Factorise the subject out of the collected terms and divide by the bracket.

Needs first: Simplifying Algebraic Fractions.

https://lightmysky.com/learn/mathematics/rearranging-formulae-when-the-subject-appears-twice-mt_Velmpnxfcj

#### Completing the Square (ages 15-16)

Write a quadratic as (x + p)² + q by halving the x coefficient and correcting the constant, then solve it by taking the square root of both sides.

Ready when they can: Write x² + 6x + 1 as (x + 3)² - 8; Solve from the completed square by taking the square root and keeping both signs; Complete the square when the x² coefficient is not 1 by taking it out first.

Needs first: Rearranging Formulae When the Subject Appears Twice, Difference of Two Squares and Perfect Square Trinomials.

https://lightmysky.com/learn/mathematics/completing-the-square-mt_rHmCfzB4Fm

#### The Quadratic Formula (ages 15-16)

Solve any quadratic with x = (-b ± √(b² - 4ac))/(2a), including ones that do not factorise, giving answers exactly or to a stated accuracy.

Ready when they can: Identify a, b and c with their signs before substituting; Give both roots, exact in surd form or rounded as the question asks; Say why the formula was the right choice for a quadratic that does not factorise.

Needs first: Completing the Square.

https://lightmysky.com/learn/mathematics/the-quadratic-formula-mt_C-4brnRYHY

#### The Discriminant and the Number of Roots (ages 15-16)

Use b² - 4ac to decide whether a quadratic has two roots, one repeated root or none, without solving it, and link that count to the graph crossing the x-axis.

Ready when they can: Work out the discriminant and state how many real roots the equation has; Explain what a discriminant of zero means for the shape of the graph; Find the value of k that gives a quadratic equal roots.

Needs first: The Quadratic Formula.

https://lightmysky.com/learn/mathematics/the-discriminant-and-the-number-of-roots-mt_uj95V0aLVS

#### Sketching Quadratic Graphs from Roots and the Turning Point (ages 15-16)

Sketch a parabola from its roots, y-intercept, line of symmetry and turning point, reading the turning point off the completed square form.

Ready when they can: Read the turning point straight from (x + p)² + q; Mark roots, y-intercept and line of symmetry on a sketch; Use the sketch to say for which x values the curve sits above the axis.

Needs first: The Discriminant and the Number of Roots, Quadratic Graphs.

https://lightmysky.com/learn/mathematics/sketching-quadratic-graphs-from-roots-and-the-turning-point-mt_RcrJIbbN2x

#### Simultaneous Equations with One Quadratic (ages 15-16)

Solve a linear and a quadratic equation together by substituting the linear one into the quadratic, and read the answers as the points where a line meets a curve.

Ready when they can: Substitute the linear equation into the quadratic and collect terms to one side; Give the answers as coordinate pairs, not just x values; Say what a single repeated solution means about the line and the curve.

Needs first: Sketching Quadratic Graphs from Roots and the Turning Point, Simultaneous Equations.

https://lightmysky.com/learn/mathematics/simultaneous-equations-with-one-quadratic-mt_D89ql2sJvc

#### Solving Linear Inequalities and Solution Sets (ages 15-16)

Solve inequalities in one variable with the balancing steps used for equations, flip the sign when multiplying or dividing by a negative, and show the answer on a number line.

Ready when they can: Solve 3(x - 2) < 12 and show the solution on a number line; Flip the inequality sign when dividing both sides by a negative number; Solve a double inequality such as -3 < 2x + 1 ≤ 7 and list the integers in it.

Needs first: Simultaneous Equations with One Quadratic, Inequalities and their solution sets.

https://lightmysky.com/learn/mathematics/solving-linear-inequalities-and-solution-sets-mt_QkG3Cw5VgM

#### Graphical Inequalities and Regions in the Plane (ages 15-16)

A linear inequality in two variables picks out a half-plane, and several of them together leave a region whose corners answer the question being asked. Drawing the boundary as solid or dashed is what records whether the boundary itself counts.

Ready when they can: Shades the region satisfying y < 2x + 1 and says why the boundary line is dashed; Finds the region satisfying three inequalities at once and lists the integer points inside it; Writes down the inequalities that describe a region already shaded on a grid.

https://lightmysky.com/learn/mathematics/graphical-inequalities-and-regions-in-the-plane-mt_sKerzcAcNy

#### Solving Quadratic Inequalities (ages 15-16)

Solve inequalities such as x² - x - 6 > 0 by finding the roots, sketching the parabola, and reading off the x values where the curve is on the required side of the axis.

Ready when they can: Find the roots first, then sketch to decide which regions satisfy the inequality; Write the answer as one or two ranges with the correct strict or inclusive signs; Explain why an upward parabola gives two separate ranges for > 0.

Needs first: Solving Linear Inequalities and Solution Sets.

https://lightmysky.com/learn/mathematics/solving-quadratic-inequalities-mt_dukJtB_0i8

#### Quadratic Sequences and Second Differences (ages 15-16)

Recognise a quadratic sequence from its constant second difference, and find the nth term rule in the form an² + bn + c.

Ready when they can: Take first and second differences to decide a sequence is quadratic; Use half the second difference as the coefficient of n²; Find the rest of the rule by comparing the sequence with the n² terms.

Needs first: Solving Quadratic Inequalities, Nth-Term Rules.

https://lightmysky.com/learn/mathematics/quadratic-sequences-and-second-differences-mt_gyZT3Tcw7U

#### Function Notation and Evaluating Functions (ages 15-16)

Read f(x) as a rule that turns each input into one output, evaluate a function at given values, and solve f(x) = k.

Ready when they can: Work out f(3) and f(-2) for a given rule; Solve f(x) = 0 for a quadratic rule; Explain why each input is allowed only one output.

Needs first: Quadratic Sequences and Second Differences.

https://lightmysky.com/learn/mathematics/function-notation-and-evaluating-functions-mt_YWKWzHK_6Z

#### Composite Functions (ages 15-16)

Apply one function to the output of another, writing fg(x) as f(g(x)), and keep the order of the two rules straight.

Ready when they can: Work out fg(2) by finding g(2) first and then applying f; Write and simplify an expression for fg(x); Show with one example that fg(x) and gf(x) usually differ.

Needs first: Function Notation and Evaluating Functions.

https://lightmysky.com/learn/mathematics/composite-functions-mt_jqGJHXgYNw

#### Inverse Functions (ages 15-16)

Find the rule that undoes a function by swapping input and output and rearranging, and see the inverse graph as a reflection in the line y = x.

Ready when they can: Find f⁻¹(x) for a linear rule by rearranging; Check an inverse by showing that ff⁻¹(x) gives back x; Describe the inverse graph as a reflection of the original in y = x.

Needs first: Composite Functions.

https://lightmysky.com/learn/mathematics/inverse-functions-mt_7k7q5ZjMb4

#### Transformations of Graphs (ages 15-16)

Describe and apply the effect of f(x) + a, f(x + a), -f(x) and af(x) on a graph, and give the coordinates of a marked point after the change.

Ready when they can: Say which way f(x + 3) moves the graph and why the shift looks backwards; Give the image of a marked turning point after a stated transformation; Match a transformed sketch to its equation.

Needs first: Inverse Functions.

https://lightmysky.com/learn/mathematics/transformations-of-graphs-mt_691_c-7Z5M

#### Recognising Cubic, Reciprocal and Exponential Graphs (ages 15-16)

Recognise and sketch the shapes of y = x³, y = 1/x and y = kˣ, and match each shape to the kind of situation it describes.

Ready when they can: Sketch y = x³ and y = 1/x, including the axes the reciprocal graph never touches; Pick the exponential curve rather than a straight line for a doubling story; Apply a stated shift or reflection to one of these shapes.

Needs first: Transformations of Graphs.

https://lightmysky.com/learn/mathematics/recognising-cubic-reciprocal-and-exponential-graphs-mt_2IJJ51rmq9

#### Domain and Range of a Function (ages 16-17)

Describe the set of inputs a function accepts and the set of outputs it can return, and say what forces a restriction: a division, a square root, or the situation being modelled.

Ready when they can: State the domain of f(x) = 1/(x - 3) and say why 3 is left out; Read the range of a quadratic from its turning point; Give a sensible domain for a function whose input is a length.

Needs first: Recognising Cubic, Reciprocal and Exponential Graphs, Function Notation and Evaluating Functions, Inverse Functions.

https://lightmysky.com/learn/mathematics/domain-and-range-of-a-function-mt_b_4zoHz8Jc

#### Modulus Functions and Modulus Equations (ages 16-17)

Read the modulus as distance from zero, sketch the V-shaped graph it produces, and solve equations and inequalities that contain one.

Ready when they can: Sketch y equals the modulus of a linear expression and mark where the graph turns; Solve a modulus equation by splitting into the two cases and rejecting solutions that fail the original; Solve a modulus inequality and write the answer as an interval or a union of intervals.

https://lightmysky.com/learn/mathematics/modulus-functions-and-modulus-equations-mt__W-aDpT5jz

#### Polynomial Division and the Factor Theorem (ages 16-17)

Divide a polynomial by a linear expression and read the remainder, then use the fact that a root gives a factor to break a cubic apart.

Ready when they can: Divide x³ - 2x² - 5x + 6 by (x - 1) and state the quotient; Use f(2) = 0 to write down a factor of a cubic; Factorise a cubic fully after finding its first root by substitution.

Needs first: Domain and Range of a Function, Solving Quadratic Equations by Factorising.

https://lightmysky.com/learn/mathematics/polynomial-division-and-the-factor-theorem-mt_haL2UkGa5C

#### Sketching a Curve from Its Factorised Form (ages 16-17)

Turn a factorised polynomial into a sketch: roots give the crossings, the constant term gives the y-intercept, the highest power decides what the ends do, and a repeated factor touches instead of crossing.

Ready when they can: Sketch y = (x + 1)(x - 2)(x - 4) with all intercepts labelled; Explain why y = x(x - 3)² touches the axis at 3 rather than crossing it; Predict the end behaviour of a quartic with a negative leading coefficient.

Needs first: Polynomial Division and the Factor Theorem, Sketching Quadratic Graphs from Roots and the Turning Point.

https://lightmysky.com/learn/mathematics/sketching-a-curve-from-its-factorised-form-mt_x4tZLdH8fh

#### The Exponential Function and the Number e (ages 16-17)

Treat y = aˣ as a family of curves: always positive, multiplied by a fixed factor per unit step, with a horizontal asymptote. One member, y = eˣ, has a gradient equal to its own value everywhere.

Ready when they can: Describe the shape and asymptote of y = 2ˣ and of y = 2⁻ˣ; Say what makes e different from any other base; Use a model of the form A e^(kt) to describe growth and decay.

https://lightmysky.com/learn/mathematics/the-exponential-function-and-the-number-e-mt_2hyjN4JfJJ

#### Logarithms as the Inverse of Exponentials (ages 16-17)

Read logₐ x as the answer to the question 'what power of a gives x'. The log graph is the exponential graph reflected in y = x, and each function undoes the other.

Ready when they can: Rewrite 2⁵ = 32 in logarithm form and back again; Explain why the logarithm of a negative number has no value; Sketch y = ln x by reflecting y = eˣ in the line y = x.

https://lightmysky.com/learn/mathematics/logarithms-as-the-inverse-of-exponentials-mt_skLQLUan0T

#### Hyperbolic Functions and Their Inverses (ages 17-18)

Build sinh and cosh from the exponential function, prove the identity that replaces the Pythagorean one, and write the inverses as logarithms.

Ready when they can: Define sinh and cosh in terms of the exponential and sketch both graphs; Prove the identity relating cosh squared and sinh squared and compare it with the circular case; Express an inverse hyperbolic function as a logarithm and state its domain.

https://lightmysky.com/learn/mathematics/hyperbolic-functions-and-their-inverses-mt_gCUl1sWi9M

#### Rational Functions, Asymptotes and Curve Sketching (ages 17-18)

Sketch a quotient of polynomials by finding its zeros, its vertical asymptotes and what it does far from the origin.

Ready when they can: Locate vertical asymptotes from the denominator's zeros and check whether a factor cancels into a hole; Decide the behaviour for large values by comparing the degrees of numerator and denominator; Combine intercepts, asymptotes and sign changes into a sketch and check it against a few points.

https://lightmysky.com/learn/mathematics/rational-functions-asymptotes-and-curve-sketching-mt_U-f9YTNb2o

#### The Imaginary Unit and Complex Arithmetic (ages 17-18)

Quadratics with no real roots stop being dead ends: i is defined so that i squared is -1, and numbers of the form a + bi add, multiply, conjugate and divide by the ordinary rules of algebra.

Ready when they can: Solve a quadratic with negative discriminant and write both roots in a + bi form; Add, multiply and divide two complex numbers, using the conjugate for division; Explain why the rules of real algebra carry over once i squared is replaced by -1.

https://lightmysky.com/learn/mathematics/the-imaginary-unit-and-complex-arithmetic-mt_Faemafn550

#### The Argand Plane, Modulus and Argument (ages 17-18)

A complex number is a point: real part across, imaginary part up. Its distance from the origin is the modulus and its angle is the argument, so multiplying becomes scaling and turning.

Ready when they can: Plot complex numbers on the Argand plane and read real and imaginary parts back; Compute modulus and argument and convert between a + bi and modulus-argument form; Show geometrically that multiplying by i is a quarter turn.

https://lightmysky.com/learn/mathematics/the-argand-plane-modulus-and-argument-mt_Wq01c5UN9e

#### Euler's Formula and the Exponential Form (ages 17-18)

e to the i theta traces the unit circle, tying the exponential function to sine and cosine. In exponential form, multiplying complex numbers means adding angles, and De Moivre's theorem falls out for free.

Ready when they can: Write a complex number in exponential form and convert back; Multiply and divide complex numbers by adding and subtracting arguments; Use De Moivre's theorem to compute a small integer power of a complex number.

https://lightmysky.com/learn/mathematics/eulers-formula-and-the-exponential-form-mt_RX2IxsnSwG

#### Roots of Polynomials and Roots of Unity (ages 17-18)

Every polynomial of degree n has n complex roots, with non-real roots of real polynomials arriving in conjugate pairs, and the nth roots of unity sit evenly spaced around the unit circle.

Ready when they can: Factor a cubic with one real root into its real root and a conjugate pair; Find all nth roots of unity for small n and place them on the Argand plane; State what the fundamental theorem of algebra promises and what it does not.

https://lightmysky.com/learn/mathematics/roots-of-polynomials-and-roots-of-unity-mt_XAISygqdQr

#### The Laws of Logarithms (ages 17-18)

Turn products into sums, quotients into differences and powers into multipliers, and combine several logarithms into one before solving or simplifying.

Ready when they can: Write log x + 2 log y as a single logarithm; Expand log(a²b / c) into separate terms; Use a change of base to evaluate a logarithm the calculator has no key for.

https://lightmysky.com/learn/mathematics/the-laws-of-logarithms-mt_5vHdWlxaqY

#### Solving Exponential Equations with Logarithms (ages 17-18)

Take logarithms of both sides to bring an unknown down from an exponent, and solve equations that are quadratic in eˣ by substitution.

Ready when they can: Solve 3ˣ = 20 to three significant figures; Solve e^(2x) - 5eˣ + 6 = 0 using a substitution; Find how long a modelled quantity takes to halve.

https://lightmysky.com/learn/mathematics/solving-exponential-equations-with-logarithms-mt_DaxxpSbDOn

#### Straightening Data with Logarithmic Graphs (ages 17-18)

Take logarithms of a model to make it linear: y = axⁿ gives a straight line for log y against log x, and y = abˣ gives one for log y against x. The gradient and intercept then return the constants.

Ready when they can: Choose the axes that straighten a given model; Recover a and n from the gradient and intercept of a log-log plot; Say what a straight log-linear plot tells you about the data.

https://lightmysky.com/learn/mathematics/straightening-data-with-logarithmic-graphs-mt_TVar2jxRMI

#### Arithmetic Series and Sigma Notation (ages 17-18)

Add the terms of a linear sequence with the pairing argument behind Sₙ = n(a + l)/2, and read and write sums in sigma notation.

Ready when they can: Find the sum of the first 50 terms of an arithmetic sequence; Explain the pairing argument that produces the formula; Write a given sum in sigma notation and evaluate it.

https://lightmysky.com/learn/mathematics/arithmetic-series-and-sigma-notation-mt_bAIPng87JO

#### Geometric Series and the Sum to Infinity (ages 17-18)

Sum a geometric sequence with the standard formula, and see that when the common ratio is between -1 and 1 the running total settles on a finite limit however many terms are added.

Ready when they can: Find the sum of the first 12 terms of a geometric sequence; Decide from the common ratio whether a sum to infinity exists; Use a / (1 - r) on a recurring decimal or a repeated-dose model.

https://lightmysky.com/learn/mathematics/geometric-series-and-the-sum-to-infinity-mt_HHxFOv6vXS

#### The Binomial Expansion (ages 16-17)

Expand (a + b)ⁿ with coefficients from Pascal's triangle or the nCr key, pick out a single term without writing the rest, and use the first few terms as an approximation when one term is small.

Ready when they can: Expand (1 + 2x)⁵ in full; Find the coefficient of a stated power without expanding everything; Approximate 1.02⁸ from the first three terms and comment on the error.

https://lightmysky.com/learn/mathematics/the-binomial-expansion-mt_z16HZkNZ8c

### Mechanics

https://lightmysky.com/learn/mathematics/areas/mechanics

#### Modelling Motion in a Straight Line (ages 16-17)

Set up a motion problem before calculating anything: choose which direction counts as positive, treat the object as a particle, and keep displacement, velocity and acceleration apart from distance, speed and everyday words like slowing down.

Ready when they can: Give both the displacement and the distance travelled for an out-and-back journey; Say what a negative velocity and a negative acceleration each mean once a direction is chosen; State the assumptions hidden in the words particle, smooth and light.

https://lightmysky.com/learn/mathematics/modelling-motion-in-a-straight-line-mt_no78_6w1rS

#### Motion Graphs: Gradients and Areas (ages 16-17)

Read the gradient of a displacement-time graph as velocity and the area under a velocity-time graph as displacement, and describe a whole journey from the shape of the graph alone.

Ready when they can: Find a velocity from the gradient of a displacement-time graph; Find a displacement from the area under a velocity-time graph, counting area below the axis as negative; Describe in words the journey shown by a given velocity-time graph.

https://lightmysky.com/learn/mathematics/motion-graphs-gradients-and-areas-mt_KhJeCMYBSL

#### The Constant-Acceleration Equations (ages 16-17)

Derive the five constant-acceleration equations from a straight-line velocity-time graph, then choose the one that uses the three quantities you know and gives the one you want.

Ready when they can: Derive v = u + at and s = (u + v)t / 2 from the velocity-time graph; List the five quantities in a problem and pick the equation that leaves out the unwanted one; Solve for time when the equation is quadratic in t and say what both roots mean.

https://lightmysky.com/learn/mathematics/the-constant-acceleration-equations-mt_Nyc3BcikQ9

#### Vertical Motion Under Gravity (ages 16-17)

Apply the constant-acceleration equations to an object thrown or dropped, taking the acceleration as g downwards and keeping one sign convention for the whole solution.

Ready when they can: Find the greatest height of a ball thrown upwards, using velocity zero at the top; Find the time for a dropped object to fall a given height; Explain what a negative root means when an object lands below its starting point.

https://lightmysky.com/learn/mathematics/vertical-motion-under-gravity-mt_IgNj9bn14O

#### Kinematics with Calculus (ages 17-18)

When the acceleration is not constant, differentiate displacement to get velocity and velocity to get acceleration, and integrate back the other way, using an initial condition to fix each constant.

Ready when they can: Differentiate s(t) twice and give the units of each result; Integrate a(t) to get v(t) and use v(0) to find the constant; Find when a particle is instantaneously at rest by solving v(t) = 0.

Needs first: The Power Rule for Differentiating Polynomials, Integration as the Reverse of Differentiation.

https://lightmysky.com/learn/mathematics/kinematics-with-calculus-mt_2kNspOOoDw

#### Forces as Vectors: Resolving and Resultants (ages 16-17)

Draw every force acting on a body as an arrow, add them as vectors to get the resultant, and split any force into components along two perpendicular directions of your choosing.

Ready when they can: Resolve a 20 N force at 30° to the horizontal into two components; Find the magnitude and direction of the resultant of two perpendicular forces; Draw a diagram showing every force on a body and nothing that is not a force.

https://lightmysky.com/learn/mathematics/forces-as-vectors-resolving-and-resultants-mt_-qDRgd2g8v

#### Equilibrium and Newton's First Law (ages 17-18)

A body with no resultant force stays still or keeps a constant velocity. Setting the components in two perpendicular directions to zero turns that into equations that find unknown forces.

Ready when they can: Show three given forces are in equilibrium by resolving in two directions; Find the tension in each of two strings holding a hanging mass; Name every force on a book resting on a table and say what exerts it.

https://lightmysky.com/learn/mathematics/equilibrium-and-newtons-first-law-mt_e6RFRQkRPo

#### Moments and the Equilibrium of a Rigid Body (ages 17-18)

Measure the turning effect of a force as force times perpendicular distance from a point, and solve a beam problem by setting both the total force and the total moment to zero.

Ready when they can: Find the moment of a force about a point using the perpendicular distance; Find both support reactions on a loaded uniform beam; Work out how far a load can move along a plank before it tips.

https://lightmysky.com/learn/mathematics/moments-and-the-equilibrium-of-a-rigid-body-mt_FX5egGL4LI

#### Newton's Second Law: Force, Mass and Acceleration (ages 17-18)

A resultant force gives an acceleration in its own direction, with F = ma. Weight is mass times g, which is why objects of different mass fall together.

Ready when they can: Find the acceleration of a 2 kg object under a 6 N resultant force; Keep mass and weight apart, with the right units for each; Find the resultant force needed to slow a moving object at a stated rate.

https://lightmysky.com/learn/mathematics/newtons-second-law-force-mass-and-acceleration-mt_SKO85AcKdb

#### Friction and the Coefficient of Friction (ages 17-18)

Model friction as a force bounded by the coefficient times the normal reaction, and decide whether a body stays put or slides.

Ready when they can: State the inequality limiting friction and say when it becomes an equality; Decide whether a body on a horizontal surface moves under a given applied force; Explain what the coefficient of friction is a property of, and what the model leaves out.

https://lightmysky.com/learn/mathematics/friction-and-the-coefficient-of-friction-mt_EwFUd9N24W

#### Newton's Second Law in Two Dimensions (ages 17-18)

Resolve the forces along the direction of motion and perpendicular to it, then apply F = ma along that direction while the perpendicular components balance. This is what makes a slope problem solvable.

Ready when they can: Find the acceleration of a block sliding down a smooth slope; Resolve perpendicular to the slope to find the normal reaction; Handle a pulling force applied at an angle to the direction of travel.

https://lightmysky.com/learn/mathematics/newtons-second-law-in-two-dimensions-mt_yNUFF3lxlj

#### Connected Particles and Pulleys (ages 17-18)

Two bodies joined by a string share one acceleration and pull on each other equally and oppositely. Write F = ma for each body, then solve the two equations together for the acceleration and the tension.

Ready when they can: Write the equation of motion for each of two connected masses; Solve the pair for the shared acceleration and the tension; Explain why the tension is the same throughout a light string over a smooth pulley.

https://lightmysky.com/learn/mathematics/connected-particles-and-pulleys-mt_pZ6zV0RFdC

#### Motion on a Rough Inclined Plane (ages 17-18)

Resolve weight along and perpendicular to a slope, include friction in the correct direction, and find the acceleration or the angle at which sliding starts.

Ready when they can: Resolve the weight into components along and perpendicular to the slope and mark friction's direction; Find the acceleration of a body sliding down a rough slope; Derive the angle of friction at which a body is on the point of slipping.

https://lightmysky.com/learn/mathematics/motion-on-a-rough-inclined-plane-mt_0rBy66HFNO

#### Projectile Motion (ages 17-18)

Split the launch velocity into horizontal and vertical parts, then run constant velocity across and constant acceleration downwards, with time as the only quantity the two share. Range, greatest height and flight time follow.

Ready when they can: Split a launch speed and angle into horizontal and vertical components; Find the time of flight from the vertical motion, then the range from the horizontal; Say what the model assumes by leaving air resistance out.

https://lightmysky.com/learn/mathematics/projectile-motion-mt_O1C-QxCSJN

### Linear Algebra

https://lightmysky.com/learn/mathematics/areas/linear-algebra

#### Systems of Linear Equations and Their Solution Sets (ages 18-19)

A linear system has no solution, exactly one, or infinitely many, and nothing else. Reading which case you are in, and describing an infinite solution set, is the starting point for the whole subject.

Ready when they can: Classify a two-variable system by the geometry of its lines; Describe an infinite solution set with a free parameter; Give an inconsistent system and say what makes it inconsistent.

https://lightmysky.com/learn/mathematics/systems-of-linear-equations-and-their-solution-sets-mt_sQL6JfR7Te

#### Gaussian Elimination and Row Echelon Form (ages 18-19)

Reduce a system to echelon form with three row operations that never change the solution set, then read pivots, free variables and the full solution off the result.

Ready when they can: Carry a system to reduced row echelon form; Identify pivot and free columns and write the general solution; Say why each row operation preserves the solution set.

https://lightmysky.com/learn/mathematics/gaussian-elimination-and-row-echelon-form-mt_PZBce3UvRm

#### Matrix Multiplication and What It Represents (ages 18-19)

A matrix records a linear rule. Multiplying matrices composes the rules, which is why the product is defined by rows against columns and why order matters.

Ready when they can: Multiply two matrices and state when the product is defined; Give two matrices whose products in the two orders differ; Read a matrix-vector product as a combination of the columns.

https://lightmysky.com/learn/mathematics/matrix-multiplication-and-what-it-represents-mt_0fJOMPlCxr

#### The Inverse of a Matrix and When It Exists (ages 18-19)

An inverse undoes the rule a matrix applies. Only square matrices with full pivot count have one, and elimination both decides the question and computes the answer.

Ready when they can: Compute an inverse by row reducing the matrix beside the identity; State several equivalent conditions for invertibility; Solve a system with an inverse and say when that is a poor method.

https://lightmysky.com/learn/mathematics/the-inverse-of-a-matrix-and-when-it-exists-mt_1K6lcfMQ_b

#### Determinants and What They Measure (ages 18-19)

The determinant is the factor by which a map scales area or volume, with a sign for orientation. It vanishes exactly when the map collapses space, which is exactly when no inverse exists.

Ready when they can: Compute a determinant by cofactor expansion and by row reduction; Interpret a determinant as an area or volume scale factor; Connect a zero determinant to a system with no unique solution.

https://lightmysky.com/learn/mathematics/determinants-and-what-they-measure-mt_fWr2D_1BdM

#### LU Factorisation, Pivoting and the Cost of a Solve (ages 20-21)

Record Gaussian elimination as a product of two triangular matrices, add pivoting for stability, and count the operations each stage costs.

Ready when they can: Factor a matrix into lower and upper triangular factors and solve by two substitutions; Explain why partial pivoting is needed even when no pivot is exactly zero; Count the operations for a factorisation and for each extra right-hand side, and say why the split matters.

https://lightmysky.com/learn/mathematics/lu-factorisation-pivoting-and-the-cost-of-a-solve-mt_5Gg2v3Oxrr

#### Vector Spaces and Subspaces (ages 18-19)

Strip vectors down to the two operations and the axioms they satisfy, so that polynomials, matrices and functions count as vectors too. A subspace is a subset closed under both operations.

Ready when they can: Check the closure conditions to decide whether a subset is a subspace; Give an example of a vector space whose elements are not arrows; Show that the solutions of a homogeneous system form a subspace.

https://lightmysky.com/learn/mathematics/vector-spaces-and-subspaces-mt_Zrddx-E6_n

#### Linear Independence, Span and Basis (ages 18-19)

Span is everything you can reach by combining vectors; independence says none of them is redundant. A basis is a set that is both, so every element has exactly one expression.

Ready when they can: Decide independence by solving a homogeneous system; Describe the span of a set of vectors geometrically; Show that coordinates with respect to a basis are unique.

https://lightmysky.com/learn/mathematics/linear-independence-span-and-basis-mt_5RGbip9yC9

#### Dimension and the Rank-Nullity Theorem (ages 18-19)

Every basis of a space has the same size, which is its dimension. For a matrix, the rank and the nullity add to the number of columns, which explains the shape of every solution set met so far.

Ready when they can: Find a basis for the column space and for the null space of a matrix; State the rank-nullity theorem and check it on an example; Predict the number of free parameters in a solution set from the rank.

https://lightmysky.com/learn/mathematics/dimension-and-the-rank-nullity-theorem-mt_aMG8PcwPAR

#### Linear Maps and Their Matrices (ages 19-20)

A linear map respects addition and scaling. Once a basis is fixed, every such map is a matrix, and the matrix columns are the images of the basis vectors.

Ready when they can: Build the matrix of a rotation or projection from images of the basis vectors; Check linearity from the two defining properties; Identify the kernel and image of a map and relate them to null space and column space.

https://lightmysky.com/learn/mathematics/linear-maps-and-their-matrices-mt_pzrfiQFdto

#### Change of Basis (ages 19-20)

The same map has different matrices in different bases. A change-of-basis matrix converts coordinates, and similar matrices are the same map seen from two viewpoints.

Ready when they can: Convert coordinates between two bases with a transition matrix; Write the matrix of a map in a new basis by conjugating; Explain what stays the same about a map when the basis changes.

https://lightmysky.com/learn/mathematics/change-of-basis-mt_HTGuJhX484

#### Eigenvalues and Eigenvectors (ages 19-20)

Some directions survive a map unchanged except for scaling. Finding them means solving the characteristic equation, and they explain what the map does far better than its entries do.

Ready when they can: Find eigenvalues from the characteristic polynomial and eigenvectors from the null space; Interpret an eigenvector geometrically for a rotation, reflection or shear; Give a real matrix with no real eigenvalues and explain the geometry.

https://lightmysky.com/learn/mathematics/eigenvalues-and-eigenvectors-mt_TVqqaw11qa

#### Diagonalisation and Powers of a Matrix (ages 19-20)

When enough independent eigenvectors exist, the map is a diagonal matrix in the eigenbasis, which makes powers, long-run behaviour and matrix exponentials easy.

Ready when they can: Diagonalise a matrix and state the two factors involved; Compute a high power of a matrix through its diagonal form; Give a matrix that cannot be diagonalised and say what fails.

https://lightmysky.com/learn/mathematics/diagonalisation-and-powers-of-a-matrix-mt_w15uCVhdhX

#### Inner Products, Length and Orthogonality (ages 19-20)

An inner product gives a general space a notion of length and angle. Orthogonal sets are independent, and orthonormal ones make coordinates cheap to compute.

Ready when they can: Verify the inner product axioms for a given rule; Show that an orthogonal set of nonzero vectors is independent; Compute coordinates in an orthonormal basis with inner products alone.

https://lightmysky.com/learn/mathematics/inner-products-length-and-orthogonality-mt_X0HPRGto4W

#### Orthogonal Projection and Least Squares (ages 20-21)

Project a vector onto a subspace to get the closest point in it. Applied to an inconsistent system, this is the least squares solution, which is where regression comes from.

Ready when they can: Project a vector onto a subspace and verify the residual is orthogonal to it; Set up the normal equations for an inconsistent system; Explain why the least squares solution minimises the residual length.

https://lightmysky.com/learn/mathematics/orthogonal-projection-and-least-squares-mt_kGvRrYJrat

#### The Gram-Schmidt Process (ages 20-21)

Turn any basis into an orthonormal one by subtracting off projections onto what has already been built, which gives the QR factorisation used by numerical solvers.

Ready when they can: Orthonormalise a small basis by hand; State what the process preserves at every stage; Read the QR factorisation off the completed process.

https://lightmysky.com/learn/mathematics/the-gram-schmidt-process-mt_nkp231EA_E

#### Symmetric Matrices and the Spectral Theorem (ages 20-21)

A real symmetric matrix has real eigenvalues and an orthonormal eigenbasis. That single fact is behind quadratic forms, covariance matrices and principal axes.

Ready when they can: Diagonalise a symmetric matrix with an orthogonal matrix; Classify a quadratic form from the signs of its eigenvalues; Explain why symmetry forces eigenvectors for distinct eigenvalues to be orthogonal.

https://lightmysky.com/learn/mathematics/symmetric-matrices-and-the-spectral-theorem-mt_sdQv4m7Nbk

#### The Singular Value Decomposition (ages 20-21)

Every matrix, square or not, factors into a rotation, a scaling and another rotation. The singular values rank the directions by how much the map stretches them, which is how low-rank approximation works.

Ready when they can: Relate singular values to eigenvalues of the matrix times its transpose; Read the rank of a matrix off its singular values; Explain how truncating the decomposition gives a best low-rank approximation.

https://lightmysky.com/learn/mathematics/the-singular-value-decomposition-mt_UsUZbM9VRK

#### Iterative Methods for Large Linear Systems (ages 23-24)

For a large sparse system, elimination costs too much and the solution is approached instead of computed. Convergence is decided by the spectrum of the iteration, and preconditioning is the act of changing that spectrum.

Ready when they can: Run one step of a splitting method and state its convergence condition; Say why the conjugate gradient method needs a symmetric positive definite matrix; Explain what a preconditioner changes and why that helps.

https://lightmysky.com/learn/mathematics/iterative-methods-for-large-linear-systems-mt_FKkxKYVGYJ

### Calculus & Analysis

https://lightmysky.com/learn/mathematics/areas/calculus-and-analysis

#### The Gradient of a Curve as a Limit (ages 16-17)

See that a curve has a different gradient at every point, and that the gradient of a chord settles on a single value as the second point slides in. That limiting value is the gradient of the tangent.

Ready when they can: Compute chord gradients on y = x² for h = 1, 0.1 and 0.01 at x = 2; Say what number the chord gradients are approaching and why it is not reached; Explain why a curve has no single gradient the way a line does.

Needs first: Lines Meeting Circles: Tangents and Chords, Recognising Cubic, Reciprocal and Exponential Graphs.

https://lightmysky.com/learn/mathematics/the-gradient-of-a-curve-as-a-limit-mt_LAlhcwVjln

#### Differentiation from First Principles (ages 16-17)

Write the chord gradient as [f(x + h) - f(x)] / h, simplify it algebraically, and let h approach zero to get the derivative. This is the definition every rule later rests on.

Ready when they can: Differentiate f(x) = x² from first principles, showing the cancellation of h; Differentiate f(x) = x³ from first principles; Say why the h in the denominator can only be cancelled while h is not zero.

Needs first: The Gradient of a Curve as a Limit, Simplifying Algebraic Fractions.

https://lightmysky.com/learn/mathematics/differentiation-from-first-principles-mt_pdfPztEjw_

#### The Power Rule for Differentiating Polynomials (ages 17-18)

Differentiate any sum of powers of x with the rule that xⁿ becomes nxⁿ⁻¹, including negative and fractional powers once the term is rewritten as a power.

Ready when they can: Differentiate y = 4x³ - 7x + 2 term by term; Rewrite 1/x² and √x as powers before differentiating; Evaluate the derivative at a given x to get the gradient there.

Needs first: Differentiation from First Principles.

https://lightmysky.com/learn/mathematics/the-power-rule-for-differentiating-polynomials-mt_l7f4j44bR3

#### The Derivative as a Rate of Change (ages 17-18)

Read dy/dx as how fast one quantity changes per unit of another, with the units to match, so a derivative answers questions about cost per item, litres per second or metres per second.

Ready when they can: State the units of dV/dt when V is in litres and t in seconds; Interpret a derivative of zero in a real context; Say what a negative derivative means for a quantity that is being modelled.

Needs first: The Power Rule for Differentiating Polynomials, Compound Units.

https://lightmysky.com/learn/mathematics/the-derivative-as-a-rate-of-change-mt_RqyLE3jrAW

#### Tangents and Normals to a Curve (ages 17-18)

Find the equation of the tangent at a point on a curve from the derivative there, and the normal from the perpendicular gradient.

Ready when they can: Find the tangent to y = x² - 3x at the point where x = 2; Find the normal at the same point and check the gradients multiply to -1; Find the point where a given tangent meets the x-axis.

Needs first: The Derivative as a Rate of Change, Parallel and Perpendicular Lines in Coordinates.

https://lightmysky.com/learn/mathematics/tangents-and-normals-to-a-curve-mt_BzMw7IT6kp

#### Increasing and Decreasing Functions (ages 17-18)

Use the sign of the derivative to say where a curve rises and where it falls, which turns a question about shape into an inequality in x.

Ready when they can: Find the interval where y = x² - 6x is decreasing; Show that a given cubic is increasing for all x; Match the sign of f'(x) to the parts of a sketched curve.

Needs first: Tangents and Normals to a Curve, Solving Quadratic Inequalities.

https://lightmysky.com/learn/mathematics/increasing-and-decreasing-functions-mt_KOrXxQvBrZ

#### Stationary Points and the Second Derivative (ages 17-18)

Solve f'(x) = 0 to locate maximum, minimum and inflection points, then use the sign of f''(x) to decide which is which.

Ready when they can: Find the stationary points of y = x³ - 3x and classify each one; Use f''(x) to distinguish a maximum from a minimum; Explain what f''(x) = 0 leaves undecided and what to check instead.

Needs first: Increasing and Decreasing Functions, Sketching a Curve from Its Factorised Form.

https://lightmysky.com/learn/mathematics/stationary-points-and-the-second-derivative-mt_VbGJEFFgfs

#### Optimisation with Calculus (ages 17-18)

Turn a worded problem into one function of one variable, use a constraint to remove the second variable, then differentiate to find the best value and justify that it is a maximum or minimum.

Ready when they can: Use a fixed perimeter to write area as a function of one side, then maximise it; Minimise the surface area of an open box of fixed volume; Check that the stationary point found is the kind the question asked for.

Needs first: Stationary Points and the Second Derivative, Rearranging Formulae When the Subject Appears Twice.

https://lightmysky.com/learn/mathematics/optimisation-with-calculus-mt_9I0ql39Lzw

#### Integration as the Reverse of Differentiation (ages 17-18)

Recover a function from its derivative by raising the power and dividing, and carry the constant of integration that differentiation destroyed. Use a known point to pin that constant down.

Ready when they can: Integrate 6x² - 4x and check the answer by differentiating it; Explain why every answer carries + c; Find the particular function whose derivative is 2x and which passes through (1, 5).

Needs first: Optimisation with Calculus, The Power Rule for Differentiating Polynomials.

https://lightmysky.com/learn/mathematics/integration-as-the-reverse-of-differentiation-mt_edtk3ArxRk

#### The Definite Integral and the Area Under a Curve (ages 17-18)

Estimate the area under a curve with rectangles, then evaluate it exactly by substituting the limits into the antiderivative. Areas below the axis come out negative and have to be handled separately.

Ready when they can: Estimate an area with rectangles and compare it with the exact value; Evaluate a definite integral using square-bracket notation; Split an integral at a root so that area below the axis is counted correctly.

https://lightmysky.com/learn/mathematics/the-definite-integral-and-the-area-under-a-curve-mt_S2IO2S7kgd

#### Areas Between Two Curves (ages 17-18)

Find where two curves meet, then integrate the difference of the two functions between those limits to get the area enclosed.

Ready when they can: Find the intersection points of a line and a parabola; Integrate the difference of the two functions between those limits; Say which function goes first in the subtraction and why.

https://lightmysky.com/learn/mathematics/areas-between-two-curves-mt_lDBZmnLK1b

#### One-Sided Limits and When a Limit Fails to Exist (ages 18-19)

Treat a limit as a two-sided agreement: what the outputs approach from the left has to match what they approach from the right. Where the two disagree, or the outputs grow without bound, no limit exists.

Ready when they can: Read the left and right limits off a piecewise graph at a jump; Give a function whose limit at a point fails because the one-sided values differ; Separate a limit that is infinite from one that fails to exist at all.

https://lightmysky.com/learn/mathematics/one-sided-limits-and-when-a-limit-fails-to-exist-mt__L0B_WQq-P

#### The Limit Laws and Indeterminate Forms (ages 18-19)

Combine limits with the rules for sums, products and quotients, and recognise the forms those rules leave undecided. A 0/0 quotient is a signal to factorise, rationalise or squeeze.

Ready when they can: Evaluate a limit by cancelling a removable factor; Clear a 0/0 form in a surd expression by rationalising; Trap a function between two others to force a limit by the squeeze theorem.

https://lightmysky.com/learn/mathematics/the-limit-laws-and-indeterminate-forms-mt_rAJs-V4Jlx

#### Locating Roots and Iterative Methods (ages 17-18)

Trap a root between two values by a change of sign, then rearrange the equation into the form x = g(x) and iterate from a starting value until the digits stop moving.

Ready when they can: Use a sign change to show a root lies in a given interval; Rearrange an equation into an iterative formula; Run an iteration to a stated accuracy and justify stopping.

https://lightmysky.com/learn/mathematics/locating-roots-and-iterative-methods-mt_2COO6TWerM

#### The Newton-Raphson Method (ages 17-18)

Follow the tangent at the current guess down to the x-axis to get the next guess, which is x - f(x)/f'(x). Note when it fails: a nearly flat tangent throws the next guess far away.

Ready when they can: Apply one step of the formula from a given starting value; Explain the formula as the x-intercept of a tangent; Describe a starting value for which the method fails and say why.

https://lightmysky.com/learn/mathematics/the-newton-raphson-method-mt_jkjJre5ETd

#### The Trapezium Rule (ages 17-18)

Estimate a definite integral by slicing the region into trapezia of equal width, and use the curvature to say whether the estimate is above or below the true value.

Ready when they can: Estimate an integral with four strips of equal width; Halve the strip width and describe what happens to the error; Decide from a sketch whether the estimate is too big or too small.

https://lightmysky.com/learn/mathematics/the-trapezium-rule-mt_rAlJ1WIRmZ

#### Continuity and the Intermediate Value Theorem (ages 18-19)

Define continuity at a point as the limit agreeing with the value there, classify the ways that can fail, and use the intermediate value theorem to guarantee a root inside an interval.

Ready when they can: State the three conditions continuity at a point requires; Classify a discontinuity as removable, jump or infinite; Use a sign change on a continuous function to guarantee a root.

https://lightmysky.com/learn/mathematics/continuity-and-the-intermediate-value-theorem-mt_kaQR6cWjbV

#### The Epsilon-Delta Definition of a Limit (ages 18-19)

State what a limit claims with no appeal to motion: for every tolerance around the limiting value there is a distance around the point that keeps outputs inside it. Prove a simple limit by producing that distance.

Ready when they can: Read an epsilon-delta statement as a challenge and a response; Produce a delta that works for a given epsilon on a linear function; Explain why the definition has to hold for every epsilon, not one small one.

https://lightmysky.com/learn/mathematics/the-epsilon-delta-definition-of-a-limit-mt_jFzRYQzCmk

#### The Product and Quotient Rules (ages 18-19)

Differentiate a product or a quotient without multiplying it out, and see where each rule comes from in the difference quotient.

Ready when they can: Differentiate x² sin x and simplify the result; Differentiate a quotient and say which factor belongs on top; Show by counterexample that the derivative of a product is not the product of the derivatives.

https://lightmysky.com/learn/mathematics/the-product-and-quotient-rules-mt_NJ7INJ0jfv

#### The Chain Rule (ages 18-19)

Differentiate a composition by multiplying the rate of the outer function by the rate of the inner one. The rule is what makes substitution, related rates and implicit differentiation possible.

Ready when they can: Differentiate (3x² + 1)⁵ and name the inner and outer functions; Apply the rule twice on a triple composition; Explain the rule as two rates multiplying, using units.

https://lightmysky.com/learn/mathematics/the-chain-rule-mt_kdhl4dmwJn

#### Derivatives of Exponential, Logarithmic and Trigonometric Functions (ages 18-19)

Establish the derivatives of the standard non-polynomial functions, including why e is the base that makes the exponential its own derivative.

Ready when they can: Differentiate e^(3x), ln(5x) and cos(2x); Say what is special about the base e in terms of gradients; Use the derivative of sin x to explain the small-angle approximation.

https://lightmysky.com/learn/mathematics/derivatives-of-exponential-logarithmic-and-trigonometric-functions-mt_695WPZKADT

#### Implicit Differentiation and Derivatives of Inverse Functions (ages 18-19)

Differentiate a relation that is not solved for y, and use the same move to get the derivative of an inverse function from the derivative of the original.

Ready when they can: Find dy/dx for x² + y² = 25 and read the gradient at a point on the circle; Derive the derivative of arcsin x from sin y = x; Explain why dy/dx appears as a factor whenever y is differentiated.

https://lightmysky.com/learn/mathematics/implicit-differentiation-and-derivatives-of-inverse-functions-mt_P4ABBGsKFT

#### Related Rates (ages 18-19)

Link two changing quantities by an equation, differentiate the equation with respect to time, and solve for the rate you cannot measure directly.

Ready when they can: Set up a relation between two quantities before differentiating anything; Differentiate a geometric formula with respect to time; Substitute the instantaneous values only after differentiating, and say why.

https://lightmysky.com/learn/mathematics/related-rates-mt_3XTIPt8Vmf

#### The Mean Value Theorem (ages 18-19)

Over an interval where a function is continuous and differentiable, some interior point has instantaneous rate equal to the average rate across the whole interval. Most facts linking a derivative to a function's behaviour rest on this.

Ready when they can: State the hypotheses and find the guaranteed point for a given function; Give a function that fails the theorem and identify the hypothesis it breaks; Use the theorem to argue that a zero derivative on an interval forces a constant function.

https://lightmysky.com/learn/mathematics/the-mean-value-theorem-mt_09iApYVelx

#### L'Hopital's Rule and Comparing Growth Rates (ages 18-19)

Resolve 0/0 and infinity over infinity limits by differentiating numerator and denominator separately, and use the result to rank how fast logarithms, powers and exponentials grow.

Ready when they can: Apply the rule twice on a limit that stays indeterminate after one pass; Rewrite a product or power indeterminate form so the rule applies; Rank ln x, x^k and e^x by growth and support the ranking with a limit.

https://lightmysky.com/learn/mathematics/lhopitals-rule-and-comparing-growth-rates-mt_Ai-A2sPIoE

#### Riemann Sums and the Definite Integral as a Limit (ages 19-20)

Build the definite integral as the limit of sums of rectangle areas, with sample points anywhere in each subinterval. This is the definition every later property of the integral is argued from.

Ready when they can: Write a Riemann sum with n subintervals in sigma notation for a given function; Compute left, right and midpoint sums for the same integral and compare them; Explain how refining the partition removes the dependence on where samples are taken.

https://lightmysky.com/learn/mathematics/riemann-sums-and-the-definite-integral-as-a-limit-mt_pwa2SRU6P9

#### The Fundamental Theorem of Calculus (ages 19-20)

Both halves: differentiating an accumulation function returns the integrand, and a definite integral can be evaluated from any antiderivative. This is why the two calculus operations undo each other.

Ready when they can: Differentiate an integral with a variable upper limit; Evaluate a definite integral by antidifferentiation and justify the step; Explain why an accumulation function is continuous even when the integrand is not.

https://lightmysky.com/learn/mathematics/the-fundamental-theorem-of-calculus-mt_EsS_ovdz2A

#### Integration by Substitution (ages 19-20)

Reverse the chain rule by renaming an inner function, changing the differential and, for a definite integral, changing the limits with it.

Ready when they can: Choose u so that du absorbs the leftover factor in the integrand; Convert the limits of a definite integral when substituting; Say why a substitution fails when the required factor is missing.

https://lightmysky.com/learn/mathematics/integration-by-substitution-mt_jH-j_XsdC7

#### Integration by Parts (ages 19-20)

Reverse the product rule to trade one integral for another that is easier, and choose the parts so the trade is an improvement.

Ready when they can: Choose u and dv so the new integral is simpler than the original; Apply the method twice and solve for the original integral when it reappears; Integrate ln x by taking dv = dx.

https://lightmysky.com/learn/mathematics/integration-by-parts-mt_v6jZVs2_tf

#### Trigonometric Integrals and Trigonometric Substitution (ages 19-20)

Handle powers of sine and cosine with identities, and clear expressions such as √(a² - x²) by substituting a trigonometric function for x.

Ready when they can: Reduce an odd power of sine by splitting off one factor and substituting; Choose the substitution that matches a sum or difference of squares; Convert the answer back to the original variable using a right triangle.

https://lightmysky.com/learn/mathematics/trigonometric-integrals-and-trigonometric-substitution-mt_JqysS41psg

#### Partial Fractions for Rational Integrands (ages 19-20)

Split a rational function into simpler fractions whose integrals are logarithms and arctangents, after checking the degree of the numerator first.

Ready when they can: Divide first when the numerator has degree at least that of the denominator; Set up the correct form for a repeated linear factor; Integrate the resulting pieces and combine the logarithms.

https://lightmysky.com/learn/mathematics/partial-fractions-for-rational-integrands-mt_PA8qxs424c

#### Improper Integrals and Their Convergence (ages 19-20)

Give meaning to an integral with an infinite limit or an unbounded integrand by evaluating a proper integral and taking a limit, then decide whether the result is finite.

Ready when they can: Rewrite an infinite-range integral as a limit and evaluate it; Decide convergence for 1/x^p on [1, ∞) and say where the cut-off sits; Handle an integrand that blows up inside the interval by splitting it.

https://lightmysky.com/learn/mathematics/improper-integrals-and-their-convergence-mt_gvtZPFRA6Z

#### Vector-Valued Functions and Motion Along a Curve (ages 19-20)

Describe a path in space by a vector that depends on one parameter. Differentiating gives velocity and acceleration, and the arc length is an integral of speed.

Ready when they can: Differentiate a vector-valued function componentwise to get velocity; Find the unit tangent at a point on a space curve; Set up the arc length of a curve as an integral of speed.

https://lightmysky.com/learn/mathematics/vector-valued-functions-and-motion-along-a-curve-mt_Xcjt6exMy3

#### Functions of Several Variables and Level Curves (ages 19-20)

Read a function of two inputs as a surface, and read the surface through its level curves. A contour map is the working picture for the rest of the spine.

Ready when they can: Sketch level curves for a function of two variables; Read steepness and flat regions off a contour map; State the domain of a function of two variables and draw it in the plane.

https://lightmysky.com/learn/mathematics/functions-of-several-variables-and-level-curves-mt_u04fZ_XiJ8

#### Partial Derivatives (ages 19-20)

Differentiate with respect to one variable while holding the others fixed. Mixed second partials agree for the functions met in practice, which is a statement worth noticing rather than assuming.

Ready when they can: Compute both first partials of a function of two variables; Interpret a partial derivative as a slope along a coordinate direction; Check that the two mixed second partials agree for a given function.

https://lightmysky.com/learn/mathematics/partial-derivatives-mt_tu11fd9Xk9

#### Tangent Planes and Linear Approximation (ages 19-20)

Replace a surface near a point by the plane its partials define, and use that plane to estimate values and propagate small errors.

Ready when they can: Write the equation of the tangent plane at a point on a surface; Estimate a function value near a known point with the linear approximation; Give a function that has both partials at a point but no tangent plane.

https://lightmysky.com/learn/mathematics/tangent-planes-and-linear-approximation-mt_EYMcjChX_m

#### The Multivariable Chain Rule (ages 19-20)

Differentiate a composition when several inputs each depend on other variables, by summing one contribution per path through the dependency diagram.

Ready when they can: Draw the dependency diagram and read the terms off it; Differentiate z = f(x, y) with x and y both functions of t; Handle two intermediate variables and two independent ones.

https://lightmysky.com/learn/mathematics/the-multivariable-chain-rule-mt_CHSHdNxPmJ

#### Directional Derivatives and the Gradient (ages 19-20)

The rate of change in an arbitrary direction is the dot product of the gradient with a unit vector, so the gradient points the steepest way uphill and sits perpendicular to level curves.

Ready when they can: Compute a directional derivative from the gradient and a unit direction; State the direction of fastest increase and its rate; Show that the gradient is perpendicular to the level curve through a point.

https://lightmysky.com/learn/mathematics/directional-derivatives-and-the-gradient-mt_LW_KckY5Ad

#### Critical Points and Optimisation in Two Variables (ages 19-20)

Find points where the gradient vanishes and classify them with the second derivative test, including the saddle point, which has no one-variable analogue.

Ready when they can: Locate all critical points by solving the gradient equal to zero; Classify a critical point with the discriminant of the second partials; Describe a saddle and say why one-variable tests miss it.

https://lightmysky.com/learn/mathematics/critical-points-and-optimisation-in-two-variables-mt_4qB5pAGeuR

#### Lagrange Multipliers (ages 19-20)

Optimise subject to a constraint by setting the gradient of the objective parallel to the gradient of the constraint, which is the moment the level curves touch.

Ready when they can: Set up the multiplier equations for a constrained problem; Explain the tangency condition in terms of level curves; Compare the multiplier method with substituting the constraint directly.

https://lightmysky.com/learn/mathematics/lagrange-multipliers-mt_0RPOBWZ1gs

#### Double Integrals over General Regions (ages 19-20)

Integrate over a plane region by iterating two single integrals, with the inner limits describing the region. Choosing the order of integration is often the whole problem.

Ready when they can: Set up an iterated integral for a region bounded by two curves; Reverse the order of integration and redraw the region to find the new limits; Compute a volume under a surface over a bounded region.

https://lightmysky.com/learn/mathematics/double-integrals-over-general-regions-mt_UKS9_AhAWw

#### Volumes of Revolution: Disks, Washers and Shells (ages 19-20)

Set up a volume as an integral of cross-sections, and choose between slicing perpendicular to the axis and using cylindrical shells based on which integral is easier.

Ready when they can: Write the integral for a solid generated by rotating a region about the x-axis; Use washers when the solid has a hole and identify both radii; Say when shells give a simpler integral than disks for the same solid.

https://lightmysky.com/learn/mathematics/volumes-of-revolution-disks-washers-and-shells-mt_mzZ22MkWD4

#### Arc Length and the Area of a Surface of Revolution (ages 19-20)

Set up the integrals that measure the length of a plane curve and the area swept when it is spun about an axis.

Ready when they can: Derive the arc length integrand from a limit of straight-line approximations; Compute the arc length of a curve given in Cartesian and in parametric form; Set up and evaluate a surface-of-revolution area integral about each axis.

https://lightmysky.com/learn/mathematics/arc-length-and-the-area-of-a-surface-of-revolution-mt_W4uujT9Z1t

#### Sequences and Their Limits (ages 19-20)

Treat a sequence as a function on the positive integers and ask what its terms approach. Monotone bounded sequences converge, which is the first place completeness is doing real work.

Ready when they can: Decide convergence for a sequence given by a formula in n; Show a recursively defined sequence is increasing and bounded above; Distinguish a sequence from the series formed by summing it.

https://lightmysky.com/learn/mathematics/sequences-and-their-limits-mt_PQl3Q6n5dc

#### Infinite Series and the Geometric Series (ages 19-20)

Define the sum of a series as the limit of its partial sums, work out the geometric and telescoping cases exactly, and use the term test to rule out convergence.

Ready when they can: Write the partial sum of a telescoping series and take its limit; State the condition under which a geometric series has a finite sum; Show that terms not tending to zero forces divergence, and that the converse fails.

https://lightmysky.com/learn/mathematics/infinite-series-and-the-geometric-series-mt_EPE-ERFFQt

#### Convergence Tests for Series of Positive Terms (ages 19-20)

Decide convergence with the integral, comparison, limit comparison, ratio and root tests, and choose the test that matches the shape of the terms.

Ready when they can: Match a p-series or a factorial to the test that settles it fastest; Use limit comparison against a known series and justify the comparison; Say what the ratio test leaves undecided when its limit equals 1.

https://lightmysky.com/learn/mathematics/convergence-tests-for-series-of-positive-terms-mt_8N49Q4BlO8

#### Alternating Series and Absolute Convergence (ages 19-20)

Handle series whose terms change sign: the alternating test, the error bound from the first omitted term, and the difference between converging absolutely and converging only conditionally.

Ready when they can: Apply the alternating series test and bound the truncation error; Give a series that converges but whose absolute version does not; Explain why absolute convergence is the stronger claim.

https://lightmysky.com/learn/mathematics/alternating-series-and-absolute-convergence-mt_sk6F4n1USH

#### Power Series and the Radius of Convergence (ages 19-20)

Read a power series as a function defined where it converges, find its radius with the ratio test, and check the endpoints separately.

Ready when they can: Find the radius of convergence of a given power series; Test both endpoints and state the full interval; Differentiate or integrate a power series term by term inside its radius.

https://lightmysky.com/learn/mathematics/power-series-and-the-radius-of-convergence-mt_RnYb0JLKbD

#### Taylor and Maclaurin Series (ages 19-20)

Build the power series of a function from its derivatives at a point, use the remainder to say how good a truncation is, and reuse the standard expansions instead of starting over.

Ready when they can: Derive the Maclaurin series of e^x, sin x or 1/(1 - x); Obtain a new series by substituting into or differentiating a known one; Bound the error of a Taylor polynomial with the remainder term.

https://lightmysky.com/learn/mathematics/taylor-and-maclaurin-series-mt_SgI9Pn9RIO

#### Double Integrals in Polar Coordinates (ages 20-21)

Integrate over circular regions by switching to polar coordinates, where the area element carries an extra factor of r.

Ready when they can: Convert a region and an integrand to polar form; Explain where the factor of r in the area element comes from; Evaluate an integral over a disc or an annulus.

https://lightmysky.com/learn/mathematics/double-integrals-in-polar-coordinates-mt_93e-KSzQMT

#### Polynomial Interpolation and Its Error Term (ages 20-21)

Fit the unique polynomial through given points, build it in Lagrange and Newton form, and bound how far it strays between the points.

Ready when they can: Construct an interpolating polynomial in both Lagrange and divided-difference form; State the error term and use it to bound the interpolation error on an interval; Show with a worked example why more equally spaced points can make the fit worse.

https://lightmysky.com/learn/mathematics/polynomial-interpolation-and-its-error-term-mt_NSnzY9Xodd

#### Numerical Quadrature: Newton-Cotes and Adaptive Rules (ages 20-21)

Derive quadrature rules by integrating an interpolating polynomial, compare their error orders, and refine only where the integrand misbehaves.

Ready when they can: Derive the trapezium and Simpson rules by integrating interpolating polynomials; Compare error orders and predict how halving the step changes each error; Explain when an adaptive rule beats a uniform one and how it decides where to refine.

https://lightmysky.com/learn/mathematics/numerical-quadrature-newton-cotes-and-adaptive-rules-mt_fT5kRCUiD5

#### The Completeness Axiom: Suprema and Infima (ages 20-21)

The rationals have gaps and the reals do not. Completeness is stated as every bounded set having a least upper bound, and it is the axiom every later theorem in analysis is traced back to.

Ready when they can: Find the supremum of a set that has no maximum; Show that the rationals fail the least-upper-bound property; Use the supremum in an argument rather than the maximum.

https://lightmysky.com/learn/mathematics/the-completeness-axiom-suprema-and-infima-mt_xjI-pIfh95

#### Convergence of Sequences, Rigorously (ages 20-21)

Prove convergence from the definition: for every tolerance there is a point in the sequence past which every term stays inside it. Limit laws become theorems with proofs rather than rules to apply.

Ready when they can: Prove a stated limit by producing N for an arbitrary epsilon; Prove that a limit is unique; Prove one of the limit laws from the definition.

https://lightmysky.com/learn/mathematics/convergence-of-sequences-rigorously-mt_yB5M-DCH8V

#### Cauchy Sequences and the Bolzano-Weierstrass Theorem (ages 20-21)

Terms that eventually crowd together converge, in the reals but not in the rationals. Every bounded sequence has a convergent subsequence, which is the workhorse behind existence proofs.

Ready when they can: Show a sequence is Cauchy without naming its limit; Give a Cauchy sequence of rationals with no rational limit; Extract a convergent subsequence from a bounded sequence.

https://lightmysky.com/learn/mathematics/cauchy-sequences-and-the-bolzano-weierstrass-theorem-mt_nreDylVkSU

#### Continuity and Uniform Continuity (ages 20-21)

Continuity as a sequence or epsilon-delta condition, then the stronger version where one delta works across the whole domain. A continuous function on a closed bounded interval is uniformly continuous and attains its bounds.

Ready when they can: Prove continuity of a function at a point from the definition; Give a continuous function that is not uniformly continuous, with the reason; State the extreme value theorem and where its hypotheses are used.

https://lightmysky.com/learn/mathematics/continuity-and-uniform-continuity-mt_plWc9raOwz

#### Differentiability and the Theorems Behind the Rules (ages 20-21)

Define the derivative as a limit, prove differentiability implies continuity, and prove Rolle and the mean value theorem. The rules used all year get their justification here.

Ready when they can: Prove that differentiability at a point forces continuity there; Give a continuous function that is not differentiable and say where the definition fails; Prove the mean value theorem from Rolle's theorem.

https://lightmysky.com/learn/mathematics/differentiability-and-the-theorems-behind-the-rules-mt_1xLEeoA69z

#### The Riemann Integral and When a Function Is Integrable (ages 20-21)

Define the integral by upper and lower sums and call a function integrable when the two meet. Continuous functions qualify; a function that is discontinuous everywhere need not.

Ready when they can: Compute upper and lower sums for a partition and compare them; State the criterion for integrability in terms of refinements; Give a bounded function that is not Riemann integrable.

https://lightmysky.com/learn/mathematics/the-riemann-integral-and-when-a-function-is-integrable-mt_Ahl2MYIA4N

#### Pointwise and Uniform Convergence (ages 20-21)

A sequence of functions can converge at every point and still lose continuity in the limit. Uniform convergence is the stronger condition that preserves continuity and permits term-by-term integration.

Ready when they can: Give a sequence of continuous functions with a discontinuous pointwise limit; State the difference between the two definitions in terms of quantifier order; Say what uniform convergence licenses that pointwise convergence does not.

https://lightmysky.com/learn/mathematics/pointwise-and-uniform-convergence-mt_iAGk1ML5MA

#### Triple Integrals and Coordinates for Solids (ages 20-21)

Integrate over a solid region, and choose cylindrical or spherical coordinates when the solid has an axis or a centre of symmetry.

Ready when they can: Set up a triple integral with the limits describing a solid; Choose between cylindrical and spherical coordinates for a given solid; State the volume element in each coordinate system and where its factors come from.

https://lightmysky.com/learn/mathematics/triple-integrals-and-coordinates-for-solids-mt_RFeK8LD_jT

#### Change of Variables and the Jacobian (ages 20-21)

Change coordinates in a multiple integral, and see the Jacobian determinant as the local factor by which area or volume is stretched.

Ready when they can: Compute a Jacobian and use it to transform a double integral to easier coordinates; Recover the polar, cylindrical and spherical area elements as Jacobians rather than as memorised facts; Design a substitution that turns an awkward region into a rectangle.

https://lightmysky.com/learn/mathematics/change-of-variables-and-the-jacobian-mt_1_LRE2cJft

#### Vector Fields and Line Integrals (ages 20-21)

Attach a vector to every point of a region, then integrate along a curve to accumulate work done by the field or mass along a wire.

Ready when they can: Sketch a simple vector field and describe its flow; Parameterise a curve and evaluate the work integral along it; Distinguish integrating a scalar along a curve from integrating a field along it.

https://lightmysky.com/learn/mathematics/vector-fields-and-line-integrals-mt_VZxKEmsVgO

#### Conservative Fields and Path Independence (ages 20-21)

Some fields are gradients of a potential function. For those, the line integral depends only on the endpoints, and there is a test to recognise them.

Ready when they can: Test a field for the mixed-partial condition on a simply connected region; Recover a potential function from a conservative field; Explain why the integral around any closed loop of a conservative field is zero.

https://lightmysky.com/learn/mathematics/conservative-fields-and-path-independence-mt_5djKpI5F33

#### Green's Theorem in the Plane (ages 20-21)

Trade a line integral around a closed plane curve for a double integral of a derivative expression over the region inside it. The first of three theorems with the same shape.

Ready when they can: State the theorem with the orientation convention for the boundary; Convert a circulation integral into a double integral and evaluate it; Use the theorem to compute an area from a boundary integral.

https://lightmysky.com/learn/mathematics/greens-theorem-in-the-plane-mt_UDgivmPVEJ

#### Divergence and Curl (ages 20-21)

Two derivative operations on a field: divergence measures net outflow at a point, curl measures local rotation. Both are the language of the theorems that follow.

Ready when they can: Compute the divergence and curl of a given field; Describe the physical reading of each at a point; Show that a conservative field has zero curl.

https://lightmysky.com/learn/mathematics/divergence-and-curl-mt_JbjW8WKOPE

#### Surface Integrals and Flux (ages 20-21)

Parameterise a surface, build its area element from a cross product, and integrate a field through it to measure flux.

Ready when they can: Parameterise a surface and compute its area element; Choose an orientation and say what the sign of the flux means; Evaluate the flux of a field through a plane or a sphere.

https://lightmysky.com/learn/mathematics/surface-integrals-and-flux-mt_b3FIxOVaTO

#### Stokes' Theorem and the Divergence Theorem (ages 20-21)

Both theorems say that integrating a derivative over a region equals integrating the original object over its boundary. With Green's theorem and the fundamental theorem, they are one statement in four settings.

Ready when they can: State each theorem and identify the region and its boundary; Convert a surface flux integral into a triple integral of divergence; Explain how all four theorems in the course share one form.

https://lightmysky.com/learn/mathematics/stokes-theorem-and-the-divergence-theorem-mt_sRojZcrw-q

#### Sigma-Algebras and Measurable Sets (ages 22-23)

A size cannot be assigned to every subset of the line, so the first move is to fix the collection of sets the size will be defined on. A sigma-algebra is closed under complement and countable union, which is exactly what limit arguments later need.

Ready when they can: Check whether a given collection of sets is a sigma-algebra; Describe the Borel sigma-algebra by what generates it, and say why generation needs an argument; Say why closure under countable unions, rather than finite unions, is the property that matters.

https://lightmysky.com/learn/mathematics/sigma-algebras-and-measurable-sets-mt_cpvegazufk

#### Outer Measure and the Construction of Lebesgue Measure (ages 22-23)

Cover a set by intervals, take the cheapest cover, and every subset gets an outer measure. The Caratheodory condition then selects the sets on which that outer measure is additive, and those sets are the measurable ones.

Ready when they can: Compute the outer measure of a countable set and of an interval; State the Caratheodory condition and use it to test a set for measurability; Describe how a non-measurable set is built and which axiom the construction relies on.

https://lightmysky.com/learn/mathematics/outer-measure-and-the-construction-of-lebesgue-measure-mt_6u5_Um71wE

#### Measurable Functions and Approximation by Simple Functions (ages 22-23)

A function is measurable when the preimage of every interval is a measurable set. Every non-negative measurable function is an increasing limit of simple functions, and that staircase is what makes an integral definable in stages.

Ready when they can: Test measurability using preimages of open rays; Build an increasing sequence of simple functions converging to a given non-negative function; Show that a pointwise limit of measurable functions stays measurable, which fails for continuous functions.

https://lightmysky.com/learn/mathematics/measurable-functions-and-approximation-by-simple-functions-mt_VwNRjXA7ro

#### The Lebesgue Integral and What It Repairs (ages 22-23)

Define the integral first for simple functions, then as a supremum over the simple functions underneath. Functions the Riemann theory cannot touch become integrable, and the value agrees with the Riemann integral wherever that one exists.

Ready when they can: Integrate a simple function directly from its defining partition; Integrate the indicator function of the rationals and say where the Riemann definition stalls; State how the two integrals relate on a bounded interval.

https://lightmysky.com/learn/mathematics/the-lebesgue-integral-and-what-it-repairs-mt_KO92nLc5YU

#### Monotone Convergence, Fatou and Dominated Convergence (ages 22-24)

Three theorems that say when a limit may be moved inside an integral, each with its own price. They are the reason this integral, and not the earlier one, is the one used in probability and in partial differential equations.

Ready when they can: Apply monotone convergence and point at the step where monotonicity is used; Give a sequence for which Fatou's inequality is strict; Find a dominating function for a given sequence, or show that none exists.

https://lightmysky.com/learn/mathematics/monotone-convergence-fatou-and-dominated-convergence-mt_7n6ZDkHeBe

#### Product Measure and Fubini's Theorem (ages 22-24)

Two measure spaces combine into one, and an integral over the product can be done one variable at a time. The hypotheses of the theorem say exactly when the order of integration is free.

Ready when they can: State the difference between the Tonelli and Fubini hypotheses; Exchange the order of a double integral and justify the exchange; Give an example where the two iterated integrals differ, and name the hypothesis that fails.

https://lightmysky.com/learn/mathematics/product-measure-and-fubinis-theorem-mt_1VzzVmMjTB

#### Lp Spaces and the Inequalities They Rest On (ages 22-24)

Functions with integrable p-th power form a normed space once functions that agree almost everywhere are treated as equal. Holder's and Minkowski's inequalities are what make the norm behave like a length.

Ready when they can: Use Holder's inequality to bound the integral of a product; Explain the identification of functions agreeing almost everywhere and why the norm forces it; Say what makes the case p equal to 2 different from every other p.

https://lightmysky.com/learn/mathematics/lp-spaces-and-the-inequalities-they-rest-on-mt_Qd8jU26qgE

#### Normed Spaces, Completeness and Banach Spaces (ages 22-24)

A vector space with a length function, plus the question of whether every Cauchy sequence in it converges. Completeness is what lets an existence proof finish by taking a limit and knowing the limit is still in the space.

Ready when they can: Verify the norm axioms for a proposed norm; Give a normed space that is not complete and name the limit it is missing; Explain why all norms agree in finite dimensions and why that argument fails in infinite dimensions.

https://lightmysky.com/learn/mathematics/normed-spaces-completeness-and-banach-spaces-mt_y_jueKnovX

#### Bounded Linear Operators and the Operator Norm (ages 23-24)

For a linear map between normed spaces, continuity and boundedness turn out to be the same condition. The operator norm records the worst stretching the map can perform on a unit vector.

Ready when they can: Prove that a linear map is continuous exactly when it is bounded; Compute the operator norm of a multiplication or integral operator; Give an unbounded linear map and explain why differentiation is the standard example.

https://lightmysky.com/learn/mathematics/bounded-linear-operators-and-the-operator-norm-mt_Qi_mbSNMMx

#### Baire Category and the Uniform Boundedness Principle (ages 23-24)

In a complete space, a countable union of nowhere dense sets cannot fill the space. That one fact upgrades pointwise bounds on a family of operators into a single uniform bound, and it is also what makes a surjective bounded operator an open map.

Ready when they can: State the category theorem and point at the step where completeness is used; Derive a uniform bound from pointwise bounds on a family of operators; Say what the open mapping and closed graph theorems add to the same argument.

https://lightmysky.com/learn/mathematics/baire-category-and-the-uniform-boundedness-principle-mt_11Rd73trAX

#### The Hahn-Banach Theorem and the Dual Space (ages 23-24)

A bounded linear functional defined on a subspace extends to the whole space without growing in norm. The dual space these functionals populate is what makes it possible to argue about a vector by testing it against everything.

Ready when they can: State the extension theorem and say what quantity is preserved; Use a functional to separate a point from a closed subspace; Identify the dual of a familiar sequence space or function space.

https://lightmysky.com/learn/mathematics/the-hahn-banach-theorem-and-the-dual-space-mt_pJuHFxkvjS

#### The Fourier Transform on the Line (ages 22-23)

Extend Fourier series from an interval to the whole line, where the sum over discrete frequencies becomes an integral over a continuum.

Ready when they can: Derive the transform as a limit of Fourier series on intervals of growing length; Compute the transform of a Gaussian and of an indicator function; State the inversion theorem and the hypotheses it needs.

https://lightmysky.com/learn/mathematics/the-fourier-transform-on-the-line-mt_BMrt5FPe3U

#### Hilbert Spaces and Orthogonal Projection in Infinite Dimensions (ages 23-24)

A complete inner-product space keeps the geometry of angles and projections when the dimension is infinite. Closest points to a closed subspace still exist and are unique, and every bounded functional is an inner product with a single fixed vector.

Ready when they can: Project onto a closed subspace and check that the residual is orthogonal to it; Expand a vector in an orthonormal basis and read off Parseval's identity; State the Riesz representation theorem and say what it identifies with what.

https://lightmysky.com/learn/mathematics/hilbert-spaces-and-orthogonal-projection-in-infinite-dimensions-mt_xmKq8SAgvy

#### Compact Self-Adjoint Operators and the Spectral Theorem (ages 23-24)

In infinite dimensions the spectrum is larger than the set of eigenvalues, so the matrix picture cannot be copied over. Compact self-adjoint operators are the case where it survives: an orthonormal basis of eigenvectors, with eigenvalues shrinking to zero.

Ready when they can: Separate the spectrum from the point spectrum with a concrete operator; State the spectral theorem for compact self-adjoint operators; Explain why the eigenvalues can accumulate only at zero.

https://lightmysky.com/learn/mathematics/compact-self-adjoint-operators-and-the-spectral-theorem-mt_P_Jr9LWFQj

#### Convolution, Plancherel and Transforming a Derivative (ages 23-24)

Establish the three properties that make the transform useful: convolution becomes multiplication, energy is preserved, and differentiation becomes multiplication by the frequency.

Ready when they can: Prove the convolution theorem and use it to compute a hard integral cheaply; State Plancherel's theorem and interpret it as the transform being unitary; Solve a linear constant-coefficient equation by transforming, dividing and inverting.

https://lightmysky.com/learn/mathematics/convolution-plancherel-and-transforming-a-derivative-mt_zSwMJrQIMt

#### Conditioning, Stability and Floating-Point Error (ages 23-24)

Conditioning says how much the answer moves when the data moves, and stability says how much an algorithm adds on top of that. Rounding error is tiny, and those two amplifiers are what make it visible.

Ready when they can: Compute a condition number and read it as an error amplifier; Tell an ill-conditioned problem apart from an unstable algorithm; Show catastrophic cancellation on a concrete subtraction.

https://lightmysky.com/learn/mathematics/conditioning-stability-and-floating-point-error-mt_q8IoCElXIV

### Complex Analysis

https://lightmysky.com/learn/mathematics/areas/complex-analysis

#### Complex Functions and the Complex Plane as a Domain (ages 19-20)

Treat a function of a complex variable as a map of the plane to itself, and set up limits and continuity in that setting.

Ready when they can: Describe the image of a line or circle under a simple complex map; Define a limit of a complex function and explain why approach from every direction is required; Split a complex function into its real and imaginary parts as two real functions of two variables.

https://lightmysky.com/learn/mathematics/complex-functions-and-the-complex-plane-as-a-domain-mt_hMo851VTEs

#### Complex Differentiability and the Cauchy-Riemann Equations (ages 19-20)

Demand a derivative independent of the direction of approach, and derive the two partial differential equations that demand forces.

Ready when they can: Derive the Cauchy-Riemann equations by comparing approach along the two axes; Show a specific function fails to be differentiable anywhere despite being smooth as a real map; State the extra continuity condition that makes the equations sufficient.

https://lightmysky.com/learn/mathematics/complex-differentiability-and-the-cauchy-riemann-equations-mt_nZNmZcl9Ss

#### Harmonic Functions and What Analyticity Forces (ages 20-21)

Show the real and imaginary parts of an analytic function each satisfy Laplace's equation, and recover one from the other.

Ready when they can: Prove that the real part of an analytic function is harmonic; Construct a harmonic conjugate for a given harmonic function; Explain why this links complex analysis to steady-state heat and potential problems.

https://lightmysky.com/learn/mathematics/harmonic-functions-and-what-analyticity-forces-mt_jqajP39XI4

#### Contour Integrals Along Parametrised Paths (ages 20-21)

Integrate a complex function along a path by parametrising it, and bound the result by length times maximum modulus.

Ready when they can: Evaluate a contour integral directly from a parametrisation; Show the value is unchanged by reparametrising and reversed by reversing the path; Apply the estimation lemma to bound an integral without evaluating it.

https://lightmysky.com/learn/mathematics/contour-integrals-along-parametrised-paths-mt_CaJ7ruAv8P

#### Cauchy's Theorem and Deforming a Contour (ages 20-21)

Prove that an analytic function integrates to zero around a closed loop it is analytic inside, and use that to slide contours freely.

Ready when they can: Derive Cauchy's theorem from Green's theorem plus the Cauchy-Riemann equations; Deform a contour past a region of analyticity without changing the integral; Explain what fails when a singularity lies inside the loop.

https://lightmysky.com/learn/mathematics/cauchys-theorem-and-deforming-a-contour-mt_aacYFVN-HH

#### Cauchy's Integral Formula and Derivatives of Every Order (ages 20-21)

Recover a function's value inside a contour from its values on the contour, then differentiate under the integral to get every derivative at once.

Ready when they can: State and apply the integral formula to evaluate a value or a derivative; Explain why complex differentiability once forces differentiability infinitely often; Deduce Liouville's theorem and, from it, the fundamental theorem of algebra.

https://lightmysky.com/learn/mathematics/cauchys-integral-formula-and-derivatives-of-every-order-mt_mViFwrFNWQ

#### Power Series and Analyticity in the Complex Plane (ages 20-21)

Expand an analytic function as a power series on a disc, and read the radius of convergence off the nearest singularity.

Ready when they can: Expand a function about a point and state the disc on which the series is valid; Explain a real series' radius of convergence by pointing at a complex singularity; Show that a zero of an analytic function is isolated unless the function is identically zero.

https://lightmysky.com/learn/mathematics/power-series-and-analyticity-in-the-complex-plane-mt_Mwxapy_pU8

#### Laurent Series and Classifying Isolated Singularities (ages 21-22)

Allow negative powers to expand a function on an annulus, and sort singularities by how the negative part behaves.

Ready when they can: Find the Laurent expansion of a function on a stated annulus; Classify a singularity as removable, a pole of stated order, or essential; Give the behaviour near an essential singularity that separates it from a pole.

https://lightmysky.com/learn/mathematics/laurent-series-and-classifying-isolated-singularities-mt_WoQV0gD1O-

#### The Residue Theorem (ages 21-22)

Reduce an integral around a closed contour to a sum of residues, one number per singularity enclosed.

Ready when they can: Compute a residue at a simple pole and at a pole of higher order; State the residue theorem with the winding number and apply it to a contour enclosing several poles; Explain why only the coefficient of the minus-one power survives the integration.

https://lightmysky.com/learn/mathematics/the-residue-theorem-mt_BN2biZ_zos

#### Evaluating Real Integrals by Residues (ages 21-22)

Close a real integral into a contour in the plane, discard the added arc with an estimate, and read the answer off the residues.

Ready when they can: Evaluate a rational real integral over the whole line by closing in a half-plane; Handle an oscillatory integrand with Jordan's lemma and justify discarding the arc; Deal with a pole on the contour by indenting around it and accounting for the half residue.

https://lightmysky.com/learn/mathematics/evaluating-real-integrals-by-residues-mt_Lj_HXtjzAh

#### The Argument Principle and Rouche's Theorem (ages 21-22)

Count zeros and poles inside a contour by watching how the argument turns, and transfer a count to a nearby function.

Ready when they can: State the argument principle and apply it to count zeros in a region; Use Rouche's theorem to locate the roots of a polynomial inside a disc; Deduce the open mapping theorem or the maximum modulus principle from the same idea.

https://lightmysky.com/learn/mathematics/the-argument-principle-and-rouches-theorem-mt_J1dC428M84

#### Conformal Maps and Mobius Transformations (ages 21-22)

See that an analytic map with nonzero derivative preserves angles, and use Mobius maps to move standard regions onto one another.

Ready when they can: Explain why a nonzero derivative makes a map angle-preserving; Build a Mobius transformation carrying three named points to three others; Map a half-plane onto a disc and use it to transfer a boundary-value problem.

https://lightmysky.com/learn/mathematics/conformal-maps-and-mobius-transformations-mt_WtHCbAT4GI

### Differential Equations

https://lightmysky.com/learn/mathematics/areas/differential-equations

#### What a Differential Equation Says and What a Solution Is (ages 19-20)

An equation relating a function to its own derivatives constrains a whole family of functions. A general solution carries arbitrary constants; an initial condition picks one member out of the family.

Ready when they can: Verify that a proposed function satisfies a given equation; State the order of an equation and the number of constants its general solution carries; Use an initial condition to fix the constants in a general solution.

https://lightmysky.com/learn/mathematics/what-a-differential-equation-says-and-what-a-solution-is-mt_tHlHg2nK3o

#### Direction Fields and Euler's Method (ages 19-20)

Draw the slope the equation prescribes at each point and the solution curves appear without any formula. Stepping along those slopes numerically is Euler's method, with error you can reason about.

Ready when they can: Sketch solution curves on a given direction field; Take several Euler steps by hand and tabulate the result; Say how halving the step size affects the error, and why the method drifts.

https://lightmysky.com/learn/mathematics/direction-fields-and-eulers-method-mt_Ak-TZOX3GR

#### Separable Equations (ages 19-20)

When the equation factors into a part in y and a part in x, separate the variables and integrate both sides. The constant of integration is where the initial condition enters.

Ready when they can: Separate and integrate an equation, keeping the constant; Apply an initial condition and state the interval where the solution is valid; Recognise an equation that cannot be separated.

https://lightmysky.com/learn/mathematics/separable-equations-mt_itSTsLTkwQ

#### First-Order Linear Equations and the Integrating Factor (ages 19-20)

Multiply through by a factor chosen to turn the left side into the derivative of a product, then integrate once. The factor is built from the coefficient of y.

Ready when they can: Write an equation in standard form and compute its integrating factor; Recognise the product rule pattern the factor creates; Solve a mixing or cooling problem set up as a linear equation.

https://lightmysky.com/learn/mathematics/first-order-linear-equations-and-the-integrating-factor-mt_BXmt2pbWp8

#### The Logistic Equation and Saturating Growth (ages 19-20)

Growth proportional to the population and to the room left produces an S-shaped curve with a carrying capacity. The model is where equilibrium solutions first appear.

Ready when they can: Solve the logistic equation for a given carrying capacity; Identify the equilibrium solutions and say which is stable; Compare logistic and exponential predictions over a long horizon.

https://lightmysky.com/learn/mathematics/the-logistic-equation-and-saturating-growth-mt_7Y_48Ga33L

#### Second-Order Linear Equations with Constant Coefficients (ages 20-21)

Try an exponential and the equation becomes a quadratic in the exponent. Real, repeated and complex roots give three shapes of general solution.

Ready when they can: Write and solve the characteristic equation; Give the general solution in each of the three root cases; Convert a complex-root solution into a decaying sine and cosine form.

https://lightmysky.com/learn/mathematics/second-order-linear-equations-with-constant-coefficients-mt_G7sMq1EHwQ

#### Nonhomogeneous Equations and Particular Solutions (ages 20-21)

The full solution is the homogeneous solution plus any particular one. Undetermined coefficients guesses the shape of the forcing; variation of parameters handles the rest.

Ready when they can: Choose a trial solution matching the forcing term; Adjust the trial when it duplicates a homogeneous solution; Use variation of parameters when no simple guess applies.

https://lightmysky.com/learn/mathematics/nonhomogeneous-equations-and-particular-solutions-mt_gbkQZte_JZ

#### Damped and Driven Oscillations (ages 20-21)

The same equation governs a mass on a spring and a series circuit. Damping decides how the free motion dies away, and driving near the natural frequency produces resonance.

Ready when they can: Classify motion as underdamped, critically damped or overdamped from the roots; Identify the transient and steady-state parts of a driven solution; Explain resonance in terms of the driving frequency and the natural frequency.

https://lightmysky.com/learn/mathematics/damped-and-driven-oscillations-mt_Y8K1njb1PH

#### Fourier Series (ages 20-21)

Any reasonable periodic function is a sum of sines and cosines. The coefficients are recovered by integrating against each one, which is what lets a system driven by a complicated periodic input be solved one frequency at a time.

Ready when they can: Compute the first Fourier coefficients of a square or sawtooth wave; Explain how orthogonality of the sines and cosines isolates each coefficient; Say what the partial sums do near a jump discontinuity.

https://lightmysky.com/learn/mathematics/fourier-series-mt_DJ3iwfj7NK

#### Series Solutions About an Ordinary Point (ages 20-21)

When the coefficients are not constant, assume a power series, match coefficients and generate a recurrence. Several named functions of physics are defined this way and no other.

Ready when they can: Substitute a power series and derive the recurrence relation; Generate the first several coefficients from initial conditions; Say what the radius of convergence means for the solution's range.

https://lightmysky.com/learn/mathematics/series-solutions-about-an-ordinary-point-mt_E6NiSd7MED

#### The Laplace Transform (ages 20-21)

An improper integral converts a function of time into a function of a new variable, turning differentiation into multiplication. Its usefulness rests on the transform being reversible.

Ready when they can: Compute the transform of a simple function from the defining integral; Use the derivative rule to see why the transform turns calculus into algebra; Read an inverse transform off a table after partial fractions.

https://lightmysky.com/learn/mathematics/the-laplace-transform-mt_8j8GXzITN0

#### Solving Initial Value Problems with Laplace Transforms (ages 21-22)

Transform the equation, solve the resulting algebra for the transform of the unknown, then invert. Initial conditions enter at the start rather than at the end, which is what makes the method suit discontinuous forcing.

Ready when they can: Transform an initial value problem and solve for the transform of the solution; Invert with partial fractions and a table; Handle a forcing term that switches on at a fixed time.

https://lightmysky.com/learn/mathematics/solving-initial-value-problems-with-laplace-transforms-mt_0BhjPVNUwl

#### Sturm-Liouville Problems and Eigenfunction Expansions (ages 21-22)

Putting a second-order boundary value problem in self-adjoint form makes its eigenfunctions orthogonal, which is why a solution can be written as a series in them at all. Fourier series is then one case rather than a trick that happened to work.

Ready when they can: Writes a given second-order equation in Sturm-Liouville form and identifies the weight function; Shows that eigenfunctions for distinct eigenvalues are orthogonal with respect to that weight; Expands a given function in the eigenfunctions of a stated boundary value problem and gets the coefficients.

https://lightmysky.com/learn/mathematics/sturm-liouville-problems-and-eigenfunction-expansions-mt_oqadAPaSsW

#### Green's Functions for Boundary Value Problems (ages 21-22)

Solve the problem once for a point source and the solution for any source is an integral against that answer. The Green's function carries the boundary conditions, so it is built from two homogeneous solutions chosen to die at the right end.

Ready when they can: Constructs the Green's function for a stated second-order operator and pair of boundary conditions; Recovers the solution for a given forcing term as an integral against the Green's function; Explains the jump condition on the derivative and where it comes from.

https://lightmysky.com/learn/mathematics/greens-functions-for-boundary-value-problems-mt_2ctFrfKIgW

#### Systems of Differential Equations and Eigenvalue Solutions (ages 21-22)

Several coupled unknowns become one vector equation. The eigenvalues of the coefficient matrix give the growth rates and the eigenvectors give the directions along which the system decouples.

Ready when they can: Write a coupled pair as a single matrix equation; Solve a two-by-two system through eigenvalues and eigenvectors; Convert a second-order equation into a first-order system.

https://lightmysky.com/learn/mathematics/systems-of-differential-equations-and-eigenvalue-solutions-mt_BbOqJ4S1ur

#### Phase Portraits, Equilibria and Stability (ages 21-22)

Draw the trajectories of a system in the plane of its unknowns. Equilibria are classified by the eigenvalues, and the same classification says whether nearby solutions return or leave.

Ready when they can: Classify an equilibrium as a node, saddle, spiral or centre from the eigenvalues; Sketch a phase portrait and mark the trajectories near equilibrium; Linearise a nonlinear system near an equilibrium and say what the linear picture can miss.

https://lightmysky.com/learn/mathematics/phase-portraits-equilibria-and-stability-mt_ULuZk4lmGr

#### Classifying Second-Order PDEs and What the Type Decides (ages 22-23)

The sign pattern of the second-order coefficients sorts equations into elliptic, parabolic and hyperbolic. The type decides which data may be prescribed and whether a solution smooths its data out or carries it along.

Ready when they can: Classify a given second-order equation from its coefficients; Match each type with a set of boundary or initial conditions that makes the problem well posed; Say which type smooths a kink in the data and which one keeps it.

https://lightmysky.com/learn/mathematics/classifying-second-order-pdes-and-what-the-type-decides-mt_hlQWbd1kzR

#### Separation of Variables and the Heat Equation (ages 22-23)

Assume the solution is a product of one-variable functions and the equation splits into ordinary ones. The boundary conditions pick out which modes are allowed, and the initial profile is matched by a series in those modes.

Ready when they can: Separate a boundary value problem into two ordinary equations; Identify the eigenvalues that the boundary conditions force; Match a given initial profile by computing its coefficients.

https://lightmysky.com/learn/mathematics/separation-of-variables-and-the-heat-equation-mt_XnPDL0X1TL

#### The Wave Equation and Its Characteristics (ages 22-23)

Along two families of lines the wave equation reduces to an ordinary derivative, and the solution reads as two fixed shapes travelling in opposite directions. A discontinuity in the data is carried along, not smoothed away.

Ready when they can: Draw the characteristics through a point and mark its domain of dependence; Apply d'Alembert's formula to given initial displacement and velocity; Contrast a travelling kink here with the same kink in the heat equation.

https://lightmysky.com/learn/mathematics/the-wave-equation-and-its-characteristics-mt_-_QCiBWg1w

#### Laplace's Equation and the Maximum Principle (ages 22-23)

A solution of Laplace's equation equals its own average over any small sphere, so it can have no interior peak. Uniqueness and stability for the boundary value problem follow from that one observation.

Ready when they can: State the mean value property and derive the maximum principle from it; Use the maximum principle to prove uniqueness for the Dirichlet problem; Explain why harmonic functions are smooth even when the boundary data is rough.

https://lightmysky.com/learn/mathematics/laplaces-equation-and-the-maximum-principle-mt_jSEkaTav1V

#### Weak Solutions and Test Functions (ages 22-24)

Multiply the equation by a smooth test function, integrate by parts, and the derivative moves off the unknown. A function with a corner can then solve an equation that in the classical sense it cannot.

Ready when they can: Move a derivative onto a test function and say why the boundary terms vanish; Show that a piecewise linear function solves a problem weakly but not classically; Say what a Sobolev space collects and why its completeness is the point.

https://lightmysky.com/learn/mathematics/weak-solutions-and-test-functions-mt_AKlC3Ol70p

#### Numerical Schemes for Evolution Equations (ages 23-24)

Replace the derivatives by differences and a differential equation becomes a recursion. Consistency and stability together give convergence, and the stability condition is what caps the time step.

Ready when they can: Derive a finite difference scheme and state its order of accuracy; Test a scheme for stability and read off the step-size restriction; Explain why an explicit scheme for the heat equation needs a small time step.

https://lightmysky.com/learn/mathematics/numerical-schemes-for-evolution-equations-mt_RuDbOapexB

### Probability

https://lightmysky.com/learn/mathematics/areas/probability

#### Likelihood Language (ages 9-10)

Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible

Ready when they can: Place five everyday events (e.g. 'the sun will rise tomorrow', 'it will snow in July', 'I'll flip heads') on a scale from impossible to certain; Use 'likely', 'unlikely', 'certain', 'impossible', and 'even chance' correctly to describe different events; Explain why pulling a red ball from a bag of mostly red balls is 'likely' but not 'certain'.

Needs first: Mathematical Precision.

https://lightmysky.com/learn/mathematics/likelihood-language-mt_iFFKZd-Vgv

#### Ordering Likelihoods (ages 9-10)

Compare the likelihood of different events and order them from least to most likely — including situations with unequal outcomes such as a bag with more of one colour than another, or a spinner with sections of different sizes — and explain reasoning using informal language

Ready when they can: Order four or more events from least likely to most likely and justify each placement; Compare likelihoods when outcomes are not equally likely — e.g. 'Drawing red from a bag with 7 red and 3 blue is more likely than drawing blue'; Explain why some events are closer to 'even chance' and others are closer to 'certain' or 'impossible'.

Needs first: Likelihood Language.

https://lightmysky.com/learn/mathematics/ordering-likelihoods-mt_UcGn2hjhYU

#### Equally Likely Outcomes (ages 9-10)

Understand that 'equally likely' means every outcome has exactly the same chance of occurring; identify whether a given situation has equally likely outcomes (a fair coin, a fair die, a spinner with equal sections) or unequally likely outcomes (a bag with more of one colour, a spinner with unequal sections)

Ready when they can: Explain that a fair coin has equally likely outcomes because heads and tails each have the same chance; Identify whether a spinner with unequal sections has equally likely outcomes or not, and explain why; Give an example of a situation with equally likely outcomes and one without, explaining the difference.

Needs first: Ordering Likelihoods.

https://lightmysky.com/learn/mathematics/equally-likely-outcomes-mt_xSgAgg9Ej_

#### Simple Chance Experiments (ages 9-10)

Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes

Ready when they can: Flip a coin 20 times, record heads and tails in a tally chart, and describe what they notice about the results; Roll a die 30 times and compare how often each number came up with what they expected; Pull counters from a bag, record results, and explain whether the outcomes matched their prediction.

Needs first: Pictograms and tally charts, Likelihood Language.

https://lightmysky.com/learn/mathematics/simple-chance-experiments-mt_J4j7d3iAfg

#### Probability as a Fraction (ages 9-10)

Describe the probability of simple equally-likely outcomes using unit fractions: the probability of rolling a 6 on a fair die is 1/6, flipping heads is 1/2, picking one specific colour from three equally represented colours is 1/3; place these fractional probabilities on a 0-to-1 probability scale

Ready when they can: State that the probability of rolling a 6 on a fair die is 1/6 and explain why; Express the probability of picking a red card from a standard deck as 26/52 or 1/2; Write the probability of a simple event as a fraction: favourable outcomes over total outcomes.

Needs first: Simple Chance Experiments, Unit fractions, Equally Likely Outcomes.

https://lightmysky.com/learn/mathematics/probability-as-a-fraction-mt_-c4Ca_nBzX

#### The 0-to-1 Probability Scale (ages 10-11)

Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages

Ready when they can: Place events on a number line from 0 (impossible) to 1 (certain), expressing positions as fractions or decimals; Explain that a probability of 0.5 means 'even chance' and connect this to the informal word 'likely'; Convert between informal language ('very unlikely') and a numerical position on the 0-to-1 scale.

Needs first: Probability as a Fraction, Comparing fractions.

https://lightmysky.com/learn/mathematics/the-0-to-1-probability-scale-mt_t0g2SlP404

#### Calculating Simple Probability (ages 10-11)

Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations

Ready when they can: Calculate the probability of drawing a blue marble from a bag of 3 blue and 7 red as 3/10; Use the formula P(event) = favourable outcomes ÷ total outcomes to solve at least three different problems; Explain why increasing the number of favourable outcomes increases the probability.

Needs first: The 0-to-1 Probability Scale, Equally Likely Outcomes.

https://lightmysky.com/learn/mathematics/calculating-simple-probability-mt_Zt30Gxi-qp

#### Experimental vs Theoretical (ages 10-11)

Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results

Ready when they can: Roll a die 60 times and compare experimental frequencies with the expected 10 per number; Explain why experimental results don't exactly match theoretical predictions but get closer with more trials; Predict what would happen if the experiment were repeated 600 times instead of 60.

Needs first: Simple Chance Experiments, Calculating Simple Probability.

https://lightmysky.com/learn/mathematics/experimental-vs-theoretical-mt_-bMnJcPJy8

#### Probabilities Sum to One (ages 10-11)

Understand that when all possible outcomes of a trial are listed, their probabilities must add up to 1; use this to find the probability of an event NOT happening: P(not A) = 1 − P(A); apply this shortcut to avoid counting all unfavourable outcomes directly

Ready when they can: List all outcomes of spinning a 4-colour spinner and verify their probabilities add up to 1; Calculate P(not rolling a 3) as 1 − 1/6 = 5/6 using the complement rule; Spot an error in a probability table where the values don't sum to 1 and explain what's wrong.

Needs first: The 0-to-1 Probability Scale, Calculating Simple Probability.

https://lightmysky.com/learn/mathematics/probabilities-sum-to-one-mt_3fwYu7imd4

#### The Probability Scale (ages 11-13)

Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible

Ready when they can: Place everyday events on a 0-to-1 probability scale with justification; Explain why a fair six-sided die gives each number a probability of 1/6; Distinguish between equally likely outcomes (fair coin) and unequally likely outcomes (biased spinner).

Needs first: One Quantity as a Fraction, Calculating Simple Probability.

https://lightmysky.com/learn/mathematics/the-probability-scale-mt_vmQJAtAFuy

#### Complementary events (ages 11-13)

Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

Ready when they can: Verify that probabilities of all outcomes listed for a spinner sum to 1; Calculate the probability of NOT rolling a 6 as 1 − 1/6 = 5/6; Identify an error in a probability distribution where the values do not sum to 1.

Needs first: Probabilities Sum to One, The Probability Scale.

https://lightmysky.com/learn/mathematics/complementary-events-mt_XfyqXLqzpx

#### Experimental probability (ages 11-13)

Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

Ready when they can: Conduct a coin-toss experiment, record results in a frequency table, and calculate relative frequencies; Compare experimental results with theoretical probability and explain discrepancies; Predict that relative frequency approaches theoretical probability as the number of trials increases.

Needs first: Experimental vs Theoretical, The Probability Scale.

https://lightmysky.com/learn/mathematics/experimental-probability-mt_sHJqh6UUya

#### Sets & Venn Diagrams (ages 12-14)

Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes

Ready when they can: List the elements in the union and intersection of two sets using a Venn diagram; Use a two-way table to enumerate all possible outcomes of two combined events; Shade regions of a Venn diagram to represent A ∪ B, A ∩ B, and A′ (complement).

Needs first: Complementary events.

https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8

#### Tree diagrams (ages 12-14)

Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

Ready when they can: List all 36 outcomes when rolling two dice and find P(total = 7); Draw a tree diagram for two successive events and multiply along branches for combined probabilities; Calculate the probability of a combined event using a sample space diagram and simplify the fraction.

Needs first: Sets & Venn Diagrams, Multiplying fractions (age 10+), Experimental probability.

https://lightmysky.com/learn/mathematics/tree-diagrams-mt_GDtFU5fyUv

#### Venn Diagrams and Counting Outcomes (ages 12-13)

Construct and interpret Venn diagrams with two or three sets to organise and count outcomes; use systematic listing and the product rule for counting to enumerate all possible outcomes of combined events

Ready when they can: Draw a two-circle Venn diagram to sort 30 students by whether they like football, like cricket, or like both; Shade the intersection A ∩ B and the union A ∪ B on a Venn diagram and explain what each region represents; Use a completed Venn diagram to calculate P(A), P(B), P(A ∩ B), and P(A ∪ B).

Needs first: Sets & Venn Diagrams.

https://lightmysky.com/learn/mathematics/venn-diagrams-and-counting-outcomes-mt_eSv_w46u6H

#### Relative Frequency and Expected Outcomes (ages 15-16)

Estimate a probability from experimental results, and use a probability to predict how many times an outcome should happen in a set number of trials.

Ready when they can: Estimate a probability as successes divided by trials; Predict the expected number of successes in 200 trials; Explain why a larger number of trials gives a better estimate.

https://lightmysky.com/learn/mathematics/relative-frequency-and-expected-outcomes-mt_OQCnzkcHUH

#### Counting Outcomes with the Product Rule (ages 15-16)

Count the outcomes of several choices made in a row by multiplying the number of options at each stage, instead of listing them all.

Ready when they can: Multiply the options at each stage to count the total outcomes; Adjust the count when an option cannot be used twice; Use the count as the denominator of a probability.

https://lightmysky.com/learn/mathematics/counting-outcomes-with-the-product-rule-mt_74gSbYIG8p

#### The Addition Rule and Mutually Exclusive Events (ages 15-16)

Use P(A or B) = P(A) + P(B) - P(A and B), and see why the subtraction disappears when two events cannot happen together.

Ready when they can: Decide whether two events are mutually exclusive before adding; Apply the addition rule and subtract the overlap where there is one; Use the fact that all outcomes sum to 1 to find a missing probability.

https://lightmysky.com/learn/mathematics/the-addition-rule-and-mutually-exclusive-events-mt_QsIusFefeE

#### Independent Events and the Multiplication Rule (ages 15-16)

Multiply probabilities for events that do not affect each other, and test whether two events really are independent before doing so.

Ready when they can: Multiply probabilities for two independent events; Test independence by checking whether one outcome changes the other's probability; Explain why 'and' multiplies while 'or' adds.

https://lightmysky.com/learn/mathematics/independent-events-and-the-multiplication-rule-mt_MK8EPHEUdN

#### Tree Diagrams Without Replacement (ages 15-16)

Draw tree diagrams for two or three stages where the first outcome changes the second, multiply along a branch, and add the routes that fit the question.

Ready when they can: Adjust the second set of branch probabilities when an item is not replaced; Multiply along a branch and add the branches that satisfy the condition; Check that the branches at each stage add to 1.

https://lightmysky.com/learn/mathematics/tree-diagrams-without-replacement-mt_NfiAY_wMwZ

#### Conditional Probability from Tables and Venn Diagrams (ages 15-16)

Work out the probability of one event given that another has happened, by restricting attention to the row, column or region the condition allows.

Ready when they can: Read a conditional probability from a two-way table using the row total as the denominator; Find a conditional probability from a region of a Venn diagram; Explain in words how P(A given B) differs from P(B given A).

https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP

#### Discrete Random Variables and Probability Distributions (ages 16-17)

A random variable attaches a number to each outcome, and its distribution lists every value the variable can take with the probability of taking it. Those probabilities have to total 1.

Ready when they can: Write the distribution of the total when two dice are added; Use the total of 1 to find a missing probability in a table; Find P(X ≥ 3) from a given distribution.

https://lightmysky.com/learn/mathematics/discrete-random-variables-and-probability-distributions-mt_yKztNkvvq3

#### Expected Value and Variance of a Discrete Random Variable (ages 16-17)

Weight each value by its probability to get the long-run mean, and use E(X²) minus the square of E(X) for the variance. Both turn a distribution into a decision about whether something is worth doing.

Ready when they can: Calculate E(X) for a given distribution; Calculate Var(X) from E(X²) and E(X); Decide whether a game with a stake is fair.

https://lightmysky.com/learn/mathematics/expected-value-and-variance-of-a-discrete-random-variable-mt_PFdo0Nm3FP

#### The Binomial Distribution (ages 16-17)

Count successes in a fixed number of independent trials that each have the same probability. The number of arrangements times the probability of one arrangement gives each term.

Ready when they can: Check the four conditions before choosing a binomial model; Calculate P(X = 3) when n = 10 and p = 0.2; Explain why sampling without replacement breaks the model.

https://lightmysky.com/learn/mathematics/the-binomial-distribution-mt_X2kVGK67Md

#### The Normal Distribution and Standardised Scores (ages 16-17)

A continuous symmetric model where most values sit near the mean. Converting a value to z = (x - μ) / σ says how many standard deviations from the mean it is, which makes different data sets comparable.

Ready when they can: Use the 68 and 95 percent facts to describe a data set; Convert a value to a z-score and say what it means; Explain why probability here is an area under the curve, not a height.

https://lightmysky.com/learn/mathematics/the-normal-distribution-and-standardised-scores-mt_Cs32DT9KnA

#### Finding Probabilities and Values from a Normal Model (ages 17-18)

Get the probability of a range of values from a normal model, and go the other way from a stated probability back to the cut-off value, sketching the region every time.

Ready when they can: Find P(X < 70) for a stated mean and standard deviation; Find the mark that only the top 10 percent beat; Find an unknown mean or standard deviation from a given probability.

https://lightmysky.com/learn/mathematics/finding-probabilities-and-values-from-a-normal-model-mt_naXMRySvos

#### Probability Spaces: Sample Spaces, Events and Axioms (ages 18-19)

Set probability on its axioms: a sample space, events as subsets, and a measure that is nonnegative, totals one and adds over disjoint events. Every rule met earlier follows from those three.

Ready when they can: Write the sample space and an event for an experiment; Derive the complement and general addition rules from the axioms; Give an assignment of probabilities that breaks the axioms and say which one.

https://lightmysky.com/learn/mathematics/probability-spaces-sample-spaces-events-and-axioms-mt_4gsBeqJtIQ

#### Conditional Probability, Independence and Bayes' Theorem (ages 18-19)

Conditioning restricts the sample space. Independence is the case where it changes nothing, and Bayes' theorem reverses the conditioning, which is how evidence updates a belief.

Ready when they can: Compute a conditional probability from a joint and a marginal; Apply Bayes' theorem to a screening test and interpret the result; Distinguish independent events from mutually exclusive ones.

https://lightmysky.com/learn/mathematics/conditional-probability-independence-and-bayes-theorem-mt_wIi_XRzwwK

#### Discrete Models Beyond the Binomial (ages 18-19)

Geometric, hypergeometric and Poisson models, and what each assumes about the trials. Choosing a model is a modelling decision, not a formula lookup.

Ready when they can: Match a situation to the geometric, hypergeometric or Poisson model; State the assumption that separates sampling with and without replacement; Use the Poisson model as a limit of the binomial for rare events.

https://lightmysky.com/learn/mathematics/discrete-models-beyond-the-binomial-mt_9zc5xYjDg_

#### Continuous Random Variables and Density Functions (ages 19-20)

For a continuous variable, probability is area under a density, so any single value has probability zero. The cumulative function and the density are linked by calculus in both directions.

Ready when they can: Verify that a function is a valid density and find a probability from it; Differentiate a cumulative function to recover the density; Explain why P(X = a) is zero and what that does not mean.

https://lightmysky.com/learn/mathematics/continuous-random-variables-and-density-functions-mt_jlf4zDTeNm

#### Expectation and Variance by Integration (ages 19-20)

The mean and variance of a continuous variable are integrals against the density, and the same linearity rules from the discrete case still hold.

Ready when they can: Compute the mean and variance of a continuous variable by integration; Use linearity of expectation without assuming independence; Find the expected value of a function of a random variable.

https://lightmysky.com/learn/mathematics/expectation-and-variance-by-integration-mt_kRSaKgp3bs

#### Joint Distributions, Covariance and Independence (ages 19-20)

Two variables have a joint distribution, from which marginals follow. Covariance measures how they move together, and independence forces zero covariance without the converse holding.

Ready when they can: Find marginal distributions from a joint table or density; Compute a covariance and interpret its sign; Give dependent variables with zero covariance.

https://lightmysky.com/learn/mathematics/joint-distributions-covariance-and-independence-mt_YyTFTAqhSF

#### Conditional Expectation Given a Sigma-Algebra (ages 22-23)

Define conditioning on information rather than on an event, as the best prediction measurable with respect to what is known.

Ready when they can: State the defining property and prove uniqueness up to a null set; Recover elementary conditional expectation as the case of a finite partition; Use the tower property and the projection interpretation on a worked example.

https://lightmysky.com/learn/mathematics/conditional-expectation-given-a-sigma-algebra-mt_i2sxZc-ER8

#### Markov Chains and the Memoryless Assumption (ages 22-24)

The next state depends on the current state and on nothing before it. That single assumption turns a process into a matrix, and questions about the far future become questions about matrix powers.

Ready when they can: Write the transition matrix for a described process; Compute an n-step transition probability; Give a process that is not Markov and say what extra memory would make it one.

https://lightmysky.com/learn/mathematics/markov-chains-and-the-memoryless-assumption-mt_2wDa_JxJ_o

#### Stationary Distributions and Long-Run Behaviour (ages 22-24)

A distribution left unchanged by one step is an eigenvector of the transition matrix for eigenvalue one. Irreducibility and aperiodicity are the conditions under which every starting distribution converges to it.

Ready when they can: Solve for a stationary distribution and check that it sums to one; Decide whether a chain is irreducible and aperiodic; Say what periodicity does to the long-run behaviour.

https://lightmysky.com/learn/mathematics/stationary-distributions-and-long-run-behaviour-mt_MGfHvUGkeh

#### Martingales and Optional Stopping (ages 23-24)

A martingale is a process whose expected next value, given everything so far, is its current value. Stopping it at a random time preserves that expectation, as long as the stopping rule is not allowed to look ahead.

Ready when they can: Check the martingale property for a given process; Apply optional stopping to compute a ruin probability; Give a stopping rule for which the theorem's hypotheses fail and the conclusion is false.

https://lightmysky.com/learn/mathematics/martingales-and-optional-stopping-mt_198uXX3jRJ

#### Brownian Motion and Its Defining Properties (ages 23-24)

Independent normal increments, continuous paths, and no derivative anywhere. It is the scaling limit of a random walk, and it is the process most continuous-time models are written against.

Ready when they can: State the defining properties and compute a covariance from them; Describe the scaling that turns a random walk into this process; Say why the paths are continuous and yet nowhere differentiable.

https://lightmysky.com/learn/mathematics/brownian-motion-and-its-defining-properties-mt_T5KtWIk07Z

### Discrete Mathematics

https://lightmysky.com/learn/mathematics/areas/discrete-mathematics

#### Counting with the Product and Sum Rules (ages 18-19)

Count a finite set by breaking the choice into independent stages to multiply, or into disjoint cases to add, and say which structure the problem has.

Ready when they can: Decide whether a counting problem splits into stages or into cases, and justify the split; Count arrangements where a later stage's options depend on an earlier choice; Detect and repair a double count caused by treating overlapping cases as disjoint.

https://lightmysky.com/learn/mathematics/counting-with-the-product-and-sum-rules-mt_3NZC5F7RKP

#### Permutations and Combinations (ages 18-19)

Count arrangements where order matters and selections where it does not, and see the second as the first divided by the arrangements you refuse to distinguish.

Ready when they can: Choose between a permutation and a combination count from the wording of a problem; Derive the combination formula from the permutation count by dividing out repeats; Count arrangements of a multiset where some objects are identical.

https://lightmysky.com/learn/mathematics/permutations-and-combinations-mt_1L58kuu-w3

#### Binomial Coefficients and Combinatorial Identities (ages 18-19)

Read the binomial coefficient as a count and prove identities about it by counting one set two ways rather than by algebra.

Ready when they can: Prove Pascal's rule by splitting the selections according to whether one element is chosen; Give a counting argument for the sum of a row of Pascal's triangle; Prove Vandermonde's identity by counting a mixed selection two ways.

https://lightmysky.com/learn/mathematics/binomial-coefficients-and-combinatorial-identities-mt_lHXFvudTh6

#### The Pigeonhole Principle (ages 19-20)

Use the observation that more objects than boxes forces a repeat to prove existence results no construction would give.

Ready when they can: State the principle and its generalised form with a ceiling; Choose the pigeons and the holes for a stated problem, which is the whole difficulty; Prove a result such as two people in a group sharing a handshake count.

https://lightmysky.com/learn/mathematics/the-pigeonhole-principle-mt_wgfpmZqzd9

#### Inclusion-Exclusion (ages 19-20)

Count a union by adding the parts, subtracting the pairwise overlaps, adding the triples back, and prove the alternating pattern is right.

Ready when they can: Apply the formula to three and to four overlapping sets; Prove the general formula by tracking how often one element is counted; Count derangements or surjections by applying the principle to a well-chosen family of sets.

https://lightmysky.com/learn/mathematics/inclusion-exclusion-mt_MgU-IMpVHA

#### Recurrence Relations and Characteristic Roots (ages 19-20)

Turn a rule that defines each term from earlier ones into a closed formula by solving the characteristic equation, including the repeated-root case.

Ready when they can: Set up a linear recurrence from a described counting process; Solve a second-order homogeneous recurrence and fit the constants to the initial values; Handle a repeated characteristic root and explain why an extra factor of n appears.

https://lightmysky.com/learn/mathematics/recurrence-relations-and-characteristic-roots-mt_q0b2bi0iAB

#### Generating Functions (ages 20-21)

Store a whole sequence as the coefficients of a power series, then use algebra on the series to answer questions about the sequence.

Ready when they can: Write the generating function of a simple sequence and read a coefficient back out; Solve a recurrence by converting it into an equation for the generating function; Explain what a product of two generating functions counts.

https://lightmysky.com/learn/mathematics/generating-functions-mt_WAX3O-HjRk

#### Graphs, Degrees and the Handshake Lemma (ages 20-21)

Define a graph as a set of vertices with a set of pairs, and prove the first theorem about it: the degrees sum to twice the number of edges.

Ready when they can: State what a graph is precisely, and distinguish simple graphs, multigraphs and directed graphs; Prove the handshake lemma and deduce that the number of odd-degree vertices is even; Decide whether two drawings represent the same graph.

https://lightmysky.com/learn/mathematics/graphs-degrees-and-the-handshake-lemma-mt_1oqO_o3bTO

#### Trees and Spanning Trees (ages 20-21)

Characterise a tree in several equivalent ways, prove the edge count, and count the labelled trees on n vertices.

Ready when they can: Prove that connected with n minus one edges, acyclic and connected, and unique paths are the same condition; Show every connected graph has a spanning tree; State Cayley's formula and outline one argument for it.

https://lightmysky.com/learn/mathematics/trees-and-spanning-trees-mt_kMWpsz44yJ

#### Euler Trails and Hamilton Cycles (ages 21-22)

Settle exactly when a graph has a walk using every edge once, and see why the analogous question about vertices has no such clean answer.

Ready when they can: State and prove the degree condition for an Euler circuit and for an Euler trail; Give sufficient conditions for a Hamilton cycle and explain why they are not necessary; Contrast the two problems in terms of how hard each is to decide.

https://lightmysky.com/learn/mathematics/euler-trails-and-hamilton-cycles-mt_RU5P5Iqekt

#### Graph Colouring and Planarity (ages 21-22)

Colour vertices so that neighbours differ, bound the colours needed, and use Euler's formula to see what a graph drawn without crossings cannot contain.

Ready when they can: Bound the chromatic number by the maximum degree and exhibit a graph meeting the bound; Prove Euler's formula for connected planar graphs; Use the edge bound from Euler's formula to show a specific graph is not planar.

https://lightmysky.com/learn/mathematics/graph-colouring-and-planarity-mt_6xy6UPBppw

#### Matchings and Hall's Theorem (ages 21-22)

Decide when every element of one side can be paired off, and prove that the obvious obstruction is the only one.

Ready when they can: State Hall's condition and check it on a small bipartite graph; Prove that Hall's condition is sufficient, not merely necessary; Recast an assignment problem as a matching and read off what blocks a full pairing.

https://lightmysky.com/learn/mathematics/matchings-and-halls-theorem-mt_hkWslW5b5U

### Abstract Algebra

https://lightmysky.com/learn/mathematics/areas/abstract-algebra

#### Groups, Subgroups and Symmetry (ages 21-22)

One operation, associative, with an identity and inverses. Symmetries of an object, permutations and modular arithmetic all satisfy the same four axioms, so anything proved once holds for all of them.

Ready when they can: Check the group axioms for a given set and operation; Describe the symmetry group of a square and list its elements; Use the subgroup test on a candidate subset.

https://lightmysky.com/learn/mathematics/groups-subgroups-and-symmetry-mt_HFAhcaGo2L

#### Homomorphisms, Cosets and Lagrange's Theorem (ages 21-22)

Maps that preserve the operation, the classes a subgroup carves out, and the counting result that a subgroup's order divides the group's. Kernels are what make quotient groups possible.

Ready when they can: Show a given map is a homomorphism and find its kernel; Partition a small group into cosets of a subgroup; Use Lagrange's theorem to rule out a subgroup of a stated size.

https://lightmysky.com/learn/mathematics/homomorphisms-cosets-and-lagranges-theorem-mt_yKiZ8sg7yN

#### Rings, Fields and Their First Properties (ages 21-22)

Two operations instead of one. Rings cover the integers and polynomials, fields are the rings where division works, and the difference explains why some equations are solvable and others are not.

Ready when they can: Decide whether a given structure is a ring, an integral domain or a field; Give a ring with zero divisors and say what breaks; Explain why the integers modulo p form a field exactly when p is prime.

https://lightmysky.com/learn/mathematics/rings-fields-and-their-first-properties-mt_BmhIook13o

#### Normal Subgroups and Quotient Groups (ages 22-23)

Cosets can be multiplied consistently exactly when the subgroup is normal. The quotient group that results turns the kernel of a homomorphism into a complete description of the map.

Ready when they can: Decide whether a subgroup is normal, by conjugation or by its index; Write the multiplication table of a small quotient group; Use the first isomorphism theorem to identify the image of a homomorphism.

https://lightmysky.com/learn/mathematics/normal-subgroups-and-quotient-groups-mt_RU7A-t7wQ5

#### Group Actions, Orbits and the Class Equation (ages 22-23)

A group acting on a set splits it into orbits, and each orbit has the size of an index of a stabiliser. Counting one set two ways with that relation proves results no direct argument reaches.

Ready when they can: Identify the orbits and stabilisers of a given action; Apply the orbit-stabiliser relation to a symmetry group; Use the class equation to show that a group of prime-power order has a nontrivial centre.

https://lightmysky.com/learn/mathematics/group-actions-orbits-and-the-class-equation-mt_urut0TFTOR

#### The Sylow Theorems and Groups of Small Order (ages 22-23)

Subgroups of prime-power order exist, are all conjugate, and their number is pinned down by two arithmetic conditions. That is enough to rule out simple groups of many orders and to finish the classification of small ones.

Ready when they can: Count the possible Sylow subgroups from the congruence and divisibility conditions; Show that no group of a given order can be simple; List the groups of a small order and justify that the list is complete.

https://lightmysky.com/learn/mathematics/the-sylow-theorems-and-groups-of-small-order-mt_vg2VYkLuz8

#### Ideals and Quotient Rings (ages 22-23)

The ring counterpart of a normal subgroup is an ideal, and quotienting by it declares its elements to be zero. Whether an ideal is prime or maximal is read directly off the ring the quotient produces.

Ready when they can: Check whether a subset of a ring is an ideal; Describe the quotient of a polynomial ring by a principal ideal; Distinguish prime from maximal in terms of the quotient ring.

https://lightmysky.com/learn/mathematics/ideals-and-quotient-rings-mt_uQBA9E1JIP

#### Polynomial Rings, Irreducibility and Unique Factorisation (ages 22-24)

Polynomials over a field divide with remainder, and that single fact forces unique factorisation into irreducibles. Deciding whether a given polynomial is irreducible over the rationals needs tests rather than inspection.

Ready when they can: Divide polynomials with remainder and read off what it says about roots; Apply Eisenstein's criterion and reduction modulo a prime; Trace the chain from division with remainder to principal ideals to unique factorisation.

https://lightmysky.com/learn/mathematics/polynomial-rings-irreducibility-and-unique-factorisation-mt_m2G9PIHj6y

#### Modules: Linear Algebra Over a Ring (ages 22-24)

A module is a vector space whose scalars form a ring rather than a field. Bases may fail to exist, and what survives is a structure theorem that delivers the Jordan form and the classification of finite abelian groups at the same time.

Ready when they can: Give a module with no basis and say which vector-space step fails; State the structure theorem for finitely generated modules over a principal ideal domain; Read the Jordan form of a matrix as one instance of that theorem.

https://lightmysky.com/learn/mathematics/modules-linear-algebra-over-a-ring-mt_0GMVp-s8wD

#### Field Extensions and Their Degrees (ages 22-24)

Adjoining a root to a field produces a larger field, which is a vector space over the smaller one. Its dimension is called the degree, and degrees multiply along a tower of extensions.

Ready when they can: Compute the degree of a simple extension from a minimal polynomial; Apply the tower law to a compound extension; Explain why a ruler and compass cannot produce the cube root of two.

https://lightmysky.com/learn/mathematics/field-extensions-and-their-degrees-mt_CjOMNt5_i0

#### Group Representations and the Group Algebra (ages 22-23)

Realise an abstract group as matrices acting on a vector space, and recognise a representation as a module over the group algebra.

Ready when they can: Write down a faithful matrix representation of a small group and check the homomorphism property; Translate between a representation, a linear action and a module over the group algebra; Identify subrepresentations and say what irreducible means in this setting.

https://lightmysky.com/learn/mathematics/group-representations-and-the-group-algebra-mt_y5JlvQGKYW

#### Maschke's Theorem and Complete Reducibility (ages 22-23)

Prove that over a field of the right characteristic every representation splits into irreducible pieces, and see exactly where the proof needs that hypothesis.

Ready when they can: Prove Maschke's theorem by averaging a projection over the group; Point at the division by the group order and give a case where the theorem fails; Apply Schur's lemma to constrain maps between irreducible representations.

https://lightmysky.com/learn/mathematics/maschkes-theorem-and-complete-reducibility-mt_FVNCwUqeTx

#### The Galois Correspondence (ages 22-24)

The symmetries of a field extension form a group whose subgroups match the intermediate fields, in reverse order. Whether that group can be built from abelian pieces is what decides if the roots can be written with radicals.

Ready when they can: List the automorphisms of a small splitting field; Match subgroups to intermediate fields in a concrete degree-four example; State what solvability of the group says about a general quintic.

https://lightmysky.com/learn/mathematics/the-galois-correspondence-mt_30kyliQR_L

#### Characters and the Orthogonality Relations (ages 23-24)

Reduce a representation to the trace of each group element, and prove the resulting functions are orthogonal for an inner product on class functions.

Ready when they can: Show a character is constant on conjugacy classes and independent of the chosen basis; Prove the first orthogonality relation for irreducible characters; Count the irreducible representations against the number of conjugacy classes.

https://lightmysky.com/learn/mathematics/characters-and-the-orthogonality-relations-mt_RleR7YGXjX

#### Decomposing a Representation from Its Character (ages 23-24)

Build the character table of a finite group and use it to read off how any representation breaks into irreducibles.

Ready when they can: Construct the character table of a small non-abelian group; Decompose a permutation representation by taking inner products with the irreducible characters; Read a normal subgroup off the table from the kernel of a character.

https://lightmysky.com/learn/mathematics/decomposing-a-representation-from-its-character-mt_ccEcWW9xAa

### Number Theory

https://lightmysky.com/learn/mathematics/areas/number-theory

#### Divisibility and the Division Algorithm (ages 18-19)

Fix what divides means, prove that division leaves a unique quotient and remainder, and use that uniqueness as the base of everything after it.

Ready when they can: Prove basic divisibility facts directly from the definition rather than by example; State and prove the division algorithm, including the uniqueness of the remainder; Use the remainder cases to prove a statement about all integers.

https://lightmysky.com/learn/mathematics/divisibility-and-the-division-algorithm-mt_UkQNs-6-40

#### Euclid's Algorithm and Bezout's Identity (ages 18-19)

Find a greatest common divisor by repeated division instead of by factorising, then run the algorithm backwards to write it as a combination of the two numbers.

Ready when they can: Run the algorithm on a large pair and explain why it terminates; Back-substitute to express the gcd as an integer combination of the inputs; Deduce Euclid's lemma and, from it, uniqueness of prime factorisation.

https://lightmysky.com/learn/mathematics/euclids-algorithm-and-bezouts-identity-mt_26hM0EnJpq

#### Modular Arithmetic and Congruence Classes (ages 19-20)

Agree to identify integers with the same remainder, check the arithmetic survives that identification, and compute in the resulting finite system.

Ready when they can: Show that addition and multiplication are well defined on congruence classes; Compute a large power modulo n by repeated squaring; Use a modulus to prove a divisibility claim or to rule out an equation having integer solutions.

https://lightmysky.com/learn/mathematics/modular-arithmetic-and-congruence-classes-mt_Lt4_Aazx2j

#### Linear Congruences and the Chinese Remainder Theorem (ages 19-20)

Solve a single linear congruence, say exactly when it is solvable, and combine congruences with coprime moduli into one.

Ready when they can: Decide when a linear congruence has a solution and count the solutions modulo n; Find a modular inverse using the extended Euclidean algorithm; Solve a system of congruences with coprime moduli and state the modulus of the combined answer.

https://lightmysky.com/learn/mathematics/linear-congruences-and-the-chinese-remainder-theorem-mt_J9_RMpwcRX

#### Fermat's Little Theorem and Euler's Theorem (ages 20-21)

Prove that raising a unit to the size of the unit group returns one, and use it to shortcut enormous modular powers.

Ready when they can: Prove Fermat's little theorem by permuting the nonzero residues; Compute Euler's totient function and state the general theorem; Reduce a huge exponent modulo the totient before computing the power.

https://lightmysky.com/learn/mathematics/fermats-little-theorem-and-eulers-theorem-mt_7wW4z4Eidx

#### Primitive Roots and the Units Modulo n (ages 20-21)

Ask when the units modulo n are generated by a single element, and settle which n admit one.

Ready when they can: Compute the order of an element modulo n and relate it to the totient; Find a primitive root modulo a small prime and use it to index the other units; State which moduli have primitive roots and give a modulus that does not.

https://lightmysky.com/learn/mathematics/primitive-roots-and-the-units-modulo-n-mt_KwTDckkMze

#### Quadratic Residues and the Law of Reciprocity (ages 21-22)

Decide which residues are squares modulo a prime, compute the Legendre symbol, and use reciprocity to answer the question quickly.

Ready when they can: List the quadratic residues modulo a small prime and count them; Apply Euler's criterion to test whether a residue is a square; Use quadratic reciprocity and the supplementary laws to evaluate a Legendre symbol.

https://lightmysky.com/learn/mathematics/quadratic-residues-and-the-law-of-reciprocity-mt_0KS9eTCY4p

#### The Distribution of Primes and What Is Still Open (ages 21-22)

Prove the primes never run out, meet the estimate for how thinly they spread, and see where the honest boundary of current knowledge sits.

Ready when they can: Give Euclid's proof that the primes are infinite and one other proof of the same fact; State the prime number theorem and use it to estimate a prime count; Describe an open problem about primes precisely enough to say what a solution would need to establish.

https://lightmysky.com/learn/mathematics/the-distribution-of-primes-and-what-is-still-open-mt_PJwm9kuQWQ

### Topology

https://lightmysky.com/learn/mathematics/areas/topology

#### Metric Spaces: Distance as an Axiom (ages 20-21)

Keep only the properties distance must have, and check how much of the analysis of the real line survives on that alone.

Ready when they can: State the metric axioms and verify them for an unfamiliar example such as a function space; Redefine convergence and continuity using only the metric; Give two metrics on one set that disagree about which sequences converge.

https://lightmysky.com/learn/mathematics/metric-spaces-distance-as-an-axiom-mt_A3TMb8wL6k

#### Open Sets, Closed Sets and Limit Points (ages 20-21)

Rebuild openness, closure and limit points from balls alone, and restate continuity as preimages of open sets.

Ready when they can: Prove that arbitrary unions and finite intersections of open sets are open; Compute the closure and the interior of a given subset; Prove that a function is continuous exactly when preimages of open sets are open.

https://lightmysky.com/learn/mathematics/open-sets-closed-sets-and-limit-points-mt_9bBdT38dbB

#### Completeness and the Contraction Mapping Theorem (ages 21-22)

Say what a complete metric space is, and prove that a contraction on one has exactly one fixed point that iteration finds.

Ready when they can: Give a metric space that is not complete and identify the missing limit; Prove the contraction mapping theorem and extract the error bound iteration gives; Apply the theorem to prove existence and uniqueness for a differential equation.

https://lightmysky.com/learn/mathematics/completeness-and-the-contraction-mapping-theorem-mt_DYsLzg-IaK

#### Compactness in Metric Spaces (ages 21-22)

Compare the open-cover and sequential definitions, prove they agree in a metric space, and see what compactness buys for continuous functions.

Ready when they can: Prove that a continuous function on a compact space is bounded and attains its bounds; Show closed and bounded is not enough for compactness outside finite dimensions; State the Heine-Borel theorem and identify exactly where its proof uses completeness.

https://lightmysky.com/learn/mathematics/compactness-in-metric-spaces-mt_dBLXU0wSN9

#### Topological Spaces: Continuity Without Distance (ages 23-24)

Declare which sets count as open and continuity can be defined with no distance anywhere in sight. One set can carry several topologies, and the choice decides which functions are continuous.

Ready when they can: Check the axioms for a proposed collection of open sets; Define continuity by preimages and reconcile it with the epsilon-delta version; Give two topologies on one set and a function continuous for one but not the other.

https://lightmysky.com/learn/mathematics/topological-spaces-continuity-without-distance-mt_D2oPq0AVhI

#### Compactness and Connectedness (ages 23-24)

Two properties that continuous maps preserve, which is why proofs lean on them so heavily. Compactness turns any open cover into a finite one, and connectedness rules out splitting a space in two.

Ready when they can: Prove that the continuous image of a compact space is compact; Use connectedness to prove an intermediate value statement; Explain why closed and bounded describes compactness in Euclidean space but not in general.

https://lightmysky.com/learn/mathematics/compactness-and-connectedness-mt_ybV1lUedHs

#### The Fundamental Group and Loops on a Circle (ages 23-24)

Loops based at a point, counted up to continuous deformation, form a group. Computing it for the circle is what proves a disc and an annulus are genuinely different spaces rather than merely drawn differently.

Ready when they can: Decide whether two given loops are homotopic; Explain why the fundamental group of the circle is the integers; Use the group to prove that two spaces are not homeomorphic.

https://lightmysky.com/learn/mathematics/the-fundamental-group-and-loops-on-a-circle-mt_zH50_L0nu4

## English

355 topics, ages 4 to 18. https://lightmysky.com/learn/english

### Handwriting & Transcription

https://lightmysky.com/learn/english/areas/handwriting-and-transcription

#### Sitting and holding a pencil (ages 4-6)

Sit correctly at a table holding a pencil comfortably and correctly; form lower-case letters in the correct direction starting and finishing in the right place

Ready when they can: Hold a pencil with a comfortable tripod or near-tripod grip; Write all 26 lowercase letters with correct starting points and direction; Maintain consistent letter size on lined paper.

https://lightmysky.com/learn/english/sitting-and-holding-a-pencil-mt_WBfj79OqXz

#### Forming Capital Letters (ages 5-6)

Form capital letters correctly; print many upper- and lowercase letters legibly

Ready when they can: Write all 26 capital letters with correct formation; Distinguish between uppercase and lowercase forms in own writing; Use appropriate sizing so capitals are taller than lowercase letters.

Needs first: Sitting and holding a pencil.

https://lightmysky.com/learn/english/forming-capital-letters-mt_H7DquwQi_F

#### Letter Formation Families (ages 5-6)

Understand which letters belong to which handwriting families based on similar formation patterns and practise letters in groups

Ready when they can: Group letters by similar strokes (e.g. c, a, d, g, o family — all start with a curve); Explain why certain letters are practised together; Form letters within the same family consistently using the shared movement pattern.

Needs first: Sitting and holding a pencil.

https://lightmysky.com/learn/english/letter-formation-families-mt_DMvKfP4uGC

#### Writing digits 0-9 (ages 5-6)

Form digits 0-9 correctly and legibly

Ready when they can: Write all digits 0-9 clearly with correct starting points; Form digits the appropriate size relative to letter height; Write numbers legibly so they can be read by others.

Needs first: Sitting and holding a pencil.

https://lightmysky.com/learn/english/writing-digits-0-9-mt_oAK9GXSfqV

#### Joining Letters (ages 6-10)

Begin to join letters using diagonal and horizontal strokes, understanding which letter pairs are best left unjoined, forming letters of correct size relative to one another

Ready when they can: Join 'in', 'un', 'it' with a diagonal stroke connecting the letters; Leave letters like 'b' unjoined when followed by certain letters, explaining why; Write with consistent letter sizing on lined paper, ascenders and descenders in proportion.

Needs first: Forming Capital Letters, Sitting and holding a pencil, Letter Formation Families.

https://lightmysky.com/learn/english/joining-letters-mt_02DH7sGXCi

#### Writing Legibly at Speed (ages 10-12)

Keep handwriting readable when the writing has to keep up with thinking, listening or a clock. Decide which joins to keep, which to drop, and when to slow down because the reader is somebody else.

Ready when they can: Take notes at listening speed and still read them back a week later; Name two joins they drop when writing fast and say why those are the safe ones to lose; Write a final copy more slowly than a draft, and say what changed about the reader.

https://lightmysky.com/learn/english/writing-legibly-at-speed-mt_2M-7dIhJOy

### Phonics & Word Reading

https://lightmysky.com/learn/english/areas/phonics-and-word-reading

#### Rhyming words (ages 4-6)

Recognise and produce rhyming words; join in with predictable phrases and rhymes in stories and poems; learn to appreciate and recite poems by heart

Ready when they can: Identify which words rhyme from a set (e.g. cat, bat, dog); Generate a word that rhymes with a given target; Join in with repeated refrains and rhyming patterns during shared reading.

https://lightmysky.com/learn/english/rhyming-words-mt_4GiE83rJF_

#### Understanding print (ages 4-6)

Demonstrate understanding that print carries meaning, follows left-to-right top-to-bottom directionality, and is organised page by page in books

Ready when they can: Track words with a finger moving left to right across the page; Turn pages in the correct sequence when handling a book; Point to where reading starts on a page.

https://lightmysky.com/learn/english/understanding-print-mt_1KCwbGvm1F

#### Knowing all letters (ages 4-6)

Recognise and name all uppercase and lowercase letters of the alphabet; name the letters in order and use letter names to distinguish between alternative spellings

Ready when they can: Name all 26 letters in both cases when shown in random order; Recite the alphabet from A to Z; Use letter names to explain spelling choices (e.g. 'Is it c or k in cat?').

Needs first: Understanding print.

https://lightmysky.com/learn/english/knowing-all-letters-mt_frDIaXzWbx

#### Single Letter Sounds (ages 4-6)

Know the primary sound for each consonant and the short and long sounds for the five major vowels; respond speedily to single-letter graphemes

Ready when they can: Say the most common sound for each consonant when shown the letter; Distinguish short vowel sounds in CVC words (e.g. /a/ in 'cat' vs /e/ in 'bed'); Associate long and short vowel sounds with common single-letter spellings.

Needs first: Knowing all letters.

https://lightmysky.com/learn/english/single-letter-sounds-mt_F978c32kDr

#### Syllables (ages 5-6)

Count, blend, and segment syllables in spoken words; divide written words into syllables as an aid to reading and spelling

Ready when they can: Clap out syllables in spoken words (e.g. 'butterfly' = 3 claps); Blend syllables to form words (e.g. 'rain' + 'bow' → 'rainbow'); Segment a word into its syllable parts orally.

https://lightmysky.com/learn/english/syllables-mt_UvNrOXny1i

#### Onsets & Rimes (ages 4-7)

Blend and segment onsets and rimes in single-syllable words; isolate and pronounce individual phonemes (initial, medial, final) in CVC words; add or substitute phonemes to make new words

Ready when they can: Blend onset and rime to say a word (e.g. /c/ + /at/ → 'cat'); Identify the first, middle, or last sound in a CVC word; Change one sound to make a new word (e.g. change /c/ in 'cat' to /b/ → 'bat').

Needs first: Rhyming words, Syllables.

https://lightmysky.com/learn/english/onsets-and-rimes-mt_PvU3eoikev

#### Consonant Digraphs (ages 4-7)

Read and spell words containing consonant digraphs and less common consonant spellings (ch, sh, th, ck, tch, ng, ph, wh, k for /k/)

Ready when they can: Read words with consonant digraphs (e.g. 'shop', 'chip', 'that'); Identify the sound made by ph (/f/) and wh (/w/) in words; Spell words ending in -ck (e.g. 'duck') and -tch (e.g. 'match').

Needs first: Single Letter Sounds, Onsets & Rimes.

https://lightmysky.com/learn/english/consonant-digraphs-mt_9-OHslmt1g

#### Blending Sounds to Read Words (ages 4-7)

Apply phonic knowledge to blend sounds in unfamiliar words containing taught grapheme-phoneme correspondences; respond speedily to graphemes for all 40+ phonemes

Ready when they can: Sound out and blend unfamiliar phonically regular words (e.g. /sh/-/o/-/p/ → 'shop'); Read words containing taught GPCs without excessive sounding out; Distinguish between similarly spelled words by identifying differing letter sounds (e.g. 'big' vs 'bag').

Needs first: Single Letter Sounds, Onsets & Rimes, Consonant Digraphs.

https://lightmysky.com/learn/english/blending-sounds-to-read-words-mt__KHQttMde3

#### Vowel Digraphs (ages 4-7)

Read and spell words containing common vowel digraphs (ai, ay, ee, ea, oa, oe, oo, oi, oy) including where a digraph can represent more than one sound

Ready when they can: Read words with vowel digraphs (e.g. 'tree', 'boat', 'rain', 'coin'); Distinguish between different sounds for the same digraph (e.g. 'oo' in 'book' vs 'moon'); Spell words using common vowel digraph patterns.

Needs first: Single Letter Sounds, Onsets & Rimes.

https://lightmysky.com/learn/english/vowel-digraphs-mt_BtMbZibZUj

#### Compound Words (ages 5-8)

Recognise and spell compound words by identifying the two component words that combine to form a single word

Ready when they can: Identify the two words in a compound (e.g. 'sunshine' = 'sun' + 'shine'); Spell compound words by combining known words; Create compound words from given word pairs.

Needs first: Blending Sounds to Read Words, Syllables.

https://lightmysky.com/learn/english/compound-words-mt_70Ys4i1AB1

#### Diphthongs and complex vowels (ages 5-6)

Read and spell words containing diphthongs and complex vowel patterns (ow, ou, ew, ue, ie, aw, au) and words ending in -y as a vowel sound

Ready when they can: Read words with variable vowel sounds (e.g. 'ow' in 'cow' vs 'snow'); Decode words with diphthongs (e.g. 'cloud', 'blue', 'pie'); Read words ending in -y pronounced as /ee/ or /igh/ (e.g. 'happy', 'my').

Needs first: Vowel Digraphs, Blending Sounds to Read Words.

https://lightmysky.com/learn/english/diphthongs-and-complex-vowels-mt_fMd7v87IiI

#### R-Controlled Vowel Sounds (ages 5-6)

Read and spell words containing r-controlled vowels (ar, er, ir, ur, or, ore) and vowel-r patterns where 'r' modifies the vowel sound

Ready when they can: Read words with r-controlled vowels (e.g. 'car', 'bird', 'fork', 'her'); Recognise that 'r' changes the vowel sound (e.g. 'cat' vs 'cart'); Spell words with common r-controlled patterns.

Needs first: Single Letter Sounds, Blending Sounds to Read Words.

https://lightmysky.com/learn/english/r-controlled-vowel-sounds-mt_a6m7PqTuJN

#### Reading Contractions (ages 5-6)

Read and understand contractions with apostrophes, knowing the apostrophe represents omitted letters

Ready when they can: Read common contractions in text (e.g. 'I'm', 'we'll', 'don't'); Match contractions to their expanded forms (e.g. 'I'm' = 'I am'); Explain that the apostrophe shows where letters are missing.

Needs first: Blending Sounds to Read Words.

https://lightmysky.com/learn/english/reading-contractions-mt_t1JXeNgKcu

#### Reading High-Frequency Words by Sight (ages 5-8)

Read common high-frequency and exception words automatically by sight, including words with irregular spelling patterns

Ready when they can: Read common exception words instantly without sounding out (e.g. 'the', 'said', 'was', 'you'); Note unusual correspondences between spelling and sound in exception words; Recognise at least 20-30 high-frequency words in connected text.

Needs first: Knowing all letters, Blending Sounds to Read Words.

https://lightmysky.com/learn/english/reading-high-frequency-words-by-sight-mt_YKkCM63fSC

#### Reading Inflectional Endings (ages 5-7)

Read words containing taught GPCs with common inflectional endings (-s, -es, -ing, -ed, -er, -est) and the prefix un-; read multi-syllable words with taught patterns

Ready when they can: Read suffixed words fluently (e.g. 'jumping', 'wanted', 'faster'); Identify the root word when a suffix is added; Read words with prefix un- (e.g. 'unhappy', 'undo').

Needs first: Blending Sounds to Read Words.

https://lightmysky.com/learn/english/reading-inflectional-endings-mt__CMXZiPfTV

#### Trigraphs (ages 5-6)

Read and spell words containing trigraphs — three-letter graphemes representing a single sound (igh, air, ear, are)

Ready when they can: Read words with trigraphs (e.g. 'night', 'chair', 'near'); Distinguish between different sounds for 'ear' (e.g. 'hear' vs 'bear'); Identify the single phoneme represented by three letters in a word.

Needs first: Consonant Digraphs, Vowel Digraphs.

https://lightmysky.com/learn/english/trigraphs-mt_roAgL1rQRF

#### Split Digraphs and Magic E (ages 5-7)

Read and spell words containing split digraphs (a-e, e-e, i-e, o-e, u-e) where a final 'e' makes the preceding vowel long

Ready when they can: Read words with split digraphs (e.g. 'cake', 'bike', 'home', 'cube'); Compare minimal pairs showing the effect of the split digraph (e.g. 'cap' vs 'cape'); Spell words with split digraphs correctly.

Needs first: Vowel Digraphs, Trigraphs.

https://lightmysky.com/learn/english/split-digraphs-and-magic-e-mt_C7abt7pRr6

#### Alternative Spellings for Known Sounds (ages 6-8)

Recognise alternative grapheme-phoneme correspondences for known phonemes (e.g., /dʒ/ as ge/dge/g, /s/ as c, /n/ as kn/gn, /r/ as wr, /ʒ/ as s), reading words with less common spellings for familiar sounds

Ready when they can: Read words with less common spellings for familiar sounds: 'badge', 'giraffe', 'city', 'knock', 'gnaw', 'write', 'treasure'; Identify that the same phoneme can be represented by different graphemes (e.g., /dʒ/ spelled g, ge, dge); Select the correct alternative GPC to decode an unfamiliar word in context.

Needs first: Consonant Digraphs, Blending Sounds to Read Words, Trigraphs, Split Digraphs and Magic E, Diphthongs and complex vowels, R-Controlled Vowel Sounds.

https://lightmysky.com/learn/english/alternative-spellings-for-known-sounds-mt_OgJPbGkrYk

#### Syllables (age 6+) (ages 6-9)

Decode words of two or more syllables by breaking them into syllable chunks, applying knowledge that every syllable must contain a vowel sound, and blending the parts together

Ready when they can: Read 'rabbit', 'thunder', 'fantastic' by breaking into syllable chunks and blending; Clap or tap syllables in a multi-syllable word, then read each chunk before blending; Identify that every syllable must contain a vowel sound.

Needs first: Blending Sounds to Read Words, Alternative Spellings for Known Sounds, Syllables.

https://lightmysky.com/learn/english/syllables-age-6-mt_kVzAFMuFc4

#### Reading fluently (ages 5-7)

Read aloud books matched to phonic ability accurately and with growing fluency; reread familiar texts to build confidence, speed, and expression

Ready when they can: Read a phonically appropriate text with 90%+ accuracy; Reread familiar texts with improved pace and expression; Read emergent-reader texts with purpose and understanding.

Needs first: Starting and Ending Sentences, Blending Sounds to Read Words, Reading High-Frequency Words by Sight.

https://lightmysky.com/learn/english/reading-fluently-mt_ZhvwM6LMBL

#### Reading with Expression and Accuracy (ages 6-10)

Read aloud with accuracy, appropriate rate, and expression (prosody), re-reading familiar texts to build fluency and confidence, and using context to self-correct

Ready when they can: Read a grade-level passage aloud with expression and appropriate pacing; Self-correct miscues during oral reading by re-reading or using context cues; Re-read a familiar book demonstrating increased fluency and confidence.

Needs first: Building sentences, Alternative Spellings for Known Sounds, Reading fluently.

https://lightmysky.com/learn/english/reading-with-expression-and-accuracy-mt_V-ldQp56bF

#### Decoding unfamiliar words (ages 7-9)

Read Y3-4 exception words with unusual spelling-sound correspondences, applying growing knowledge of morphology and etymology to decode unfamiliar exception words

Ready when they can: Read exception words from the Y3-4 statutory word list accurately (e.g. 'business', 'caught', 'knowledge', 'different'); Identify unusual letter-sound correspondences in exception words and explain why the word does not follow common GPC rules; Use growing knowledge of morphology and etymology to attempt unfamiliar exception words (e.g. recognise the root 'know' in 'knowledge').

Needs first: Reading High-Frequency Words by Sight, Root Words & Inflections, Syllables (age 6+).

https://lightmysky.com/learn/english/decoding-unfamiliar-words-mt_14OR-MhGJ9

#### Prefixes and suffixes (ages 7-9)

Read words containing common prefixes and suffixes from the Y3-4 programme, applying knowledge of root words, prefixes and suffixes (morphology and etymology) to read aloud and understand new words

Ready when they can: Read words with common prefixes (dis-, mis-, re-, pre-) and suffixes (-ation, -ous, -ly) by identifying the root word first; Apply morphological knowledge to attempt unfamiliar words (e.g. recognise 'happy' inside 'unhappiness'); Explain how a prefix or suffix changes the meaning or word class of a root word (e.g. 'care' → 'careless' → 'carelessly').

Needs first: Reading Inflectional Endings, Basic Nouns & Verbs, Adjectives vs adverbs.

https://lightmysky.com/learn/english/prefixes-and-suffixes-mt_HrgDjxcWvf

### Spelling & Word Study

https://lightmysky.com/learn/english/areas/spelling-and-word-study

#### Phonics Vocabulary (ages 4-7)

Know and use the vocabulary of phonics and word structure — phoneme, grapheme, GPC (grapheme-phoneme correspondence), blend, segment, digraph, CVC, vowel, consonant, syllable, root word, suffix, prefix, and homophone — and understand that these words describe the building blocks that phonics instruction is built on

Ready when they can: Say the sounds for common graphemes (e.g. 'sh', 'ch', 'th', 'ee', 'igh') and use 'phoneme' and 'grapheme' correctly when explaining; Blend sounds together to read an unfamiliar word and explain what they are doing using the word 'blend'; Segment a word into its individual sounds for spelling and use the term 'segment' to describe the process.

https://lightmysky.com/learn/english/phonics-vocabulary-mt_EqXlZfB4jp

#### Segmenting words into sounds (ages 4-7)

Segment spoken words into phonemes and spell CVC and simple phonetically regular words by writing a letter or letters for each sound

Ready when they can: Write CVC words from dictation (e.g. 'cat', 'bed', 'hot'); Segment words into individual sounds before choosing letters to write; Spell simple words phonetically drawing on sound-letter knowledge.

Needs first: Phonics Vocabulary, Single Letter Sounds, Onsets & Rimes, Sitting and holding a pencil.

https://lightmysky.com/learn/english/segmenting-words-into-sounds-mt_BhYJZUsErp

#### Spelling Verb Endings (ages 5-6)

Spell words with common suffixes (-s/-es for plurals and third person verbs, -ing, -ed, -er, -est) where no change to the root word is needed

Ready when they can: Add -s or -es correctly to make plurals (e.g. 'cats', 'boxes'); Spell words with -ing and -ed endings (e.g. 'jumping', 'helped'); Add -er and -est to adjectives (e.g. 'quicker', 'quickest').

Needs first: Segmenting words into sounds, Phonics Vocabulary.

https://lightmysky.com/learn/english/spelling-verb-endings-mt_QdMMLRYWhn

#### The Prefix un- (ages 5-6)

Spell words using the prefix un- to change meaning; understand that un- creates opposites or reverses actions

Ready when they can: Spell words with un- prefix correctly (e.g. 'unhappy', 'unfair', 'undo'); Explain how un- changes the meaning of a word; Create new words by adding un- to known words.

Needs first: Segmenting words into sounds, Phonics Vocabulary.

https://lightmysky.com/learn/english/the-prefix-un-mt_zBUcAPDRPM

#### Tricky words (ages 5-8)

Spell common exception words from memory that do not follow regular phonic patterns, including the days of the week

Ready when they can: Correctly spell high-frequency irregular words (e.g. 'said', 'the', 'was'); Write all seven days of the week correctly; Recall and write exception words in dictated sentences.

Needs first: Segmenting words into sounds, Knowing all letters.

https://lightmysky.com/learn/english/tricky-words-mt_Jq0MjURrRC

#### Alternative Spellings for Sounds (ages 6-9)

Spell words using alternative grapheme choices for known phonemes, learning new spellings for sounds already encountered (e.g., /ɔ:/ as 'a' before ll, /ʌ/ as 'o', words ending -tion), including distinguishing common homophones

Ready when they can: Spell 'ball', 'call', 'walk' using alternative grapheme /ɔ:/ as 'a' before ll; Distinguish homophones in writing: 'there/their/they’re', 'here/hear', 'quite/quiet'; Spell words ending in -tion correctly: 'station', 'fiction', 'motion'.

Needs first: Segmenting words into sounds, Phonics Vocabulary, Single Letter Sounds, Alternative Spellings for Known Sounds.

https://lightmysky.com/learn/english/alternative-spellings-for-sounds-mt_p_jxNLdus4

#### Spelling Contracted Forms (ages 6-7)

Spell contracted forms correctly by placing the apostrophe where letters are omitted (can't, didn't, I'll, it's, etc.)

Ready when they can: Write 'can't' for 'cannot', 'didn't' for 'did not' with apostrophe correctly placed; Distinguish 'it's' (it is) from 'its' (possessive) in a sentence; Expand a contraction back to its full form and explain which letters are missing.

Needs first: Segmenting words into sounds, Reading Contractions.

https://lightmysky.com/learn/english/spelling-contracted-forms-mt_IntmJBg4VQ

#### Suffixes (ages 6-7)

Apply suffix spelling rules that require changes to the root word: dropping final -e before vowel suffixes, changing -y to -i, doubling final consonants in short-vowel words; use suffixes -ment, -ness, -ful, -less, -ly

Ready when they can: Spell 'hoping' (drop e), 'cried' (y to i), 'running' (double consonant) applying the correct rule; Add -ful, -less, -ness, -ly correctly: 'careful', 'hopeless', 'sadness', 'slowly'; Identify which suffix rule to apply to a given root word and explain why.

Needs first: Segmenting words into sounds, Phonics Vocabulary, Spelling Verb Endings, Split Digraphs and Magic E.

https://lightmysky.com/learn/english/suffixes-mt_FYK8m6eHQm

#### Homophones (ages 7-9)

Distinguish and correctly spell common homophones and near-homophones encountered at Y3-4 level (e.g., accept/except, affect/effect, brake/break, grate/great), including using the /eɪ/ sound spelt ei, eigh, or ey

Ready when they can: Spell pairs of homophones correctly in context (e.g., 'there/their/they're', 'brake/break', 'grate/great'); Choose the correct homophone to complete a sentence (e.g., 'The dog wagged its/it's tail'); Spell words with the /eɪ/ sound as ei, eigh, or ey (e.g., vein, eight, they, neighbour).

Needs first: Phonics Vocabulary, Alternative Spellings for Sounds, Reading High-Frequency Words by Sight.

https://lightmysky.com/learn/english/homophones-mt_37QCuGOxFe

#### Prefixes (age 7+) (ages 7-10)

Spell words with a range of prefixes (dis-, mis-, un-, re-, pre-, anti-, auto-, super-) understanding how each prefix modifies the root word's meaning without changing its spelling

Ready when they can: Spell words with prefixes dis-, mis-, re- correctly without altering the root (e.g., disappoint, misspell, return); Add prefixes un-, pre-, anti-, auto-, super- to root words and use the new word in a sentence (e.g., unhappy, preview, autograph); Explain how a prefix changes the meaning of a root word (e.g., 'dis-' means 'not' or 'opposite of').

Needs first: Suffixes, The Prefix un-.

https://lightmysky.com/learn/english/prefixes-age-7-mt_T6nrrf2K43

#### Spelling Word Lists (age 7+) (ages 7-9)

Spell words from the statutory word list for Years 3 and 4, including commonly misspelt words that do not follow regular patterns

Ready when they can: Spell at least 20 words from the Y3-4 statutory list correctly (e.g., accident, believe, different, favourite, imagine); Identify tricky parts of statutory words and use a strategy to remember them (e.g., 'separate' has 'a rat' in the middle); Use statutory list words accurately in own writing across subjects.

Needs first: Tricky words, Alternative Spellings for Sounds.

https://lightmysky.com/learn/english/spelling-word-lists-age-7-mt_O2dS6gvClw

#### Suffixes (age 7+) (ages 7-9)

Spell words using productive suffixes (-ation, -ly, -ous) and less common sound-spelling correspondences (/ɪ/ as y, /ʌ/ as ou, endings sounding like /ʒə/, /tʃə/, /ʒən/, /ʃən/) introduced in the Year 3-4 programme

Ready when they can: Spell words with suffixes -ation (e.g., information, sensation), -ly (e.g., sadly, gently, happily), and -ous (e.g., famous, enormous, various); Spell words with less common vowel patterns: /ɪ/ as y (e.g., myth, gym), /ʌ/ as ou (e.g., young, touch, double); Spell words with endings /ʒə/ as -sure (e.g., measure, treasure), /tʃə/ as -ture (e.g., creature, furniture), /ʒən/ as -sion (e.g., division, television).

Needs first: Suffixes, Spelling Verb Endings.

https://lightmysky.com/learn/english/suffixes-age-7-mt_tHtjfjjFrl

#### Spellings from Greek, French and Latin (ages 8-10)

Spell words with etymological letter patterns from Greek (ch = /k/), French (ch = /ʃ/, -gue, -que), and Latin (sc = /s/) origins

Ready when they can: Spell words with Greek ch such as 'scheme', 'chorus', 'chemist', 'echo' and explain the /k/ sound pattern; Spell words with French ch such as 'chef', 'chalet', 'machine' and -gue/-que endings like 'league', 'unique'; Spell words with Latin sc such as 'science', 'scene', 'discipline' and identify the silent letter pattern.

Needs first: Suffixes (age 7+).

https://lightmysky.com/learn/english/spellings-from-greek-french-and-latin-mt_y8sicbhMci

#### Advanced Spelling Conventions (ages 9-10)

Spell words using assorted Y5-6 conventions: doubling after -fer when the stress remains (referring but reference), using hyphens to join prefixes to root words (co-ordinate, re-enter), the /iː/ sound spelt ei after c (receive, ceiling), and the letter string ough representing different sounds (though, through, thought, thorough, plough)

Ready when they can: Apply the -fer doubling rule: double the r when the syllable is stressed (referring, preferred, transferred) but not when stress shifts (reference, preference); Use hyphens correctly when a prefix ends with the same letter the root begins with (re-enter, co-own) or to avoid ambiguity (re-cover vs recover); Read and spell words containing ough by recognising its multiple pronunciations: /oʊ/ (though), /uː/ (through), /ɔː/ (thought), /ʌf/ (rough), /aʊ/ (plough).

Needs first: Prefixes (age 7+), Spellings from Greek, French and Latin.

https://lightmysky.com/learn/english/advanced-spelling-conventions-mt_U_HQXCnAaG

#### Homophones (age 9+) (ages 9-10)

Distinguish and correctly spell homophones and commonly confused words at Y5-6 level (e.g., affect/effect, practice/practise, advice/advise, complement/compliment, aisle/isle, led/lead), including confused words such as to/too/two and there/their/they're

Ready when they can: Select the correct spelling from a pair of homophones by analysing meaning in context, e.g. 'The doctor's advice (noun) was to practise (verb) daily'; Spell commonly confused words accurately by applying word-class clues: advise/advice, practise/practice, licence/license (verb ends in -ise, noun ends in -ice); Identify and correct homophone errors in extended writing, including to/too/two, there/their/they're, whose/who's, and its/it's.

Needs first: Homophones.

https://lightmysky.com/learn/english/homophones-age-9-mt_u3OuIXqmAo

#### Silent Letters in Words (ages 9-10)

Spell words containing silent letters that are remnants of earlier pronunciation or etymology, recognising common silent-letter patterns and using word origins to remember them

Ready when they can: Identify and spell words with silent initial consonants: knight, know, write, wrap, gnaw, psalm, applying knowledge that these letters were once pronounced; Spell words with silent internal letters: doubt (b), island (s), muscle (c), solemn (n), using etymological connections to aid memory (e.g. doubt from Latin dubitare); Use word families and etymology to remember silent letters, e.g. sign is related to signal where the g is pronounced.

Needs first: Spellings from Greek, French and Latin.

https://lightmysky.com/learn/english/silent-letters-in-words-mt_XK7NYt61cO

#### Spelling -able & -ible (ages 9-10)

Spell words ending in -able/-ible and the corresponding adverb forms -ably/-ibly, applying patterns to determine which suffix to use based on the root word

Ready when they can: Apply the guideline that -able is typically used with complete root words (enjoyable, comfortable) while -ible is used with incomplete roots (visible, possible), noting key exceptions; Convert -able/-ible adjectives into adverbs by changing the ending to -ably/-ibly, e.g. comfortable → comfortably, possible → possibly, terrible → terribly; Determine whether to drop or retain the final -e of the root when adding -able, e.g. adorable (drop e) vs changeable (keep e before soft g).

Needs first: Suffixes (age 7+).

https://lightmysky.com/learn/english/spelling-able-and-ible-mt_9hBs430cU4

#### Spelling Word Lists (age 9+) (ages 9-10)

Spell words from the statutory word list for Years 5 and 6, including words with irregular or uncommon spelling patterns that must be learned individually

Ready when they can: Spell high-frequency words from the Y5-6 list accurately in dictated sentences, e.g. accommodate, committee, correspond, exaggerate, immediately, necessary; Use look-cover-write-check and mnemonic strategies to learn words with tricky patterns such as 'separate' (a rat in separate), 'rhythm' (rhythm helps your two hips move); Identify and self-correct misspellings of statutory list words when proof-reading extended writing.

Needs first: Spelling Word Lists (age 7+).

https://lightmysky.com/learn/english/spelling-word-lists-age-9-mt_sJyZW4qYUG

#### Suffixes (age 9+) (ages 9-10)

Spell words with Latin and French suffix patterns: endings sounding like /ʃəs/ spelt -cious or -tious (e.g., precious, cautious), /ʃəl/ spelt -cial or -tial (e.g., official, essential), and words ending in -ant/-ance/-ancy vs -ent/-ence/-ency (e.g., observant/observance, confident/confidence)

Ready when they can: Apply the pattern that -cious follows a vowel (spacious, gracious) while -tious follows a consonant (cautious, ambitious), noting common exceptions like anxious; Choose between -cial (usually after a vowel: special, official) and -tial (usually after a consonant: essential, partial) when spelling words with the /ʃəl/ ending; Select -ant/-ance or -ent/-ence by checking whether the root ends in a hard c or g sound (-ant: significant) or a soft c or g sound (-ent: innocent), and by applying word-family strategies.

Needs first: Suffixes (age 7+).

https://lightmysky.com/learn/english/suffixes-age-9-mt_2X9Cd38eSJ

#### Apostrophes for possession (ages 6-8)

Use the possessive apostrophe with singular nouns to show ownership (e.g., the girl's book, the dog's bone)

Ready when they can: Write 'the cat's tail' to show the tail belongs to the cat; Distinguish plural -s ('the cats ran') from possessive 's ('the cat's bed') in writing; Add a possessive apostrophe to a singular noun in a dictated sentence.

Needs first: Regular Plural Nouns, Spelling Contracted Forms, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/apostrophes-for-possession-mt_Z3G_97fnha

#### Spelling from Dictation (ages 5-8)

Write simple sentences from memory when dictated by the teacher, applying taught GPCs, spelling rules, and common exception words

Ready when they can: Write a dictated sentence using phonically plausible spellings; Include correct spelling of taught exception words in dictation; Apply sentence punctuation in dictated writing.

Needs first: Segmenting words into sounds, Phonics Vocabulary, Tricky words, Starting and Ending Sentences.

https://lightmysky.com/learn/english/spelling-from-dictation-mt_AhfyJoTQtY

#### Apostrophes for possession (age 7+) (ages 7-10)

Use the possessive apostrophe accurately with both regular and irregular plural nouns (e.g., the girls' bags, the children's toys), distinguishing singular from plural possession

Ready when they can: Place the apostrophe correctly in plural possessives: 'the dogs' kennel' vs 'the dog's kennel'; Write possessive forms of irregular plurals correctly (e.g. 'children's', 'women's', 'mice's'); Distinguish singular possession (the boy's hat) from plural possession (the boys' hats) in dictated sentences.

Needs first: Irregular Plural Nouns, Apostrophes for possession.

https://lightmysky.com/learn/english/apostrophes-for-possession-age-7-mt_HdI1y5KsBl

#### Using a Dictionary to Check Spellings (ages 7-11)

Use the first two or three letters of a word to check its spelling in a dictionary; consult reference materials including beginning dictionaries to verify and correct spellings

Ready when they can: Locate a word in a dictionary using its first two or three letters (e.g., find 'beautiful' by looking up 'be-'); Check and correct a misspelling by comparing with the dictionary entry (e.g., look up 'freind' → 'friend'); Use a glossary or beginning dictionary to confirm spelling of a word used in own writing.

Needs first: Knowing all letters, Non-Fiction Text Features.

https://lightmysky.com/learn/english/using-a-dictionary-to-check-spellings-mt_6W5zzDIGZH

#### Applying Spelling Rules to Complex Words (ages 11-14)

Spell correctly and consistently, applying the spelling patterns and rules from KS1-2 to increasingly complex vocabulary encountered in KS3 reading and subject-specific study

Ready when they can: Spell subject-specific vocabulary correctly when encountered in new domains (e.g., 'parliament', 'photosynthesis', 'algorithm'); Apply known spelling rules and etymological patterns to unfamiliar words; Use proofreading strategies to identify and correct spelling errors in own extended writing.

Needs first: Spelling Word Lists (age 9+), Spellings from Greek, French and Latin, Hyphens in Prefixed Words, Advanced Spelling Conventions, Homophones (age 9+), Silent Letters in Words, Spelling -able & -ible, Suffixes (age 9+).

https://lightmysky.com/learn/english/applying-spelling-rules-to-complex-words-mt_4PA9IrxtCQ

#### Proofreading Under Time Pressure (ages 14-16)

Find your own errors in the minutes left at the end, not the ones a reader would find in a week. Know which mistakes you personally make, look for those first, and read in the way that exposes them rather than in the way that reads smoothly past them.

Ready when they can: Keep a short list of the errors they make repeatedly and check for those first; Read a draft in a way that breaks the flow, backwards by sentence or aloud, and catch what silent reading missed; Correct spelling, apostrophes and sentence boundaries in a timed piece without rewriting whole sentences.

https://lightmysky.com/learn/english/proofreading-under-time-pressure-mt_F3XNYambhL

### Grammar & Punctuation

https://lightmysky.com/learn/english/areas/grammar-and-punctuation

#### Building sentences (ages 4-6)

Understand that words combine to make sentences — a sentence expresses a complete thought; produce and expand complete sentences in speech and writing

Ready when they can: Distinguish between complete sentences and fragments; Compose a complete sentence with a subject and verb; Expand a simple sentence by adding detail.

https://lightmysky.com/learn/english/building-sentences-mt_N8CpN1EJrP

#### Spaces Between Words (ages 4-6)

Separate words with spaces in writing; understand that spaces mark word boundaries in print

Ready when they can: Leave clear finger-spaces between words when writing; Count the number of words in a written sentence by identifying spaces; Correct writing that has missing spaces between words.

Needs first: Understanding print, Building sentences.

https://lightmysky.com/learn/english/spaces-between-words-mt_of2GggtxFl

#### Basic Nouns & Verbs (ages 5-6)

Use frequently occurring nouns (people, places, things) and verbs (action words) appropriately in speech and writing

Ready when they can: Use common nouns accurately in sentences (e.g. 'dog', 'school', 'book'); Use action verbs appropriately (e.g. 'run', 'eat', 'play'); Identify nouns and verbs in simple sentences when prompted.

https://lightmysky.com/learn/english/basic-nouns-and-verbs-mt_yBJyCfhtem

#### Joining Words with 'And' (ages 5-7)

Join words and clauses using the conjunction 'and' to create longer sentences

Ready when they can: Combine two simple sentences using 'and' (e.g. 'I like cats and dogs'); Join two related clauses with 'and' (e.g. 'We went to the park and we played'); Use 'and' in lists of items within a sentence.

Needs first: Building sentences.

https://lightmysky.com/learn/english/joining-words-with-and-mt_YXVQaufkKO

#### Regular Plural Nouns (ages 5-6)

Form and use regular plural nouns orally and in writing by adding -s or -es; understand that plural means more than one

Ready when they can: Say and write correct plural forms (e.g. 'one cat, two cats'; 'one wish, two wishes'); Choose -s or -es correctly based on the ending sound; Explain that plural nouns name more than one.

Needs first: Basic Nouns & Verbs.

https://lightmysky.com/learn/english/regular-plural-nouns-mt_18qkgxr_-T

#### Starting and Ending Sentences (ages 5-8)

Begin sentences with a capital letter and end them with the appropriate mark (full stop, question mark, or exclamation mark); recognise and name end punctuation

Ready when they can: Write sentences beginning with a capital letter; Choose and use the correct end punctuation for statements, questions, and exclamations; Identify and name full stops, question marks, and exclamation marks when reading.

Needs first: Spaces Between Words.

https://lightmysky.com/learn/english/starting-and-ending-sentences-mt_QEr24lqzvH

#### Capitals for Names, Days and I (ages 5-7)

Use capital letters for proper nouns (names of people, places) the days of the week, and the personal pronoun 'I'

Ready when they can: Capitalise names of people and places consistently in writing; Write the pronoun 'I' as a capital letter; Capitalise days of the week (e.g. 'Monday').

Needs first: Starting and Ending Sentences.

https://lightmysky.com/learn/english/capitals-for-names-days-and-i-mt_uM6q_KBWKy

#### Grammar words: letter, word, sentence (ages 5-6)

Use basic grammatical terminology when discussing reading and writing: letter, capital letter, word, singular, plural, sentence, punctuation, full stop, question mark, exclamation mark

Ready when they can: Name punctuation marks correctly when pointed out in text; Use terms like 'capital letter' and 'full stop' when editing writing; Explain what a 'sentence' is using the correct term.

Needs first: Building sentences, Starting and Ending Sentences.

https://lightmysky.com/learn/english/grammar-words-letter-word-sentence-mt_TfOiog-ALs

#### Apostrophes: Contraction and Possession (ages 6-7)

Use apostrophes in writing for both contraction (marking omitted letters) and singular possession, distinguishing the two uses

Ready when they can: Use apostrophes correctly in both 'don't' and 'Sam's bag' within the same piece of writing; Explain the difference between apostrophe for contraction and apostrophe for possession; Correct misplaced or missing apostrophes in a set of sentences.

Needs first: Spelling Contracted Forms, Starting and Ending Sentences, Apostrophes for possession.

https://lightmysky.com/learn/english/apostrophes-contraction-and-possession-mt_mKAZTqItRG

#### Commas in lists (ages 6-11)

Use commas to separate items in a list within a sentence (e.g., 'I bought apples, bananas, and oranges')

Ready when they can: Write a sentence containing a list of 3+ items separated by commas: 'I bought apples, bananas, and oranges'; Identify where commas should go in an unpunctuated list sentence; Explain that commas separate items in a list so the reader knows each item.

Needs first: Building sentences, Starting and Ending Sentences.

https://lightmysky.com/learn/english/commas-in-lists-mt_ntqNLHsj5n

#### Determiners and articles (ages 6-7)

Use determiners (articles a/an/the and demonstratives this/that/these/those) correctly before nouns

Ready when they can: Use 'a' before consonant sounds and 'an' before vowel sounds correctly: 'a ball', 'an apple'; Distinguish 'this/these' (near) from 'that/those' (far) when pointing to objects; Select the correct article (a/an/the) to complete a sentence.

Needs first: Basic Nouns & Verbs.

https://lightmysky.com/learn/english/determiners-and-articles-mt_RioBUxHz1X

#### Four Types of Sentences (ages 6-7)

Understand and use the four sentence types — statement, question, exclamation, and command — recognising how grammatical patterns indicate sentence function

Ready when they can: Write or identify a statement, question, exclamation, and command from a set of sentences; Match each sentence type to its correct end punctuation mark; Transform a statement into a question or command on request.

Needs first: Starting and Ending Sentences.

https://lightmysky.com/learn/english/four-types-of-sentences-mt_u1-UfD0rTH

#### Pronouns (ages 6-7)

Use personal, possessive, and indefinite pronouns correctly (e.g., I/me/my, they/them/their, anyone/everything), replacing nouns to avoid repetition

Ready when they can: Replace a repeated noun with a pronoun: 'The dog was happy. He wagged his tail.'; Use I/me correctly in subject and object position in a sentence; Choose the correct possessive pronoun (my/his/her/their) to match the noun it replaces.

Needs first: Building sentences, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/pronouns-mt_sZXPK1FnRB

#### Subject-verb agreement (ages 6-7)

Use singular and plural nouns with matching verbs in sentences, maintaining subject-verb agreement (e.g., 'He hops' vs 'We hop')

Ready when they can: Write 'The dog runs' (singular) and 'The dogs run' (plural) with correct verb agreement; Correct subject-verb agreement errors in sentences: fix 'The children plays' to 'The children play'; Choose the correct verb form to match a singular or plural subject in a gap-fill exercise.

Needs first: Regular Plural Nouns, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/subject-verb-agreement-mt_u7Jxjjatkh

#### Choosing A or An (ages 7-8)

Use the correct form of the indefinite article — 'a' before words beginning with a consonant sound and 'an' before words beginning with a vowel sound (e.g., a rock, an open box, an hour, a unicorn)

Ready when they can: Choose 'a' or 'an' correctly before nouns beginning with consonant or vowel sounds (e.g., 'a ball', 'an egg', 'an umbrella'); Apply the rule to tricky words where spelling and sound differ (e.g., 'an hour' because /h/ is silent, 'a uniform' because /juː/ starts with a consonant sound); Correct errors in a/an usage in given sentences (e.g., change 'a orange' to 'an orange').

Needs first: Determiners and articles, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/choosing-a-or-an-mt_2l06snztdP

#### Irregular Plural Nouns (ages 7-9)

Form and use irregular plural nouns (e.g., children, teeth, mice, geese) in addition to regular plurals, recognising that some nouns have irregular plural forms that do not follow the -s/-es pattern

Ready when they can: Form and use irregular plural nouns correctly (e.g. child→children, tooth→teeth, mouse→mice, goose→geese); Identify collective nouns that name a group (e.g. 'a flock of birds', 'a group of children', 'a pack of wolves'); Correct over-regularised plurals in writing (e.g. change 'mouses' to 'mice', 'foots' to 'feet').

Needs first: Regular Plural Nouns.

https://lightmysky.com/learn/english/irregular-plural-nouns-mt_nFBLNoChD0

#### Pronouns for clarity (ages 7-9)

Choose pronouns for clarity and cohesion, avoiding ambiguity and repetition; use reflexive pronouns correctly (e.g., myself, ourselves, himself)

Ready when they can: Replace repeated nouns with pronouns to improve cohesion: rewrite 'Sam picked up Sam's bag' as 'Sam picked up his bag'; Use reflexive pronouns correctly in sentences (e.g. 'I made it myself', 'They helped themselves'); Identify and fix ambiguous pronoun references (e.g. 'Tom told Jack he was late' — who was late?).

Needs first: Pronouns.

https://lightmysky.com/learn/english/pronouns-for-clarity-mt_9yFAtUkoYr

#### Abstract nouns (ages 8-9)

Understand and use abstract nouns to name ideas, qualities, and states that cannot be perceived by the senses

Ready when they can: Sort words like 'freedom', 'table', 'courage', 'pencil', 'childhood' into abstract and concrete noun categories; Complete sentences using appropriate abstract nouns: 'Her _____ (brave → bravery) inspired the whole team'; Write three sentences each containing a different abstract noun (e.g. 'honesty', 'friendship', 'happiness').

Needs first: Basic Nouns & Verbs.

https://lightmysky.com/learn/english/abstract-nouns-mt_8bIXVKTdtK

#### Agreement in sentences (ages 8-10)

Ensure subject-verb agreement and pronoun-antecedent agreement within and across sentences

Ready when they can: Correct 'The group of children were laughing' to 'The group of children was laughing' and explain the singular subject; Choose the correct pronoun in 'Each student must bring ____ (his or her / their) book' and explain the antecedent link; Identify and fix three agreement errors in a short paragraph, explaining each correction.

Needs first: Pronouns for clarity, Subject-verb agreement.

https://lightmysky.com/learn/english/agreement-in-sentences-mt_2NfIKEYdbm

#### Plural vs Possessive in Nouns (ages 8-9)

Distinguish between the plural -s suffix and the possessive -'s suffix in nouns

Ready when they can: Sort words like 'dogs', 'dog's', and 'dogs'' into plural, singular possessive, and plural possessive categories; Explain why 'the cats bowl' is incorrect and supply the correct form ('the cat's bowl' or 'the cats' bowl') for a given meaning; Write two sentences using the same noun — one as a plural and one as a possessive.

Needs first: Apostrophes: Contraction and Possession, Apostrophes for possession.

https://lightmysky.com/learn/english/plural-vs-possessive-in-nouns-mt_bn5ggh84qD

#### Converting Words into Verbs (ages 9-10)

Convert nouns and adjectives into verbs by adding suffixes -ate, -ise (-ize), and -ify, understanding how word class changes affect sentence construction

Ready when they can: Add -ate, -ise, or -ify to nouns or adjectives to form verbs, e.g. pollen → pollinate, advert → advertise, simple → simplify; Choose the correct verb-forming suffix for a given root and use the resulting verb in a sentence, e.g. 'They needed to classify the animals' from 'class'; Identify the word-class change when a suffix converts a noun or adjective into a verb and explain how this affects the sentence structure.

Needs first: Suffixes (age 7+), Basic Nouns & Verbs.

https://lightmysky.com/learn/english/converting-words-into-verbs-mt_p3tZiUaWAa

#### Verb Prefixes and Meaning (ages 9-10)

Use verb prefixes (dis-, de-, mis-, over-, re-) to change verb meaning, understanding how each prefix modifies the action expressed by the root verb

Ready when they can: Add verb prefixes to change meaning, e.g. dis- (disagree, disappear), de- (decompose, defrost), mis- (misunderstand, misbehave), over- (overlook, overreact), re- (redo, reconsider); Select the appropriate verb prefix to express a specific meaning shift such as negation (dis-/mis-), reversal (de-/un-), repetition (re-), or excess (over-); Distinguish verb prefixes from noun/adjective prefixes and explain how adding a prefix to a verb changes the action described.

Needs first: Prefixes (age 7+), Basic Nouns & Verbs.

https://lightmysky.com/learn/english/verb-prefixes-and-meaning-mt_qw6mhOl-Qy

#### Colons and Semicolons in Lists (ages 10-11)

Use a colon to introduce a list and semi-colons to separate items within lists, particularly when list items contain internal commas or are complex phrases

Ready when they can: Introduce a list with a colon after an independent clause such as 'You will need the following items:'; Use semi-colons to separate list items that contain commas such as locations with city and country; Punctuate complex lists in formal writing maintaining clarity and consistency.

Needs first: Commas in lists.

https://lightmysky.com/learn/english/colons-and-semicolons-in-lists-mt_uycuqPaiJ1

#### Bullet Point Punctuation (ages 10-11)

Punctuate bullet points consistently to list information clearly, applying conventions for capitalisation, end punctuation, and parallel structure across items

Ready when they can: Create bullet point lists with consistent capitalisation and punctuation throughout; Use full stops for bullet points that are complete sentences and no punctuation for fragments; Maintain parallel grammatical structure across all items in a bulleted list.

Needs first: Commas in lists, Colons and Semicolons in Lists.

https://lightmysky.com/learn/english/bullet-point-punctuation-mt_wUyAZJikAA

#### Prepositions (ages 5-7)

Understand and use the most frequently occurring prepositions of location and direction (e.g. to, from, in, out, on, off, for, by, with)

Ready when they can: Use prepositions correctly in sentences (e.g. 'on the table', 'under the bed'); Follow instructions involving prepositions (e.g. 'Put the book on the shelf'); Describe positions using prepositional phrases.

Needs first: Listening and responding.

https://lightmysky.com/learn/english/prepositions-mt_VY3rBq8RyP

#### Question Words (ages 5-6)

Understand and use question words (who, what, where, when, why, how) to form and answer questions

Ready when they can: Ask questions using appropriate question words; Answer who, what, where, when questions about familiar topics; Recognise that question words signal a question is being asked.

Needs first: Listening and responding.

https://lightmysky.com/learn/english/question-words-mt_6lHBTwQPrS

#### Subordinate clauses (ages 6-9)

Use subordination (when, if, that, because) and co-ordination (or, and, but) to join clauses and create compound and complex sentences

Ready when they can: Write 'I stayed inside because it was raining' using a subordinating conjunction; Use 'but' and 'or' to join ideas: 'I wanted to play but it was raining'; Use 'when' and 'if' clauses in writing: 'If it stops raining, we can go outside'.

Needs first: Listening and responding, Four Types of Sentences, Joining Words with 'And'.

https://lightmysky.com/learn/english/subordinate-clauses-mt_wq-1OJ_8s5

#### Expressing Time, Place and Cause (ages 7-8)

Use conjunctions (when, before, after, while, so, because), adverbs (then, next, soon, therefore) and prepositions (before, after, during, in, because of) to express time, place and cause within and across sentences

Ready when they can: Use time conjunctions to connect clauses (e.g., 'We went inside because it was raining', 'After the bell rang, we lined up'); Use adverbs of time and cause within sentences (e.g., 'First, she opened the door. Then, she stepped outside. Therefore, she got wet.'); Use prepositions of time and cause in phrases (e.g., 'during the lesson', 'before lunch', 'because of the rain').

Needs first: Prepositions, Subordinate clauses.

https://lightmysky.com/learn/english/expressing-time-place-and-cause-mt_uorNrPTh6U

#### Fronted Adverbials and Commas (ages 8-9)

Use fronted adverbials to vary sentence openings and punctuate them with commas

Ready when they can: Write a sentence beginning with a time adverbial, e.g. 'Later that day, the children ran home'; Rewrite 'The fox crept through the garden at midnight' with the adverbial fronted and a comma placed correctly; Identify and correct a missing comma after a fronted adverbial in 'Before breakfast she packed her bag'.

Needs first: Commas in lists, Expressing Time, Place and Cause.

https://lightmysky.com/learn/english/fronted-adverbials-and-commas-mt_0QJoKWABdC

#### Commas Before Joining Words (ages 9-11)

Use a comma before a coordinating conjunction (and, but, or, so, yet) when joining two independent clauses in a compound sentence

Ready when they can: Place a comma before the coordinating conjunction in a compound sentence, e.g. 'I wanted to go outside, but it was raining'; Distinguish compound sentences (two independent clauses) from simple sentences with compound predicates, e.g. 'She sang and danced' needs no comma but 'She sang a song, and he played the piano' does; Edit writing to insert missing commas before coordinating conjunctions in compound sentences.

Needs first: Commas in lists, Subordinate clauses.

https://lightmysky.com/learn/english/commas-before-joining-words-mt_j2idD_jq73

#### Commas to avoid ambiguity (ages 9-10)

Use commas to clarify meaning and avoid ambiguity in sentences where the absence of a comma could cause misreading

Ready when they can: Insert a comma to prevent ambiguity, e.g. 'Let's eat, Grandma' vs 'Let's eat Grandma' or 'Most of the time, travellers worry about their bags'; Identify sentences where a missing comma changes the meaning and explain the two possible readings; Use commas after introductory elements (adverbial phrases, subordinate clauses) to prevent misreading of the main clause.

Needs first: Fronted Adverbials and Commas, Commas in lists.

https://lightmysky.com/learn/english/commas-to-avoid-ambiguity-mt_VMS3kDQ8sA

#### Fixing Fragments & Run-Ons (ages 9-10)

Recognise and correct sentence fragments (incomplete sentences lacking a subject or predicate) and run-on sentences (two or more independent clauses joined without proper punctuation or conjunctions)

Ready when they can: Identify a sentence fragment by checking whether it has both a subject and a predicate, e.g. recognise 'Running through the park' as a fragment and correct to 'The dog was running through the park'; Identify a run-on sentence where two independent clauses are fused without punctuation or a conjunction, e.g. 'I like cats I also like dogs' and correct using a full stop, comma + conjunction, or semicolon; Edit a paragraph to fix fragments and run-ons, choosing the most effective correction strategy for each error.

Needs first: Building sentences, Subordinate clauses.

https://lightmysky.com/learn/english/fixing-fragments-and-run-ons-mt_7oZ2YenzhX

#### Relative Clauses (ages 9-10)

Form and use relative clauses beginning with relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why) to add detail, qualify nouns, and create complex sentences

Ready when they can: Combine a main clause with a relative clause using 'who' or 'which' to add information about a noun, e.g. 'The dog, which had a red collar, barked loudly'; Choose the correct relative pronoun (who for people, which for things, where for places, when for times) and identify the noun it refers back to; Recognise that a relative clause beginning with 'that' can often replace 'who' or 'which' in defining clauses, e.g. 'The book that I read' vs 'The book which I read'.

Needs first: Pronouns for clarity, Subordinate clauses.

https://lightmysky.com/learn/english/relative-clauses-mt_YQ64pzcLDl

#### Commas After Introductory Elements (ages 10-11)

Use a comma to separate an introductory element from the rest of the sentence, including introductory words, phrases, and clauses

Ready when they can: Place commas after introductory adverbs such as 'However' or 'Therefore' at the start of sentences; Use commas after introductory prepositional phrases like 'In the morning' or 'After the game'; Punctuate introductory dependent clauses correctly such as 'When the bell rang, we left'.

Needs first: Fronted Adverbials and Commas, Commas in lists.

https://lightmysky.com/learn/english/commas-after-introductory-elements-mt_0wUwxyBs5y

#### Conjunctions, Prepositions and Interjections (ages 10-11)

Explain the function of conjunctions, prepositions, and interjections in general and in particular sentences, understanding how each word class contributes to meaning

Ready when they can: Identify conjunctions, prepositions, and interjections in sentences and explain their function; Explain how removing a preposition or conjunction changes the meaning of a sentence; Use interjections appropriately to convey emotion in dialogue or informal writing.

Needs first: Expressing Time, Place and Cause, Prepositions, Subordinate clauses.

https://lightmysky.com/learn/english/conjunctions-prepositions-and-interjections-mt_LN_g2b3d34

#### Correlative Conjunctions (ages 10-11)

Use correlative conjunctions correctly in sentences, pairing words such as either/or, neither/nor, both/and, not only/but also, and whether/or

Ready when they can: Write sentences using each pair of correlative conjunctions correctly; Ensure parallel structure when using correlative conjunctions in complex sentences; Identify and correct errors in correlative conjunction usage in given sentences.

Needs first: Subordinate clauses.

https://lightmysky.com/learn/english/correlative-conjunctions-mt_S7CnyZCnxg

#### Punctuating Clauses (ages 10-11)

Use semi-colons, colons, and dashes to mark boundaries between independent clauses, choosing the appropriate punctuation based on the relationship between the clauses

Ready when they can: Join two related independent clauses using a semi-colon in place of a conjunction; Use a colon to introduce an explanation or elaboration of the first clause; Replace commas with dashes to create stronger pauses between clauses for emphasis.

Needs first: Commas Before Joining Words, Subordinate clauses.

https://lightmysky.com/learn/english/punctuating-clauses-mt_xYjD_kA70s

#### The subjunctive mood (ages 10-11)

Use the subjunctive form in formal writing and speech to express wishes, demands, suggestions, or hypothetical situations (e.g., 'If I were you', 'I suggest that he go', 'Were they to arrive')

Ready when they can: Write sentences using 'If I were' to express hypothetical conditions; Transform informal sentences into formal equivalents using subjunctive forms such as 'I recommend that she attend'; Identify subjunctive mood in formal texts such as legal documents or formal letters.

Needs first: Subordinate clauses.

https://lightmysky.com/learn/english/the-subjunctive-mood-mt_k7VtbWdfDO

#### Varying Sentence Structure (ages 10-11)

Expand, combine, and reduce sentences for meaning, reader interest, and style, using techniques such as embedding clauses, using appositives, and varying sentence length

Ready when they can: Combine two simple sentences into one complex sentence using subordination; Expand a simple sentence by adding descriptive phrases and clauses; Reduce wordy sentences by removing redundant words while preserving meaning.

Needs first: Subordinate clauses, Relative Clauses.

https://lightmysky.com/learn/english/varying-sentence-structure-mt_ZO2iP89cld

#### Punctuating Direct Speech (ages 7-10)

Punctuate direct speech using inverted commas (speech marks), understanding that direct speech records the exact words spoken and must be enclosed in punctuation marks

Ready when they can: Place inverted commas around the spoken words in a sentence (e.g., "Let's go!" shouted Tom.); Write a sentence containing direct speech with correct punctuation including a reporting clause (e.g., Mum said, "Time for bed."); Identify direct speech in a text and explain what the inverted commas show.

Needs first: Rehearsing and Varying Sentences, Starting and Ending Sentences, Four Types of Sentences.

https://lightmysky.com/learn/english/punctuating-direct-speech-mt_-mw3JeIjhU

#### Brackets and dashes for parenthesis (ages 9-10)

Use brackets, dashes, and commas to indicate parenthesis — additional information inserted into a sentence that could be removed without changing the sentence's core meaning

Ready when they can: Insert a parenthetical phrase using paired brackets, e.g. 'The oldest building (built in 1642) stands in the town square'; Use paired dashes to add an aside or extra detail within a sentence, e.g. 'My brother — who is older than me — lives in London'; Choose between brackets, dashes, and commas for parenthesis based on how much emphasis the aside should receive, recognising that dashes give most prominence and brackets give least.

Needs first: Punctuating Direct Speech, Commas in lists.

https://lightmysky.com/learn/english/brackets-and-dashes-for-parenthesis-mt_m3-eXac3aP

#### Commas with yes, no, and names (ages 10-11)

Use commas to set off the words yes and no, to set off tag questions, and to indicate direct address in sentences

Ready when they can: Write sentences using commas with yes and no at the beginning such as 'Yes, I understand'; Punctuate tag questions correctly such as 'It's cold today, isn't it?'; Use commas to set off names in direct address such as 'Sarah, please pass the salt'.

Needs first: Punctuating Direct Speech, Commas in lists, Four Types of Sentences.

https://lightmysky.com/learn/english/commas-with-yes-no-and-names-mt_AfIzLRvMgW

#### Punctuating Titles of Works (ages 10-11)

Use underlining, quotation marks, or italics to indicate titles of works, applying conventions for different types of works such as books, stories, poems, songs, and articles

Ready when they can: Use italics or underlining for titles of books, films, and albums; Use quotation marks for titles of short works such as poems, songs, and articles; Apply title formatting conventions consistently in a piece of writing.

Needs first: Punctuating Direct Speech, Capitals for Names, Days and I.

https://lightmysky.com/learn/english/punctuating-titles-of-works-mt_Q2Eud_PPz6

#### Advanced Punctuation for Clarity (ages 11-14)

Use punctuation confidently and accurately for effect and clarity — including semicolons to link related clauses, colons to introduce lists or explanations, dashes and parentheses for parenthetical information, ellipsis for omission or suspense, and commas for coordinate adjectives and nonrestrictive elements

Ready when they can: Use a semicolon to link two closely related independent clauses without a conjunction; Set off a nonrestrictive clause with commas and explain why the commas are needed; Use a colon to introduce an explanation or elaboration, and a dash for a dramatic aside.

Needs first: Brackets and dashes for parenthesis, Colons and Semicolons in Lists, Punctuating Clauses, Plural vs Possessive in Nouns, Commas to avoid ambiguity, Commas After Introductory Elements, Apostrophes for possession (age 7+).

https://lightmysky.com/learn/english/advanced-punctuation-for-clarity-mt_lsO9O-_eZH

#### Expanded noun phrases (ages 6-7)

Use expanded noun phrases to describe and specify, adding adjectives and other modifiers before a noun (e.g., 'the blue butterfly', 'the old, creaky door')

Ready when they can: Expand 'the cat' into 'the fluffy black cat' by adding adjectives; Use noun phrases with two or more modifiers in independent writing; Choose precise adjectives to make a noun phrase more vivid: e.g., 'a tiny, shivering kitten'.

Needs first: Defining Words, Building sentences, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/expanded-noun-phrases-mt_cU3LcEVkBQ

#### Grammar Terms: Nouns, Verbs and Tense (ages 6-7)

Use and understand Year 2 grammatical terminology in discussion: noun, noun phrase, statement, question, exclamation, command, compound, suffix, adjective, adverb, verb, tense (past/present), apostrophe, comma

Ready when they can: Use the term 'noun phrase' when discussing expanded noun phrases in own writing; Identify adjectives, adverbs, and verbs in sentences using correct terminology; Explain what 'tense' means and give an example of past and present tense.

Needs first: Expanded noun phrases, Apostrophes: Contraction and Possession, Commas in lists, Grammar words: letter, word, sentence, Four Types of Sentences.

https://lightmysky.com/learn/english/grammar-terms-nouns-verbs-and-tense-mt_qzwQAOfurw

#### Adjectives vs adverbs (ages 7-8)

Use adjectives and adverbs correctly, choosing between them depending on whether a noun or verb/adjective is being modified (e.g., 'She ran quickly' vs 'She is quick')

Ready when they can: Choose the correct form: 'The dog is (slow/slowly)' vs 'The dog walks (slow/slowly)'; Identify whether a word is modifying a noun (adjective) or a verb (adverb) in a given sentence; Expand sentences by adding both an adjective and an adverb: 'The tall boy ran quickly'.

Needs first: Expanded noun phrases.

https://lightmysky.com/learn/english/adjectives-vs-adverbs-mt_j351evNNnB

#### Grammar Terms: Clauses and Conjunctions (ages 7-9)

Use and understand Year 3 grammatical terminology accurately when discussing reading and writing: preposition, conjunction, word family, prefix, clause, subordinate clause, direct speech, consonant letter, vowel letter, inverted commas/speech marks

Ready when they can: Use the terms 'clause' and 'subordinate clause' to identify parts of a multi-clause sentence (e.g., point to the subordinate clause in 'I stayed inside because it rained'); Use the terms 'conjunction', 'preposition', and 'prefix' correctly when explaining word/sentence choices in own writing; Distinguish between consonant letters and vowel letters and use the terms 'direct speech' and 'inverted commas' when discussing punctuation.

Needs first: Grammar Terms: Nouns, Verbs and Tense, Subordinate clauses.

https://lightmysky.com/learn/english/grammar-terms-clauses-and-conjunctions-mt_B8JOz79O6t

#### Comparatives & Superlatives (ages 8-9)

Form and use comparative and superlative adjectives and adverbs, choosing correctly between them

Ready when they can: Form comparatives and superlatives for 'big' (bigger/biggest), 'beautiful' (more/most beautiful), and 'good' (better/best); Choose the correct form in 'She runs _____ (faster/more fast) than her brother' and explain the rule; Write sentences using both a comparative adverb ('more carefully') and a superlative adjective ('tallest') correctly.

Needs first: Adjectives vs adverbs.

https://lightmysky.com/learn/english/comparatives-and-superlatives-mt_X1L9DoUwjF

#### Expanded noun phrases (age 8+) (ages 8-10)

Expand noun phrases with modifying adjectives, nouns, and preposition phrases to add detail

Ready when they can: Expand 'the teacher' to 'the strict maths teacher with curly hair' using adjective, noun, and preposition phrase; Write a sentence containing a noun phrase with at least three modifiers, e.g. 'the old stone bridge over the river'; Identify the head noun and its modifiers in 'the tiny grey kitten under the table'.

Needs first: Expanded noun phrases, Prepositions.

https://lightmysky.com/learn/english/expanded-noun-phrases-age-8-mt_EbiGRVK8uR

#### Grammar Terms: Pronouns and Determiners (ages 8-9)

Know and use Year 4 grammar terminology including determiner, pronoun, possessive pronoun, and adverbial

Ready when they can: Label the determiner, pronoun, and adverbial in 'She quickly opened her present on the table'; Explain the difference between a possessive pronoun ('mine', 'theirs') and other pronouns ('I', 'they'); Use the terms 'determiner' and 'adverbial' accurately when discussing a classmate's writing.

Needs first: Grammar Terms: Clauses and Conjunctions.

https://lightmysky.com/learn/english/grammar-terms-pronouns-and-determiners-mt_J5cx6S_eT9

#### Adjective Order in Sentences (ages 9-10)

Order adjectives within sentences according to conventional English patterns (opinion-size-age-shape-colour-origin-material-purpose) to produce natural-sounding descriptions

Ready when they can: Arrange multiple adjectives before a noun in conventional order, e.g. 'a lovely little old rectangular green French silver whittling knife' simplified to classroom examples like 'a small red bag' not 'a red small bag'; Identify when adjective order sounds unnatural and rearrange to match English conventions, e.g. correct 'the wooden big table' to 'the big wooden table'; Apply the size-before-colour-before-material pattern in descriptive writing, e.g. 'a tall grey stone castle' rather than 'a stone grey tall castle'.

Needs first: Expanded noun phrases (age 8+), Adjectives vs adverbs, Comparatives & Superlatives.

https://lightmysky.com/learn/english/adjective-order-in-sentences-mt_VVx0hPPSKi

#### Expanded noun phrases (age 9+) (ages 9-10)

Form and use prepositional phrases (preposition + noun phrase) to add detail about time, location, or direction within sentences, recognising how they function as adjective or adverb phrases

Ready when they can: Identify the preposition and noun phrase within a prepositional phrase, e.g. in 'under the old bridge', 'under' is the preposition and 'the old bridge' is the noun phrase; Add prepositional phrases to expand sentences with detail about where, when, or how, e.g. 'The cat slept' → 'The cat slept on the warm windowsill throughout the afternoon'; Distinguish prepositional phrases functioning as adjectives (modifying nouns: 'the house on the hill') from those functioning as adverbs (modifying verbs: 'she ran across the field').

Needs first: Fronted Adverbials and Commas, Expanded noun phrases (age 8+), Expressing Time, Place and Cause, Prepositions, Choosing A or An.

https://lightmysky.com/learn/english/expanded-noun-phrases-age-9-mt_7SfQuXgNtd

#### Grammar Terms: Modal Verbs and Clauses (ages 9-10)

Know and use Year 5 grammar terminology accurately when discussing reading and writing: modal verb, relative pronoun, relative clause, parenthesis, bracket, dash, cohesion, ambiguity

Ready when they can: Label a relative clause in a sentence and identify the relative pronoun that introduces it, using correct terminology; Explain why a pair of brackets or dashes creates a parenthesis and describe its function using the term 'parenthesis'; Use the terms 'modal verb', 'cohesion', and 'ambiguity' when discussing how a writer has achieved particular effects in a text.

Needs first: Grammar Terms: Pronouns and Determiners.

https://lightmysky.com/learn/english/grammar-terms-modal-verbs-and-clauses-mt_-tcJeAhK5k

#### Hyphens in Prefixed Words (ages 10-11)

Use hyphens to avoid ambiguity in compound modifiers and prefixed words, distinguishing between meanings that change based on hyphen placement

Ready when they can: Distinguish between 'man eating shark' and 'man-eating shark' by adding or removing hyphens; Use hyphens with prefixes to clarify meaning such as 'recover' versus 're-cover'; Apply hyphens correctly in compound adjectives before nouns such as 'well-known author'.

Needs first: Compound Words, Expanded noun phrases.

https://lightmysky.com/learn/english/hyphens-in-prefixed-words-mt_QpmVikVaqY

#### Phrases & Clauses (ages 11-13)

Understand and analyse the function of phrases (noun, verb, adjectival, adverbial, prepositional) and clauses (main, subordinate, relative) in general and in specific sentences, including recognising and correcting misplaced and dangling modifiers

Ready when they can: Identify a prepositional phrase acting as an adverbial and explain its role in the sentence; Distinguish between a main clause and a subordinate clause and explain their relationship; Spot a dangling modifier in a sentence and rewrite it to remove the ambiguity.

Needs first: Expanded noun phrases (age 8+), Relative Clauses, Expanded noun phrases (age 9+).

https://lightmysky.com/learn/english/phrases-and-clauses-mt_IdFxLz-UW9

#### Pronoun Case and Reference (ages 11-13)

Use pronouns in the proper case (subjective, objective, possessive) and use intensive pronouns like 'myself'; recognise and correct shifts in pronoun number and person, and vague pronouns whose antecedent is unclear

Ready when they can: Choose the correct pronoun case in tricky spots (e.g. 'between you and me', not 'between you and I'); Fix a shift in person or number mid-sentence (e.g. rewriting 'If a student works hard, you will improve'); Rewrite a sentence with a vague pronoun so the reference is clear (e.g. 'Ana told Mia that Mia's essay had won').

Needs first: Pronouns for clarity, Grammar Terms: Pronouns and Determiners, Agreement in sentences.

https://lightmysky.com/learn/english/pronoun-case-and-reference-mt_C7Tkco_WdO

#### Types of Sentences (ages 11-14)

Choose among and construct simple, compound, complex, and compound-complex sentences to signal different relationships among ideas, varying sentence patterns deliberately for meaning, interest, and style

Ready when they can: Combine short sentences into a complex sentence using a subordinating conjunction for effect; Rewrite a passage of monotonous simple sentences using a mix of sentence types for variety and flow; Identify the sentence type (simple, compound, complex, compound-complex) of given examples and explain the effect of each.

Needs first: Phrases & Clauses, Relative Clauses, Fixing Fragments & Run-Ons, Correlative Conjunctions.

https://lightmysky.com/learn/english/types-of-sentences-mt_T9IXrlxfx2

#### Past, Present and Progressive Tense (ages 6-9)

Use verbs to convey past and present tense correctly and consistently, including the progressive form (e.g., she is drumming, he was shouting), understanding how tense indicates time

Ready when they can: Write a passage consistently in past tense without switching to present; Use progressive forms correctly: 'was running', 'is jumping' to show ongoing actions; Identify verbs in a sentence and change them from past to present tense or vice versa.

Needs first: Revising and editing, Building sentences, Grammar Terms: Nouns, Verbs and Tense, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/past-present-and-progressive-tense-mt_enj1sMcfOT

#### Irregular past tense verbs (ages 7-8)

Form and use the past tense of frequently occurring irregular verbs correctly (e.g., sat, hid, told, went, came, ran), recognising that these do not follow the regular -ed pattern

Ready when they can: Supply the correct past tense of common irregular verbs: go→went, see→saw, run→ran, tell→told; Correct over-regularised forms in writing (e.g. change 'goed' to 'went', 'hided' to 'hid'); Write a short recount using at least five irregular past-tense verbs accurately.

Needs first: Past, Present and Progressive Tense.

https://lightmysky.com/learn/english/irregular-past-tense-verbs-mt_KIG5FQI5fC

#### Simple Past, Present and Future (ages 8-9)

Form and use the simple past, present, and future verb tenses consistently in writing

Ready when they can: Rewrite 'I walk to school' in past tense ('I walked') and future tense ('I will walk'); Identify and correct inconsistent tense in 'Yesterday she walks to the shop and bought milk'; Write a three-sentence paragraph maintaining consistent future tense throughout.

Needs first: Past, Present and Progressive Tense, Irregular past tense verbs.

https://lightmysky.com/learn/english/simple-past-present-and-future-mt_Of-WsrRQ8B

#### The Present Perfect Tense (ages 7-11)

Use the present perfect form of verbs in contrast to the simple past tense, understanding how the present perfect indicates an action completed at an unspecified time or with ongoing relevance (e.g., 'He has gone out' vs 'He went out')

Ready when they can: Form the present perfect using 'has/have' + past participle (e.g., 'She has eaten', 'They have finished'); Choose between simple past and present perfect to match the intended meaning (e.g., 'I ate lunch' vs 'I have eaten lunch'); Identify the present perfect form in a text and explain why the author used it instead of simple past.

Needs first: Past, Present and Progressive Tense, Simple Past, Present and Future, Subject-verb agreement.

https://lightmysky.com/learn/english/the-present-perfect-tense-mt_7D-vlii8F-

#### Standard English Verbs (ages 8-9)

Use Standard English verb inflections in place of non-standard local forms

Ready when they can: Correct 'we was playing' to 'we were playing' and explain why the standard form is needed in writing; Choose the standard form in pairs such as 'I did / I done', 'she has / she have', 'they were / they was'; Rewrite a short passage replacing three non-standard verb forms with their Standard English equivalents.

Needs first: Past, Present and Progressive Tense.

https://lightmysky.com/learn/english/standard-english-verbs-mt_ay0qkGj0jg

#### Modal Verbs and Possibility (ages 9-10)

Understand and use modal verbs (can, may, must, might, shall, will, could, should, would) and modal adverbs (perhaps, surely, certainly) to indicate degrees of possibility, necessity, and permission

Ready when they can: Select a modal verb to express certainty, probability, or possibility in a sentence, e.g. 'It will rain' vs 'It might rain' vs 'It could rain'; Replace a modal verb with a modal adverb to achieve a similar effect, e.g. 'He might come' → 'Perhaps he will come'; Distinguish between modals expressing permission (may, can), obligation (must, should), and possibility (might, could) in context.

Needs first: The Present Perfect Tense, Standard English Verbs, Past, Present and Progressive Tense, Simple Past, Present and Future.

https://lightmysky.com/learn/english/modal-verbs-and-possibility-mt_N9zffZxuu5

#### Progressive and Continuous Tenses (ages 9-10)

Form and use the progressive (continuous) verb tenses — past progressive (was walking), present progressive (am walking), and future progressive (will be walking) — to convey ongoing actions at different times

Ready when they can: Write sentences using past progressive to describe an action that was ongoing at a particular time, e.g. 'She was reading when the phone rang'; Distinguish present progressive from simple present, e.g. 'I am eating lunch' (right now) vs 'I eat lunch at noon' (habitual); Form the future progressive using 'will be' + present participle to describe an action that will be ongoing, e.g. 'Tomorrow at 3pm I will be travelling'.

Needs first: Past, Present and Progressive Tense, Simple Past, Present and Future.

https://lightmysky.com/learn/english/progressive-and-continuous-tenses-mt_mkDqmejLMw

#### Active and passive voice (ages 10-11)

Use the passive voice to shift focus from the agent to the action or recipient, understanding how passive constructions affect the presentation of information in formal and objective writing

Ready when they can: Convert active sentences to passive voice and explain the change in emphasis; Identify passive constructions in news reports and scientific writing; Choose between active and passive voice based on purpose and audience.

Needs first: Past, Present and Progressive Tense, Subject-verb agreement.

https://lightmysky.com/learn/english/active-and-passive-voice-mt_gbTyzvnWzr

#### Choosing Tenses for Precise Meaning (ages 10-11)

Use verb tense to convey various times, sequences, states, and conditions, selecting tenses deliberately to express the precise timing and nature of actions and events

Ready when they can: Write a paragraph using multiple tenses to show the sequence of past, present, and future events; Choose between simple, progressive, and perfect tenses to express duration or completion; Explain why a specific tense is appropriate for expressing a condition or hypothetical situation.

Needs first: The Present Perfect Tense, Progressive and Continuous Tenses.

https://lightmysky.com/learn/english/choosing-tenses-for-precise-meaning-mt_mpktt3wj1M

#### Consistent verb tense (ages 10-11)

Recognise and correct inappropriate shifts in verb tense within and across sentences and paragraphs, maintaining consistency unless a shift is required by meaning

Ready when they can: Identify and correct unnecessary tense shifts in a given paragraph; Edit own writing to ensure consistent tense use throughout a narrative; Explain when a tense shift is appropriate such as when describing a flashback.

Needs first: Progressive and Continuous Tenses, Choosing Tenses for Precise Meaning, Simple Past, Present and Future.

https://lightmysky.com/learn/english/consistent-verb-tense-mt_npRaYRhU2V

#### Grammar Terms: Voice and Punctuation (ages 10-11)

Know and use Year 6 grammatical terminology accurately: subject, object, active voice, passive voice, synonym, antonym, ellipsis, hyphen, colon, semi-colon, bullet points

Ready when they can: Define and give examples of subject and object in sentences; Explain the difference between active and passive voice using correct terminology; Use terms such as ellipsis, colon, and semi-colon accurately when discussing punctuation choices.

Needs first: Active and passive voice, Grammar Terms: Modal Verbs and Clauses.

https://lightmysky.com/learn/english/grammar-terms-voice-and-punctuation-mt_hzkNpp2PdV

#### Literary and Language Terminology (ages 11-14)

Discuss reading, writing, and spoken language with precise and confident use of linguistic and literary terminology — including terms for word classes, sentence types, clause types, literary devices, and text-level features

Ready when they can: Use terms like 'subordinate clause', 'relative pronoun', 'metaphor', 'alliteration' accurately in discussion; Explain the difference between a simile and a metaphor using correct terminology; Use metalanguage (e.g., 'the author employs enjambment to...') confidently when writing about texts.

Needs first: Grammar Terms: Voice and Punctuation, Phrases & Clauses, Conjunctions, Prepositions and Interjections.

https://lightmysky.com/learn/english/literary-and-language-terminology-mt_HCweOHWSiu

#### Verb Voice and Mood (ages 12-14)

Understand and use active and passive voice deliberately, and recognise verb moods (indicative, imperative, subjunctive, conditional) and their effects — choosing the appropriate voice and mood for purpose and audience

Ready when they can: Rewrite an active sentence in the passive voice and explain when the passive is more appropriate; Identify the subjunctive mood in a formal text (e.g., 'If I were...', 'It is essential that he be...'); Explain why a scientific report typically uses passive voice while a personal narrative uses active.

Needs first: Active and passive voice, The subjunctive mood, Modal Verbs and Possibility.

https://lightmysky.com/learn/english/verb-voice-and-mood-mt_N5tciHU8cE

#### Grammar for Effect (ages 11-14)

Analyse the effectiveness and impact of grammatical features in texts read — understanding how authors make deliberate grammatical choices (sentence length, passive voice, fronted adverbials, listing) to create specific effects on the reader

Ready when they can: Explain how an author's use of short, simple sentences creates tension or urgency in a passage; Analyse why an author uses a list of three (tricolon) in a persuasive text and evaluate its impact; Identify a grammatical choice in a text (e.g., present tense for immediacy) and explain the effect on the reader.

Needs first: Text Features & Presentation, Verb Voice and Mood, Types of Sentences, Varying Sentence Structure.

https://lightmysky.com/learn/english/grammar-for-effect-mt_N5tiL3uIeq

#### Verbals: Gerunds, Participles and Infinitives (ages 12-14)

Explain what gerunds, participles and infinitives are and the job each does in a particular sentence: a gerund acting as a subject ('Swimming is fun'), a participle describing a noun, an infinitive expressing purpose

Ready when they can: Identify a gerund and explain its role (e.g. 'running' as the subject of 'Running keeps me fit'); Spot a participle used as an adjective (e.g. 'the broken window', 'a barking dog'); Explain what an infinitive is doing in a sentence (e.g. 'to win' showing purpose in 'She trained to win').

Needs first: Phrases & Clauses, The Present Perfect Tense.

https://lightmysky.com/learn/english/verbals-gerunds-participles-and-infinitives-mt_bz_7yQVJaw

#### Standard English (ages 11-13)

Know and understand the differences between spoken and written language — including differences in formality, register, grammar, and vocabulary — and between Standard English and other varieties of English, using Standard English confidently in writing and speech

Ready when they can: Explain three differences between how we speak informally and how we write formally (e.g., contractions, slang, sentence completeness); Identify features of Standard English and explain why it is used in formal contexts; Rewrite an informal spoken passage (e.g., a text message) in formal written Standard English.

Needs first: Choosing Formal Vocabulary, Reflecting on Your Language Use.

https://lightmysky.com/learn/english/standard-english-mt_S2fP8rUwrl

#### Cohesion within paragraphs (ages 9-11)

Use cohesive devices within a paragraph — including pronouns, adverbials (then, after that, firstly), and synonyms — to link sentences and build a coherent flow of ideas

Ready when they can: Replace repeated nouns with pronouns or synonyms to maintain cohesion without ambiguity, e.g. 'The explorer found a cave. She examined it carefully'; Use adverbials of sequence (firstly, then, next, finally) and cause (therefore, as a result, consequently) to connect ideas within a paragraph; Identify where cohesion breaks down in a paragraph and insert appropriate linking devices to improve the flow.

Needs first: Pronouns for clarity, Organising Writing into Paragraphs.

https://lightmysky.com/learn/english/cohesion-within-paragraphs-mt_4-vfMgmCVB

#### Linking paragraphs with adverbials (ages 9-11)

Link ideas across paragraphs using adverbials of time (later, meanwhile, after a while), place (nearby, far away, beyond the wall), and number (secondly, finally, in addition) to guide the reader through a multi-paragraph text

Ready when they can: Begin a new paragraph with an adverbial of time to signal a shift in time or sequence, e.g. 'Meanwhile, back at the castle...' or 'Several hours later, the storm finally passed'; Use adverbials of place to move the reader to a new location between paragraphs, e.g. 'Beyond the forest, the land was flat and dry'; Use numbering or addition adverbials to structure non-fiction across paragraphs, e.g. 'The first reason... The second reason... In addition...'.

Needs first: Fronted Adverbials and Commas, Cohesion within paragraphs.

https://lightmysky.com/learn/english/linking-paragraphs-with-adverbials-mt_uvILgZq9HN

#### Paragraph Cohesion (ages 10-11)

Link ideas across paragraphs using a wider range of cohesive devices including word repetition, grammatical connections such as adverbials, and ellipsis to create coherent extended texts

Ready when they can: Use adverbials such as 'on the other hand' and 'as a consequence' to connect paragraphs; Apply ellipsis to avoid repetition while maintaining clarity across sentences; Create cohesion by repeating key words or using synonyms to link ideas between paragraphs.

Needs first: Linking paragraphs with adverbials.

https://lightmysky.com/learn/english/paragraph-cohesion-mt_hjtbA3g-Nn

#### Sentence Craft for Rhythm and Emphasis (ages 14-15)

Control where the weight of a sentence falls: hold the key word until the end, front an idea for emphasis, and use a short sentence only where the rhythm earns it.

Ready when they can: Rewrite a sentence so its strongest word lands last, and say what the change does; Place a short sentence after long ones for a stated effect rather than by habit; Vary the openings of consecutive sentences without adding padding.

https://lightmysky.com/learn/english/sentence-craft-for-rhythm-and-emphasis-mt_4opgg-pdsr

#### Levels of Language: A Framework for Description (ages 16-18)

Describe a text at more than one level: word choice, grammar, sound, layout, and what is meant beyond what is said. The levels exist so that a description can be checked by somebody else.

Ready when they can: Describe one short text at three levels and keep the observations separate; Use a grammatical term correctly about a real sentence from the text; Say what a description at one level misses that another level catches.

https://lightmysky.com/learn/english/levels-of-language-a-framework-for-description-mt_affit49cOP

### Reading Comprehension

https://lightmysky.com/learn/english/areas/reading-comprehension

#### Book Features and Author's Reasons (ages 5-8)

Identify front cover, back cover, and title page of a book; identify the reasons an author gives to support points in informational text

Ready when they can: Point to and name parts of a book (front cover, back cover, title page); Use the title page to find the title, author, and illustrator; Identify a reason the author gives for a claim in a simple non-fiction text.

Needs first: Understanding print.

https://lightmysky.com/learn/english/book-features-and-authors-reasons-mt_XeMZdf2Y9W

#### Listening to Texts Read Aloud (ages 5-10)

Listen to and discuss poems, stories, and non-fiction at a level beyond independent reading; confirm understanding of texts read aloud by asking and answering questions about key details

Ready when they can: Answer questions about a story or non-fiction text read aloud by the teacher; Discuss events, characters, or ideas from chapter books read to the class; Ask for clarification when something in a read-aloud is not understood.

https://lightmysky.com/learn/english/listening-to-texts-read-aloud-mt_mLPEMpYb_R

#### Characters, settings, and events (ages 5-8)

Identify characters, settings, and major events in stories; become familiar with key stories, fairy tales, and traditional tales and retell them with key details in sequence

Ready when they can: Name the main characters in a story; Describe where and when a story takes place; Retell a familiar story including beginning, middle, and end events.

Needs first: Listening to Texts Read Aloud.

https://lightmysky.com/learn/english/characters-settings-and-events-mt_sSQlLOnAow

#### Predicting what happens next (ages 4-10)

Predict what might happen next in a story based on what has been read so far; discuss the significance of titles and events

Ready when they can: Make a prediction before turning the page and explain reasoning; Discuss why a title fits or hints at the story content; Revise predictions as new information is encountered in the text.

Needs first: Characters, settings, and events.

https://lightmysky.com/learn/english/predicting-what-happens-next-mt_8-POYyg7GJ

#### Different Types of Texts (ages 5-7)

Recognise common types of texts (storybooks, poems, non-fiction); name the author and illustrator and define the role of each in telling or presenting a text

Ready when they can: Distinguish between a story, a poem, and a non-fiction book; Point to and name the author and illustrator on the cover; Explain that the author writes the words and the illustrator makes the pictures.

Needs first: Listening to Texts Read Aloud.

https://lightmysky.com/learn/english/different-types-of-texts-mt_gZIo5oiBMt

#### Main Topic of Informational Texts (ages 5-7)

Identify the main topic and retell key details of informational texts; describe connections between individuals, events, ideas, or pieces of information

Ready when they can: State what a non-fiction text is mostly about in one sentence; List two or three important facts learned from an informational text; Explain how two events or ideas in a text are connected.

Needs first: Listening to Texts Read Aloud.

https://lightmysky.com/learn/english/main-topic-of-informational-texts-mt_aFvsj35QzC

#### Pictures and Text Working Together (ages 5-9)

Describe the relationship between illustrations and the text in which they appear; use pictures to support and extend comprehension

Ready when they can: Use pictures to predict or confirm story events; Describe what is happening in an illustration and how it relates to the text; Explain how an illustration adds information not stated in words.

Needs first: Understanding print.

https://lightmysky.com/learn/english/pictures-and-text-working-together-mt_OlhMP7ShFT

#### Reading between the lines (ages 5-10)

Ask and answer questions about key details in literary and informational texts; make simple inferences based on what characters say and do

Ready when they can: Answer 'who', 'what', 'where' questions about a text using evidence; Infer a character's feelings from their actions (e.g. 'She's sad because she's crying'); Make logical guesses about unstated information using text clues.

Needs first: Characters, settings, and events.

https://lightmysky.com/learn/english/reading-between-the-lines-mt_E5KC4AnRLW

#### Main Topic & Key Details (ages 6-10)

Identify the main topic of a multi-paragraph informational text, determine the focus of specific paragraphs, and explain how key details support the main idea

Ready when they can: Identify the main topic of a multi-paragraph informational text and state the focus of individual paragraphs; Describe how specific details and facts in the text support the main idea; Explain how events, ideas, or steps in a text are connected (e.g. cause-effect, sequence, comparison).

Needs first: Main Topic of Informational Texts.

https://lightmysky.com/learn/english/main-topic-and-key-details-mt_QCWWmDMYZR

#### Non-Fiction Text Features (ages 6-9)

Recognise different non-fiction text structures and features (headings, contents, glossary, index), understanding how texts are organised to present information

Ready when they can: Use a contents page to find information on a specific topic in a non-fiction book; Identify the purpose of headings, glossary, and index in an information text; Recognise that non-fiction books can be structured as lists, time order, or question-and-answer.

Needs first: Main Topic of Informational Texts, Book Features and Author's Reasons.

https://lightmysky.com/learn/english/non-fiction-text-features-mt_ZhUuT__i2H

#### Retelling Stories with Structure (ages 6-8)

Retell stories including key details in sequence, describe characters, settings, and major events using evidence from the text, and describe the overall structure of a story (beginning, middle, ending)

Ready when they can: Retell a familiar story in order, including at least three key details from beginning, middle, and end; Describe a character's appearance, actions, or personality using details from the text; Explain how the beginning of a story introduces the characters and setting, and how the ending concludes the action.

Needs first: Characters, settings, and events, Reading with Expression and Accuracy.

https://lightmysky.com/learn/english/retelling-stories-with-structure-mt_zlSoIKPyId

#### Story Sequence and Central Message (ages 6-8)

Discuss the sequence of events in narrative texts and how items of information are related in non-fiction, retelling stories including key details and demonstrating understanding of central message or lesson

Ready when they can: Retell a story in correct sequence with beginning, middle, and end; Identify the central message or lesson of a story; Explain how two pieces of information in a non-fiction text are connected.

Needs first: Main Topic of Informational Texts, Reading between the lines, Listening to Texts Read Aloud, Characters, settings, and events, Reading with Expression and Accuracy.

https://lightmysky.com/learn/english/story-sequence-and-central-message-mt_VEwM7ClYYE

#### Story Lessons and Morals (ages 7-8)

Determine the central message, lesson, or moral of a story, fable, or folktale, explaining what the story teaches the reader and supporting the interpretation with key details from the text

Ready when they can: State the lesson or moral of a fable in one sentence (e.g. 'The Tortoise and the Hare teaches that slow and steady wins the race'); Explain what a story's central message is using at least two details from the text as support; Distinguish the central message from a summary of events — explain what the story means, not just what happens.

Needs first: Reading between the lines, Retelling Stories with Structure.

https://lightmysky.com/learn/english/story-lessons-and-morals-mt_v33BwiyRnd

#### Why the author wrote it (ages 8-9)

Distinguish one's own point of view from that of the author of an informational text and identify the author's purpose

Ready when they can: Read an opinion article and state the author's point of view, then state one's own and explain how they differ; Identify whether an author's purpose is to inform, persuade, or entertain, citing evidence from the text; Explain how word choices in an informational text reveal the author's attitude toward the topic.

Needs first: Book Features and Author's Reasons.

https://lightmysky.com/learn/english/why-the-author-wrote-it-mt_OltpfaX7l6

#### Firsthand and Secondhand Accounts (ages 9-10)

Compare and contrast a firsthand account (autobiography, diary, letter) with a secondhand account (biography, textbook, news report) of the same event or topic, identifying differences in focus and information provided

Ready when they can: Explain the difference between a firsthand account (written by someone who experienced the event) and a secondhand account (written by someone who researched it), using specific examples; Compare a diary entry and a textbook passage about the same historical event, identifying what each account includes, omits, and emphasises; Analyse how the perspective of the writer (participant vs observer/researcher) affects the information provided, the language used, and the overall tone.

Needs first: Why the author wrote it.

https://lightmysky.com/learn/english/firsthand-and-secondhand-accounts-mt_j32D5DZX7x

#### How authors support their points (ages 9-10)

Explain how an author of an informational text uses reasons and evidence to support particular points, evaluating whether the reasoning is sound and the evidence is relevant and sufficient

Ready when they can: Identify the key points an author makes in an informational text and list the specific reasons and evidence provided to support each point; Evaluate whether the evidence an author uses (facts, statistics, examples, expert opinions) is relevant to the point being made and sufficient to be convincing; Distinguish between well-supported claims backed by evidence and unsupported opinions or assertions in an informational text.

Needs first: Why the author wrote it.

https://lightmysky.com/learn/english/how-authors-support-their-points-mt_k-V37x3zsF

#### Text & Media Connections (ages 9-10)

Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions from the text

Ready when they can: Compare a passage from a book with a film or audio adaptation, identifying specific moments where the visual or oral version matches or departs from the written text; Explain how a film, illustration, or dramatic performance interprets a scene from a story, citing specific textual descriptions the adaptation reflects; Identify details in the written text (descriptions of setting, character appearance, dialogue) that a visual or oral presentation brings to life, and note any differences.

Needs first: Pictures and Text Working Together.

https://lightmysky.com/learn/english/text-and-media-connections-mt_t06dHX2ZYw

#### Multiple Accounts of Events (ages 10-11)

Analyse multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent

Ready when they can: Compare two news articles about the same event and identify differences in perspective; Explain how the author's background or purpose affects their account of an event; Identify which facts are consistent across accounts and which details differ based on viewpoint.

Needs first: Firsthand and Secondhand Accounts.

https://lightmysky.com/learn/english/multiple-accounts-of-events-mt_5FREdVoS8s

#### Supporting ideas with evidence (ages 10-11)

Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which specific points

Ready when they can: Match each of an author's main points with the evidence used to support it; Evaluate whether the evidence provided adequately supports the author's argument; Identify points in a text that lack sufficient evidence or reasoning.

Needs first: How authors support their points.

https://lightmysky.com/learn/english/supporting-ideas-with-evidence-mt_S3XMQOYt_D

#### Spotting Facts and Opinions (ages 6-8)

Tell the difference between a statement of fact (something anyone can check) and a statement of opinion (what someone thinks or feels), and start noticing which is which in simple books, adverts and conversations

Ready when they can: Sort simple statements into facts and opinions (e.g. 'spiders have eight legs' vs 'spiders are scary'); Explain how a fact could be checked (e.g. by counting, looking in a book, or asking an expert); Use opinion words to signal their own view (e.g. 'I think', 'my favourite').

Needs first: Main Topic of Informational Texts, Expressing & Justifying Opinions.

https://lightmysky.com/learn/english/spotting-facts-and-opinions-mt_jJBprWe2pe

#### Fact vs opinion (ages 10-11)

Distinguish between statements of fact and statements of opinion in texts, recognising how authors blend factual information with subjective viewpoints

Ready when they can: Identify and label statements as fact or opinion in a newspaper article; Explain why a statement is a fact by citing verifiable evidence or why it is an opinion; Recognise persuasive techniques that present opinions as if they were facts.

Needs first: Why the author wrote it, Spotting Facts and Opinions.

https://lightmysky.com/learn/english/fact-vs-opinion-mt_V6456X6pJE

#### Discussing Texts as a Group (ages 5-10)

Participate in discussions about what is read, taking turns and listening to others; explain understanding clearly; actively engage in group reading activities

Ready when they can: Share ideas about a book in a group discussion; Listen to and respond to others' opinions about a text; Take turns speaking and build on what classmates have said about a book.

Needs first: Listening and responding, Listening to Texts Read Aloud.

https://lightmysky.com/learn/english/discussing-texts-as-a-group-mt_thsY1ZesaU

#### Themes and messages (ages 7-10)

Identify recurring themes (good vs evil, friendship, bravery) and conventions (once upon a time, moral at the end, hero's journey) across a wide range of books including fairy stories, myths, legends and traditional tales

Ready when they can: Identify a common theme across two different stories (e.g., 'Both "Jack and the Beanstalk" and "The Three Billy Goats Gruff" are about bravery overcoming a threat'); Name literary conventions found in fairy tales and myths (e.g., 'once upon a time', magical numbers like three, a quest or journey, good triumphing over evil); Explain how the same theme can appear in different genres (e.g., friendship in a realistic story vs a myth).

Needs first: Characters, settings, and events, Discussing Texts as a Group, Story Lessons and Morals.

https://lightmysky.com/learn/english/themes-and-messages-mt_yHQacItlhf

#### Morals in Fables, Folktales and Myths (ages 8-9)

Explain how the central message, lesson, or moral of a story is conveyed through key details across diverse text types including fables, folktales, and myths

Ready when they can: Retell a fable and identify the moral, citing three key details that convey it; Compare how two myths from different cultures convey a similar central message through different events; Explain the difference between the topic of a story and its central message or lesson.

Needs first: Story Lessons and Morals, Themes and messages.

https://lightmysky.com/learn/english/morals-in-fables-folktales-and-myths-mt_H0ajATAlus

#### Themes Across Cultures and Traditions (ages 9-10)

Compare and contrast the treatment of similar themes, topics, and story patterns (e.g., good vs evil, quest narratives, trickster tales) in stories, myths, and traditional literature from different cultures

Ready when they can: Compare how two myths or folk tales from different cultures treat a similar theme (e.g., creation, heroism, the importance of honesty) and explain both similarities and differences; Identify recurring story patterns across cultures such as the trickster figure, the quest, or the transformation, providing specific examples from texts read; Explain how cultural context shapes the way a universal theme is expressed differently in stories from various traditions.

Needs first: Themes and messages.

https://lightmysky.com/learn/english/themes-across-cultures-and-traditions-mt_tX0R4-4WXy

#### How Authors Treat Similar Themes (ages 10-11)

Compare and contrast stories in the same genre on their approaches to similar themes and topics, identifying how different authors treat common ideas

Ready when they can: Compare how two mystery stories create suspense using different techniques; Identify common themes in adventure stories and explain how each author develops them differently; Analyse how two authors from the same genre approach the theme of friendship or courage.

Needs first: Themes Across Cultures and Traditions.

https://lightmysky.com/learn/english/how-authors-treat-similar-themes-mt_jO0gHMk7Ti

#### Self-Correcting While Reading (ages 5-11)

Check that text makes sense while reading and self-correct inaccurate reading by re-reading or using context

Ready when they can: Notice when reading does not make sense and stop to re-read; Self-correct errors mid-sentence (e.g. 'Wait, that doesn't sound right'); Use meaning, sentence structure, and visual cues together to monitor reading.

Needs first: Monitoring Comprehension, Blending Sounds to Read Words, Feeling of not understanding, Building sentences, Reading with Expression and Accuracy.

https://lightmysky.com/learn/english/self-correcting-while-reading-mt_rQ2YJJi4uh

#### Main Ideas & Note-Taking (ages 7-10)

Identify main ideas drawn from more than one paragraph and summarise them; retrieve and record information from non-fiction texts using notes, tables or other methods

Ready when they can: Read a multi-paragraph non-fiction text and state the main idea of each paragraph in one sentence; Summarise a text of 3+ paragraphs in 2-3 sentences capturing the key points; Retrieve specific information from a non-fiction text and record it using a simple table or notes (e.g., 'Name: hedgehog, Habitat: woodland, Diet: insects').

Needs first: Reading between the lines, Self-Correcting While Reading, Story Sequence and Central Message, Non-Fiction Text Features.

https://lightmysky.com/learn/english/main-ideas-and-note-taking-mt_sMAcZW6vWM

#### Finding Theme and Summarising (ages 9-11)

Determine the theme of a story, drama, or poem from details in the text, and provide an objective summary that captures the key events without personal opinions

Ready when they can: Identify the theme of a story (e.g. courage, friendship, overcoming adversity) by examining what characters learn, how they change, and what the author emphasises across the whole text; Distinguish theme from topic: explain that a topic might be 'war' while the theme is 'the cost of conflict on families'; Summarise a story, chapter, or poem objectively, including only key events and details without inserting personal opinions or minor details.

Needs first: Morals in Fables, Folktales and Myths, Main Ideas & Note-Taking.

https://lightmysky.com/learn/english/finding-theme-and-summarising-mt_A0htaNaK7b

#### Summarising Non-Fiction Main Ideas (ages 10-11)

Determine two or more main ideas of an informational text and explain how they are supported by key details, then summarise the text without personal opinions

Ready when they can: Identify the main ideas in each section of an informational article; List key details that support each main idea in a multi-paragraph text; Write an objective summary capturing the main ideas without adding personal opinions.

Needs first: Main Ideas & Note-Taking.

https://lightmysky.com/learn/english/summarising-non-fiction-main-ideas-mt_XnRhhEqJLJ

#### Tracing Theme Across a Text (ages 11-14)

Determine and analyse the theme or central idea of a text, trace how it develops across the text through key details and events, and provide an objective summary distinct from personal opinion

Ready when they can: Identify a theme in a novel and explain how specific events develop it across the plot; Distinguish between the topic of a text (what it is about) and the theme (what it is saying); Write a concise, objective summary of a chapter or article without inserting personal opinion.

Needs first: Main Ideas & Note-Taking, Themes and messages, Finding Theme and Summarising.

https://lightmysky.com/learn/english/tracing-theme-across-a-text-mt_wGxq92Na5g

#### Connecting reading to experience (ages 5-7)

Link what is read or heard to own experiences; draw on background knowledge and vocabulary to support understanding of texts

Ready when they can: Make text-to-self connections (e.g. 'This reminds me of when I...'); Use personal experience to understand a character's feelings; Relate events in a story to own life to deepen comprehension.

Needs first: Thinking Before Starting, Listening to Texts Read Aloud, Reading for Meaning.

https://lightmysky.com/learn/english/connecting-reading-to-experience-mt_5n-O41lUgn

#### Expressive and Sensory Language (ages 6-9)

Recognise recurring literary language in stories and poetry, identify words and phrases that suggest feelings or appeal to the senses, and discuss favourite words and phrases

Ready when they can: Spot recurring story language such as 'Once upon a time' and 'happily ever after'; Identify sensory words and phrases in a poem: 'the icy wind howled'; Share a favourite word or phrase from a story and explain why it appeals.

Needs first: Discussing and Questioning New Words, Listening to Texts Read Aloud, Shades of Meaning.

https://lightmysky.com/learn/english/expressive-and-sensory-language-mt_fL1Xz8ostr

#### Text Features & Presentation (ages 7-10)

Identify how language choices, text structure and presentational features (illustrations, diagrams, bold print, layout) contribute to the overall meaning and effect of a text

Ready when they can: Explain how an author's word choices create a particular effect (e.g., 'The author uses "crept" instead of "walked" to make it feel sneaky and tense'); Identify how a text's structure helps the reader (e.g., 'The headings help you find information quickly', 'The story builds suspense before the ending'); Explain how a presentational feature contributes to meaning (e.g., 'The bold words are important vocabulary', 'The diagram shows how the water cycle works').

Needs first: Expressive and Sensory Language, Non-Fiction Text Features.

https://lightmysky.com/learn/english/text-features-and-presentation-mt_aVZJhPbc_1

#### Structural terminology (ages 8-9)

Use structural terminology (chapter, scene, stanza) to refer to parts of literary texts and describe how each successive part builds on earlier sections

Ready when they can: Identify chapters, scenes, or stanzas in a given text and use the correct term for each; Explain how the second stanza of a poem builds on the mood established in the first; Describe how a specific chapter advances the plot by referring to events in earlier chapters.

Needs first: Text Features & Presentation, Different Types of Texts.

https://lightmysky.com/learn/english/structural-terminology-mt_ujwtRoYJ34

#### How Parts Build a Whole Text (ages 10-11)

Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a story, drama, or poem, analysing how each part contributes to the whole

Ready when they can: Map the structure of a novel showing how each chapter advances plot or character development; Explain how individual stanzas in a poem build toward a central theme or message; Analyse how scenes in a play work together to develop conflict and resolution.

Needs first: Structural terminology.

https://lightmysky.com/learn/english/how-parts-build-a-whole-text-mt_PetJM-AYz9

#### Purpose, audience, and context (ages 11-14)

Identify the purpose, audience, and context of a text and use this knowledge to support comprehension — recognising how writing aimed at different audiences (academic, popular, persuasive) uses different conventions, register, and tone

Ready when they can: Identify the intended audience and purpose of a text and explain how the language choices reflect this; Compare a newspaper article and a scientific report on the same topic, noting differences in register and structure; Explain how knowing the historical or social context of a text deepens understanding.

Needs first: Text Features & Presentation, Fact vs opinion.

https://lightmysky.com/learn/english/purpose-audience-and-context-mt_jIcgbCmziD

#### Cultural Allusions and Word Meaning (ages 9-10)

Determine the meaning of words and phrases as used in literary texts, including understanding references to mythology and cultural allusions (e.g., Herculean, Achilles' heel)

Ready when they can: Explain the meaning of an allusion drawn from mythology when encountered in a text, e.g. identify that 'Herculean task' means an extremely difficult task, referencing Hercules' legendary labours; Use context and knowledge of word parts to determine the meaning of unfamiliar words in a poem or story, explaining how the word contributes to tone or meaning; Identify when an author is using a word figuratively rather than literally and explain the intended meaning in context.

Needs first: Expressive and Sensory Language, Literal vs Figurative Language.

https://lightmysky.com/learn/english/cultural-allusions-and-word-meaning-mt_ZanQuV90qi

#### Inferring Characters' Feelings and Motives (ages 7-10)

Draw inferences from independently-read texts, such as inferring characters' feelings, thoughts and motives from their actions, and justifying inferences with evidence from the text

Ready when they can: Infer a character's feelings or motives from their actions and dialogue (e.g. 'She slammed the door — how is she feeling?'); Justify an inference by quoting or pointing to specific evidence in the text; Distinguish between what is explicitly stated and what must be inferred from clues in the text.

Needs first: Predicting what happens next, Reading between the lines, Self-Correcting While Reading, Story Sequence and Central Message, Domain Vocabulary Across Subject Areas.

https://lightmysky.com/learn/english/inferring-characters-feelings-and-motives-mt_ukLvUD8DFA

#### Quoting Accurately from Texts (ages 10-11)

Quote accurately from literary and informational texts when explaining what the text says explicitly and when drawing inferences, using quotation marks and citations correctly

Ready when they can: Select and copy exact words from a text to support an inference about character motivation; Use quotation marks correctly when incorporating textual evidence into written responses; Introduce quotes with signal phrases such as 'The author states' or 'According to the text'.

Needs first: Inferring Characters' Feelings and Motives.

https://lightmysky.com/learn/english/quoting-accurately-from-texts-mt_ak_ZgoMKRQ

#### How Language Choices Affect the Reader (ages 10-11)

Evaluate how authors use language including figurative language, considering the impact of word choices, imagery, and literary devices on the reader

Ready when they can: Explain how a specific metaphor or simile affects the reader's understanding or emotions; Evaluate an author's choice of descriptive language and its impact on atmosphere; Compare how different authors use figurative language to achieve similar effects.

Needs first: Expressive and Sensory Language, Similes & Metaphors.

https://lightmysky.com/learn/english/how-language-choices-affect-the-reader-mt_furAIwoO9t

#### Forms of Poetry and Performance (ages 7-10)

Recognise different forms of poetry (free verse, narrative poetry, haiku) and discuss their features; prepare poems and play scripts to read aloud and perform with understanding through intonation, tone, volume and action

Ready when they can: Name at least two different forms of poetry and describe a feature of each (e.g., 'narrative poetry tells a story', 'free verse does not have a regular rhyme or rhythm'); Recognise the form of a given poem and explain how you identified it (e.g., 'This is a narrative poem because it has characters and a plot'); Prepare and perform a poem or play script extract showing understanding through changes in intonation, volume, and expression.

Needs first: Reading with Expression and Accuracy, Writing Poetry.

https://lightmysky.com/learn/english/forms-of-poetry-and-performance-mt_gR5_n99Ntt

#### Poems, Drama & Prose (ages 9-10)

Explain major differences between poems, drama, and prose, identifying structural elements unique to each form: verse, rhythm, and meter in poetry; cast of characters, dialogue, and stage directions in drama; chapters and paragraphs in prose

Ready when they can: Compare a poem, a play script, and a prose passage on a similar theme, identifying the structural features unique to each form (e.g. stanzas vs scenes vs chapters); Identify and explain the function of structural elements in drama: cast list, stage directions (in italics or brackets), dialogue format, and scene divisions; Describe how structural elements of poetry such as verse, rhythm, meter, and line breaks affect how a poem is read aloud and how meaning is conveyed.

Needs first: Forms of Poetry and Performance, Structural terminology.

https://lightmysky.com/learn/english/poems-drama-and-prose-mt_4IxR66uGLc

#### Connecting Ideas in Texts (ages 8-9)

Describe connections between events, ideas, or concepts in informational text using time, sequence, cause-and-effect, and comparison language, and identify logical connections between sentences and paragraphs

Ready when they can: Read a science text and identify three cause-and-effect relationships using signal words like 'because', 'as a result'; Explain the sequence of steps in a technical procedure using time-order language ('first', 'next', 'finally'); Describe how two paragraphs in a text are connected (e.g. comparison, cause/effect, or sequence).

Needs first: Main Topic & Key Details, Scaled picture graphs and bar graphs.

https://lightmysky.com/learn/english/connecting-ideas-in-texts-mt_w4wKFP3jud

#### Combining information from texts (ages 9-10)

Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably, combining and comparing what each source contributes

Ready when they can: Read two informational texts on the same topic and identify information that appears in both, information unique to each, and any contradictions between them; Combine key details from two sources into a coherent summary or short report that draws on both texts; Explain how reading a second text on the same topic added to, confirmed, or challenged understanding gained from the first text.

Needs first: Connecting Ideas in Texts.

https://lightmysky.com/learn/english/combining-information-from-texts-mt_8FwtdJzeDh

#### Explaining Events & Ideas (ages 9-10)

Explain events, procedures, ideas, or concepts in an informational text, including what happened and why, by citing specific textual evidence about causes, effects, and steps in a process

Ready when they can: Explain a historical event described in an informational text by identifying both what happened and the causes leading to it, using specific details from the text; Describe the steps in a procedure or process presented in an informational text, explaining why each step is necessary based on information in the text; Identify cause-and-effect relationships between ideas or events in an informational passage and explain them using evidence from the text.

Needs first: Connecting Ideas in Texts.

https://lightmysky.com/learn/english/explaining-events-and-ideas-mt_nKS_vCYrg3

#### Structure of information texts (ages 9-10)

Describe the overall structure of an informational text (chronology, comparison, cause/effect, problem/solution) and explain how the author's chosen structure helps convey information and ideas

Ready when they can: Identify which organisational structure an informational text uses (chronological order, compare/contrast, cause/effect, or problem/solution) and cite textual features that signal it; Explain how signal words (first, then, finally for chronology; however, similarly for comparison; because, as a result for cause/effect; the solution was for problem/solution) reveal text structure; Compare two informational texts on the same topic that use different structures and explain how each structure affects the way information is presented to the reader.

Needs first: Structural terminology, Connecting Ideas in Texts.

https://lightmysky.com/learn/english/structure-of-information-texts-mt_oVwNnjYPUY

#### Comparing Structure in Information Texts (ages 10-11)

Compare and contrast the overall structure of events, ideas, concepts, or information in two or more informational texts, identifying patterns such as chronology, comparison, cause/effect, or problem/solution

Ready when they can: Identify the organisational structure of two texts on the same topic; Explain how one text uses cause/effect while another uses problem/solution to present information; Analyse why an author chose a particular structure for their informational text.

Needs first: Structure of information texts.

https://lightmysky.com/learn/english/comparing-structure-in-information-texts-mt_-1okUh0Jdv

#### Explaining Relationships in Texts (ages 10-11)

Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in historical, scientific, or technical texts based on specific information

Ready when they can: Explain the cause-and-effect relationship between events in a historical text; Describe how a scientific process involves sequential steps that depend on each other; Identify how key individuals in a text influenced events or other people.

Needs first: Connecting Ideas in Texts.

https://lightmysky.com/learn/english/explaining-relationships-in-texts-mt_iv-BJS9W60

#### Synthesising across multiple texts (ages 10-11)

Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably, combining information without plagiarising

Ready when they can: Combine information from three sources into a coherent paragraph using own words; Create a fact sheet that synthesises key information from multiple texts on one topic; Present information orally that draws on multiple sources while crediting the sources.

Needs first: Combining information from texts.

https://lightmysky.com/learn/english/synthesising-across-multiple-texts-mt_kJ4xXKL_nO

#### Analysing Text Structure (ages 11-14)

Analyse how a text's structure — including its overall organisation, use of chapters, stanzas, scenes, paragraphs, or sections — contributes to its meaning, style, and development of ideas

Ready when they can: Explain how a non-chronological structure (e.g., flashback, frame narrative) creates suspense or surprise; Analyse the role of a specific paragraph in developing and refining a key concept in a non-fiction text; Compare how two texts use different structures (e.g., epistolary vs. linear narrative) and the effect of each.

Needs first: Text Features & Presentation, Comparing Structure in Information Texts, How Parts Build a Whole Text.

https://lightmysky.com/learn/english/analysing-text-structure-mt_II6iw4BmJI

#### Following Multi-Step Procedures (ages 11-14)

Follow a written multi-step procedure precisely when carrying out experiments, taking measurements or performing technical tasks: read the whole procedure first, work through the steps in order, and notice when a result signals a missed step

Ready when they can: Carry out a science experiment by following the written method step by step without skipping ahead; Follow technical instructions exactly (e.g. assembling a model or setting up software from a written guide); Spot when a result does not match what the instructions predicted and retrace the steps to find the error.

Needs first: Structure of information texts.

https://lightmysky.com/learn/english/following-multi-step-procedures-mt_b_3jwAsZ7a

#### Analysing Connections in Informational Texts (ages 12-14)

Analyse how individuals, events and ideas interact in informational texts: how an idea shapes a person's actions, how events influence one another, and how authors use comparisons, analogies and categories to connect or distinguish them

Ready when they can: Explain how an idea in a text influenced a person or event (e.g. how the dream of flight drove the Wright brothers' experiments); Identify where an author uses a comparison or analogy to link two ideas (e.g. describing the internet as a highway); Trace how an author separates similar people or ideas into categories and explain why the distinction matters.

Needs first: Explaining Relationships in Texts, Connecting Ideas in Texts, Explaining Events & Ideas.

https://lightmysky.com/learn/english/analysing-connections-in-informational-texts-mt_1F3cnUHjMb

#### Interpreting visual information in texts (ages 9-10)

Interpret information presented visually, orally, or quantitatively in informational texts (e.g., charts, graphs, diagrams, timelines, animations) and explain how it contributes to understanding the text

Ready when they can: Read and interpret data from a chart, graph, or table included in an informational text and explain how it supports or extends the written information; Explain how a diagram, map, or timeline in an informational text helps the reader understand the topic in ways that words alone might not; Synthesise information from both the written text and a visual element (graph, illustration, infographic) to draw a conclusion that neither source provides independently.

Needs first: Reading and Comparing Bar Graphs, Pictures and Text Working Together.

https://lightmysky.com/learn/english/interpreting-visual-information-in-texts-mt_KbCCmLmxYN

#### Multimedia elements in texts (ages 10-11)

Analyse how visual and multimedia elements contribute to the meaning, tone, or beauty of a text such as graphic novels, multimedia presentations, or illustrated editions of fiction and poetry

Ready when they can: Explain how illustrations in a graphic novel convey emotion or advance the story; Analyse how visual elements such as colour and layout affect the tone of a multimedia text; Compare how the same scene is portrayed in text versus in visual or audio format.

Needs first: Pictures and Text Working Together, Interpreting visual information in texts.

https://lightmysky.com/learn/english/multimedia-elements-in-texts-mt_xsk3iuNVVI

#### Comparing Texts Across Media (ages 12-14)

Compare a written text with its audio, video or multimedia version, analysing how each medium portrays the subject; weigh the advantages and disadvantages of different mediums for presenting a particular topic or idea

Ready when they can: Compare a speech's written text with a recording of it, noting how delivery changes the impact (e.g. pauses adding urgency); Explain what a video version of a text adds or loses compared with the print version; Recommend the best medium for presenting a topic and justify the choice (e.g. a diagram-rich webpage over a podcast for explaining an engine).

Needs first: Text & Media Connections, Multimedia elements in texts, Summarising Spoken and Media Presentations.

https://lightmysky.com/learn/english/comparing-texts-across-media-mt_wpLz5Y17cJ

#### Recommending Books (ages 9-10)

Recommend books to peers, giving reasons for choices based on knowledge of a wide range of genres, authors, and themes, and making comparisons within and across books

Ready when they can: Recommend a book to a peer by explaining its genre, theme, and what makes it engaging, comparing it to other books the peer has enjoyed; Justify a book recommendation by referring to specific features such as the author's style, the plot structure, or how a theme is developed; Maintain a reading log or book review collection that captures key responses to books read and serves as a reference for future recommendations.

Needs first: Listening to Texts Read Aloud, Reflecting After Learning, Themes and messages.

https://lightmysky.com/learn/english/recommending-books-mt_0MfpLj0Uhb

#### Comparing Books (ages 10-11)

Make comparisons within and across books, identifying similarities and differences in themes, characters, settings, and authorial choices across multiple texts

Ready when they can: Compare how two authors develop similar themes using different narrative techniques; Identify similarities and differences between characters across books by the same author; Analyse how settings function differently in two texts from the same genre.

Needs first: Recommending Books, Themes and messages.

https://lightmysky.com/learn/english/comparing-books-mt_sUVOS2jH3J

#### Critical comparison across texts (ages 11-14)

Make critical comparisons across texts — comparing themes, characters, settings, styles, or arguments in two or more works, including texts from different periods, genres, or cultures

Ready when they can: Compare how two novels treat a shared theme (e.g., growing up) using specific evidence from both; Analyse how a modern retelling draws on and transforms elements from a traditional story or myth; Compare conflicting accounts of the same event in two non-fiction texts and evaluate which is more convincing.

Needs first: Comparing Books, Tracing Theme Across a Text, How Authors Treat Similar Themes.

https://lightmysky.com/learn/english/critical-comparison-across-texts-mt_1GF5MeNZPA

#### Wide Independent Reading Across Genres (ages 11-14)

Read widely and independently across fiction and non-fiction — including whole novels, short stories, plays, poetry, and non-fiction from different genres, periods, and cultures — building stamina, breadth, and personal taste as a reader

Ready when they can: Choose books independently that offer appropriate challenge and genuine interest; Read at least two Shakespeare plays and a range of pre-1914 and contemporary literature during KS3; Maintain a personal reading record and articulate preferences with reasons.

Needs first: Recommending Books.

https://lightmysky.com/learn/english/wide-independent-reading-across-genres-mt_9k1qcpvVi_

#### Using Multiple Sources (ages 10-11)

Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or solve a problem efficiently

Ready when they can: Use search features, indexes, and headings to locate specific information across sources; Synthesise information from two or more sources to answer a research question; Evaluate which source provides the most relevant information for a given question.

Needs first: Reading tables, Non-Fiction Text Features.

https://lightmysky.com/learn/english/using-multiple-sources-mt_JVVKT-_AD9

#### Justifying Views About Texts (ages 10-11)

Provide reasoned justifications for views about texts, supporting interpretations and opinions with evidence and logical arguments

Ready when they can: State an opinion about a character's motivations and support it with three pieces of textual evidence; Construct a reasoned argument about an author's message using quotes from the text; Respond to an alternative interpretation by providing counter-evidence from the text.

Needs first: Building and critiquing a mathematical argument, Inferring Characters' Feelings and Motives.

https://lightmysky.com/learn/english/justifying-views-about-texts-mt_IX37F4rNed

#### Using and Evaluating Textual Evidence (ages 11-14)

Cite specific textual evidence to support analysis of what a text says explicitly and what can be inferred, distinguishing between strong and weak evidence and explaining how the evidence supports a point

Ready when they can: Identify a relevant quotation to support an inference about a character's feelings; Explain why one piece of evidence is stronger than another for supporting a claim; Use embedded quotations in a written response to back up an analytical point.

Needs first: Justifying Views About Texts, Quoting Accurately from Texts, Supporting ideas with evidence.

https://lightmysky.com/learn/english/using-and-evaluating-textual-evidence-mt_dmFnJzxKwz

#### Evaluating Arguments in Non-Fiction (ages 11-14)

Evaluate arguments and claims in non-fiction texts — assess whether reasoning is sound, evidence is relevant and sufficient, distinguish between fact and opinion, and recognise bias, propaganda, and rhetorical techniques

Ready when they can: Identify the main claim in an argument text and evaluate whether the evidence presented is sufficient; Spot logical fallacies or irrelevant evidence introduced to distract from weak reasoning; Compare two opposing arguments on the same issue and evaluate which is more convincing, with reasons.

Needs first: Using and Evaluating Textual Evidence, Purpose, audience, and context, Multiple Accounts of Events.

https://lightmysky.com/learn/english/evaluating-arguments-in-non-fiction-mt_gMSFymQlrW

#### Figurative Language and Literary Devices (ages 11-14)

Determine the meaning of figurative and connotative language in context, analyse the impact of specific word choices on meaning and tone, and identify literary devices such as metaphor, simile, personification, allusion, and irony

Ready when they can: Identify a metaphor or simile in a passage and explain its effect on the reader; Explain how an author's word choice creates a particular tone (e.g., menacing, humorous, melancholic); Recognise an allusion to a myth, the Bible, or another text and explain what it adds to the meaning.

Needs first: Using and Evaluating Textual Evidence, How Language Choices Affect the Reader.

https://lightmysky.com/learn/english/figurative-language-and-literary-devices-mt_DVSHx3YMkN

#### Poetic forms and conventions (ages 11-14)

Recognise and understand poetic conventions — including form (sonnet, ballad, free verse), metre, rhyme scheme, stanza structure, imagery, and sound devices (alliteration, assonance, onomatopoeia) — and analyse how poets use them for effect

Ready when they can: Identify the form of a poem (e.g., sonnet, haiku, ballad) and explain its key structural features; Analyse how a poet uses rhythm or sound devices to reinforce meaning or mood; Explain how enjambment or a caesura affects the pace and emphasis of a line.

Needs first: Figurative Language and Literary Devices, Forms of Poetry and Performance, Poems, Drama & Prose.

https://lightmysky.com/learn/english/poetic-forms-and-conventions-mt_aClzPBiS9k

#### Effect-Led Analysis of a Writer's Choices (ages 14-15)

Treat every language feature as a decision the writer made, and argue what that decision does to a reader. The move here is away from labelling devices and towards explaining effect.

Ready when they can: Explain what one word does to the reader without naming any device; Swap a word in a quoted line for a near synonym and say what the swap costs; Drop a device that has been spotted correctly but does nothing for the point being argued.

https://lightmysky.com/learn/english/effect-led-analysis-of-a-writers-choices-mt_rONa89oLc4

#### How a News Story Is Framed (ages 14-16)

A report is a set of choices before it is a set of facts: which event was covered, whose account leads, what the headline promises, what the last paragraph quietly concedes. Two accurate reports of one event can leave opposite impressions.

Ready when they can: Name whose voice leads a report and whose appears only near the end; Show where a headline claims more than the body of the report supports; Compare two reports of one event and state the difference in framing without calling either one false.

https://lightmysky.com/learn/english/how-a-news-story-is-framed-mt_fh7yPuodva

#### Inference and Implication in Close Reading (ages 14-16)

Read what a text implies but never states, building a chain of inferences from small details. The test is whether the text can bear the reading or the reader has supplied it.

Ready when they can: Infer something about a character from a detail the narrator passes over without comment; Point at the exact words that support an inference, and at the ones that only seem to; Give up a plausible reading once it turns out nothing in the text supports it.

https://lightmysky.com/learn/english/inference-and-implication-in-close-reading-mt_ZsYmlv5QuC

#### Analysing Tone and Its Shifts (ages 14-16)

Name a text's tone precisely, show which diction and syntax produce it, and find the line where the tone turns. A shift in tone is usually where the meaning of a passage sits.

Ready when they can: Choose a precise tone word (wry, resigned, indignant) rather than a general one such as sad; Locate the sentence where tone changes and explain what causes the change; Show how sentence length or punctuation builds tone, not only vocabulary.

https://lightmysky.com/learn/english/analysing-tone-and-its-shifts-mt_mZSdiW9z1W

#### Analysing Structural Choices in Whole Texts (ages 14-16)

Read structure as a sequence of decisions: where a text starts, how its focus narrows or widens, where the perspective moves, and what the ending does with the opening. Position carries meaning independently of content.

Ready when they can: Describe how the focus of an extract moves from wide to narrow and what the move does; Explain the effect of where a moment sits (first line, midpoint, last line), not what it contains; Link an ending back to the opening and say what the return changes.

https://lightmysky.com/learn/english/analysing-structural-choices-in-whole-texts-mt_siYSy_kXUU

#### Comparing Characters Across Stories (ages 5-9)

Compare and contrast the adventures and experiences of characters in familiar stories; identify similarities and differences between two texts on the same topic

Ready when they can: Identify what two stories have in common (e.g. 'Both have a bear character'); Compare information from two books about the same topic; Discuss how characters' experiences are similar or different across stories.

Needs first: Connecting New & Old Ideas, Main Topic of Informational Texts, Feelings Change and Differ, Characters, settings, and events, Spotting Patterns.

https://lightmysky.com/learn/english/comparing-characters-across-stories-mt_GLY3R3YSlf

#### Characters' Viewpoints and Responses (ages 6-8)

Identify and compare characters' points of view, recognise who is narrating a story, describe how characters respond to events and challenges, and compare characters' experiences across different stories or versions of the same story

Ready when they can: Identify who is telling a story and explain how you know (e.g. 'The wolf is telling the story because he says I'); Describe how a character responds to a problem or challenge using evidence from the text (e.g. 'When the bridge broke, she decided to swim across'); Compare how two characters from different stories react to a similar situation (e.g. how two heroes show bravery in different ways).

Needs first: Connecting reading to experience, Seeing Someone Else's Point of View, Comparing Characters Across Stories, Retelling Stories with Structure.

https://lightmysky.com/learn/english/characters-viewpoints-and-responses-mt_xjl6AEhnjk

#### Character Traits and Motivation (ages 8-9)

Analyse character traits, motivations, and feelings using text evidence, and distinguish one's own point of view from that of the narrator or characters

Ready when they can: Identify two character traits from a story and cite the specific actions or dialogue that reveal each trait; Explain why a character made a particular decision by linking their motivation to events in the text; Describe where one's own opinion about a character differs from the narrator's portrayal and explain why.

Needs first: Inferring Characters' Feelings and Motives, Characters' Viewpoints and Responses.

https://lightmysky.com/learn/english/character-traits-and-motivation-mt_KmPZ5diLEP

#### In-Depth Character and Setting Analysis (ages 9-10)

Describe in depth a character, setting, or event in a story or drama, drawing on specific details from the text such as a character's thoughts, words, actions, and interactions

Ready when they can: Write a detailed character description drawing on evidence from multiple points in the text, including what the character says, does, thinks, and how others respond to them; Describe a setting in depth by citing specific sensory details, figurative language, and mood clues the author provides; Explain how a key event affects the characters and plot development, citing specific textual details about actions, reactions, and consequences.

Needs first: Character Traits and Motivation.

https://lightmysky.com/learn/english/in-depth-character-and-setting-analysis-mt_Eehl12cSnN

#### Narrator's Point of View (ages 9-10)

Compare and contrast the point of view from which different stories are narrated, including distinguishing between first-person and third-person narration and explaining how the narrator's perspective shapes the reader's understanding

Ready when they can: Identify whether a story is told in first person (I/we) or third person (he/she/they) and explain how this affects what the reader knows about characters' thoughts and feelings; Compare two versions of a story or event told from different points of view and explain how each narrator's perspective changes what is emphasised, omitted, or revealed; Explain why an author might choose first-person narration (immediacy, personal voice) versus third-person narration (broader view, objectivity) for a particular story.

Needs first: Character Traits and Motivation, Characters' Viewpoints and Responses.

https://lightmysky.com/learn/english/narrators-point-of-view-mt_E_OryWIYkn

#### Comparing Characters, Settings and Events (ages 10-11)

Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details about how characters interact, settings influence action, or events connect

Ready when they can: Create a Venn diagram comparing two characters' traits using textual evidence; Explain how a change in setting affects the mood and characters' actions in a story; Analyse how two events in a narrative are connected through cause and effect.

Needs first: In-Depth Character and Setting Analysis.

https://lightmysky.com/learn/english/comparing-characters-settings-and-events-mt_WRlJ0-hAOG

#### Different viewpoints in texts (ages 10-11)

Describe how a narrator's or speaker's point of view influences how events are described, recognising the difference between limited and omniscient narration and how perspective shapes storytelling

Ready when they can: Identify whether a story uses first-person or third-person narration and explain the effect; Explain how events would be described differently if told from another character's perspective; Analyse how the narrator's knowledge or bias affects what information the reader receives.

Needs first: Narrator's Point of View.

https://lightmysky.com/learn/english/different-viewpoints-in-texts-mt_LCJNRaRXtW

#### Plot Structure and Character Development (ages 11-14)

Analyse how plot structure unfolds through episodes or key events, and how characters develop, respond to challenges, and change over the course of a narrative — including the relationship between character, setting, and plot

Ready when they can: Trace how a character's attitude changes across a story and identify the turning points; Explain how a specific incident in a drama propels the action or provokes a decision; Analyse how the setting influences a character's behaviour or the mood of a scene.

Needs first: Using and Evaluating Textual Evidence, Inferring Characters' Feelings and Motives, Comparing Characters, Settings and Events.

https://lightmysky.com/learn/english/plot-structure-and-character-development-mt_Hqz5y_tWz2

#### Narrative Perspective and Unreliable Narrators (ages 11-14)

Analyse point of view and narrative perspective — including first person, third person limited and omniscient, and unreliable narrator — and how the author's or narrator's perspective shapes the reader's understanding and creates effects such as suspense, irony, or humour

Ready when they can: Identify the narrative perspective of a text and explain how it limits or expands the reader's knowledge; Explain how dramatic irony arises when the reader knows something a character does not; Compare how the same event might be told differently from two characters' perspectives.

Needs first: Using and Evaluating Textual Evidence, Plot Structure and Character Development, Different viewpoints in texts.

https://lightmysky.com/learn/english/narrative-perspective-and-unreliable-narrators-mt_x2sWtfTeYT

#### Understanding drama and performance (ages 11-14)

Understand how dramatists communicate meaning through performance — including staging, direction, set design, lighting, and actors' choices — and how different productions can interpret the same script differently

Ready when they can: Explain how a director's staging choices (e.g., set, lighting, blocking) affect the audience's understanding; Compare two productions or adaptations of the same play and evaluate different interpretive choices; Analyse how a filmed or live production stays faithful to or departs from the original script.

Needs first: Plot Structure and Character Development, Narrative Perspective and Unreliable Narrators, Poems, Drama & Prose.

https://lightmysky.com/learn/english/understanding-drama-and-performance-mt_tIi6L1n7kF

#### Building an Analytical Paragraph (ages 14-16)

Write a paragraph of analysis that holds one point, embeds short quotations inside its own sentences, and keeps returning to the argument instead of retelling the text.

Ready when they can: Embed a quotation of a few words inside a sentence so the whole reads as one sentence; Follow a quotation with analysis of its language rather than a restatement of the event; Delete a sentence of plot summary from a paragraph and lose nothing.

https://lightmysky.com/learn/english/building-an-analytical-paragraph-mt_g6V2qZrdWR

#### Poetry: Imagery and the Speaker's Voice (ages 15-16)

Read a poem through its images and its speaker: who is talking, at what distance from the poet, and how a run of images carries the poem's argument.

Ready when they can: Distinguish the speaker of a poem from the poet who wrote it; Trace one image as it develops across stanzas and say what it accumulates; Explain the effect of an image that sits oddly against the rest of the poem.

https://lightmysky.com/learn/english/poetry-imagery-and-the-speakers-voice-mt_RYvng3ESeS

#### Poetry: Form, Sound, and Line as Meaning (ages 15-16)

Explain how a poem's shape carries meaning: the pull between metre and speech rhythm, what a line break does to the word left hanging, what a form promises, and where the poet breaks it.

Ready when they can: Explain what a line break does to the word at the end of the line; Say what a regular form sets up and what a departure from it signals; Tie a sound pattern to sense rather than calling it musical.

https://lightmysky.com/learn/english/poetry-form-sound-and-line-as-meaning-mt_16EYLKp49Q

#### Comparing Two Poems (ages 15-16)

Compare poems by method rather than by checklist: find the concern they share, then argue how each poet handles it differently, moving between the two inside a paragraph.

Ready when they can: State a shared concern precisely enough that the two poems answer it differently; Move between poems within one paragraph instead of writing two separate halves; Use a comparative link that carries an argument (where one softens the loss, the other refuses to).

https://lightmysky.com/learn/english/comparing-two-poems-mt__cGKUS-Mlo

#### Drama: Stagecraft as Method (ages 15-16)

Analyse a play as something staged: entrances and exits, silence, what an audience sees before it hears, dramatic irony, and stage directions read as part of the writing.

Ready when they can: Explain what the audience knows that a character does not, and what the gap does to a scene; Analyse a stage direction as an authorial choice rather than a note for the crew; Explain the effect of an entrance, an exit, or a silence at a specific point.

https://lightmysky.com/learn/english/drama-stagecraft-as-method-mt_RYVZd0zENq

#### Reading Nineteenth-Century Prose Unseen (ages 15-16)

Work out an unfamiliar older extract with no notes: unpick long sentences, infer archaic vocabulary from its surroundings, and hold the sense of a passage whose syntax delays the point.

Ready when they can: Reduce a long periodic sentence to its main clause plus its qualifications; Infer an unfamiliar word from the sentence around it and test the guess against the rest of the passage; Put a dense paragraph into one plain sentence before starting to analyse it.

https://lightmysky.com/learn/english/reading-nineteenth-century-prose-unseen-mt_9kI4W1A79W

#### Context That Serves the Reading (ages 15-16)

Use what was true when a text was written to sharpen a reading of its language, and keep the context tied to the text instead of writing a paragraph of history beside it.

Ready when they can: Use one contextual fact to explain a specific word or moment in the text; Reject a contextual point that adds nothing to the reading in hand; Explain how a first audience might have heard a line differently from a reader today.

https://lightmysky.com/learn/english/context-that-serves-the-reading-mt_xjq2wvDyYF

#### Comparing Writers' Viewpoints Across Non-Fiction (ages 15-16)

Compare two non-fiction texts on one subject, often written a century apart: what each writer thinks, how each makes a reader feel it, and where their methods diverge.

Ready when they can: State each writer's attitude in a phrase, not just the subject they share; Compare methods (anecdote against statistic, mockery against restraint), not only opinions; Support one comparative point with an extract from each text.

https://lightmysky.com/learn/english/comparing-writers-viewpoints-across-non-fiction-mt_ORnNTCIy4T

#### Critical Evaluation of a Writer's Success (ages 15-16)

Answer the question that asks how far you agree: judge how well a writer achieves a stated effect, and support the verdict with the text's own methods rather than with taste.

Ready when they can: Commit to a judgement instead of listing what the writer does; Concede a point that weakens the judgement, then answer it; Support an evaluation with a method from the text, not with whether it was enjoyable.

https://lightmysky.com/learn/english/critical-evaluation-of-a-writers-success-mt_opMDJ3ov_i

#### Close Reading at Depth (ages 16-18)

Work a short passage until the reading is dense: several strands tracked at once, and the detail that resists a first reading given weight rather than passed over.

Ready when they can: Read one passage three times, each pass following a different strand, and keep the notes apart; Give weight to a word that does not fit the reading instead of ignoring it; Say which of two readings the passage supports better, and what decides it.

https://lightmysky.com/learn/english/close-reading-at-depth-mt_FG1xqyBhdk

#### From Noticing to a Literary Thesis (ages 16-18)

Turn a page of annotations into one arguable claim about the text, narrow enough to defend at essay length and open enough that a reader could disagree.

Ready when they can: Reduce a page of notes to one sentence somebody could argue against; Reject a thesis that only restates what the text obviously does; Narrow a thesis until the essay can actually defend it in its length.

https://lightmysky.com/learn/english/from-noticing-to-a-literary-thesis-mt_51UHXhXCo6

#### Checking a Claim Before You Repeat It (ages 14-16)

Trace a claim back to whoever first made it, then check whether anyone independent says the same. Most of the work is leaving the page you are on: a confident sentence with no traceable origin is the normal shape of something false.

Ready when they can: Follow a claim from where it was met back to the first source that carries it, and say where the trail stops; Find a second source that is genuinely independent rather than a copy of the first; Say what would have to be true for the claim to hold, and whether the sources found show it.

https://lightmysky.com/learn/english/checking-a-claim-before-you-repeat-it-mt_alX03luQ-m

#### Images and Charts as Argument (ages 15-16)

A photograph is cropped, a chart has an axis, a caption tells the reader what to see. Each of those is an argument made without a sentence, and each can be checked the way a sentence can.

Ready when they can: Say what a caption asks the reader to conclude that the image alone does not show; Spot an axis or a scale that makes a difference look larger than it is; Explain what a crop excludes and how the excluded part would change the reading.

https://lightmysky.com/learn/english/images-and-charts-as-argument-mt_X1vajiAqrM

#### Sustaining a Literary Argument Across an Essay (ages 16-18)

Hold one thesis through a whole essay: every paragraph advances the case, quotation stays short and embedded, and the order follows the argument rather than the order of the book.

Ready when they can: Order paragraphs by the argument rather than by where the quotations appear in the text; Open each paragraph with a sentence that moves the thesis on; Cut a paragraph that is interesting in itself but does not serve the thesis.

https://lightmysky.com/learn/english/sustaining-a-literary-argument-across-an-essay-mt_GeEKS_WMne

#### Free Indirect Style and Narrative Distance (ages 16-18)

Read prose where a narrator's words and a character's thoughts run together, and judge how close the narration stands to the character at any moment. That distance is a choice, and it moves.

Ready when they can: Point at a sentence where whose words they are is unclear, and explain what the blur does; Track where narration moves closer to a character and where it pulls back; Separate a character's judgement from the narrator's in a passage that carries both.

https://lightmysky.com/learn/english/free-indirect-style-and-narrative-distance-mt_r3DLUmwC6G

#### Scanning a Line: Metre, Stress, and Substitution (ages 16-18)

Mark the stresses in a line of verse, name the pattern it sets up, and find where the poet departs from it. The departures are usually where the reading starts.

Ready when they can: Mark stressed and unstressed syllables across four lines and name the metre; Find a substituted foot and explain what the interruption does to the sense; Read a line aloud against its metre and say which wins, the pattern or the speech.

https://lightmysky.com/learn/english/scanning-a-line-metre-stress-and-substitution-mt_jF8TId2BYf

#### Genre as a Set of Expectations (ages 17-18)

Treat a genre as the promises a reader brings to a text, then read what the writer does with them: met, delayed, or refused.

Ready when they can: State what a reader expects of a genre before reading a text placed in it; Find a point where a text refuses a convention and explain the effect of the refusal; Argue that a text sits in two genres at once and say what each reading gains.

https://lightmysky.com/learn/english/genre-as-a-set-of-expectations-mt_2OD97Y6LmG

#### Tragedy: The Shape of the Fall (ages 17-18)

Read tragedy as a genre with a shape: a protagonist with something to lose, a fall an audience can see coming, and an ending that asks what the loss bought. Then test the shape on a play that does not fit it.

Ready when they can: Locate the point in a play after which the fall can no longer be stopped; Explain what a protagonist's flaw costs, using the play's own language rather than a definition; Judge whether a modern text is a tragedy and say which parts of the shape it keeps.

https://lightmysky.com/learn/english/tragedy-the-shape-of-the-fall-mt_PBjNKW9yUC

#### Reading Through a Critical Lens (ages 17-18)

Use a critical approach as a set of questions to put to a text: who holds power here, whose work goes unseen, whose story is left out. A lens is a way of asking, not a verdict to apply.

Ready when they can: Put the questions one critical approach asks to a text and record what surfaces; Read a single passage through two lenses and say what each brings out that the other misses; Drop a lens that produces nothing the text supports.

https://lightmysky.com/learn/english/reading-through-a-critical-lens-mt_ceYRZV1vOe

#### Arguing With Published Criticism (ages 17-18)

Read what a critic has written about a text as a position to test: agreed with in part, answered where it stops holding. The essay stays yours, and the critic gives it something to push against.

Ready when they can: State a critic's claim in one sentence before responding to it; Agree with part of a critical reading and show where it stops holding; Use a critic to sharpen an argument rather than to settle it.

https://lightmysky.com/learn/english/arguing-with-published-criticism-mt_RHkHphHUHO

#### Comparing Whole Texts Around a Question (ages 17-18)

Build a comparison of two whole texts from one critical question, with the argument moving between them instead of taking each in turn. A difference counts when it answers the question.

Ready when they can: Frame a question that both texts answer differently; Move between texts inside a paragraph, using the second to test a claim about the first; Drop a difference that is real but says nothing about the question.

https://lightmysky.com/learn/english/comparing-whole-texts-around-a-question-mt_lUatQWgP2g

#### Working an Unseen Text Against the Clock (ages 17-18)

Meet a text you have never read and produce an argued response in a fixed time: one pass for sense, a decision about what to write on, and three moves worth making rather than everything noticed.

Ready when they can: Split a fixed time into reading, planning, and writing, and hold to the split; Choose three points to develop and leave the rest of the annotations unused; Write an opening claim before the reading feels finished.

https://lightmysky.com/learn/english/working-an-unseen-text-against-the-clock-mt_9yk_tpun2R

### English Thinking

https://lightmysky.com/learn/english/areas/english-thinking

#### Reading for Meaning (ages 5-6)

Understand that reading is about making meaning, not just saying words correctly — a text that can be decoded but not understood has not been read

Ready when they can: Simple View of Reading (Gough & Tunmer); reading comprehension research on comprehension-decoding separation.

Needs first: Feeling of not understanding.

https://lightmysky.com/learn/english/reading-for-meaning-mt_scBgiMKhG_

#### Monitoring Comprehension (ages 6-8)

Notice the difference between decoding words and actually understanding them — recognise when you've read the words but not grasped the meaning, and do something about it

Ready when they can: comprehension monitoring research; Metacognitive Monitoring in Reading Comprehension (MDPI 2024).

Needs first: Feeling of not understanding, Reading for Meaning.

https://lightmysky.com/learn/english/monitoring-comprehension-mt_GugVunb2lI

#### Author's word choices (ages 7-9)

Recognise how an author's deliberate choices — of words, structure, tone, and perspective — create particular effects on you as a reader

Ready when they can: authorial awareness research; Understanding Author's Purpose (Firkins); collaborative multilayered text interpretation in 5-8 year olds.

Needs first: Connecting New & Old Ideas, Monitoring Comprehension.

https://lightmysky.com/learn/english/authors-word-choices-mt_QB4qIGJIIj

#### Inference vs Explicit Meaning (ages 7-9)

Distinguish between what a text explicitly says and what you have inferred, assumed, or read in — knowing which is which is fundamental to honest comprehension

Ready when they can: inference vs literal comprehension development research; online inference making and comprehension monitoring (PMC 2021).

Needs first: Teaching It Back, Monitoring Comprehension.

https://lightmysky.com/learn/english/inference-vs-explicit-meaning-mt_lp3qyEujIv

#### Knowing What You Don't Know (ages 8-10)

Monitor your own vocabulary gaps — notice words you half-know, distinguish confident from uncertain knowledge, and develop strategies to resolve the uncertainty

Ready when they can: Noticing Unfamiliar Words Assessment research (grade 2+); word consciousness and vocabulary metacognition research; Building Word Knowledge e-Book (PMC 2019).

Needs first: Inference vs Explicit Meaning, Analysing Your Own Errors.

https://lightmysky.com/learn/english/knowing-what-you-dont-know-mt_LH714Riydn

#### Reviewing Own Writing (ages 8-10)

Evaluate whether your own writing achieves the effect you intended on a reader — go beyond checking for correctness to asking whether it actually works

Ready when they can: writing self-evaluation research grades 3-5; metacognitive awareness of writing (Frontiers 2025).

Needs first: Author's word choices, Understanding Why.

https://lightmysky.com/learn/english/reviewing-own-writing-mt_U_8iVFZuHH

#### Reflecting on Your Language Use (ages 10-11)

Reflect on yourself as a language user — how your reading, writing, and speaking shift across audiences, purposes, and contexts, and where you want to develop further

Ready when they can: metalinguistic awareness development; register and audience awareness research.

Needs first: Knowing What You Don't Know, Reviewing Own Writing, Reflecting After Learning.

https://lightmysky.com/learn/english/reflecting-on-your-language-use-mt_haNr13NIuN

#### Choosing How to Read a Text (ages 12-14)

Match the reading to the job: skim to see whether a text is worth the time, scan for one fact, read closely when the wording carries the argument, reread when the first pass did not hold. Reading everything at one speed wastes the hours that the hard texts need.

Ready when they can: Say before starting which of skim, scan or close read the task needs, and why; Switch approach mid-text when the first choice stops working, and name the moment it stopped; Justify rereading a paragraph rather than pressing on, pointing at what did not resolve.

https://lightmysky.com/learn/english/choosing-how-to-read-a-text-mt_P8WoRvRp1m

#### Holding an Interpretation (ages 15-16)

Accept that a text supports more than one reading, argue for the one you hold, and drop it when the evidence says you should. A reading is a position, not a right answer to be found.

Ready when they can: Offer an alternative reading of the same lines and weigh it against your own; Say what would have to be true in the text for a rival reading to win; Abandon a reading after finding evidence against it, and say what changed your mind.

https://lightmysky.com/learn/english/holding-an-interpretation-mt_pH7ZCyH5cU

#### Reading Beyond the Set Texts (ages 17-18)

Build your own reading around the texts you are taught: books chosen because they argue with each other, notes a later essay can use, and a question of your own that comes out of the reading.

Ready when they can: Choose a second text because it argues with a set text, and say how; Keep a reading note that is still usable months later, rather than a summary; Turn a pattern noticed across your own reading into a question worth writing on.

https://lightmysky.com/learn/english/reading-beyond-the-set-texts-mt_ZegdyfwUov

#### Framing a Research Question (ages 17-18)

Turn an interest into a question a study can answer: narrow enough to investigate, open enough to have more than one answer, and answerable with material you can actually get hold of.

Ready when they can: Narrow a broad interest into a question answerable in the time available; Reject a question whose answer is already settled, or that nothing could test; Say what evidence would answer the question before collecting any.

https://lightmysky.com/learn/english/framing-a-research-question-mt_IEMPNTY48g

### Vocabulary

https://lightmysky.com/learn/english/areas/vocabulary

#### Discussing and Questioning New Words (ages 5-11)

Ask and answer questions about unknown words in texts; discuss word meanings and link new vocabulary to words already known

Ready when they can: Ask 'What does ___ mean?' when meeting unfamiliar words during reading; Use context and pictures to work out what a new word might mean; Explain a new word by connecting it to a known word (e.g. 'enormous means really really big').

https://lightmysky.com/learn/english/discussing-and-questioning-new-words-mt_6-MYToNZ39

#### Using New Vocabulary (ages 5-9)

Use words and phrases acquired through conversations, being read to, and responding to texts in own speech and writing

Ready when they can: Incorporate new vocabulary from read-alouds into conversations; Attempt to use interesting or topic-specific words in own writing; Use newly learned words appropriately in different contexts.

Needs first: Discussing and Questioning New Words.

https://lightmysky.com/learn/english/using-new-vocabulary-mt_NP101Zl-4g

#### Word Parts as Clues (ages 5-8)

Use knowledge of common inflections and affixes (-ed, -s, un-, -er) as clues to the meaning of unknown words; understand how the prefix un- changes meaning

Ready when they can: Recognise that -ed signals past tense (e.g. 'jumped' = already happened); Explain how un- makes a word mean the opposite (e.g. 'unhappy' = not happy); Use word parts to figure out the meaning of an unfamiliar word.

Needs first: Discussing and Questioning New Words, Reading Inflectional Endings.

https://lightmysky.com/learn/english/word-parts-as-clues-mt_aw0PldeT_L

#### Root Words & Inflections (ages 6-9)

Identify frequently occurring root words and their inflectional forms (e.g., look/looks/looked/looking), using affixes as clues to word meaning and understanding how suffixes create nouns and adjectives

Ready when they can: Identify 'play' as the root in 'played', 'playing', 'player'; Explain that '-ful' in 'careful' means 'full of care'; Use '-ness' and '-er' to form nouns from root words: 'sad → sadness', 'teach → teacher'.

Needs first: Word Parts as Clues, Suffixes, Basic Nouns & Verbs.

https://lightmysky.com/learn/english/root-words-and-inflections-mt_UEe3MC5RZc

#### Word Families and Root Words (ages 7-9)

Explore word families based on common root words, understanding how words are related in form and meaning through shared roots, prefixes and suffixes (e.g., solve → solution, solver, dissolve, insoluble)

Ready when they can: Generate at least 4 words in a word family from a given root (e.g., from 'play': player, playful, replay, playground); Explain how members of a word family are connected in meaning (e.g., 'solve, solution, dissolve all relate to finding answers or breaking apart'); Use knowledge of a word family to predict the meaning of an unfamiliar member (e.g., knowing 'act' helps understand 'actor', 'action', 'react').

Needs first: Word Parts as Clues, Root Words & Inflections.

https://lightmysky.com/learn/english/word-families-and-root-words-mt_p1imGSFgJT

#### Formal and Informal English (ages 7-10)

Recognise and compare formal and informal uses of English, understanding that language choices vary based on audience, purpose and context

Ready when they can: Identify whether a spoken or written example uses formal or informal language (e.g., 'Dear Sir' vs 'Hey mate'); Rewrite an informal sentence in a more formal way (e.g., change 'Can I have some?' to 'May I please have some?'); Explain why formal language might be used in one situation and informal in another (e.g., a letter to the headteacher vs a note to a friend).

Needs first: Describing Aloud, Using New Vocabulary.

https://lightmysky.com/learn/english/formal-and-informal-english-mt_86DyHo9zO3

#### Choosing Formal Vocabulary (ages 10-11)

Distinguish between formal and informal vocabulary, selecting words appropriate for formal speech and writing such as 'discover' instead of 'find out' and 'request' instead of 'ask for'

Ready when they can: Replace informal words with formal equivalents in a given text; Identify formal vocabulary choices in official letters and reports; Write the same message twice using formal vocabulary for a letter and informal vocabulary for a text message.

Needs first: Formal and Informal English.

https://lightmysky.com/learn/english/choosing-formal-vocabulary-mt_h3vmvQW5Wa

#### Dialects & Registers (ages 10-11)

Compare and contrast the varieties of English used in stories, dramas, or poems, including dialects and registers, understanding how language varies by region, context, and purpose

Ready when they can: Identify dialect features in character dialogue and explain their effect; Compare formal and informal registers in different types of texts; Explain how an author uses language variety to develop character or setting.

Needs first: Formal and Informal English.

https://lightmysky.com/learn/english/dialects-and-registers-mt_1ro8W1cZYn

#### Sorting & Categorising Words (ages 5-8)

Sort common objects and words into categories to understand how concepts relate; demonstrate understanding of opposites (antonyms) for common verbs and adjectives

Ready when they can: Group words or objects by category (e.g. animals, foods, colours); Identify and produce opposite pairs (e.g. 'big/small', 'hot/cold', 'go/stop'); Explain why items belong together in a category.

Needs first: How Many in Total?.

https://lightmysky.com/learn/english/sorting-and-categorising-words-mt_oL9s_bufDp

#### Shades of Meaning (ages 5-9)

Distinguish shades of meaning among verbs describing similar actions and among adjectives differing in intensity; make real-life connections between words and their use

Ready when they can: Compare similar verbs by acting them out (e.g. 'walk', 'march', 'strut', 'prance'); Order adjectives by intensity (e.g. big, huge, gigantic); Connect vocabulary to personal experiences (e.g. note things at school that are 'colourful').

Needs first: Sorting & Categorising Words.

https://lightmysky.com/learn/english/shades-of-meaning-mt_VLu59hpQ4T

#### Defining Words (ages 6-9)

Define words by category and by one or more key attributes (e.g., 'a duck is a bird that swims'), making real-life connections between words and their use

Ready when they can: Define 'tiger' as 'a large cat with stripes' — naming category and key attribute; Connect the word 'cozy' to real-life examples: places at home that feel cozy; Sort words into categories and explain why each word belongs.

Needs first: Discussing and Questioning New Words, Sorting & Categorising Words.

https://lightmysky.com/learn/english/defining-words-mt_f_dMmvzxwo

#### Literal vs Figurative Language (ages 8-9)

Distinguish literal from nonliteral (figurative) language in context and interpret common idioms and phrases

Ready when they can: Identify whether 'It's raining cats and dogs' is literal or nonliteral and explain what it means; Read a passage and circle three phrases used nonliterally, restating each in literal terms; Explain the difference between 'She was on fire' (figurative — performing well) and 'The log was on fire' (literal).

Needs first: Expressive and Sensory Language, Shades of Meaning.

https://lightmysky.com/learn/english/literal-vs-figurative-language-mt_SUOhjmRqv9

#### Antonyms & Synonyms (ages 9-11)

Demonstrate understanding of words by relating them to their antonyms (opposites) and synonyms (words with similar meanings), using synonym and antonym relationships to refine vocabulary and improve precision in writing

Ready when they can: Generate synonyms and antonyms for given words and explain subtle differences between synonyms, e.g. happy/joyful/ecstatic differ in intensity; Use a thesaurus to find synonyms and select the most precise word for a given context, e.g. choosing 'sprinted' rather than 'ran' to convey speed; Replace overused words in writing with more precise synonyms and explain how the substitution changes the tone or emphasis.

Needs first: Shades of Meaning.

https://lightmysky.com/learn/english/antonyms-and-synonyms-mt_E5YbLvMgLL

#### Domain Vocabulary Across Subject Areas (ages 9-11)

Acquire and use accurately academic and domain-specific vocabulary relevant to grade-level topics, including words that signal precise meaning in informational texts across subject areas

Ready when they can: Identify and define academic vocabulary (e.g., compare, contrast, summarise, evidence, interpret) used across multiple subject areas and use these words accurately in discussion and writing; Determine the meaning of domain-specific words encountered in science, social studies, or maths texts (e.g., ecosystem, democracy, numerator) using context, glossaries, and prior knowledge; Use newly acquired academic and domain-specific vocabulary in sentences that demonstrate understanding of precise meaning and appropriate context.

Needs first: Discussing and Questioning New Words, Defining Words.

https://lightmysky.com/learn/english/domain-vocabulary-across-subject-areas-mt_WzOyJFKDIu

#### Greek and Latin Roots for Word Meaning (ages 9-11)

Use knowledge of Greek and Latin affixes (prefixes and suffixes) and roots as clues to determine the meaning of unfamiliar words, building a bank of common roots and their meanings

Ready when they can: Identify common Greek and Latin roots in unfamiliar words and use root meaning to infer word meaning, e.g. 'aqua' (water) in aquarium/aquatic, 'dict' (say) in predict/dictionary; Break a multi-morpheme word into prefix + root + suffix to determine meaning, e.g. un- (not) + believe + -able = not able to be believed; Use knowledge of Greek-origin prefixes (auto-, tele-, micro-) and Latin-origin prefixes (inter-, trans-, sub-) to decode and define unfamiliar vocabulary in context.

Needs first: Word Families and Root Words, Prefixes (age 7+), Prefixes and suffixes.

https://lightmysky.com/learn/english/greek-and-latin-roots-for-word-meaning-mt_x_Lg4RASVU

#### Idioms & Proverbs (ages 9-11)

Recognise and interpret common idioms (break the ice, hit the nail on the head), adages (actions speak louder than words), and proverbs (a stitch in time saves nine), understanding their figurative meanings and when to use them

Ready when they can: Explain the figurative meaning of common idioms encountered in texts, e.g. 'let the cat out of the bag' means to reveal a secret, not literally releasing a cat; Interpret the meaning and intended lesson of adages and proverbs, e.g. explain that 'the early bird catches the worm' advises that acting promptly gives an advantage; Use context clues to determine the meaning of an unfamiliar idiom or proverb encountered during reading and verify using a reference source.

Needs first: Literal vs Figurative Language.

https://lightmysky.com/learn/english/idioms-and-proverbs-mt_IoGOSAQ8bz

#### Similes & Metaphors (ages 9-11)

Understand and identify similes (comparisons using like or as) and metaphors (direct comparisons stating something is something else) in texts, explaining how each creates imagery and conveys meaning

Ready when they can: Identify similes in a text by locating comparisons using 'like' or 'as' and explain what two things are being compared and what quality is highlighted, e.g. 'The snow was like a white blanket'; Identify metaphors in a text and explain the implied comparison, e.g. in 'Time is a thief', explain that time is compared to a thief because it takes things away; Explain how a simile or metaphor in a poem or story creates a particular image or feeling for the reader that a literal description would not achieve.

Needs first: Expressive and Sensory Language, Literal vs Figurative Language.

https://lightmysky.com/learn/english/similes-and-metaphors-mt_hJW7hVflm3

#### Using a Thesaurus to Choose Words (ages 10-11)

Use a thesaurus to find synonyms and extend vocabulary choices, selecting the most appropriate word based on context, connotation, and register

Ready when they can: Use a thesaurus to find three alternatives for overused words in own writing; Select the most appropriate synonym from thesaurus options based on context and tone; Explain why one synonym is more suitable than another for a specific sentence.

Needs first: Using a Dictionary to Check Spellings, Antonyms & Synonyms.

https://lightmysky.com/learn/english/using-a-thesaurus-to-choose-words-mt_saW7PxtPxw

#### Vocabulary Strategies (ages 11-14)

Determine the meaning of unknown and multiple-meaning words and phrases using a flexible range of strategies — including context clues, Greek and Latin affixes and roots, reference materials, and verification of inferred meaning

Ready when they can: Use context clues (the overall meaning of a sentence, a word’s position or function) to infer the meaning of an unfamiliar word; Break down a word using known Greek or Latin roots and affixes to deduce its meaning (e.g., 'malevolent' = mal- (bad) + volent (wishing)); Look up a word in a dictionary to verify or refine an inferred meaning.

Needs first: Using a Thesaurus to Choose Words, Spellings from Greek, French and Latin, Converting Words into Verbs, Verb Prefixes and Meaning, Decoding unfamiliar words.

https://lightmysky.com/learn/english/vocabulary-strategies-mt_WZnwITSWr8

#### Academic Vocabulary (ages 11-14)

Acquire and use accurately a broad range of general academic vocabulary and domain-specific words — drawing new vocabulary from reading and listening and deploying it consciously in writing and speech to achieve particular effects

Ready when they can: Use academic vocabulary (e.g., analyse, evaluate, justify, convey, imply) accurately and appropriately in essay writing; Incorporate domain-specific terms from a subject studied (e.g., 'photosynthesis', 'legislature') into explanatory writing; Draw a new word or phrase from a text read and use it consciously in own writing or speech.

Needs first: Choosing Formal Vocabulary, Vocabulary Strategies, Abstract nouns, Greek and Latin Roots for Word Meaning.

https://lightmysky.com/learn/english/academic-vocabulary-mt_OLwNsTI6C7

#### Advanced Figurative Language (ages 11-14)

Understand and interpret figurative language, word relationships, and nuances in word meaning — including allusion, irony, pun, oxymoron, and extended metaphor — and distinguish between connotation and denotation when analysing or choosing words

Ready when they can: Explain the connotative difference between words with similar denotations (e.g., thrifty vs. stingy vs. economical); Identify irony or an allusion in a text and explain what it adds to the meaning; Analyse an extended metaphor across a paragraph or poem and explain how it develops an idea.

Needs first: Figurative Language and Literary Devices, Antonyms & Synonyms, Cultural Allusions and Word Meaning, Idioms & Proverbs.

https://lightmysky.com/learn/english/advanced-figurative-language-mt_MlmIrLb_7x

#### Patterns of Language and Semantic Fields (ages 14-16)

Track a run of related words across a passage as one deliberate pattern, and say what the pattern builds that no single word would. Where a writer breaks their own pattern is often the point.

Ready when they can: Group words from an extract into a field (disease, machinery, imprisonment) and name it; Explain what a pattern accumulates across a whole passage rather than in one line; Spot where the writer departs from the pattern and say why the departure lands.

https://lightmysky.com/learn/english/patterns-of-language-and-semantic-fields-mt_p1Wzl_KM7p

#### How Language Varies: Register, Dialect, and Sociolect (ages 16-18)

Separate the kinds of variation in English: the situation a speaker is in, the place they come from, and the groups they belong to. Real speech mixes all three at once.

Ready when they can: Attribute a feature of a transcript to situation, region, or group, and defend the choice; Find where one speaker shifts variety inside a conversation and say what prompted it; Describe a dialect feature in grammatical terms rather than calling it wrong.

https://lightmysky.com/learn/english/how-language-varies-register-dialect-and-sociolect-mt_SJ9T1azPop

#### Language Change Over Time (ages 16-18)

Track how English has changed: meanings that narrowed or drifted, words borrowed and coined, spelling settled by print, grammar quietly simplified. Change is measurable in texts, not just asserted.

Ready when they can: Date a short text roughly from its vocabulary, spelling, and grammar, giving the evidence; Trace one word whose meaning narrowed or broadened and say what pushed it; Explain one change through a cause outside the language, such as trade, print, or migration.

https://lightmysky.com/learn/english/language-change-over-time-mt_o8mC_j0E2J

#### Attitudes to Language Change (ages 17-18)

Weigh the familiar claim that English is getting worse against what the evidence shows, and separate a judgement about language from a judgement about the people using it.

Ready when they can: Restate a complaint about language use as a claim that can be tested; Find evidence for and against one claim that a usage is new or wrong; Show where a criticism of somebody's speech is really a criticism of the speaker.

https://lightmysky.com/learn/english/attitudes-to-language-change-mt_IJ9Tv9T3Ua

#### Language and Power in Public Discourse (ages 17-18)

Who gets to name things, and what the naming does. Political and institutional language distributes blame, hides an agent behind a passive, and turns contested choices into settled facts, all with ordinary grammar.

Ready when they can: Find the sentence where an agent has been removed and say who it was; Compare two labels for one group and describe what each label assumes; Describe a piece of official or campaign language at the grammatical level rather than only judging its intent.

https://lightmysky.com/learn/english/language-and-power-in-public-discourse-mt_nOBe8ExZx-

### Speaking & Listening

https://lightmysky.com/learn/english/areas/speaking-and-listening

#### Expressing & Justifying Opinions (ages 4-6)

Articulate and justify answers, arguments, and opinions; participate in discussions, presentations, performances, role play, and debates

Ready when they can: State an opinion and give a reason (e.g. 'I think ... because ...'); Participate in a class presentation or performance with confidence; Explain thinking when answering a question rather than just giving a one-word answer.

https://lightmysky.com/learn/english/expressing-and-justifying-opinions-mt_S0hzjAeLSK

#### Listening and responding (ages 4-11)

Listen and respond appropriately to adults and peers; follow agreed-upon rules for discussion such as listening to others and taking turns speaking

Ready when they can: Demonstrate attentive listening by making eye contact and responding relevantly; Follow classroom discussion rules (e.g. raise hand, wait for turn); Show understanding of what was said by paraphrasing or responding appropriately.

https://lightmysky.com/learn/english/listening-and-responding-mt_mB7DVai-Uf

#### Exploring Ideas Through Talk (ages 4-6)

Use spoken language to develop understanding through speculating, hypothesising, imagining, and exploring ideas; use strategies to build vocabulary through talk

Ready when they can: Wonder aloud about possibilities (e.g. 'What if...' or 'I think it might be because...'); Try out new vocabulary in conversation after hearing it in a story or lesson; Explore ideas through talk before committing them to writing.

Needs first: Feeling of not understanding.

https://lightmysky.com/learn/english/exploring-ideas-through-talk-mt_n6GhzDPllD

#### Asking Questions (ages 4-11)

Ask relevant questions to extend understanding; ask and answer questions to seek help, get information, or clarify something not understood

Ready when they can: Ask a question when something is unclear or more information is needed; Answer questions with relevant and specific information; Request clarification politely (e.g. 'Can you explain that again?').

Needs first: Question Words, Listening and responding, Exploring Ideas Through Talk.

https://lightmysky.com/learn/english/asking-questions-mt_f8n4txtLej

#### Group discussions (ages 4-11)

Participate actively in collaborative conversations staying on topic; continue a conversation through multiple exchanges; maintain attention in discussions

Ready when they can: Stay on topic during a conversation for multiple turns; Build on what another speaker has said (e.g. 'I agree because...'); Maintain focus and contribute meaningfully in group discussions.

Needs first: Listening and responding, Exploring Ideas Through Talk.

https://lightmysky.com/learn/english/group-discussions-mt_wwdRhPyz6s

#### Describing Aloud (ages 4-8)

Describe familiar people, places, things, and events with detail; speak audibly and express thoughts, feelings, and ideas clearly; give well-structured descriptions and explanations

Ready when they can: Describe a familiar person or place using several details; Speak clearly and loudly enough for the whole group to hear; Organise ideas logically when sharing information or telling about an event.

Needs first: Expressing & Justifying Opinions, Group discussions.

https://lightmysky.com/learn/english/describing-aloud-mt_4A7FYmvVhA

#### Reciting Poetry (ages 6-10)

Learn poems by heart and recite with appropriate intonation, adding visual displays to descriptions when appropriate, and producing complete sentences in spoken presentations

Ready when they can: Recite a poem from memory with expression and clear enunciation; Add a drawing or visual display to support an oral description or presentation; Present information to the class using complete sentences and audible voice.

Needs first: Describing Aloud, Expressing & Justifying Opinions.

https://lightmysky.com/learn/english/reciting-poetry-mt_ZBMcX2oRor

#### Reporting & Recounting (ages 8-11)

Report on a topic or recount an experience with organised facts and descriptive details, speaking clearly at an understandable pace

Ready when they can: Deliver a one-minute oral report on a chosen topic, including at least three organised facts; Recount a personal experience using descriptive details and a clear beginning, middle, and end; Self-assess a recorded presentation for pace, clarity, and inclusion of relevant details.

Needs first: Describing Aloud, Reciting Poetry.

https://lightmysky.com/learn/english/reporting-and-recounting-mt_ds2TOtP8I1

#### Paraphrasing What You Hear (ages 9-10)

Paraphrase portions of a text read aloud or information presented in diverse media and formats, capturing the key ideas accurately in one's own words

Ready when they can: Listen to a passage read aloud and restate the main idea and key details in own words without looking at the original text; Paraphrase information from a short video, podcast, or presentation, identifying the central message and supporting details; Distinguish between paraphrasing (restating in own words) and copying, demonstrating the ability to capture meaning without repeating exact wording.

Needs first: Main Ideas & Note-Taking.

https://lightmysky.com/learn/english/paraphrasing-what-you-hear-mt_-DuXzMVVXQ

#### Adapting Speech to Context (ages 10-11)

Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation while adjusting tone, vocabulary, and style for different audiences

Ready when they can: Present the same information formally to a panel and informally to peers; Adjust vocabulary and sentence structure when speaking to different audiences; Identify contexts that require formal English and those where informal speech is appropriate.

Needs first: Choosing Formal Vocabulary.

https://lightmysky.com/learn/english/adapting-speech-to-context-mt_bkvB7QYKwg

#### Building on Others in Discussions (ages 10-11)

Pose and respond to specific questions in discussions, making comments that contribute to the discussion and elaborate on the remarks of others

Ready when they can: Ask follow-up questions that build on another speaker's comment; Respond to a classmate's idea by adding supporting evidence or a related example; Redirect a discussion by posing a question that connects to the main topic.

Needs first: Asking Questions.

https://lightmysky.com/learn/english/building-on-others-in-discussions-mt_LNYTNpJOGT

#### Multimedia Presentations (ages 10-11)

Include multimedia components and visual displays in presentations when appropriate to enhance the development of main ideas or themes

Ready when they can: Select graphics, images, or sound that support and clarify main ideas in a presentation; Create slides or visual aids that enhance rather than distract from the spoken content; Integrate multimedia elements smoothly into an oral presentation.

Needs first: Reciting Poetry.

https://lightmysky.com/learn/english/multimedia-presentations-mt_VtqvUORa8K

#### Summarising Spoken and Media Presentations (ages 10-11)

Summarise a written text read aloud or information presented in diverse media and formats including visually, quantitatively, and orally

Ready when they can: Summarise the main points of a video or audio presentation in own words; Identify key information from a graph, chart, or infographic and explain it orally; Listen to a passage read aloud and provide an accurate summary of the content.

Needs first: Paraphrasing What You Hear.

https://lightmysky.com/learn/english/summarising-spoken-and-media-presentations-mt_A4YUbzUFan

#### Engaging Listeners and Valuing Viewpoints (ages 7-8)

Gain, maintain and monitor the interest of listeners when speaking; consider and evaluate different viewpoints, attending to and building on others' contributions; begin to select appropriate language for different situations

Ready when they can: Use strategies to engage listeners during a presentation (e.g., make eye contact, vary tone and pace, ask the audience a question); Listen to a peer's viewpoint and respond by agreeing, disagreeing, or extending their idea with a reason (e.g., 'I agree with Priya because… but I also think…'); Choose more formal language for a class presentation and more informal language for a group discussion, explaining the difference.

Needs first: Teaching It Back, Expressing & Justifying Opinions, Group discussions, Reciting Poetry.

https://lightmysky.com/learn/english/engaging-listeners-and-valuing-viewpoints-mt_sXRHr7tfS5

#### Preparing for and Explaining in Discussions (ages 8-11)

Come to discussions prepared, draw on preparation and known information, and explain ideas in light of the discussion

Ready when they can: Read assigned material and prepare three discussion points or questions before a group conversation; During discussion, refer explicitly to the text or preparation notes to support a point; After a group exchange, explain how one's own thinking changed or was confirmed by others' contributions.

Needs first: Engaging Listeners and Valuing Viewpoints, Group discussions.

https://lightmysky.com/learn/english/preparing-for-and-explaining-in-discussions-mt_yrMniCJu_S

#### Identifying Reasons Behind a Speaker's Points (ages 9-10)

Identify the reasons and evidence a speaker provides to support particular points, evaluating whether the reasoning is logical and the evidence is relevant

Ready when they can: Listen to a speaker's argument or presentation and list the specific reasons and evidence provided to support each main point; Evaluate whether the reasons a speaker gives are logical and whether the evidence cited is relevant to the claim being made; Ask follow-up questions that probe the strength of a speaker's reasoning, e.g. 'What evidence supports that claim?' or 'Are there other explanations?'.

Needs first: Why the author wrote it, Engaging Listeners and Valuing Viewpoints.

https://lightmysky.com/learn/english/identifying-reasons-behind-a-speakers-points-mt_iodbOOmEQs

#### Drawing Conclusions from Discussion (ages 10-11)

Review the key ideas expressed in discussions and draw conclusions in light of information and knowledge gained from the discussion

Ready when they can: Summarise the main points made by different speakers in a group discussion; Draw a conclusion that synthesises multiple viewpoints expressed in the discussion; Explain how the discussion changed or confirmed initial understanding of a topic.

Needs first: Preparing for and Explaining in Discussions.

https://lightmysky.com/learn/english/drawing-conclusions-from-discussion-mt_Cc-QHVo747

#### Evaluating a Speaker's Argument (ages 10-11)

Summarise the points a speaker makes and explain how each claim is supported by reasons and evidence, evaluating the logic and relevance of the support

Ready when they can: Identify the main claim in a spoken presentation and the evidence used to support it; Evaluate whether a speaker's reasons logically support their main argument; Explain which pieces of evidence most effectively support a speaker's points.

Needs first: Identifying Reasons Behind a Speaker's Points.

https://lightmysky.com/learn/english/evaluating-a-speakers-argument-mt_on7FHCDmi-

#### Advanced Collaborative Discussions (ages 12-14)

Take part in demanding group discussions: arrive prepared with evidence from reading or research, follow agreed rules and roles, pose questions that connect several speakers' ideas, and qualify or justify views when new evidence emerges

Ready when they can: Bring notes or evidence from reading into a discussion and refer to them when making a point; Ask a question that links what two earlier speakers said (e.g. 'Maya's point about cost seems to clash with Leo's — can both be right?'); Adjust or defend a position when someone presents new evidence, explaining the reasoning aloud.

Needs first: Building on Others in Discussions, Preparing for and Explaining in Discussions, Drawing Conclusions from Discussion.

https://lightmysky.com/learn/english/advanced-collaborative-discussions-mt_4oegcJcRlQ

#### Speaking Formally and Giving Presentations (ages 11-14)

Use Standard English confidently in formal and informal spoken contexts — give short speeches and presentations expressing own ideas clearly, keeping to the point, and adapting register and vocabulary to the audience

Ready when they can: Deliver a 2-3 minute presentation on a topic with a clear opening, organised points, and a conclusion; Adapt language between formal and informal registers depending on the context and audience; Maintain eye contact, appropriate pace, and clear articulation when speaking to a group.

Needs first: Standard English, Reporting & Recounting, Adapting Speech to Context.

https://lightmysky.com/learn/english/speaking-formally-and-giving-presentations-mt_z07UNAIsNc

#### Multimedia in Presentations (ages 12-14)

Integrate multimedia and visual displays into presentations with intent: choose clips, images, charts and sound that clarify information, strengthen claims and evidence, and add interest rather than decoration

Ready when they can: Choose a chart or image because it makes a specific claim clearer, and say so when presenting; Place a short clip or audio at the exact point in a talk where it strengthens the argument; Cut a flashy visual that does not support the message (e.g. dropping an animation that distracts from the data).

Needs first: Multimedia Presentations, Speaking Formally and Giving Presentations.

https://lightmysky.com/learn/english/multimedia-in-presentations-mt_7LrPGIbf8Z

#### Performing Scripts & Poetry (ages 11-14)

Improvise, rehearse, and perform play scripts and poetry — using role, intonation, tone, volume, mood, silence, stillness, and action to generate language, explore meaning, and add impact to performance

Ready when they can: Perform a scene from a play using appropriate intonation, volume, and pauses to convey character and mood; Use improvisation to explore how a character might respond in a new situation; Rehearse and perform a poem aloud, using pace and emphasis to bring out the meaning.

Needs first: Understanding drama and performance.

https://lightmysky.com/learn/english/performing-scripts-and-poetry-mt_ylFTYS80d1

#### Formal Debates (ages 12-14)

Participate in formal debates and structured discussions — presenting a position with supporting evidence, responding to others’ points, summarising and building on what has been said, and following rules of discussion

Ready when they can: Present an argument in a debate with a clear claim supported by evidence; Respond to an opposing point by summarising it fairly before offering a counterargument; Build on a previous speaker’s idea by extending, questioning, or challenging it constructively.

Needs first: Persuasive Writing, Speaking Formally and Giving Presentations, Evaluating a Speaker's Argument.

https://lightmysky.com/learn/english/formal-debates-mt_Yrjn8jAt1c

#### Weighing a Spoken Argument as You Hear It (ages 14-16)

A speaker sets the pace, so the listening has to keep up: hold the line of argument, note the step that was asserted rather than shown, and keep a question in reserve until the speaker has finished making the case.

Ready when they can: Take notes that record the structure of a talk, not only its facts; Name the one step in a spoken argument that was assumed rather than supported; Hold a question until the speaker finishes, and put it in a form the speaker can answer.

https://lightmysky.com/learn/english/weighing-a-spoken-argument-as-you-hear-it-mt_eSTvUWJufm

#### Speaking to a Brief and Taking Questions (ages 15-16)

Prepare and deliver a formal spoken presentation to a set brief, then answer unrehearsed questions from listeners without abandoning the position taken.

Ready when they can: Deliver a prepared presentation from notes rather than reading a script out; Answer a question that challenges the argument, conceding where the challenge is fair; Adjust pace and emphasis in delivery so the key point is the one heard.

https://lightmysky.com/learn/english/speaking-to-a-brief-and-taking-questions-mt_ykCrDCiVIy

#### Seminar Discussion on Shared Reading (ages 16-18)

Talk about a text everyone in the room has read: bring a reading rather than an opinion, quote to make a point rather than to fill time, and change position out loud when somebody shows you something you missed.

Ready when they can: Open with a reading of a specific passage rather than a general view of the text; Answer the strongest version of another reading before disagreeing with it; Say aloud what changed your mind and which passage did it.

https://lightmysky.com/learn/english/seminar-discussion-on-shared-reading-mt_pezM0VweIi

#### Child Language: How Speech Develops (ages 17-18)

Follow how children get from single words to grammar: what they overgeneralise, what the people around them do, and what an error reveals about the rule a child has built.

Ready when they can: Explain what a child's error shows about a rule they have worked out; Put samples of child speech into a plausible order of development and justify it; Weigh one account of how children learn language against a piece of evidence.

https://lightmysky.com/learn/english/child-language-how-speech-develops-mt_GC3OSei4tC

#### Discourse Analysis: How Conversation Is Organised (ages 17-18)

Read a transcript of real talk for its structure: how turns get handed over, how a topic opens and is dropped, how speakers repair themselves, and who does the work of keeping it going.

Ready when they can: Mark turn-taking, overlaps, and pauses in a transcript and say what the pattern shows; Find where a topic changes and identify who changed it; Explain a feature of spontaneous speech as organisation rather than as error.

https://lightmysky.com/learn/english/discourse-analysis-how-conversation-is-organised-mt_MKUDTyGxXP

#### Gathering and Transcribing Language Data (ages 17-18)

Collect real language to work on: a sample that fits the question, transcribed consistently, with permission from the people whose speech is being used.

Ready when they can: Choose a sample that could answer the question and say what it leaves out; Transcribe a minute of speech with pauses and overlaps marked the same way throughout; Ask for consent and anonymise a speaker before using their words.

https://lightmysky.com/learn/english/gathering-and-transcribing-language-data-mt_fxbiLHyXW4

### Writing Composition

https://lightmysky.com/learn/english/areas/writing-composition

#### Sharing and Publishing Your Writing (ages 5-11)

Read own writing aloud clearly enough to be heard by peers and the teacher; use digital tools to produce and publish writing

Ready when they can: Read own sentences aloud with clear voice and appropriate expression; Share a piece of writing by reading it to the class; Type simple words or sentences using a computer or tablet.

Needs first: Reading fluently.

https://lightmysky.com/learn/english/sharing-and-publishing-your-writing-mt_nYU6x2E2T8

#### Writing Process Vocabulary (ages 5-8)

Know and use the vocabulary of the writing process — compose, plan, draft, revise, edit, proofread, genre, audience, purpose, narrative, recount, instruction, paragraph, sequence, and detail — and understand that these words describe distinct steps and decisions that all writers make, not just tasks to tick off

Ready when they can: Use 'compose', 'revise', and 'edit' correctly when describing the stages of writing; Explain who the 'audience' is for a piece of writing and how that changes what they write; Describe the purpose of a piece of writing (to persuade, inform, entertain, or instruct) and match their language to it.

https://lightmysky.com/learn/english/writing-process-vocabulary-mt_o8ciHks8t2

#### Shared Research Projects (ages 5-9)

Participate in shared research and writing projects; recall information from experiences or gather information from sources to answer a question

Ready when they can: Contribute ideas and information to a class writing project; Draw or write facts learned from personal experience about a topic; Help gather information from books or adults for a group research task.

Needs first: Listening to Texts Read Aloud, Writing Process Vocabulary.

https://lightmysky.com/learn/english/shared-research-projects-mt_4A4RpX-Go9

#### Writing Craft Vocabulary (ages 8-11)

Know and use the vocabulary of writing craft and effect — form, structure, register, tone, voice, coherence, cohesion, argument, evidence, perspective, rhetoric, technique, formal, informal, and style — and understand that these words describe choices writers make intentionally to achieve a particular effect on the reader

Ready when they can: Explain the difference between 'formal register' and 'informal register' and give an example of when each is appropriate; Use terms like 'coherence', 'cohesion', and 'paragraph structure' accurately when discussing or improving their own writing; Identify the 'purpose', 'audience', and 'form' of a piece of writing and explain how these shape the language choices.

Needs first: Writing Process Vocabulary.

https://lightmysky.com/learn/english/writing-craft-vocabulary-mt_82KKv0Fca3

#### Saying Sentences Before Writing Them (ages 5-6)

Say out loud what is going to be written; compose sentences orally before writing them down as preparation for independent writing

Ready when they can: Say a complete sentence aloud before attempting to write it; Rehearse a sentence orally more than once to hold it in memory; Practise sentences with a partner before writing independently.

Needs first: Describing Aloud, Building sentences, Writing Process Vocabulary.

https://lightmysky.com/learn/english/saying-sentences-before-writing-them-mt_PJyCGJz5Hv

#### Writing opinions (ages 5-7)

Compose opinion pieces using drawing, dictating, or writing that name a topic or book and state a preference or opinion about it

Ready when they can: State an opinion clearly (e.g. 'My favourite animal is a dog because...'); Give at least one reason for an opinion; Draw, dictate, or write to express a preference about a book or topic.

Needs first: Writing Process Vocabulary, Saying Sentences Before Writing Them.

https://lightmysky.com/learn/english/writing-opinions-mt_91f1XFvGZq

#### Writing to inform (ages 5-7)

Compose informative or explanatory texts using drawing, dictating, or writing that name a topic and supply some information about it

Ready when they can: Write or dictate two or three facts about a familiar topic; Label diagrams or drawings with informative details; Name a topic and provide relevant details about it.

Needs first: Writing Process Vocabulary, Saying Sentences Before Writing Them.

https://lightmysky.com/learn/english/writing-to-inform-mt__MDiDU9Vck

#### Basic Informational Writing (ages 6-11)

Compose informative or explanatory texts that introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section

Ready when they can: Write an informative text that introduces a topic clearly and groups related information together; Use facts, definitions, and concrete details to develop and explain points about the topic; Provide a concluding statement or section that wraps up the information presented.

Needs first: Writing Craft Vocabulary, Writing to inform.

https://lightmysky.com/learn/english/basic-informational-writing-mt_hp2qJ-QRBn

#### Structured Opinion Writing (ages 6-11)

Compose opinion pieces that introduce a topic, state a clear point of view, provide organised reasons linked with connecting words, and include a concluding statement or section

Ready when they can: Write an opinion piece that introduces the topic, states a clear opinion, and provides at least two reasons; Use linking words (because, and, also, for example) to connect the opinion to supporting reasons; End an opinion piece with a concluding statement that restates or reinforces the opinion.

Needs first: Writing Craft Vocabulary, Writing opinions.

https://lightmysky.com/learn/english/structured-opinion-writing-mt_WKxX-b86Vr

#### Rehearsing and Varying Sentences (ages 7-8)

Compose and rehearse sentences orally before writing, progressively building varied and rich vocabulary and an increasing range of sentence structures including dialogue

Ready when they can: Rehearse a sentence containing dialogue aloud before writing it (e.g. 'Let's go!' shouted Tom); Orally compose sentences with varied openers (e.g. time adverbials, subordinate clauses) before writing; Try out two or three different ways to express the same idea orally and choose the most effective version to write.

Needs first: Writing Process Vocabulary, Saying Sentences Before Writing Them.

https://lightmysky.com/learn/english/rehearsing-and-varying-sentences-mt_FGCFUCqJBB

#### Vivid Word Choices (ages 8-10)

Choose precise and vivid words and phrases to create specific effects in writing

Ready when they can: Replace vague words in 'The nice man went to the big house' with more precise alternatives and explain the effect; Write two versions of the same scene — one with plain language and one with carefully chosen words for suspense or humour; Select from a word bank the most effective verb and adjective for a given sentence, justifying each choice.

Needs first: Writing Craft Vocabulary, Formal and Informal English, Rehearsing and Varying Sentences.

https://lightmysky.com/learn/english/vivid-word-choices-mt_LMX-nZETLM

#### Writing a Précis (ages 10-11)

Precis longer passages by summarising the main ideas and key information concisely while maintaining the essential meaning and removing non-essential detail

Ready when they can: Reduce a three-paragraph text to a single paragraph capturing all main points; Identify and remove redundant information while preserving essential meaning; Write a precis that is no more than one-third the length of the original text.

Needs first: Main Ideas & Note-Taking.

https://lightmysky.com/learn/english/writing-a-precis-mt_curkA82CmO

#### Writing Poetry (ages 6-7)

Write poetry, exploring patterns of language, rhyme and rhythm, and learning poems by heart for recitation with appropriate intonation

Ready when they can: Write a simple poem using rhyming couplets or a repeated pattern; Recite a poem from memory with expression and appropriate intonation; Identify rhyme and rhythm patterns in poems read aloud.

Needs first: Rhyming words, Expressive and Sensory Language, Writing Process Vocabulary, Saying Sentences Before Writing Them, Reciting Poetry.

https://lightmysky.com/learn/english/writing-poetry-mt_YNe6siFTFq

#### Simple Stories with Beginning and Ending (ages 5-7)

Write simple narratives by sequencing sentences to describe events in order; narrate a single event or linked events with a beginning, middle, and ending or reaction

Ready when they can: Write a short story with at least three sequenced sentences; Use time words like 'first', 'then', 'next' to order events; Include a reaction or ending to a narrative (e.g. 'I felt happy').

Needs first: Rote counting to 100, Writing Process Vocabulary, Saying Sentences Before Writing Them, Characters, settings, and events, Sitting and holding a pencil.

https://lightmysky.com/learn/english/simple-stories-with-beginning-and-ending-mt_nDAcXoPa0c

#### Narrative Writing (ages 7-11)

Write narratives with developed settings, characters and plot, using dialogue and description to develop experiences and show character responses to situations

Ready when they can: Write a narrative that includes a described setting, at least one developed character, and a clear plot with a problem and resolution; Use dialogue to show what characters say and reveal their personality or feelings; Use descriptive details and temporal words to organise events into a clear sequence with a satisfying ending.

Needs first: Writing Craft Vocabulary, Simple Stories with Beginning and Ending.

https://lightmysky.com/learn/english/narrative-writing-mt_vauULTecMH

#### Short Research Projects (ages 8-11)

Conduct short research projects that build knowledge about a topic, gather information from print and digital sources, and take brief organised notes

Ready when they can: Generate three research questions about an assigned topic and identify two sources for each; Take brief notes from a print source, sorting key facts into provided categories; Write a short summary paragraph synthesising information gathered from two different sources.

Needs first: Shared Research Projects, Writing Craft Vocabulary, Scaled picture graphs and bar graphs, Main Ideas & Note-Taking.

https://lightmysky.com/learn/english/short-research-projects-mt_FW9_8F52bw

#### Evidence-Based Writing (ages 9-11)

Draw evidence from informational texts to support analysis, reflection, and research in writing, applying grade-level reading standards to non-fiction

Ready when they can: Write a research-based paragraph or short report that cites specific facts, details, and evidence from informational texts to support key points; Synthesise information from two informational sources into a written summary that accurately represents both, noting areas of agreement and difference; Paraphrase information from informational texts accurately and cite sources appropriately, avoiding plagiarism.

Needs first: Short Research Projects, Main Topic & Key Details.

https://lightmysky.com/learn/english/evidence-based-writing-mt_ZxdfRbwkKM

#### Literary Evidence in Writing (ages 9-11)

Draw evidence from literary texts to support analysis, reflection, and research in writing, applying grade-level reading standards to literature

Ready when they can: Write a response to a literary text that includes direct quotations and specific details from the text as evidence to support a claim or observation; Explain how a character's actions or dialogue reveal their traits or motivations, citing specific passages from the story as evidence; Compare how two literary texts treat a similar theme, using textual evidence from both to support the comparison.

Needs first: Short Research Projects, Inferring Characters' Feelings and Motives, Domain Vocabulary Across Subject Areas.

https://lightmysky.com/learn/english/literary-evidence-in-writing-mt_sdmm_m60qX

#### Research & Note-Taking (ages 10-11)

Gather relevant information from print and digital sources, summarise or paraphrase information in notes and finished work, and provide a basic bibliography or list of sources

Ready when they can: Take organised notes from multiple sources using own words rather than copying; Create a bibliography listing sources used in a research project; Paraphrase key information from a source without changing the meaning.

Needs first: Writing a Précis, Short Research Projects.

https://lightmysky.com/learn/english/research-and-note-taking-mt_dRLP8g0SAg

#### Digital Writing and Publishing (ages 11-14)

Use technology to produce and publish writing: type fluently over long stretches, link to and cite sources, lay out ideas and their relationships clearly on screen, and collaborate with others in shared documents

Ready when they can: Type extended pieces fluently enough that the keyboard does not interrupt their thinking; Add working links and citations to sources in a published piece (e.g. linking to the article a claim came from); Collaborate in a shared document (e.g. commenting on a partner's draft and resolving suggested edits).

Needs first: Sharing and Publishing Your Writing, Research & Note-Taking.

https://lightmysky.com/learn/english/digital-writing-and-publishing-mt_dN7QLqqJ4j

#### Responding to Writing Feedback (ages 5-7)

With teacher guidance, re-read own writing aloud to check it sounds right; listen and respond to questions and suggestions from teacher or peers to add detail, clarify meaning, and strengthen writing — this is the scaffolded beginning of writing self-evaluation, not an independent skill

Ready when they can: Reread own writing and spot a missing word or unclear sentence; Add a detail in response to a question (e.g. 'Can you tell me more about...?'); Make at least one improvement to a piece based on feedback.

Needs first: Checking Your Own Work, Feeling of not understanding, Simple Stories with Beginning and Ending, Writing Process Vocabulary, Reviewing Own Writing.

https://lightmysky.com/learn/english/responding-to-writing-feedback-mt_OyOYHlZ2_T

#### Revising and editing (ages 6-7)

Proof-read own writing to check for errors in spelling, grammar, and punctuation; evaluate and revise writing with teacher/peer support, re-reading to ensure meaning is clear and tense is consistent

Ready when they can: Re-read own writing and spot a missing full stop or capital letter; Identify and correct a tense inconsistency in a piece of writing; Discuss improvements with a partner and make at least one revision to strengthen the writing.

Needs first: Writing Process Vocabulary, Responding to Writing Feedback, Alternative Spellings for Sounds, Starting and Ending Sentences.

https://lightmysky.com/learn/english/revising-and-editing-mt_I65kFjWwnF

#### Revising and editing (age 8+) (ages 8-9)

Read back your own writing critically and independently — notice where meaning is unclear, where a word could be stronger, or where the reader might be confused; make revisions without needing teacher prompts, using your own judgment about what is and isn't working

Ready when they can: Reread a paragraph silently and independently identify at least one place where meaning could be clearer or a word choice improved; Make a revision that goes beyond spelling/punctuation — changing a sentence for clarity or effect; Explain in their own words why they changed something ('I thought the reader wouldn't understand what I meant').

Needs first: Teaching It Back, Writing Craft Vocabulary, Sharing and Publishing Your Writing, Responding to Writing Feedback.

https://lightmysky.com/learn/english/revising-and-editing-age-8-mt_HWYAspz-LK

#### Revising and editing (age 7+) (ages 7-11)

Evaluate and edit writing by assessing effectiveness, proposing changes to grammar and vocabulary for consistency, and proof-reading for spelling, grammar and punctuation errors at Y3-4 level

Ready when they can: Read own or a peer's writing aloud and suggest specific improvements to vocabulary or sentence structure; Propose changes to grammar and word choice to improve clarity and consistency across a piece of writing; Proof-read writing at Y3-4 level for spelling, punctuation, and grammatical errors and correct them independently.

Needs first: Writing Craft Vocabulary, Revising and editing (age 8+), Revising and editing.

https://lightmysky.com/learn/english/revising-and-editing-age-7-mt_pis4novXWQ

#### Planning, Revising and Editing Writing (ages 11-14)

Plan, revise, and edit writing to improve coherence and effectiveness — considering how the writing reflects its intended audience and purpose, amending vocabulary, grammar, and structure, and proofreading for accurate spelling, punctuation, and grammar

Ready when they can: Revise a draft to improve paragraph structure, adding or removing material for coherence; Edit sentence-level issues including word choice, grammar, and punctuation before finalising; Reflect on whether the writing achieves its intended effect on the target audience and adjust accordingly.

Needs first: Literary and Language Terminology, Revising and editing (age 8+), Revising and editing (age 7+), Analysing Your Own Errors, Reflecting After Learning.

https://lightmysky.com/learn/english/planning-revising-and-editing-writing-mt_av-uRBrhwT

#### Building Writing Stamina (ages 6-7)

Write about real events and for different purposes, developing stamina for sustained writing across genres beyond narrative (e.g., recounts, letters, instructions)

Ready when they can: Write a recount of a school trip using temporal connectives (first, then, after that); Write a simple set of instructions with numbered steps; Sustain writing for an extended period across a full page without stopping.

Needs first: Joining Letters, Expressing Feelings with Words, Writing to inform, Simple Stories with Beginning and Ending, Writing Process Vocabulary.

https://lightmysky.com/learn/english/building-writing-stamina-mt_lIs10UMkPG

#### Organising Writing into Paragraphs (ages 7-10)

Organise writing into paragraphs, grouping related material around a theme, and use simple organisational devices such as headings and sub-headings in non-narrative writing

Ready when they can: Divide a piece of writing into paragraphs, each focused on one main idea or aspect of the topic; Use headings and sub-headings to organise a non-fiction text (e.g., a report about animals with sections 'Habitat', 'Diet', 'Appearance'); Identify where a new paragraph should begin in a given text and explain why (e.g., 'A new paragraph starts here because the topic changes from appearance to diet').

Needs first: Building Writing Stamina, Simple Stories with Beginning and Ending, Writing Process Vocabulary.

https://lightmysky.com/learn/english/organising-writing-into-paragraphs-mt_AvJMWQbDsr

#### Planning Ideas Before Writing (ages 6-10)

Plan before writing by saying aloud or noting down what will be written, writing down ideas and key words, and encapsulating ideas sentence by sentence before composing

Ready when they can: Verbally rehearse sentences before writing them down; Jot key words or ideas in a planning format (e.g., story map) before drafting; Write a simple plan with beginning, middle, and end for a story.

Needs first: Describing Aloud, Organising Writing into Paragraphs, Building Writing Stamina, Simple Stories with Beginning and Ending, Writing Process Vocabulary, Saying Sentences Before Writing Them.

https://lightmysky.com/learn/english/planning-ideas-before-writing-mt_9P9o6d0Qm3

#### Choosing Form and Tone for Your Audience (ages 9-10)

Identify the audience for and purpose of writing before beginning, selecting the appropriate form, tone, and register to match the intended reader and communicative goal

Ready when they can: Determine the audience (e.g., peers, teacher, younger children, a public audience) and purpose (to persuade, inform, entertain, or explain) before drafting and explain how these choices affect language and structure; Select an appropriate form for the writing task (letter, report, story, instructions, review) based on audience and purpose; Adjust vocabulary, sentence length, and level of formality to suit the identified audience, e.g. using simpler language for younger readers and more formal language for an official letter.

Needs first: Writing Craft Vocabulary, Formal and Informal English, Planning Ideas Before Writing, Author's word choices, Planning a Task.

https://lightmysky.com/learn/english/choosing-form-and-tone-for-your-audience-mt_v5DyOEpbbr

#### Writing for an audience (ages 9-11)

Produce clear and coherent writing in which the development and organisation are appropriate to the task, purpose, and audience, maintaining a consistent style and structure throughout

Ready when they can: Identify the task, purpose, and audience before writing and make deliberate choices about structure, tone, and vocabulary to suit them; Organise ideas logically so that the writing flows from introduction through development to conclusion, with each section serving a clear purpose; Review a draft to check that the organisation, style, and level of formality are consistent and appropriate for the intended reader.

Needs first: Writing Craft Vocabulary, Planning Ideas Before Writing, Organising Writing into Paragraphs.

https://lightmysky.com/learn/english/writing-for-an-audience-mt_cB7hV8sw7X

#### Layout and Formatting in Informational Writing (ages 10-11)

Use layout devices including headings, sub-headings, columns, bullets, and tables to structure text and guide the reader through informational and explanatory writing

Ready when they can: Organise an informational text using headings and sub-headings to separate sections; Present comparative information using a table with clear row and column headers; Use columns and bullet points to display information in a scannable format.

Needs first: Writing Craft Vocabulary, Organising Writing into Paragraphs.

https://lightmysky.com/learn/english/layout-and-formatting-in-informational-writing-mt_AHAFw-atka

#### Planning Narratives (ages 10-11)

Plan narrative writing by considering how authors have developed characters and settings, drawing on techniques observed in texts read, heard, or performed

Ready when they can: Identify specific authorial techniques for character development from a mentor text; Plan a character using techniques such as showing through action borrowed from a studied author; Analyse how an author builds setting and apply similar techniques in planning own narrative.

Needs first: Connecting New & Old Ideas, Writing Craft Vocabulary, Choosing Form and Tone for Your Audience.

https://lightmysky.com/learn/english/planning-narratives-mt_j6ENpc8--_

#### Cohesion and Transitions Across Writing (ages 11-14)

Use varied transitions, cohesive devices, and paragraph-linking strategies to create coherence across a whole piece of writing — including temporal transitions, causal connectives, and techniques for signalling shifts in argument, time, or setting

Ready when they can: Use a range of causal and logical connectives (consequently, nevertheless, as a result) appropriately across a discursive essay; Signal a shift in time or setting within a narrative using a transitional phrase or paragraph break; Link paragraphs using a cohesive device such as a topic sentence that refers back to the previous paragraph.

Needs first: Paragraph Cohesion, Linking paragraphs with adverbials, Consistent verb tense, Pronoun Case and Reference.

https://lightmysky.com/learn/english/cohesion-and-transitions-across-writing-mt_tn1rY9GbEZ

#### Developed Informational and Explanatory Writing (ages 11-14)

Write informative and explanatory texts that examine a topic and convey ideas clearly — organising information logically with headings and formatting, developing the topic with relevant facts, definitions, details, and quotations, and using precise vocabulary

Ready when they can: Organise an explanatory essay with a clear introduction, logical body paragraphs, and a conclusion; Develop a topic using well-chosen facts, definitions, concrete details, and quotations from sources; Use domain-specific vocabulary and formatting (headings, graphics) to aid the reader's comprehension.

Needs first: Layout and Formatting in Informational Writing, Writing for an audience, Cohesion and Transitions Across Writing, Choosing Form and Tone for Your Audience, Bullet Point Punctuation.

https://lightmysky.com/learn/english/developed-informational-and-explanatory-writing-mt_zCUIJLdK_s

#### Research & Source Evaluation (ages 11-14)

Summarise and organise material from reading and research — gathering relevant information from multiple sources, assessing credibility, integrating evidence without plagiarising, and supporting ideas with factual detail

Ready when they can: Take notes from multiple sources on a topic and organise them under logical headings; Paraphrase information from a source accurately without copying word-for-word; Assess whether a source is credible and relevant before including it in research writing.

Needs first: Writing a Précis, Research & Note-Taking, Literary Evidence in Writing, Developed Informational and Explanatory Writing, Punctuating Titles of Works, Summarising Non-Fiction Main Ideas, Synthesising across multiple texts, Using Multiple Sources.

https://lightmysky.com/learn/english/research-and-source-evaluation-mt_Qcsl1Z1x0l

#### Writing Character & Dialogue (ages 11-14)

Write narratives that develop real or imagined experiences using effective technique — including establishing context and point of view, developing characters through dialogue, pacing, and description, using varied transitions, and providing a reflective conclusion

Ready when they can: Open a narrative by establishing setting, point of view, and a hook that engages the reader; Use dialogue, pacing, and descriptive detail to develop characters and advance the plot; Craft a conclusion that reflects on the narrated events rather than simply ending the action.

Needs first: Planning Narratives, Cohesion and Transitions Across Writing, Narrative Writing, Commas with yes, no, and names.

https://lightmysky.com/learn/english/writing-character-and-dialogue-mt_BLzNxSSdWu

#### Writing Across Genres (ages 11-14)

Write for a range of purposes and audiences beyond narrative — including scripts, poetry, personal and formal letters, notes for talks, and other forms — selecting the appropriate form, register, and conventions for each

Ready when they can: Write a formal letter using appropriate layout, salutation, register, and sign-off conventions; Compose a script with stage directions, character names, and realistic dialogue; Adapt writing style (vocabulary, sentence structure, tone) to suit different audiences and purposes.

Needs first: Writing Character & Dialogue, Choosing Form and Tone for Your Audience.

https://lightmysky.com/learn/english/writing-across-genres-mt_9lN0SpKlEH

#### Writing Techniques for Effect (ages 11-14)

Apply growing knowledge of vocabulary, grammar, and text structure to writing — drawing on literary and rhetorical devices from reading (e.g., rhetorical questions, tricolon, anaphora, contrast) to enhance impact

Ready when they can: Use a rhetorical question or tricolon deliberately in a persuasive piece and explain the intended effect; Employ varied sentence openings and structures to maintain reader interest across a whole piece; Draw on a literary device encountered in reading and apply it consciously in own writing.

Needs first: Writing Across Genres, Figurative Language and Literary Devices, Vivid Word Choices.

https://lightmysky.com/learn/english/writing-techniques-for-effect-mt_s6-6FYb5UQ

#### Persuasive Writing (ages 11-14)

Write arguments to support claims with clear reasons and relevant evidence — including introducing claims, acknowledging counterclaims, organising reasons logically, maintaining a formal style, and providing a concluding statement

Ready when they can: Write an argument essay with a clear claim supported by at least three pieces of evidence; Acknowledge and respond to a counterclaim rather than ignoring opposing views; Use linking words and phrases (however, furthermore, consequently) to connect claims, reasons, and evidence.

Needs first: Writing for an audience, Evaluating Arguments in Non-Fiction, Justifying Views About Texts, Writing Techniques for Effect, Cohesion and Transitions Across Writing, Choosing Form and Tone for Your Audience.

https://lightmysky.com/learn/english/persuasive-writing-mt_Qxyikkkzam

#### Precision and Economy (ages 14-16)

Say more in fewer words: choose the exact verb and noun, drop intensifiers doing no work, and cut any phrase whose removal costs nothing.

Ready when they can: Replace a weak verb plus adverb with one exact verb; Cut a tenth of a draft's words without losing any meaning; Catch vague nouns (thing, aspect, situation) and name what is actually meant.

https://lightmysky.com/learn/english/precision-and-economy-mt_6IiH44N01F

#### Paragraph Shape and Deliberate Breaks (ages 14-16)

Decide where paragraphs start and stop for effect: one movement per paragraph, a break placed to shift time, focus, or speaker, and the one-line paragraph kept rare.

Ready when they can: Split an overlong paragraph at the point where its focus changes; Use a very short paragraph once in a piece and justify where it sits; Open a paragraph with a sentence that moves the piece on rather than repeating the last one.

https://lightmysky.com/learn/english/paragraph-shape-and-deliberate-breaks-mt_3C7NH2XOkg

#### Register Control for a Named Reader (ages 14-16)

Hold one register across a whole piece for a specific reader and purpose, shift it only on purpose, and notice where formality has slipped.

Ready when they can: Write the same content for two different readers and account for every change made; Find a slip into casual phrasing inside a formal draft and repair it; Break register once for a deliberate effect and explain the choice.

https://lightmysky.com/learn/english/register-control-for-a-named-reader-mt_aDiwZqqMS7

#### Descriptive Writing: Selected Detail (ages 14-16)

Build a place or a moment from a few exact details instead of a pile of adjectives, and control what the reader looks at and in what order.

Ready when they can: Describe a scene with three concrete details and at most one adjective each; Move the reader's attention deliberately, from a wide view down to one small thing; Replace a stated feeling with a detail that produces it in the reader.

https://lightmysky.com/learn/english/descriptive-writing-selected-detail-mt_dKL2VQQAIb

#### Shaping a Short Narrative (ages 15-16)

Give a short story a shape that fits its length: open inside the situation, hold to one moment or one turn, and end without explaining the point.

Ready when they can: Open in the middle of the action and supply the background later; Cut a story down to one turning point and keep it whole; End on an image or a line of dialogue instead of a summary of the meaning.

https://lightmysky.com/learn/english/shaping-a-short-narrative-mt_IqahcVf6dV

#### Sustaining a Narrative Voice (ages 15-16)

Write in a voice that is not your own and keep it: a narrator with consistent vocabulary and outlook, held at a deliberate distance from the writer behind them.

Ready when they can: Keep one narrator's word choices consistent across a whole piece; Let a narrator reveal something they do not understand about themselves; Repair a line where the writer's own voice has replaced the narrator's.

https://lightmysky.com/learn/english/sustaining-a-narrative-voice-mt_Lecl8HXETd

#### Rhetoric in Persuasion, Used Sparingly (ages 15-16)

Use rhetorical method where it carries the argument: an anecdote that earns a claim, a repetition placed once, a direct address that suits the reader. Devices used for display get cut.

Ready when they can: Open a persuasive piece with a concrete case rather than a general claim; Place a repeated structure once, at the point of most pressure; Remove a rhetorical question that adds nothing to the argument.

https://lightmysky.com/learn/english/rhetoric-in-persuasion-used-sparingly-mt_QFPbIBjdzu

#### Structuring an Argument (ages 15-16)

Order an argument so it builds: one line of thought, each paragraph advancing it, the opposing case answered rather than mentioned, and the strongest ground held back to the end.

Ready when they can: State the line of argument in one sentence before drafting; Answer a counter-argument at its strongest rather than a weak version of it; Order paragraphs so a later point depends on an earlier one.

https://lightmysky.com/learn/english/structuring-an-argument-mt_HYPdD7Zqxu

#### Using Researched Evidence in Argument (ages 15-16)

Fold source material into your own argument: choose evidence that changes what a reader believes, attribute it inside the sentence, and keep the argument in your own voice.

Ready when they can: Introduce a source in the sentence so the reader knows where the claim comes from; Keep the one figure or quotation that does the work and drop the rest; Follow evidence with the inference drawn from it instead of moving straight on.

https://lightmysky.com/learn/english/using-researched-evidence-in-argument-mt_heDDfyi4O6

#### Editing for Effect (ages 15-16)

Redraft to change how a piece lands, not only to correct it: read it aloud, cut what stalls, and ask whether the effect intended is the effect produced.

Ready when they can: Read a draft aloud and mark every place the reading stumbles; Make one structural change in a redraft, such as moving or deleting a paragraph; Name the effect intended and point to where the draft fails to produce it.

https://lightmysky.com/learn/english/editing-for-effect-mt_1YPl7I-wrO

#### Writing to a Reader Who Decides (ages 16-18)

A personal statement, an application, a formal request: writing where the reader has something you want and a stack of other people's pages beside yours. What is left out matters as much as what is claimed, and every claim has to survive being checked.

Ready when they can: Write an opening that says something only this writer could say; Replace an unsupported claim about themselves with the evidence a reader could verify; Cut a paragraph that flatters the reader instead of answering what was asked.

https://lightmysky.com/learn/english/writing-to-a-reader-who-decides-mt_MdOd8lS2ZV

#### Building a Source Base for a Long Essay (ages 17-18)

Assemble the reading behind a long piece: enough to know what has already been said, judged for reliability, and recorded so that every claim can be traced back to its page.

Ready when they can: Find a source that disagrees with the argument being built and read it properly; Keep a reference that lets a reader find the exact page months later; Drop a source that is easy to reach but adds nothing to the question.

https://lightmysky.com/learn/english/building-a-source-base-for-a-long-essay-mt_d1WQaNVDuN

#### Signposting and Sections in a Long Essay (ages 17-18)

Keep a long piece navigable: sections that each do one job, an opening that says where the piece is going, and links that remind a reader how the paragraph in front of them serves the question.

Ready when they can: Give every section of a long draft a one-line job and check that none does two; Write an opening that tells a reader the question and the route through it; Add a link back to the question at the point a reader is most likely to lose the thread.

https://lightmysky.com/learn/english/signposting-and-sections-in-a-long-essay-mt_8AOy_cfuot

#### Revising at Length (ages 17-18)

Revise a long piece by diagnosis: read for the argument first, move or cut whole sections, and leave the sentence work until the shape has settled.

Ready when they can: Summarise your own draft in one paragraph and find where the draft does not match the summary; Move or delete a whole section and repair the joins it leaves; Hold back line editing until the structural pass is done, and say why.

https://lightmysky.com/learn/english/revising-at-length-mt_RiDXGhZWak

## Computing

260 topics, ages 5 to 24. https://lightmysky.com/learn/computing

### Artificial Intelligence

https://lightmysky.com/learn/computing/areas/artificial-intelligence

#### Computers in Everyday Life (ages 5-7)

Identifying computers in everyday life — not just laptops but phones, tablets, smart speakers, traffic lights, washing machines; what makes something a computer

Ready when they can: Point out at least five everyday objects that contain computers; Explain what all computers have in common (they follow instructions and process information); Sort a set of objects into 'contains a computer' and 'does not contain a computer'.

https://lightmysky.com/learn/computing/computers-in-everyday-life-mt_XbGfVhfiUz

#### Real-World Robots (ages 5-7)

What a robot really is — not the sci-fi version; robots in factories, robot vacuum cleaners, robot arms in surgery; that robots follow instructions given by people

Ready when they can: Describe what a robot is (a machine that follows instructions to do a task); Name at least three real robots and what they do; Explain that robots are not alive and do not have feelings — they follow instructions people wrote.

Needs first: Computers in Everyday Life.

https://lightmysky.com/learn/computing/real-world-robots-mt_jvJ35MmCvK

#### Smart Versus Not-Smart Devices (ages 5-7)

Sorting objects into 'smart' (can sense and respond) and 'not smart' (just sits there); a toaster vs a smart speaker; introduction to the idea that some machines can sense and respond to the world

Ready when they can: Sort a set of objects into 'smart' (responds to input) and 'not smart' (does the same thing every time); Explain what makes a smart speaker different from a regular radio; Give an example of a machine that senses something and responds (automatic door, motion-sensor light).

Needs first: Computers in Everyday Life.

https://lightmysky.com/learn/computing/smart-versus-not-smart-devices-mt_WRRv1ABECC

#### Step-by-Step Instructions (ages 5-7)

Step-by-step instructions for everyday tasks (making a sandwich, brushing teeth); that if instructions are wrong or missing, things go wrong; computers follow instructions exactly

Ready when they can: Write or describe step-by-step instructions for a simple everyday task; Predict what goes wrong if a step is missing or in the wrong order; Explain that a computer follows instructions exactly — it cannot guess what you meant.

Needs first: Computers in Everyday Life.

https://lightmysky.com/learn/computing/step-by-step-instructions-mt__p5n8z5soJ

#### Voice Assistants and How They Work (ages 5-7)

What happens when you talk to Alexa, Siri, or Google Assistant; they listen, try to understand, look up answers; sometimes they get it wrong; they are tools, not alive

Ready when they can: Describe the steps that happen when you ask a voice assistant a question (it listens, processes words, finds an answer, speaks back); Give an example of a time a voice assistant might get something wrong; Explain that a voice assistant is a computer program, not a person — it doesn't understand or feel.

Needs first: Step-by-Step Instructions, Smart Versus Not-Smart Devices.

https://lightmysky.com/learn/computing/voice-assistants-and-how-they-work-mt_u6SYiVx7FX

#### AI in Daily Life (ages 5-7)

Spotting AI in daily life: face unlock on a phone, video recommendations, spelling auto-correct, automatic doors that detect people; technology that seems to 'know' things

Ready when they can: Identify at least five examples of AI in their daily life; Explain that these technologies use patterns and data, not magic or real thinking; Describe one way AI makes their life easier and one time it might not work perfectly.

Needs first: Voice Assistants and How They Work, Smart Versus Not-Smart Devices.

https://lightmysky.com/learn/computing/ai-in-daily-life-mt_AzTrT5ySCx

#### Data and Information for Computers (ages 7-9)

What data is: information that computers use — numbers, words, pictures, sounds; everything a computer knows comes from data that people give it

Ready when they can: Define data as information stored in a computer (numbers, text, images, sounds); Give at least three examples of data they create every day (photos, messages, search queries); Explain that a computer only knows what it has been given — it has no knowledge of its own.

Needs first: AI in Daily Life, Step-by-Step Instructions.

https://lightmysky.com/learn/computing/data-and-information-for-computers-mt_kH1DzOPsXG

#### Patterns and Classification (ages 7-9)

Humans are great at spotting patterns; computers can learn to spot patterns too, but they need lots of examples; sorting and classification activities as the basis of machine learning

Ready when they can: Sort a set of items into categories and explain the rules they used; Explain that computers learn patterns by looking at many examples; Describe why a computer needs more examples than a human to learn the same pattern.

Needs first: Data and Information for Computers.

https://lightmysky.com/learn/computing/patterns-and-classification-mt_ofOGCQ7FWj

#### AI in Computer Games (ages 7-9)

How computer game characters 'decide' what to do; simple rule-based AI vs learning AI; NPCs, difficulty adjustment; AI as the opponent in chess or board games

Ready when they can: Explain how a computer opponent in a game decides its moves; Describe the difference between a game character that follows fixed rules and one that learns from the player; Give an example of AI making a game more fun (adjusting difficulty, generating levels).

Needs first: Patterns and Classification, Step-by-Step Instructions.

https://lightmysky.com/learn/computing/ai-in-computer-games-mt_fT4G0QloX5

#### Machine Learning Basics (ages 7-9)

How machine learning works at a conceptual level: show the computer many examples, it finds patterns, then it makes predictions about new things; hands-on experience with Teachable Machine or similar tool

Ready when they can: Describe the three steps of machine learning in simple terms (give examples, find patterns, make predictions); Train a simple model using a tool like Teachable Machine and describe what happened; Explain why showing more and better examples makes the model more accurate.

Needs first: Patterns and Classification.

https://lightmysky.com/learn/computing/machine-learning-basics-mt_K6qtan847r

#### AI Mistakes and Limitations (ages 7-9)

Machines make mistakes; they only know what they've been shown; bad training data leads to bad results; AI is not magic — just maths on data; showing edge cases and failures

Ready when they can: Give an example of AI making a mistake (voice assistant mishearing, auto-correct error, wrong recommendation); Explain that AI mistakes happen because of gaps or errors in training data; Describe why AI is not magic — it follows mathematical rules applied to data.

Needs first: Machine Learning Basics.

https://lightmysky.com/learn/computing/ai-mistakes-and-limitations-mt_bPFToj0OhZ

#### Humans Versus Machines (ages 7-9)

Comparing human and machine capabilities: creativity, empathy, common sense vs speed, memory, repetition; the Turing Test (simplified); what makes humans unique

Ready when they can: Name at least three things humans are better at than computers (creativity, empathy, common sense); Name at least three things computers are better at than humans (speed, memory, repetitive tasks); Describe the Turing Test in simple terms (can a computer fool a person into thinking it's human?).

Needs first: Real-World Robots, Machine Learning Basics.

https://lightmysky.com/learn/computing/humans-versus-machines-mt_oajUvqAiBJ

#### Recommendation Systems and Filter Bubbles (ages 7-9)

How recommendation systems work: YouTube, Netflix, and shop websites track what you click and find patterns; filter bubbles; the difference between helpful suggestions and manipulation

Ready when they can: Explain how YouTube or Netflix decides what to suggest next; Describe what a 'filter bubble' is (only seeing things similar to what you already like); Give one benefit and one risk of recommendation systems.

Needs first: Data and Information for Computers, Patterns and Classification.

https://lightmysky.com/learn/computing/recommendation-systems-and-filter-bubbles-mt_EedcpioR0v

#### Bias in AI Systems (ages 9-11)

If training data is biased, AI will be biased; examples: facial recognition working better for some skin tones, translation assuming gender; where bias comes from and whether we can fix it

Ready when they can: Explain what bias in AI means using a real-world example; Describe how biased training data leads to biased AI results; Suggest one way to reduce bias in an AI system (use more diverse data, test with different groups).

Needs first: AI Mistakes and Limitations.

https://lightmysky.com/learn/computing/bias-in-ai-systems-mt__BbOjiY5A5

#### AI and Fairness in Decisions (ages 9-11)

Whether AI should make important decisions about people: jobs, loans, justice; who is responsible when AI makes unfair decisions; introduction to algorithmic fairness

Ready when they can: Give an example of an important decision that AI might help make (hiring, medical diagnosis, loan approval); Explain why letting AI make decisions about people can be risky if the system is biased; Suggest who should be responsible if an AI system makes an unfair decision.

Needs first: Bias in AI Systems, Humans Versus Machines.

https://lightmysky.com/learn/computing/ai-and-fairness-in-decisions-mt_cVp_nop-5L

#### Deepfakes and AI-Generated Content (ages 9-11)

Deepfakes, AI-generated images and text; how to spot them and why they matter; the importance of checking sources; not everything online is real

Ready when they can: Explain what a deepfake is and give an example of AI-generated content; Describe at least two clues that might reveal an image or text was AI-generated; Explain why it matters that AI can create realistic fake content.

Needs first: AI Mistakes and Limitations, Machine Learning Basics.

https://lightmysky.com/learn/computing/deepfakes-and-ai-generated-content-mt_tzMr83pS8v

#### Designing Fair AI Rules (ages 9-11)

Design thinking applied to AI ethics: if you were designing an AI system, what rules would you give it? Who should it help? What should it not be allowed to do?

Ready when they can: Propose at least three rules for a hypothetical AI system they are designing; Explain why AI designers need to think about who might be harmed, not just who benefits; Describe one real example of AI being used responsibly and one where it was not.

Needs first: AI and Fairness in Decisions.

https://lightmysky.com/learn/computing/designing-fair-ai-rules-mt_1z-gJBJFlM

#### How a Chatbot Picks Its Next Word (ages 12-13)

A chatbot is not looking an answer up. It reads what has been written so far, picks a likely next word, feeds that back in and does it again, from patterns taken out of a very large amount of text.

Ready when they can: Describe the loop of picking one word at a time and feeding it back in; Say where the patterns came from, and that none of them is a rule a person typed in; Explain why the same question can come back with two different answers.

https://lightmysky.com/learn/computing/how-a-chatbot-picks-its-next-word-mt_1Zbhamhzai

#### What a Trained Model Is: Weights, Not Rules (ages 14-15)

A trained model is a large set of numbers fitted to examples, not a list of rules somebody wrote out. That is why nobody can point at the line that produced a given answer, and why more examples change what it does without anyone editing logic.

Ready when they can: Contrast a rule a person could write with a number fitted from data, on the same task; Say what training changes inside a model and what stays fixed once it has finished; Explain why a model cannot give the reason for an answer the way a program can be read.

https://lightmysky.com/learn/computing/what-a-trained-model-is-weights-not-rules-mt_3_1toZUxak

#### Training Data: Where It Came From and What It Leaves Out (ages 14-15)

What a model can do is bounded by what it was shown. Who is in the data, who is missing, when it was collected and whose permission was asked all decide what the model is fit for.

Ready when they can: Name three things about a dataset that change what a model trained on it can be trusted with; Give a case where a group missing from the data shows up later as worse performance for those people; Say what a cut-off date means for questions about recent events.

https://lightmysky.com/learn/computing/training-data-where-it-came-from-and-what-it-leaves-out-mt_1Lw0TMHShk

#### Writing a Prompt That Says What You Actually Want (ages 14-16)

A model answers the request in front of it, not the one in the asker's head. Stating the task, the audience, the format and the limits turns a vague request into one whose answer can be judged.

Ready when they can: Rewrite a vague request so the wanted format, length and audience are stated; Supply the material the model needs rather than assuming it knows the particular case; Say, before reading the answer, what would make that answer wrong.

https://lightmysky.com/learn/computing/writing-a-prompt-that-says-what-you-actually-want-mt_dJ5-SDX3Ck

#### AI and the Future of Work (ages 9-11)

How AI is changing the world of work: some jobs disappear, new ones are created, many change; jobs AI can't do (yet); what skills matter in an AI world

Ready when they can: Name at least two jobs that AI is changing or replacing and two new jobs AI has created; Explain why creativity, empathy, and problem-solving are skills that matter more in an AI world; Describe how AI might change a specific job they know about (teacher, doctor, farmer) without replacing it.

Needs first: Jobs People Do, Bias in AI Systems, Humans Versus Machines.

https://lightmysky.com/learn/computing/ai-and-the-future-of-work-mt__AWSThGJ0d

#### AI Data Collection and Privacy (ages 9-11)

What data AI systems collect about you; who has it and why it matters; cookies, tracking, smart speakers always listening; your data is valuable

Ready when they can: Name at least three types of personal data that AI systems collect; Explain why personal data is valuable to companies; Describe one step they can take to protect their privacy online.

Needs first: Recommendation Systems and Filter Bubbles, Scams & Online Safety.

https://lightmysky.com/learn/computing/ai-data-collection-and-privacy-mt_HopZomN12L

#### Checking a Model's Claim Against a Source (ages 15-16)

The cost of a wrong answer falls on whoever passes it on. Picking the claims that carry weight, finding them in a source that is not the model, and dropping what cannot be found is the whole of the check.

Ready when they can: Pick out which claims in an answer carry the weight, instead of checking every sentence; Find a named claim in an independent source, or record that it could not be found; Say why a reference the model produced is not evidence that the reference exists.

https://lightmysky.com/learn/computing/checking-a-models-claim-against-a-source-mt_Qh4Pnnfqv2

#### AI and the Environment (ages 9-11)

AI needs huge amounts of energy and water to train; data centres and their environmental cost; but AI can also help — predicting weather, monitoring deforestation, optimising energy; trade-offs

Ready when they can: Explain that training AI models uses a lot of electricity and water; Give at least two examples of AI being used to help the environment; Describe the trade-off between AI's environmental cost and its environmental benefits.

Needs first: Designing Fair AI Rules, Climate Change Basics, Machine Learning Basics.

https://lightmysky.com/learn/computing/ai-and-the-environment-mt_ZpCcTU8j_o

#### The Future of AI (ages 9-11)

What AI might do in 10 years; what we want it to do and what we're worried about; children as future designers and decision-makers about AI; hopeful, empowered framing

Ready when they can: Describe at least two ways AI might be used in the future that don't exist yet; Explain one thing they would want AI to do and one thing they would want it not to do; Describe why it matters that young people understand AI — because they will shape how it is used.

Needs first: Designing Fair AI Rules, AI and the Future of Work, AI and the Environment.

https://lightmysky.com/learn/computing/the-future-of-ai-mt__LiAEHt9nk

#### Why a Chatbot Can Be Confidently Wrong (ages 12-13)

A sentence that sounds likely and a sentence that is true are not the same thing, and the model has no way to tell them apart. Invented facts, names and references come out in exactly the tone of correct ones.

Ready when they can: Give an example of an answer that reads well and is wrong, and say what would have caught it; Say why the confidence of an answer carries no information about whether it is right; Check one claim from a model's answer against a source that is not the model.

https://lightmysky.com/learn/computing/why-a-chatbot-can-be-confidently-wrong-mt_TMHNkprrks

#### Using an AI Tool on Schoolwork Without Cheating Yourself (ages 13-14)

An AI tool can draft, explain or check, and each of those changes what the learner ends up knowing. Deciding in advance which part of the work is yours, and saying what the tool did, is what keeps the help honest.

Ready when they can: Name a use that helps learning and one that replaces it, for the same piece of work; State before starting which part of a task will be done without the tool, and hold to it; Write one line saying what the tool was used for, in a form a teacher could check.

https://lightmysky.com/learn/computing/using-an-ai-tool-on-schoolwork-without-cheating-yourself-mt_fjlXx-hkp_

#### What You Owe a Reader When a Model Helped (ages 15-16)

Work a model helped produce still carries its author's name. What the reader is owed is a plain statement of what the tool did and what the author checked, in whatever form the setting asks for.

Ready when they can: Write a one-line disclosure for a piece of work, saying what the tool did; Say which parts of a submission the author stays answerable for whatever the tool did; Name a setting where use has to be declared and one where it does not, and say what makes the difference.

https://lightmysky.com/learn/computing/what-you-owe-a-reader-when-a-model-helped-mt_VsUSovHzfI

#### Agents That Take Actions, Not Just Answer (ages 15-16)

Once a model can send a message, spend money or change a file, a wrong answer stops being a wrong answer and becomes a wrong action. What the tool is allowed to reach sets how bad a mistake can get.

Ready when they can: Separate what a model can do with text alone from what it can do with a tool attached to it; Name an action that should need a person to confirm it, and say what makes it that kind of action; Explain why limiting what an agent can reach matters more than trusting it to behave well.

https://lightmysky.com/learn/computing/agents-that-take-actions-not-just-answer-mt_D7KzIdIsjb

### Computing Fundamentals

https://lightmysky.com/learn/computing/areas/computing-fundamentals

#### Simple Programs: Sequences and Instructions (ages 5-8)

Write, run and fix simple programs by putting instructions in order: plan a sequence of steps, predict what the program will do before running it, and hunt down the step that went wrong when it doesn't behave as expected

Ready when they can: Build a short program by arranging instructions in order (e.g., move forward, turn left, move forward to guide a floor robot to a goal); Predict what a simple program will do before pressing run, then check the prediction against what actually happens; Find and fix the wrong or missing step when a program doesn't do what was intended, rather than starting again from scratch.

Needs first: Step-by-Step Instructions.

https://lightmysky.com/learn/computing/simple-programs-sequences-and-instructions-mt_IUvBwahibH

#### Creating Digital Content (ages 6-10)

Use technology purposefully to create and manage digital work: write and edit documents, make pictures, slides and simple videos, save files where they can be found again, and choose or combine the right software for the job

Ready when they can: Create a piece of digital work with a purpose (e.g., a poster, a slideshow about a topic, a short animation); Save work with a sensible name, organise files into folders, and find a piece of work again days later; Choose and combine software for a task (e.g., take photos, then put them into a slideshow with captions).

Needs first: Computers in Everyday Life.

https://lightmysky.com/learn/computing/creating-digital-content-mt_dfhHVURsn6

#### Networks and the Internet (ages 8-11)

How computer networks work: connected computers can share information, the internet is a network of networks, and services like the world wide web, email and video calls all travel over it as data passed from machine to machine

Ready when they can: Explain the difference between the internet (the connected computers) and the world wide web (one service that runs on it); Describe how a message or web page travels from one computer to another through cables, wifi and routers; Name several services the internet provides (e.g., web pages, email, video calls, online games) and what they have in common.

Needs first: Data and Information for Computers.

https://lightmysky.com/learn/computing/networks-and-the-internet-mt_JmrMg6v8V_

#### Programming with Loops and Variables (ages 8-11)

Design and debug programs that use repetition, selection and variables: repeat actions with loops, branch with if-blocks, keep score in a variable, and break a bigger problem into smaller parts that can be programmed one at a time

Ready when they can: Use a loop instead of repeating the same blocks (e.g., 'repeat 4' to draw a square); Use an if-block so the program responds to input (e.g., 'if the sprite touches the wall, bounce'); Store and update a value in a variable, such as a score that goes up or a countdown timer.

Needs first: Simple Programs: Sequences and Instructions.

https://lightmysky.com/learn/computing/programming-with-loops-and-variables-mt_9x5zgShXPg

#### Searching and Evaluating Online (ages 8-11)

Search the web effectively and judge what comes back: choose precise search words, understand that results are selected and ranked by a program rather than checked by a person, and weigh whether a page is trustworthy and relevant

Ready when they can: Refine a search by changing keywords when the first results aren't useful (e.g., 'Saturn rings facts' instead of 'space'); Explain that search results are ranked by a program and that the top result is not automatically the best or truest; Check who wrote a page and compare it with a second source before believing a surprising claim.

Needs first: Networks and the Internet.

https://lightmysky.com/learn/computing/searching-and-evaluating-online-mt_S-XboPwA8k

#### Events: Programs That React to What the User Does (ages 12-13)

A program does not have to run from top to bottom. A handler sits waiting for a click, a key press or a collision, and runs only when that thing happens.

Ready when they can: Attach one handler to a key press and another to a click in the same program, and say which runs when; Explain why an event-driven program looks like it is doing nothing until the user acts; Fix a program where the handler was attached to the wrong object or the wrong event.

https://lightmysky.com/learn/computing/events-programs-that-react-to-what-the-user-does-mt_HFtGUhZHz4

#### Conditions That Combine: And, Or and Not (ages 12-13)

One test is often not enough. Joining tests with and, or and not lets a single decision depend on several things at once, and each joiner changes when the branch is taken.

Ready when they can: Write a condition true only when two things hold at once, and one true when either holds; Say what not turns each of those into, with a case that shows the difference; Find the case that breaks a condition that used or where it needed and.

https://lightmysky.com/learn/computing/conditions-that-combine-and-or-and-not-mt_ZYdtXQZy5r

#### Inside the Box: Input, Processing, Storage and Output (ages 12-13)

Every computer, from a phone to the controller in a washing machine, does the same four jobs: take data in, work on it, keep it, and send results out. Naming which part does which job explains what any device is.

Ready when they can: Sort the parts of a named device into input, processing, storage and output; Trace one piece of data through all four, for a task such as taking a photo and saving it; Say why memory and storage are not the same job, using a case where the power is lost.

https://lightmysky.com/learn/computing/inside-the-box-input-processing-storage-and-output-mt_Oms8067Pnm

#### Random Numbers and Programs That Differ Each Run (ages 12-13)

A random value makes a program behave differently every time it runs. That is what games and simulations need, and it changes what counts as having tested the program.

Ready when they can: Use a random number in a chosen range so that nothing lands outside the screen or the allowed values; Run the same program three times and say what stayed the same and what changed; Explain why 'it worked when I ran it' is weaker evidence once a random value is involved.

https://lightmysky.com/learn/computing/random-numbers-and-programs-that-differ-each-run-mt_t8GTOW3hyN

#### Finding a Bug by Changing One Thing at a Time (ages 12-13)

Changing several things at once hides which change mattered. Working one change at a time, with a prediction written down before each run, finds the fault and says what caused it.

Ready when they can: State what the program should do and what it does instead, before touching any code; Make one change, predict the result, run it, and record whether the prediction held; Narrow a fault to a single block or line and say which change proved it.

https://lightmysky.com/learn/computing/finding-a-bug-by-changing-one-thing-at-a-time-mt_DMgajrUSy_

#### Why a Computer Works with Only Two Symbols (ages 12-13)

Inside the machine every value is a pattern of switches that are either on or off. Two states can be told apart reliably in a circuit, which is the reason a computer counts in twos rather than tens.

Ready when they can: Explain why two states are easier for a circuit to keep apart than ten; Count how many patterns a given number of switches can make, and check that it doubles with each extra switch; Say what a bit is and what a byte is, without converting any numbers.

https://lightmysky.com/learn/computing/why-a-computer-works-with-only-two-symbols-mt_r0wLIjpi5R

#### An Agreed Code: How the Same Bits Mean Letters or Colours (ages 12-13)

A pattern of bits means nothing on its own. It becomes a letter, a colour or a note only because a code says so, and both ends have to be using the same code.

Ready when they can: Invent a code for a small set of symbols and use it to send a short message to someone holding the same code; Show what comes out when the two ends use different codes for the same bits; Give two things the same bit pattern could stand for in two different files.

https://lightmysky.com/learn/computing/an-agreed-code-how-the-same-bits-mean-letters-or-colours-mt_IQY-PHtZVZ

#### Reading a Program Someone Else Wrote (ages 13-14)

Most code a person meets was written by somebody else. Working out what an unfamiliar program does, and then changing it on purpose, is a different skill from writing one from a blank screen.

Ready when they can: Say in one sentence what an unfamiliar short program does, before running it; Point at the part that would have to change to alter one named behaviour; Make that change without breaking the rest, and say what was checked afterwards.

https://lightmysky.com/learn/computing/reading-a-program-someone-else-wrote-mt_VdxhuxjBSn

#### Spotting a Mistake in Stored or Sent Data (ages 13-14)

Data gets corrupted on the way, so systems send extra bits that only fit when nothing has changed. A parity bit or a check digit catches an error without anybody reading the message.

Ready when they can: Add a parity bit to a row, and find the flipped bit in a grid using row and column parity; Work out the check digit of a short product code and show that one wrong digit fails it; Say what error detection can and cannot do, using a case where two errors cancel out.

https://lightmysky.com/learn/computing/spotting-a-mistake-in-stored-or-sent-data-mt_wKwax55eo-

#### Addresses on a Network: Naming a Machine and Naming a Page (ages 13-14)

For one machine to send data to another it needs an address that is unique on the network. A web address is a different kind of name, one that has to be looked up and turned into a machine address before anything can be sent.

Ready when they can: Say what an address has to promise for a message to arrive, and why two machines on one network cannot share one; Break a web address into the part naming a machine and the part naming a page on it; Describe why the name has to be looked up first, and what happens if the lookup fails.

https://lightmysky.com/learn/computing/addresses-on-a-network-naming-a-machine-and-naming-a-page-mt_tGgw0Vhd8b

#### Writing an Algorithm Down: Flowcharts and Pseudocode (ages 13-14)

An algorithm can be recorded before any code exists, as a flowchart or as pseudocode. Both fix the order, the decisions and the repetitions, so the plan can be checked on paper and argued about with someone else.

Ready when they can: Draw a flowchart for a task with at least one decision and one repetition, using the right shape for each; Write the same algorithm as pseudocode and show the two agree step for step; Find a missing or out-of-order step by walking the flowchart with a test value.

https://lightmysky.com/learn/computing/writing-an-algorithm-down-flowcharts-and-pseudocode-mt_RCm-4b4Lof

### Digital Literacy

https://lightmysky.com/learn/computing/areas/digital-literacy

#### Typing Without Looking at the Keys (ages 8-10)

Finding keys by feel instead of by eye frees a writer's attention for what they are writing. It is built by short regular practice with settled fingering, not by chasing speed.

Ready when they can: Rest the fingers on the home row and reach nearby keys without looking down; Type a short familiar sentence with eyes on the screen rather than the keyboard; Hold accuracy steady while speed comes up over weeks, rather than trading one for the other.

https://lightmysky.com/learn/computing/typing-without-looking-at-the-keys-mt_BJ_yVASyuV

#### Where a File Lives: Folders, Names and Backups (ages 9-11)

Files sit inside folders inside other folders, and the path is the address that says which one. A name that describes the work, a place that makes sense and a second copy elsewhere are what make work findable later.

Ready when they can: Read a path and say which folder a file is in and what that folder is inside; Move a file and copy a file, and say what is different about the result; Say what the extension tells the machine, and what having only one copy risks.

https://lightmysky.com/learn/computing/where-a-file-lives-folders-names-and-backups-mt_UvLO9CA3BY

#### Spreadsheets: Rows, Columns and a Formula That Updates Itself (ages 11-13)

A spreadsheet holds values in cells and formulas that refer to those cells by name. Change one value and everything computed from it recalculates, which is what makes a sheet a model rather than a table.

Ready when they can: Write a formula that refers to cells rather than to numbers typed into the formula; Change one input and predict, before looking, which cells will change; Copy a formula down a column and say what happened to the references it contains.

https://lightmysky.com/learn/computing/spreadsheets-rows-columns-and-a-formula-that-updates-itself-mt_iWyPF0-Abz

#### Sorting and Filtering a Table to Answer a Question (ages 12-13)

A table of a few hundred rows will not answer a question by being read. Sorting brings the extremes to the top and filtering drops the rows that do not bear on the question, and what is left is the answer.

Ready when they can: Turn a question into the sort or the filter that would answer it, before touching the data; Sort by one column and say why the other columns had to move with it; Filter on two conditions and say how many rows survived and why.

https://lightmysky.com/learn/computing/sorting-and-filtering-a-table-to-answer-a-question-mt_6-UzZXVWwV

#### Passwords, Logins and Keeping an Account Yours (ages 9-11)

An account is only as private as the way into it. Length beats cleverness in a password, one password reused spreads a single break across every account, and a second factor stops most of what is left.

Ready when they can: Say why a long passphrase is harder to guess than a short password with symbols in it; Explain what goes wrong when the same password is used on several sites; Describe what a second factor adds, and name something it does not protect against.

https://lightmysky.com/learn/computing/passwords-logins-and-keeping-an-account-yours-mt_ohI6ct6tO4

#### Reusing Someone Else's Work: Licences and Giving Credit (ages 11-13)

Images, music and text found online belong to whoever made them, and a licence says what other people may do with it. Reading that licence, and naming the source, is what separates reuse from taking.

Ready when they can: Find the licence on a piece of online media and say what it allows and what it forbids; Credit a reused image so a reader could find the original; Say why 'it was on the internet' does not settle whether a thing may be reused.

https://lightmysky.com/learn/computing/reusing-someone-elses-work-licences-and-giving-credit-mt_SeLxugBmM7

### Programming

https://lightmysky.com/learn/computing/areas/programming

#### Variables and Assignment in Text Code (ages 14-15)

Storing a value under a name in written code, then replacing it later. The name holds whatever was last assigned to it, which is how a program remembers anything.

Ready when they can: Assign a value to a name and print it back out; Predict what a name holds after two assignments in a row; Pick names that say what the value means instead of single letters.

https://lightmysky.com/learn/computing/variables-and-assignment-in-text-code-mt_uLHLaX8BQq

#### Input, Output and Type Conversion (ages 14-15)

Reading what a user types, printing results back, and converting typed text into a number before doing arithmetic with it.

Ready when they can: Read a value from the user and store it in a variable; Convert typed input to a whole number or a decimal before calculating with it; Explain why adding two typed numbers without converting them joins them as text.

https://lightmysky.com/learn/computing/input-output-and-type-conversion-mt_lZmkGSELbC

#### Arithmetic in Code: Integer Division and Remainder (ages 14-15)

The arithmetic a program actually offers, including whole-number division and the remainder, and the order operators are applied in.

Ready when they can: Work out the result of an expression mixing multiplication, addition and brackets; Use whole-number division and remainder to split a total, such as seconds into minutes and seconds; Say which operator runs first without running the code.

https://lightmysky.com/learn/computing/arithmetic-in-code-integer-division-and-remainder-mt_ZPnPrLGPmT

#### Boolean Expressions and Comparison Operators (ages 14-15)

Expressions that come out true or false: comparisons between values, and the way and, or and not combine them.

Ready when they can: Write a condition that is true only inside a range of values; Predict the value of a condition that joins two comparisons with and or or; Rewrite a condition using not without changing what it means.

https://lightmysky.com/learn/computing/boolean-expressions-and-comparison-operators-mt_0aIh-DPCZ4

#### Selection with if, elif and else (ages 14-16)

Making a program take one path or another according to a condition, including several branches tested in order until one fits.

Ready when they can: Write an if and else that react to a value the user typed; Use a chain of branches so exactly one of several messages appears; Explain why reordering the branches changes the result.

https://lightmysky.com/learn/computing/selection-with-if-elif-and-else-mt_zylJ-p9g1g

#### Count-Controlled Loops (ages 14-16)

Repeating a block a known number of times, with a loop variable that takes each value of a range in turn.

Ready when they can: Write a loop that repeats a fixed number of times; Use the loop variable inside the body, for example to print a times table; Say how many times a loop over a given range will run, before running it.

https://lightmysky.com/learn/computing/count-controlled-loops-mt_r1eXTWI_6j

#### Condition-Controlled Loops (ages 15-16)

Repeating for as long as a condition stays true, for when the number of repeats is not known in advance, and making sure something inside the loop can make the condition false.

Ready when they can: Write a loop that keeps asking until the input is valid; Point at the line that lets the loop end, and say what happens without it; Choose between a counted loop and a condition-controlled loop for a described task.

https://lightmysky.com/learn/computing/condition-controlled-loops-mt_LjxO2n3Fy6

#### Strings: Indexing, Slicing and Length (ages 15-16)

Treating text as a sequence of characters that can be measured, indexed from zero, and cut into parts.

Ready when they can: Get the first, last and middle characters of a string; Take a slice and predict exactly where it starts and stops; Use the length of a string inside a loop or a condition.

https://lightmysky.com/learn/computing/strings-indexing-slicing-and-length-mt_33hA050_Qz

#### Lists: Many Values Under One Name (ages 15-16)

Holding a whole collection of values in a single variable, then reading and changing items by their position.

Ready when they can: Create a list and read an item by its index; Add and remove items, and say how the positions shift; Explain why one list beats twenty separate variables for the same data.

https://lightmysky.com/learn/computing/lists-many-values-under-one-name-mt_ipB6kmyK85

#### Traversing a List to Build a Result (ages 15-16)

Looping over every item in a collection while carrying a running result: a total, a count, or the largest value seen so far.

Ready when they can: Total the numbers in a list with a loop and a running variable; Count how many items match a condition; Find the largest value without a built-in function, and justify the starting value.

https://lightmysky.com/learn/computing/traversing-a-list-to-build-a-result-mt_lusbjHFt95

#### Defining a Function with Parameters (ages 15-16)

Giving a named block of code a job of its own and passing values into it, so the same steps run on different data.

Ready when they can: Define a function and call it more than once with different arguments; Decide which values the function needs as parameters; Replace a repeated block with a single call.

https://lightmysky.com/learn/computing/defining-a-function-with-parameters-mt_pyo7yBg4H3

#### Return Values and Variable Scope (ages 15-16)

Sending a result back out of a function, and the rule that a name created inside a function does not exist outside it.

Ready when they can: Return a value and store it in a variable where the call happened; Explain why a variable made inside a function cannot be printed after it ends; Tell apart a function that prints from a function that returns.

https://lightmysky.com/learn/computing/return-values-and-variable-scope-mt_jivtTHpZc7

#### Decomposing a Problem into Subprograms (ages 15-16)

Splitting a task into parts small enough to write and check one at a time, then wiring the parts together into the whole program.

Ready when they can: Break a described program into three or four named jobs before writing any code; Write each part as its own function and test it on its own; State what each part takes in and what it gives back.

https://lightmysky.com/learn/computing/decomposing-a-problem-into-subprograms-mt_P293LckCnd

#### Tracing a Program by Hand (ages 15-16)

Following code line by line with a table of the variables, to say what it does and where it goes wrong. Errors that stop the program are found differently from errors that give a wrong answer.

Ready when they can: Fill in a trace table for a loop and give the final output; Find the line responsible for a wrong result; Tell a syntax error from a logic error by what the computer does with each.

https://lightmysky.com/learn/computing/tracing-a-program-by-hand-mt__rsnZ5Goow

#### Linear Search (ages 15-16)

Looking for a value by checking items one after another until it is found or the collection runs out, and counting the checks that takes in the best and worst case.

Ready when they can: Write a loop that reports the position of a value, or reports that it is absent; Say how many comparisons the worst case needs for a list of a given length; Explain why this search works on data in any order.

https://lightmysky.com/learn/computing/linear-search-mt_32LwZIhSiB

#### Binary Search on Sorted Data (ages 15-16)

Finding a value in sorted data by halving the range that is still in play at every step, and the reason the method breaks on unsorted data.

Ready when they can: Step through a binary search on a sorted list and count the checks; Say what happens to the range still being searched after each comparison; Explain why the data must be sorted, and when that sorting cost is worth paying.

https://lightmysky.com/learn/computing/binary-search-on-sorted-data-mt_3avV-VasFZ

#### Functions at Depth: Default and Keyword Arguments (ages 16-17)

Giving a parameter a default so callers can leave it out, and naming arguments at the call so their order stops mattering. This is how one function serves several jobs without a second copy of the code.

Ready when they can: Write a function with a default parameter and call it with and without that argument; Call a function with named arguments given out of order and predict the result; Say why a default that is a shared collection can surprise the caller.

https://lightmysky.com/learn/computing/functions-at-depth-default-and-keyword-arguments-mt_SR8RhRmYhz

#### Dictionaries: Values Found by Key (ages 16-17)

A collection where each value is stored under a key of the programmer's choosing instead of a position. Looking a value up by key stays fast however many pairs are stored.

Ready when they can: Build a dictionary, read a value by key, and add or replace a pair; Loop over keys and values to produce a summary such as a word count; Say when a dictionary suits the data better than a list, and when it does not.

https://lightmysky.com/learn/computing/dictionaries-values-found-by-key-mt_mofpj0n5AM

#### Classes and Objects: Bundling Data with Behaviour (ages 16-18)

A class describes what every object of its kind holds and what it can do; an object is one filled-in copy of that description. The constructor sets the starting state and the methods are the only code that changes it.

Ready when they can: Define a class with a constructor and two methods, then create two objects from it; Say what belongs to the object and what belongs to the class; Rewrite a loose group of variables and functions as one class, and say what improved.

https://lightmysky.com/learn/computing/classes-and-objects-bundling-data-with-behaviour-mt_kRvg7LZ_kk

#### Inheritance and Overriding Behaviour (ages 16-18)

A class can extend another, taking its fields and methods and replacing the ones it needs to do differently. Shared behaviour is written once, and the differences sit in the class they belong to.

Ready when they can: Write a subclass that adds one field and overrides one method; Predict which version of a method runs for an object of the subclass; Say when two classes should share a parent and when they should not.

https://lightmysky.com/learn/computing/inheritance-and-overriding-behaviour-mt_wBp7j_B6fj

#### Designing with Objects: Deciding What Each Class Owns (ages 16-18)

Reading a problem description and deciding which things deserve a class, what each one is responsible for, and where the boundaries between them fall. The judgement is about responsibility, not about syntax.

Ready when they can: Pull candidate classes and responsibilities out of a written problem description; Defend a boundary: say why one piece of data belongs to this class and not that one; Spot a class that has taken on two unrelated jobs and split it.

https://lightmysky.com/learn/computing/designing-with-objects-deciding-what-each-class-owns-mt_De_gpvpOzg

#### Reading and Writing Files, Including CSV (ages 17-18)

Opening a file, reading it line by line or writing to it, and closing it again, plus the row-and-column shape of CSV. This is where a program's data starts outliving the run that produced it.

Ready when they can: Read a text file line by line and build a result from it; Write records to a CSV file and read them back into objects or dictionaries; Say what closing a file does, and what a relative path depends on.

https://lightmysky.com/learn/computing/reading-and-writing-files-including-csv-mt_j5qb4FdkdI

#### Exceptions: Raising, Catching and Recovering (ages 17-18)

Signalling a failure by raising an exception, and handling it where the caller knows what to do about it. Catching everything and carrying on hides faults, so the choice of what to catch is the real skill.

Ready when they can: Catch a specific exception around a risky operation and recover from it; Raise an exception when a function is given input it cannot work with; Explain why catching every exception and continuing is usually the wrong repair.

https://lightmysky.com/learn/computing/exceptions-raising-catching-and-recovering-mt_hEVa1JRrGu

#### Unit Tests: Deciding What Is Worth Testing (ages 17-18)

Writing small automated checks that call one function with chosen inputs and assert what should come back. The value is in the cases picked: the boundary, the empty input, the failure that should be raised.

Ready when they can: Write tests for one function covering a normal case, a boundary and an error case; Change the function so a test fails, and read what the failure tells you; Say why a test that only repeats the code's own logic proves nothing.

https://lightmysky.com/learn/computing/unit-tests-deciding-what-is-worth-testing-mt_tuIQecq5Le

#### Debugging as a Method: Reproduce, Isolate, Fix (ages 17-18)

Working from a fault to its cause by a repeatable route: reproduce it reliably, cut the program down until the fault is cornered, then change one thing and check. Guessing edits is the habit this replaces.

Ready when they can: Turn a vague fault report into a repeatable set of steps that shows it every time; Narrow a bug down by halving the suspect region rather than reading the whole file; State a hypothesis about the cause, then design the one check that would refute it.

https://lightmysky.com/learn/computing/debugging-as-a-method-reproduce-isolate-fix-mt_2JGE4ICRf6

#### The Project Arc: Building a Program in Stages (ages 17-18)

Taking a project from a written aim to working software in stages: a thin version that runs end to end, then features added one at a time, each kept working. Refactoring is the step that keeps the code liveable as it grows.

Ready when they can: Break an aim into stages where every stage leaves a program that still runs; Keep a small backlog and say what the next stage is and why it is next; Refactor once the shape of the code has drifted, without changing what it does.

https://lightmysky.com/learn/computing/the-project-arc-building-a-program-in-stages-mt_hACOaB3nA_

### Algorithms & Data Structures

https://lightmysky.com/learn/computing/areas/algorithms-and-data-structures

#### Counting Operations to Compare Algorithms (ages 16-17)

Working out how many comparisons or swaps a method performs on an input of a given size, and writing that count as a formula in n. Two algorithms can then be compared without running either one.

Ready when they can: Count the comparisons a search makes on the same list of 64 by two different methods; Write the operation count of a loop as a formula in the input size n; Explain why a timed run on one laptop is weaker evidence than a count.

https://lightmysky.com/learn/computing/counting-operations-to-compare-algorithms-mt_JkN961niFG

#### Big-O Notation and Orders of Growth (ages 16-17)

Describing how the work an algorithm does grows with the size of its input, keeping only the term that dominates and dropping constants. It gives O(1), O(log n), O(n), O(n log n) and O(n squared) as a way to compare methods at any scale.

Ready when they can: Turn an operation count such as 3n + 7 into its big-O form and say what was dropped and why; Put O(1), O(log n), O(n), O(n log n) and O(n squared) in order of growth; Predict what happens to the work when the input doubles, for each of those orders.

https://lightmysky.com/learn/computing/big-o-notation-and-orders-of-growth-mt_mkqgxhJ509

#### Quadratic Sorts: Bubble and Insertion (ages 16-17)

Two sorting methods that work by comparing neighbouring values, one bubbling the largest to the end each pass and one placing each value into an already sorted front. Both do work proportional to n squared, which is where big-O first bites.

Ready when they can: Trace one full pass of bubble sort and one insertion step on the same six values; Count the comparisons each method makes and match the count to O(n squared); Say when insertion sort beats bubble sort, and what nearly sorted input does to each.

https://lightmysky.com/learn/computing/quadratic-sorts-bubble-and-insertion-mt_cBUIBa15jQ

#### Stacks: Last In, First Out (ages 16-18)

A collection where the only value within reach is the one added most recently. Push puts a value on top, pop takes it off, and that single restriction is what makes undo, back buttons and bracket checking straightforward.

Ready when they can: Trace the contents of a stack through a run of pushes and pops; Implement push and pop over a list and say what a pop from an empty stack should do; Match a task such as undo history or bracket matching to the last-in-first-out rule.

https://lightmysky.com/learn/computing/stacks-last-in-first-out-mt_Evw7zeJE6Q

#### Queues: First In, First Out (ages 16-18)

A collection where values leave in the order they arrived: enqueue at the back, dequeue at the front. The circular queue keeps the front from drifting off the end of the storage.

Ready when they can: Trace a queue through a run of enqueue and dequeue operations; Give the order the same four values come back out of a queue and out of a stack; Explain why a print spooler or a network buffer needs arrival order kept.

https://lightmysky.com/learn/computing/queues-first-in-first-out-mt_4U1bT0JW4g

#### Linked Lists and Nodes That Point (ages 16-18)

Storing a sequence as nodes that each hold a value and a reference to the next node. Inserting in the middle costs two pointer changes, but reaching the five hundredth item means walking there one node at a time.

Ready when they can: Draw the pointer changes needed to insert and to delete a node in the middle; Compare the cost of insertion and of access for a linked list and for an array; Say what a null next reference marks and what happens if it is lost.

https://lightmysky.com/learn/computing/linked-lists-and-nodes-that-point-mt_HvY7_-M2Zj

#### Hash Tables and Near-Constant Lookup (ages 16-18)

Turning a key into a slot number with a hash function, so a value is reached by calculation instead of by searching. Two keys can land in the same slot, and the table needs a rule for what happens when they do.

Ready when they can: Apply a small hash function to several keys and place them in a table of slots; Describe one collision rule, such as chaining or probing, and run it on a clash; Explain why lookup stays close to constant time until the table gets crowded.

https://lightmysky.com/learn/computing/hash-tables-and-near-constant-lookup-mt_7v94MJEdmJ

#### Recursion and the Call Stack (ages 17-18)

A function that calls itself on a smaller version of the same problem, with a base case that stops the descent. Every call that has not returned yet waits on the call stack, which is why deep recursion runs out of room.

Ready when they can: Write a recursive function with a base case and a case that shrinks the input; Trace the call stack for a small input and say which call returns first; Rewrite a simple loop as recursion, and say what a missing base case causes.

https://lightmysky.com/learn/computing/recursion-and-the-call-stack-mt_VGjfeF3F2e

#### Merge Sort and Divide and Conquer (ages 17-18)

Sorting by splitting the data in half, sorting each half the same way, then merging two sorted halves in one pass. The splitting gives log n levels and each level costs n, which is where O(n log n) comes from.

Ready when they can: Merge two sorted lists into one and count the comparisons the merge needs; Draw the split-and-merge tree for eight values and count its levels; Explain why O(n log n) beats O(n squared) badly once the input is large.

https://lightmysky.com/learn/computing/merge-sort-and-divide-and-conquer-mt_OAutL4c7_l

#### Trees and Binary Search Trees (ages 17-18)

A structure of nodes with one root and no cycles, and the binary search tree rule that keeps smaller values left and larger values right. Walking the tree left, node, right returns the values in sorted order.

Ready when they can: Insert a run of values into an empty binary search tree and draw the result; Search for a value and count the comparisons against the tree's height; Walk a tree in order and show that the output comes out sorted.

https://lightmysky.com/learn/computing/trees-and-binary-search-trees-mt_7PGHiAY54b

#### Graphs and How to Store Them (ages 17-18)

Nodes joined by edges, with the edges possibly directed and possibly carrying a weight. The same graph can be held as an adjacency matrix or as an adjacency list, and the choice decides which questions are cheap to ask.

Ready when they can: Write the same small graph as an adjacency matrix and as an adjacency list; Say which storage suits a sparse graph and which suits a dense one, with the reason; Model a real situation, such as a route map, as nodes, edges and weights.

https://lightmysky.com/learn/computing/graphs-and-how-to-store-them-mt_tSO-F1sTuu

#### Breadth-First and Depth-First Search (ages 17-18)

Two ways to visit every node reachable from a start point: one takes a queue and spreads out level by level, the other takes a stack and follows one path as far as it goes. The choice of structure is the whole difference between them.

Ready when they can: Give the visit order both searches produce on the same graph from the same start; Explain why swapping the queue for a stack turns one search into the other; Say why visited nodes must be recorded, and what happens on a cycle if they are not.

https://lightmysky.com/learn/computing/breadth-first-and-depth-first-search-mt_q8IEzoBhzy

#### Dijkstra's Shortest Path (ages 17-18)

Finding the cheapest route through a weighted graph by always settling the nearest unsettled node next and relaxing the distances to its neighbours. Fewest hops and cheapest cost stop being the same answer once edges carry weights.

Ready when they can: Run the algorithm on a small weighted graph, keeping the table of best-known distances; Say why the nearest unsettled node can be fixed and never revised; Give a graph where the fewest-hops route is not the cheapest route.

https://lightmysky.com/learn/computing/dijkstras-shortest-path-mt_GvUzbY92qL

#### Loop Invariants and Proving an Algorithm Correct (ages 18-19)

A loop invariant is a statement that holds before a loop starts, survives every pass, and gives the wanted result once the loop stops. Stating one turns the claim that code seems to work into an argument that it works on every input.

Ready when they can: State the invariant for an insertion sort and check it at entry, after a pass, and at exit; Use an invariant to argue a summing loop is right for a list of any length; Find the input that breaks a proposed invariant and repair the statement.

https://lightmysky.com/learn/computing/loop-invariants-and-proving-an-algorithm-correct-mt_fWnstju2ns

#### Asymptotic Notation Made Precise (ages 18-19)

The definition behind big-O: f(n) is O(g(n)) when some constant multiple of g stays above f from some input size onward. Big-Omega bounds from below and big-Theta bounds from both sides, so a claim about growth becomes something a student can argue for rather than assert.

Ready when they can: Name a constant and a starting size that make a given big-O claim true; Say what big-Omega and big-Theta each add to a big-O statement; Explain why an O(n squared) method can still beat an O(n) one on small inputs.

https://lightmysky.com/learn/computing/asymptotic-notation-made-precise-mt_B0Z6Syy8Ve

#### Recurrence Relations and the Master Theorem (ages 18-20)

A recursive algorithm's cost is written as an equation that refers to itself, such as T(n) = 2T(n/2) + n. Solving it by expansion, by a recursion tree, or by the master theorem gives the running time without tracing a single call.

Ready when they can: Write the recurrence for merge sort and for binary search from the code; Expand a recurrence into a tree and sum the work level by level; Apply the master theorem and say which of its cases a given recurrence falls in.

https://lightmysky.com/learn/computing/recurrence-relations-and-the-master-theorem-mt_aOvLPV7rR8

#### Divide and Conquer as a Design Method (ages 18-20)

Split the input, solve the pieces the same way, and spend the remaining effort combining. Seen as a method rather than as one sorting trick, it produces fast multiplication, closest-pair search, and selection without sorting.

Ready when they can: Design a divide and conquer solution to a problem the learner has not seen solved that way; Say where the work sits for a given split: mostly in the split, the combine, or the leaves; Explain why splitting into pieces of unequal size can still pay off.

https://lightmysky.com/learn/computing/divide-and-conquer-as-a-design-method-mt_YITRNb-HTE

#### Randomised Quicksort and Expected Running Time (ages 19-20)

Quicksort partitions around a pivot, and its worst case is quadratic. Choosing the pivot at random makes the bad case a matter of luck rather than of input, and the expected running time is n log n whatever the adversary supplies.

Ready when they can: Partition an array around a pivot in place and state the invariant of the partition loop; Construct the input that makes a fixed-pivot quicksort quadratic; Explain what randomising the pivot changes, and what it does not.

https://lightmysky.com/learn/computing/randomised-quicksort-and-expected-running-time-mt_fcKF7zfzpX

#### The Comparison-Sorting Lower Bound (ages 19-20)

Any sort that only compares pairs of elements is a decision tree with n factorial leaves, so its height is at least n log n. This is a statement about every possible algorithm, not about the ones anybody has written.

Ready when they can: Draw the decision tree of a comparison sort on three elements and count its leaves; Argue from the leaf count to a bound on the tree's height; Explain how counting sort beats the bound without contradicting it.

https://lightmysky.com/learn/computing/the-comparison-sorting-lower-bound-mt_7AfUsPV-jW

#### Heaps and Priority Queues (ages 19-20)

A binary heap keeps the smallest item at the root using an array and a simple shape rule, so insert and extract both cost log n. It gives a sort that meets the comparison bound and, more usefully, a queue ordered by importance rather than by arrival.

Ready when they can: Insert into a heap and restore the heap property by sifting up; Extract the minimum and restore the property by sifting down; Say why a heap is stored in an array with no pointers at all.

https://lightmysky.com/learn/computing/heaps-and-priority-queues-mt_W-ofiMiXWs

#### Amortised Analysis (ages 19-21)

Some operations are occasionally expensive and usually cheap, so the worst case of one call overstates the cost of a run of calls. Amortised analysis charges the rare expensive step to the many cheap ones and reports the average per operation over any sequence.

Ready when they can: Show that a dynamic array that doubles on overflow appends in constant amortised time; Use the accounting method to place a credit on each cheap operation; Explain why an amortised bound is a worst-case claim, not an average-case one.

https://lightmysky.com/learn/computing/amortised-analysis-mt_1zLrl5RKGr

#### Greedy Choice and the Exchange Argument (ages 19-21)

A greedy method takes the locally best option and never reconsiders. It is right only when a proof says so, and the usual proof takes any optimal solution and swaps its first choice for the greedy one without making it worse.

Ready when they can: Solve interval scheduling greedily and prove the earliest-finish rule with an exchange; Find a coin system where taking the largest coin first gives the wrong answer; Say what property a problem must have before a greedy rule can be correct.

https://lightmysky.com/learn/computing/greedy-choice-and-the-exchange-argument-mt_9Fj28VDAV-

#### Union-Find and Minimum Spanning Trees (ages 20-21)

Kruskal's method sorts the edges and adds any that joins two separate pieces, which needs a structure that answers whether two vertices are already connected. Union-find answers it in almost constant time using a forest with path compression.

Ready when they can: Run Kruskal's method on a small weighted graph and say why each rejected edge was rejected; Perform union and find operations and show what path compression changes; Explain why the cut property makes the greedy edge choice safe.

https://lightmysky.com/learn/computing/union-find-and-minimum-spanning-trees-mt_zOJei4yCtr

#### Dynamic Programming: Optimal Substructure and Overlapping Subproblems (ages 20-21)

When a problem's best answer is built from best answers to smaller versions, and the same smaller versions keep reappearing, storing each answer once turns an exponential recursion into a polynomial one. The two conditions are what decide whether the method applies.

Ready when they can: Turn a naive recursive Fibonacci into a memoised one and count the calls saved; State the subproblem and the recurrence before writing any code; Say which of the two conditions fails for a problem where the method does not apply.

https://lightmysky.com/learn/computing/dynamic-programming-optimal-substructure-and-overlapping-subproblems-mt__hWkCDnzNY

#### Dynamic Programming on Two Sequences (ages 20-21)

Longest common subsequence and edit distance both fill a grid where each cell asks one question about the last character of each string. The table gives the answer, and walking back through it gives the alignment that produced it.

Ready when they can: Fill an edit distance table for two short words and read the answer off the corner; Trace back through the table to recover the actual edits; Say what each of the three choices in the recurrence corresponds to.

https://lightmysky.com/learn/computing/dynamic-programming-on-two-sequences-mt_uNUgHcKKQN

#### Dynamic Programming with a Capacity: Knapsack (ages 20-22)

The knapsack table is indexed by item and by remaining capacity, which makes its size depend on the numbers in the input rather than on how many there are. That is why the method is called pseudo-polynomial and why doubling the weights doubles the work.

Ready when they can: Fill a knapsack table for five items and read off which items were taken; Explain why the table has capacity as one of its axes; Say why an input written with larger numbers costs more without holding more items.

https://lightmysky.com/learn/computing/dynamic-programming-with-a-capacity-knapsack-mt_T5pbU_DpdC

#### Shortest Paths with Negative Weights and Between All Pairs (ages 20-22)

Dijkstra's greedy choice fails once an edge can reduce a cost, so Bellman-Ford relaxes every edge n minus one times instead, and reports a negative cycle if anything still improves. Floyd-Warshall answers every pair at once by asking which intermediate vertices are allowed.

Ready when they can: Build a graph with a negative edge where Dijkstra returns the wrong distance; Run Bellman-Ford and say what an improvement on the last pass proves; Explain what the third index in the Floyd-Warshall recurrence stands for.

https://lightmysky.com/learn/computing/shortest-paths-with-negative-weights-and-between-all-pairs-mt_e8szFezaxO

#### Network Flow and the Max-Flow Min-Cut Theorem (ages 21-22)

Flow pushes as much as possible from a source to a sink without exceeding any edge's capacity. Augmenting paths in a residual graph find the maximum, and the theorem says that maximum equals the cheapest set of edges whose removal disconnects the two.

Ready when they can: Find a maximum flow by repeatedly augmenting along paths in the residual graph; Identify the minimum cut and check its capacity equals the flow; Model bipartite matching as a flow problem and read the matching off the answer.

https://lightmysky.com/learn/computing/network-flow-and-the-max-flow-min-cut-theorem-mt_momRV9lK1n

#### Finite State Machines and What They Recognise (ages 17-18)

A machine with a fixed set of states that moves between them as it reads one input symbol at a time, drawn as a state transition diagram or written as a table. It has no memory beyond the state it is in, which fixes what it can and cannot recognise.

Ready when they can: Draw a state transition diagram for a simple device and give the matching table; Decide whether a given input string is accepted by a machine; Say why counting unlimited nested brackets is beyond any fixed set of states.

https://lightmysky.com/learn/computing/finite-state-machines-and-what-they-recognise-mt_gIk7tQ229w

#### Turing Machines and the Universal Machine (ages 17-18)

A machine with a fixed set of states plus an unlimited tape it can read, write and move along. Adding the tape is enough to compute anything any computer can, and one such machine can read another's description and run it.

Ready when they can: Run a small Turing machine on a starting tape and give the tape when it halts; Say what the tape adds that a fixed set of states alone cannot provide; Explain what a universal machine does, and why that is what a computer is.

https://lightmysky.com/learn/computing/turing-machines-and-the-universal-machine-mt_vS_QC1tCSM

#### The Halting Problem: A Task No Program Can Do (ages 17-18)

There is no program that can take any program and its input and always say correctly whether it will finish. The proof feeds the checker its own description, and the contradiction is where computability stops.

Ready when they can: State the halting problem precisely, including what the checker is given; Follow the self-reference step and say where the contradiction appears; Tell an undecidable problem apart from one that is merely slow.

https://lightmysky.com/learn/computing/the-halting-problem-a-task-no-program-can-do-mt_KeuKGHFWqr

#### Reductions: Solving One Problem by Turning It into Another (ages 21-22)

A reduction converts every instance of one problem into an instance of another, so a solver for the second answers the first. Read forwards it reuses an algorithm, and read backwards it transfers hardness from a problem nobody can solve quickly.

Ready when they can: Reduce bipartite matching to maximum flow and state what the conversion costs; Explain why a reduction has to run quickly for the argument to mean anything; Say which direction of a reduction proves easiness and which proves hardness.

https://lightmysky.com/learn/computing/reductions-solving-one-problem-by-turning-it-into-another-mt_PAwby3ZyAr

#### P, NP and What NP-Complete Means (ages 21-22)

P holds the problems solvable in polynomial time and NP the ones whose proposed answers can be checked that fast. NP-complete problems are the hardest in NP: every other NP problem reduces to them, so a fast method for one would be a fast method for all.

Ready when they can: Give a certificate for a yes-instance of a named NP problem and check it in polynomial time; Explain what would follow if any single NP-complete problem had a polynomial algorithm; Say why NP-hard and NP-complete are not the same claim.

https://lightmysky.com/learn/computing/p-np-and-what-np-complete-means-mt_wwmNVG_VnB

#### Living with NP-Hardness: Approximation and Heuristics (ages 21-22)

Hardness rules out an exact fast method for every input, not a useful answer. An approximation algorithm carries a proved ratio to the optimum, while a heuristic carries no promise and has to be judged by measurement.

Ready when they can: Run a 2-approximation for vertex cover and argue the factor from the matching it builds; Distinguish an approximation with a proved ratio from a heuristic without one; Choose between exact, approximate and heuristic for a stated deadline and input size.

https://lightmysky.com/learn/computing/living-with-np-hardness-approximation-and-heuristics-mt_tZ82ty6h2u

#### Randomised Algorithms and the Probabilistic Method (ages 22-23)

An algorithm allowed to flip coins can be simpler and faster than any deterministic one known, at the price of a guarantee about expectation rather than about every run. The same idea proves objects exist by showing a random one works with positive probability.

Ready when they can: Separate an algorithm that is always correct and sometimes slow from one that is fast and sometimes wrong; Compute the expected running time of a randomised routine on a worst-case input; Use a counting argument over a random object to show something with a wanted property exists.

https://lightmysky.com/learn/computing/randomised-algorithms-and-the-probabilistic-method-mt_4ShN_WlT0-

#### Concentration Bounds and a High-Probability Guarantee (ages 22-23)

An expectation says nothing about how often the answer lands far from it. Markov, Chebyshev and the Chernoff bound each buy a sharper statement for a stronger assumption, and they are what turn an average-case claim into one that holds on nearly every run.

Ready when they can: Apply Markov, Chebyshev and a Chernoff bound to the same quantity and compare what each yields; Say what independence buys in the Chernoff bound and what happens without it; Turn an expected-time result into a high-probability one and state the failure probability.

https://lightmysky.com/learn/computing/concentration-bounds-and-a-high-probability-guarantee-mt_WIltjK12oW

#### Approximation Ratios and How One Is Proved (ages 22-23)

An approximation algorithm comes with a proved bound on how far its answer can sit from the best one, and the proof almost never mentions the optimum directly. It bounds the optimum from one side with something computable, then bounds the algorithm against that.

Ready when they can: State what a ratio guarantees and what it says nothing about; Prove a ratio by comparing both the algorithm and the optimum to a computable bound; Give an instance where the bound is tight and say what that tightness means.

https://lightmysky.com/learn/computing/approximation-ratios-and-how-one-is-proved-mt_8pmBztDkFD

#### Linear Programming, Duality and Rounding (ages 22-23)

Relaxing integer decisions to fractions gives a problem that can be solved, and its optimum bounds the integer one. Duality supplies the certificate that a solution is optimal, and rounding turns the fractional answer back into a real one at a cost that can be bounded.

Ready when they can: Write a combinatorial problem as a linear program and state its dual; Use a dual solution as a certificate for a bound on the primal; Round a fractional solution and bound what the rounding lost.

https://lightmysky.com/learn/computing/linear-programming-duality-and-rounding-mt_rsj6G8iydV

#### Complexity Beyond NP: Space, Randomness and the Hierarchy (ages 22-24)

NP is one class among many. Alternating quantifiers give the polynomial hierarchy, bounded space gives classes with surprising collapses, and allowing randomness gives classes widely believed to add nothing. Most of the relations between them are conjectures with consequences.

Ready when they can: Place a stated problem in the right level by counting its quantifier alternations; Say what would follow if the hierarchy collapsed; State what is believed about randomised polynomial time and why the belief is not a proof.

https://lightmysky.com/learn/computing/complexity-beyond-np-space-randomness-and-the-hierarchy-mt_ADfgl9UGpO

#### SAT Solvers and What Makes Search Practical (ages 22-24)

Satisfiability is the canonical hard problem, and yet solvers decide industrial instances with millions of clauses. They search, and when they fail they learn a clause explaining the failure, which prunes the region that produced it. The worst case is unchanged; practice is not.

Ready when they can: Encode a small constraint problem into clauses and say what a satisfying assignment means for it; Explain what conflict-driven clause learning adds to plain backtracking; Say why a solver being fast on real instances contradicts nothing about NP-completeness.

https://lightmysky.com/learn/computing/sat-solvers-and-what-makes-search-practical-mt_d46m2LD443

### Computer Systems

https://lightmysky.com/learn/computing/areas/computer-systems

#### Binary Numbers and Place Value (ages 14-15)

Counting with two digits, where each column is worth twice the column to its right. Converting both ways between binary and decimal.

Ready when they can: Convert an 8-bit binary number to decimal; Convert a decimal number below 256 into 8 bits; State the largest value 8 bits can hold, and why that is the limit.

https://lightmysky.com/learn/computing/binary-numbers-and-place-value-mt_t67akIKBmI

#### Adding Binary Numbers and Overflow (ages 14-15)

Adding binary numbers column by column with a carry, and what happens when the answer needs more bits than the space it has.

Ready when they can: Add two 8-bit binary numbers, carrying correctly; Spot an addition whose result no longer fits in 8 bits; Describe what a program shows when a value overflows.

https://lightmysky.com/learn/computing/adding-binary-numbers-and-overflow-mt_dBS2OoQscq

#### Hexadecimal as Binary Shorthand (ages 14-15)

Writing four bits as one of sixteen digits, so long binary values can be read and typed by people without anything being lost.

Ready when they can: Convert between binary and hexadecimal in groups of four bits; Convert a two-digit hexadecimal number to decimal; Point at a place hex actually shows up, such as a colour code.

https://lightmysky.com/learn/computing/hexadecimal-as-binary-shorthand-mt_OV6PHdnU6N

#### Character Sets: Storing Text as Numbers (ages 14-15)

Every character has an agreed number, and the text on screen is those numbers drawn by a font. A shared standard is what lets two machines read the same file, and one byte per character stopped being enough.

Ready when they can: Explain what a character set is and why both machines have to use the same one; Work out the code of a letter given the code of another letter in the same run; Say why scripts beyond Latin, and emoji, needed a larger standard.

https://lightmysky.com/learn/computing/character-sets-storing-text-as-numbers-mt_839VNNZlp2

#### Bitmap Images: Pixels, Resolution and Colour Depth (ages 14-16)

A picture stored as a grid of pixels, each one a binary colour value. Resolution and colour depth decide both how it looks and how big the file is.

Ready when they can: Explain what resolution controls and what colour depth controls; Work out the size of an uncompressed image from its dimensions and colour depth; Predict what happens to a picture blown up past its resolution.

https://lightmysky.com/learn/computing/bitmap-images-pixels-resolution-and-colour-depth-mt_-Tr40QK8sN

#### Sampling Sound into Numbers (ages 14-16)

Recording sound by measuring the wave thousands of times a second and storing each measurement as a binary number. Sample rate and bit depth change the quality and the size together.

Ready when they can: Explain what a sample is and what the sample rate counts; Say what a higher sample rate or bit depth does to quality and to file size; Explain why a digital recording can never hold the whole wave.

https://lightmysky.com/learn/computing/sampling-sound-into-numbers-mt_yTA4W-yFjy

#### Compression: Lossy and Lossless (ages 15-16)

Making a file smaller either by storing the same information in fewer bits, or by dropping detail people are unlikely to miss. Which of the two is safe depends on the file.

Ready when they can: Describe a lossless method, such as recording runs of repeated values; Explain what lossy compression throws away and why it cannot be put back; Choose the right kind for a photo, a song and a file of code.

https://lightmysky.com/learn/computing/compression-lossy-and-lossless-mt_lx2U-B9CFa

#### Logic Gates and Truth Tables (ages 15-16)

The and, or and not circuits that everything else is built from, and the table that fixes what each one outputs for every possible input.

Ready when they can: Complete the truth table for AND, OR and NOT; Work out the output of two gates wired together; Match a written condition to the gates that would compute it.

https://lightmysky.com/learn/computing/logic-gates-and-truth-tables-mt_o2N0-q3A4Q

#### Inside the CPU: Fetch, Decode, Execute (ages 15-16)

The cycle a processor repeats: fetch the next instruction from memory, work out what it means, carry it out. Clock speed, cores and cache each change how fast that goes.

Ready when they can: Put the three stages of the cycle in order and say what each does; Explain what a higher clock speed buys, and what extra cores buy; Explain why both instructions and data sit in memory while a program runs.

https://lightmysky.com/learn/computing/inside-the-cpu-fetch-decode-execute-mt_YT-FSWnUKR

#### Memory and Storage: RAM, ROM and the Backing Store (ages 15-16)

Where a machine keeps things: fast memory that empties at power off for what is running now, permanent storage for what has to survive. Speed, size and cost pull against each other.

Ready when they can: Say what is lost when the power goes and what is not; Explain why a program is copied from storage into memory before it runs; Compare storage kinds on speed, capacity and durability for a stated use.

https://lightmysky.com/learn/computing/memory-and-storage-ram-rom-and-the-backing-store-mt_AiXGJioO_S

#### Packets and Protocols on a Network (ages 15-16)

Data crosses a network cut into numbered packets that travel separately and are put back together at the far end. Protocols are the agreed rules that let machines from different makers understand each other.

Ready when they can: Explain why data is sent in packets, and what a packet carries besides the data; Describe what happens when a packet is lost or arrives out of order; Say what a protocol is, and what two named ones are for.

https://lightmysky.com/learn/computing/packets-and-protocols-on-a-network-mt_IffXVDtfLX

#### How a Web Page Reaches Your Screen (ages 15-16)

The path from typing an address to seeing a page: the name looked up as an address, a request sent to a server, a reply of files the browser assembles.

Ready when they can: Put the steps in order from pressing enter to a finished page; Explain what the name lookup is for and what breaks without it; Tell apart what the browser does from what the server does.

https://lightmysky.com/learn/computing/how-a-web-page-reaches-your-screen-mt_8JveAW2Mg7

#### Cyber Threats and How Systems Defend (ages 15-16)

The usual ways systems are attacked, from tricking a person into handing over a password to feeding a program input it trusted too far, and the defence that answers each one.

Ready when they can: Match a threat to the defence that actually addresses it; Explain why people are attacked more often than the code is; Say what makes a password hard to guess, and why reusing one is the bigger risk.

https://lightmysky.com/learn/computing/cyber-threats-and-how-systems-defend-mt_zMJzhIdEWd

#### Boolean Algebra and Simplifying Logic Expressions (ages 16-17)

Writing a circuit as an algebraic expression and rearranging it with the laws of Boolean algebra, including De Morgan's, to reach a shorter expression with the same truth table. Fewer gates means less silicon and less delay.

Ready when they can: Rewrite NOT over an AND using De Morgan's laws and check the result against a truth table; Simplify an expression of three variables and count the gates saved; Turn a written condition into an expression and then into gates.

https://lightmysky.com/learn/computing/boolean-algebra-and-simplifying-logic-expressions-mt_9MrE1N63D5

#### Logic Circuits That Add and Remember (ages 16-17)

The half adder and full adder that turn gates into binary arithmetic with a carry, and the flip-flop that holds one bit after its input has gone. Feedback is what turns a circuit into storage.

Ready when they can: Give the sum and carry a full adder produces for each combination of its three inputs; Chain full adders to add two four-bit numbers and show where overflow appears; Explain what a flip-flop holds and why feedback is needed to hold it.

https://lightmysky.com/learn/computing/logic-circuits-that-add-and-remember-mt_zPgkt6zf-i

#### Assembly Language and the Instruction Set (ages 16-18)

The instructions a processor actually offers: load, store, add, compare, branch, halt, each naming a register or an address. A line of high-level code turns into several of them.

Ready when they can: Hand-run a short assembly listing and give the final register and memory contents; Write a counting loop using compare and branch instructions; Translate one line of high-level code into the instructions it needs.

https://lightmysky.com/learn/computing/assembly-language-and-the-instruction-set-mt_bzmsfvdzwp

#### Registers, Buses and the Fetch-Execute Cycle in Detail (ages 16-18)

What each register holds during one cycle, from the program counter and the address and data registers through to the accumulator, and what travels on the address, data and control buses. A branch is just an instruction writing to the program counter.

Ready when they can: Walk one instruction through the cycle, naming the register holding each value at each step; Say what a branch does to the program counter and when that happens in the cycle; Explain what a wider address bus or data bus changes about the machine.

https://lightmysky.com/learn/computing/registers-buses-and-the-fetch-execute-cycle-in-detail-mt_yjy3eSStzH

#### Network Layers and the Protocol Stack (ages 17-18)

A network is split into layers, each with one job and each talking only to the layer above and below: application, transport, internet, link. A message gains a header at each layer on the way down and loses it on the way up.

Ready when they can: Say which layer a named protocol belongs to and what that layer is responsible for; Follow a message down the stack at the sender and back up at the receiver; Explain what the split buys: one layer can change without the others being rewritten.

https://lightmysky.com/learn/computing/network-layers-and-the-protocol-stack-mt_O3Ew6c2ynD

#### IP Addressing and How Routers Choose a Path (ages 17-18)

How an address splits into a network part and a host part, and how a router uses its forwarding table to pick the next hop without knowing the whole route. No single machine holds a map of the internet.

Ready when they can: Split an address with a subnet mask into its network and host parts; Decide from a small forwarding table which link a packet leaves on; Explain why two packets of one message can take different routes and still arrive.

https://lightmysky.com/learn/computing/ip-addressing-and-how-routers-choose-a-path-mt_l0dRGocXGw

#### Relational Databases: Tables, Keys and Relationships (ages 17-18)

Data held as tables of rows, with a primary key that identifies one row and a foreign key that points at a row in another table. The relationships between tables are the design, not an afterthought.

Ready when they can: Choose a primary key for a table and justify why it identifies a row; Link two tables with a foreign key and name the relationship as one-to-many or many-to-many; Say what goes wrong when the same fact is stored in two places.

https://lightmysky.com/learn/computing/relational-databases-tables-keys-and-relationships-mt_i7pZV6H902

#### Normalisation to Third Normal Form (ages 17-18)

Splitting tables until every field depends on the key, the whole key, and nothing but the key. Each step removes a way the data could contradict itself after an update.

Ready when they can: Take an unnormalised table through first, second and third normal form; Name the update, insert or delete problem that each step removes; Say when a designer might accept a repeated field on purpose.

https://lightmysky.com/learn/computing/normalisation-to-third-normal-form-mt_cbRXVW6KxX

#### SQL: Selecting, Filtering and Ordering Rows (ages 17-18)

Asking a database for the rows and columns you want with SELECT, WHERE and ORDER BY. The query says what is wanted, and the database decides how to fetch it.

Ready when they can: Write a query that returns named columns for the rows matching a condition; Combine conditions with AND, OR and NOT and predict which rows survive; Sort results and limit them, and say what changes when the order is reversed.

https://lightmysky.com/learn/computing/sql-selecting-filtering-and-ordering-rows-mt_lDVVG2AKzs

#### SQL: Joining Tables and Summarising Groups (ages 17-18)

Pulling rows from two tables together on a matching key, and collapsing many rows into one answer with COUNT, SUM and GROUP BY. This is the payoff for having split the tables in the first place.

Ready when they can: Join two tables on a foreign key and say which rows the join drops; Count or total rows per group and read the result table; Explain why a join with no matching condition returns far too many rows.

https://lightmysky.com/learn/computing/sql-joining-tables-and-summarising-groups-mt_0QPZDE2KuS

#### Instruction Set Architecture as a Contract (ages 18-19)

The instruction set is the promise the hardware makes to every program: these operations exist, these registers are visible, this is how memory is addressed. Everything below it can be rebuilt without breaking a single compiled program, and that separation is why chips can change while software does not.

Ready when they can: Name what an instruction set fixes and what it deliberately leaves to the implementation; Compare a load-store design with one that operates directly on memory and say what each costs; Explain why two chips with different internals can run the same binary.

https://lightmysky.com/learn/computing/instruction-set-architecture-as-a-contract-mt_pbwHRePY5M

#### The Memory Hierarchy and Why Caching Works (ages 18-19)

Fast memory is small and small memory is fast, so machines stack registers, caches, main memory and disk. The stack pays off only because programs reuse what they touched recently and touch neighbours next, which is what locality means.

Ready when they can: Order the levels of the hierarchy by size and by access time; Identify temporal and spatial locality in a piece of loop code; Predict which of two loops over the same array runs faster and say why.

https://lightmysky.com/learn/computing/the-memory-hierarchy-and-why-caching-works-mt_0f5ArFPlxP

#### Pipelining and the Cost of a Hazard (ages 18-20)

Splitting instruction handling into stages lets one instruction start before the last has finished, raising throughput without making any single instruction faster. Dependencies between neighbouring instructions and unresolved branches force stalls, which is the price of the arrangement.

Ready when they can: Draw a pipeline diagram for five instructions and count the cycles saved; Spot a data hazard between two neighbouring instructions and say how forwarding helps; Explain why a mispredicted branch throws away work.

https://lightmysky.com/learn/computing/pipelining-and-the-cost-of-a-hazard-mt_GI_fPY9d6s

#### Many Cores and the Limit on Speedup (ages 19-20)

When one core stops getting faster, machines add cores, and the gain then depends on how much of the work can actually run at the same time. The serial fraction sets a ceiling that no number of cores can lift.

Ready when they can: Compute the best possible speedup for a program that is one tenth serial; Distinguish work that splits across cores from work that splits across data lanes; Explain why adding cores can make a program slower.

https://lightmysky.com/learn/computing/many-cores-and-the-limit-on-speedup-mt_dy3-K9dV19

#### What an Operating System Is: Privilege and System Calls (ages 19-20)

An operating system exists because programs cannot be trusted with the hardware directly. The processor runs in two modes, ordinary code cannot touch devices, and a system call is the one controlled doorway from a program into the kernel.

Ready when they can: Trace what happens on a system call, from the trap to the return; Name three things a program in user mode is not allowed to do; Explain why a library call and a system call cost different amounts.

https://lightmysky.com/learn/computing/what-an-operating-system-is-privilege-and-system-calls-mt_0kMavEKxpX

#### Processes, Context Switches and What They Cost (ages 19-20)

A process is a running program plus everything the kernel remembers about it: registers, memory map, open files. Swapping one for another means saving all of that and loading another set, which is cheap in instructions and expensive in lost cache.

Ready when they can: List what the kernel has to save and restore on a context switch; Follow a process through the ready, running and blocked states; Explain why a switch costs more than the register copying suggests.

https://lightmysky.com/learn/computing/processes-context-switches-and-what-they-cost-mt_oiOwHKUoXG

#### Scheduling: Deciding Which Process Runs Next (ages 19-21)

A scheduler chooses from the ready processes, and every rule it could use favours something: throughput, response time, or fairness. Round robin, shortest job first and priority with ageing each make that trade differently.

Ready when they can: Work out average waiting time for a job set under two different policies; Show how a long-running job starves under strict priority, and how ageing fixes it; Say which policy suits an interactive machine and which suits a batch one.

https://lightmysky.com/learn/computing/scheduling-deciding-which-process-runs-next-mt_QZYzfVIcP6

#### Virtual Memory and Address Translation (ages 19-21)

Every process is given its own address space, and the hardware translates its addresses into real ones through a page table on every access. This is what stops one program reading another's memory and what lets a program use more memory than the machine has.

Ready when they can: Translate a virtual address to a physical one given a page table and page size; Explain what the translation lookaside buffer caches and why it matters; Say what isolation the page table gives and what it does not.

https://lightmysky.com/learn/computing/virtual-memory-and-address-translation-mt_B-PiAyderj

#### Paging, Page Faults and Replacement Policies (ages 20-21)

When a page is not resident the hardware raises a fault and the kernel fetches it, possibly evicting another. Which page leaves is a policy question, and a bad answer produces thrashing, where the machine spends its time moving pages instead of running code.

Ready when they can: Count the faults a reference string causes under least recently used and under first in first out; Explain what thrashing looks like from outside the machine; Say why the optimal policy can be described but not implemented.

https://lightmysky.com/learn/computing/paging-page-faults-and-replacement-policies-mt_nEEuGL89Ze

#### File Systems: Names, Blocks and Metadata (ages 20-21)

A file system turns a flat array of blocks into names, directories and permissions. An inode or equivalent record holds where the blocks are and who may touch them, while the directory is just a table mapping names to those records.

Ready when they can: Follow a path name to the blocks that hold the file's bytes; Explain what a hard link is in terms of the record it points at; Say why deleting a large file can be instant while writing it was slow.

https://lightmysky.com/learn/computing/file-systems-names-blocks-and-metadata-mt_jN4u3idvF3

#### Crash Consistency and the Journal (ages 20-22)

A file operation touches several blocks, and a crash between them leaves the file system in a state no correct sequence could produce. A journal writes the intention down first, so recovery can either finish the operation or discard it whole.

Ready when they can: Describe an inconsistent state a crash could leave halfway through a file move; Order the journal writes and the real writes and say why the order matters; Explain what recovery does with a journal entry that has no commit record.

https://lightmysky.com/learn/computing/crash-consistency-and-the-journal-mt_I9DT0TUmiu

#### Threads and Shared Memory (ages 20-21)

Threads inside one process share an address space and everything in it, which makes them cheap to switch between and dangerous to reason about. The gain is a program that keeps working while one part waits; the cost is that any two threads can touch the same variable.

Ready when they can: Say what threads in one process share and what each keeps to itself; Explain why creating a thread is cheaper than creating a process; Identify a variable in a small program that two threads could reach at once.

https://lightmysky.com/learn/computing/threads-and-shared-memory-mt_N4EGNbN6Xh

#### Race Conditions and Mutual Exclusion (ages 20-22)

When two threads read, change and write the same value, the result depends on timing that nobody controls. A critical section is the stretch that must not be interleaved, and a lock is the usual way to enforce that, at the cost of everything waiting.

Ready when they can: Interleave two increment sequences to produce a lost update; Place a lock around the smallest region that fixes the race; Explain why a check followed by an action can be wrong even when both are correct.

https://lightmysky.com/learn/computing/race-conditions-and-mutual-exclusion-mt_hygT74jJDE

#### Deadlock and the Four Conditions (ages 20-22)

Deadlock needs mutual exclusion, holding while waiting, no preemption, and a cycle of waiting. Removing any one of the four prevents it, which is why a fixed lock ordering is the usual answer in real code.

Ready when they can: Draw the wait-for graph of a deadlocked pair of threads and find the cycle; Break a given deadlock by removing one of the four conditions; Explain how a global lock ordering prevents the cycle from forming.

https://lightmysky.com/learn/computing/deadlock-and-the-four-conditions-mt_CsMOA4sBb1

#### Message Passing and Asynchronous Work (ages 21-22)

Instead of sharing memory and guarding it, threads or processes can own their state and send messages. Queues, channels and event loops trade the race conditions of shared memory for questions about ordering, buffering and back pressure.

Ready when they can: Rewrite a lock-based counter as a single owner served by a message queue; Say what a bounded queue does when the producer outruns the consumer; Compare the failure modes of shared memory and of message passing.

https://lightmysky.com/learn/computing/message-passing-and-asynchronous-work-mt_twcpO-945r

#### Lexing and Parsing: From Text to a Syntax Tree (ages 21-22)

A compiler's front end first groups characters into tokens, which a state machine can do, then arranges those tokens into a tree according to a grammar. The tree is where operator precedence stops being a rule to memorise and becomes a shape.

Ready when they can: Tokenise a line of source and name the token kind of each piece; Draw the syntax tree for an arithmetic expression with mixed precedence; Write a grammar rule that makes an operator left associative.

https://lightmysky.com/learn/computing/lexing-and-parsing-from-text-to-a-syntax-tree-mt_-ZlCxZ3SOh

#### Semantic Analysis and the Intermediate Representation (ages 21-22)

A tree that parses can still be wrong: an undeclared name, a type mismatch, a call with the wrong arity. After those checks the compiler lowers the tree into a simpler representation, which is what lets one front end serve several targets.

Ready when they can: Name three errors a parser accepts and a semantic pass rejects; Explain what a symbol table holds and when it is consulted; Say why lowering to an intermediate form is worth the extra pass.

https://lightmysky.com/learn/computing/semantic-analysis-and-the-intermediate-representation-mt_f2z_WQxfiw

#### Code Generation and What an Optimiser May Change (ages 21-22)

The back end turns the intermediate form into instructions, assigns registers, and rearranges work. Every rearrangement is allowed only if the observable behaviour stays the same, which is why an optimiser can reorder arithmetic but not a write to a device.

Ready when they can: Hand-generate instructions for a small expression and assign registers to the temporaries; Name two transformations an optimiser is allowed to make and say what justifies each; Explain why an optimiser must not remove a read that looks unused.

https://lightmysky.com/learn/computing/code-generation-and-what-an-optimiser-may-change-mt__ZSPwP4hfA

#### Cloud-Native Architecture: Containers, Schedulers and the Control Loop (ages 23-24)

A deployment is described as a desired state and a controller works continuously to close the gap. Containers make a process portable, a scheduler decides where it runs, and the control loop is what turns a crashed replica into a replaced one with nobody being paged.

Ready when they can: Say what a container isolates and what it shares with the host; Describe the reconcile loop and why it is written to be safe to run repeatedly; Explain why declaring the desired state beats issuing the steps to reach it.

https://lightmysky.com/learn/computing/cloud-native-architecture-containers-schedulers-and-the-control-loop-mt_nV1LgSRsh_

#### Observability and Tail Latency Across Services (ages 23-24)

Once a request touches a dozen services, an average tells nobody anything. Traces follow one request across process boundaries, percentiles expose the slow tail, and a request that fans out inherits the worst of everything it waited on.

Ready when they can: Read a distributed trace and say which span holds the latency; Explain why the mean hides a problem that the ninety-ninth percentile shows; Say why a request fanning out to many services is slower than any one of them typically is.

https://lightmysky.com/learn/computing/observability-and-tail-latency-across-services-mt_NT5tmumdfA

#### Type Soundness: Progress and Preservation (ages 23-24)

A language is defined by a small-step semantics saying how a program takes one step. Soundness is two lemmas over that definition: a well-typed program is never stuck, and taking a step preserves its type. Together they say the errors the type system rules out cannot occur at run time.

Ready when they can: Read a small-step rule and say what it asserts about one step of evaluation; State progress and preservation and say what each rules out on its own; Give a language feature that breaks soundness and say which lemma it breaks.

https://lightmysky.com/learn/computing/type-soundness-progress-and-preservation-mt_nAAHVPNaVJ

#### The Impacts of Computing: Law, Ethics and the Environment (ages 15-16)

What computing does beyond the machine: the rules on holding people's data, the choices behind who a system serves well, and the energy and materials a device costs.

Ready when they can: State one legal duty an organisation has over personal data it holds; Argue both sides of a case where a useful system harms some group; Account for a device's environmental cost across making it, running it and throwing it away.

https://lightmysky.com/learn/computing/the-impacts-of-computing-law-ethics-and-the-environment-mt_veX-psjipc

### Machine Learning

https://lightmysky.com/learn/computing/areas/machine-learning

#### Joint, Marginal and Conditional Probability (ages 18-19)

Learning from data means reasoning about several uncertain quantities at once. The joint distribution holds everything, the marginal sums out what is not of interest, and the conditional is what remains once something is known.

Ready when they can: Read a joint table and compute both marginals and a conditional from it; Say what independence means as a statement about the joint distribution; Show that a conditional probability and its reverse are usually different numbers.

https://lightmysky.com/learn/computing/joint-marginal-and-conditional-probability-mt__Rj-hOSMEw

#### Bayes' Rule and Updating a Belief (ages 18-19)

Bayes' rule turns the probability of evidence given a cause into the probability of the cause given the evidence. It explains why a test that is right almost always can still be wrong most of the time it fires, when what it looks for is rare.

Ready when they can: Compute a posterior from a prior, a likelihood and a rate of false positives; Explain the base rate effect on a rare condition with an accurate test; Update a belief twice with two pieces of evidence and get the same answer either order.

https://lightmysky.com/learn/computing/bayes-rule-and-updating-a-belief-mt_A4p5--f7Io

#### Likelihood and the Maximum Likelihood Estimate (ages 18-20)

Given data and a family of models, the likelihood is how probable the data would be under each candidate. Choosing the candidate that maximises it is where most fitting procedures come from, including the least squares line.

Ready when they can: Write the likelihood of a run of coin flips as a function of the bias; Maximise a simple likelihood and check the answer against intuition; Explain why the likelihood is a function of the parameter, not of the data.

https://lightmysky.com/learn/computing/likelihood-and-the-maximum-likelihood-estimate-mt_crcBnSqkTE

#### Data as a Matrix: Rows, Features and the Target (ages 18-20)

Almost every method takes the same shape of input: one row per example, one column per feature, and a separate target column. Getting real data into that shape means encoding categories, scaling columns onto comparable ranges, and deciding what one row is.

Ready when they can: Turn a table with text categories into a numeric feature matrix; Say why scaling matters when features are measured in different units; Decide what one row should represent for a stated prediction question.

https://lightmysky.com/learn/computing/data-as-a-matrix-rows-features-and-the-target-mt_KEN-TU1Gpn

#### Linear Regression by Least Squares (ages 19-20)

Fit a straight relationship by choosing coefficients that make the sum of squared residuals as small as possible. With several features the same idea gives a plane or hyperplane, and each coefficient reads as the effect of one feature with the others held fixed.

Ready when they can: Fit a line by least squares and interpret its slope in the units of the data; Extend to two features and say what each coefficient means; Plot residuals and say what a pattern in them reveals about the fit.

https://lightmysky.com/learn/computing/linear-regression-by-least-squares-mt_QRRkpIrwWs

#### Gradient Descent: Following the Slope Downhill (ages 19-20)

When no formula gives the best parameters, start somewhere and repeatedly step against the slope of the error. The step size decides whether the search creeps, oscillates or diverges, and this one procedure trains almost everything that follows.

Ready when they can: Run gradient descent by hand on a one-parameter error function for three steps; Show what too large and too small a step size each do to the search; Say why the method finds a local minimum and what that costs.

https://lightmysky.com/learn/computing/gradient-descent-following-the-slope-downhill-mt_EjfIT1WgMX

#### Logistic Regression and the Decision Boundary (ages 19-21)

For a yes-or-no target, squeeze a linear score through a function that returns a probability, and fit by maximising likelihood. Where that probability crosses a chosen threshold is the decision boundary, and moving the threshold trades one kind of mistake for the other.

Ready when they can: Turn a linear score into a probability and read off the predicted class; Draw the decision boundary of a two-feature logistic model; Say what moving the threshold does to each kind of error.

https://lightmysky.com/learn/computing/logistic-regression-and-the-decision-boundary-mt_FaVIaT7xl2

#### Overfitting and the Bias-Variance Trade-off (ages 19-21)

A model flexible enough to fit the noise will do it, and then fail on anything new. Error splits into bias from a model too simple to represent the pattern and variance from a model too sensitive to the particular sample it saw.

Ready when they can: Show training error falling while held-out error rises as flexibility grows; Attribute a stated failure to bias or to variance and say why; Explain why more training data helps variance more than it helps bias.

https://lightmysky.com/learn/computing/overfitting-and-the-bias-variance-trade-off-mt_xznyNxeNNw

#### Regularisation: Charging for Complexity (ages 20-21)

Add a penalty on the size of the coefficients to the thing being minimised, and the fit pulls back from chasing noise. A squared penalty shrinks everything smoothly, an absolute one drives some coefficients to zero and selects features on the way.

Ready when they can: Add a penalty term and show what happens to the coefficients as it grows; Say why the two common penalties behave differently at zero; Explain why features have to be scaled before a penalty is fair.

https://lightmysky.com/learn/computing/regularisation-charging-for-complexity-mt_RVgsDP0XzP

#### Cross-Validation and Honest Model Selection (ages 20-21)

Every choice made by looking at a set of data uses that set up, so the score on it stops being an estimate of future performance. Splitting into folds, and holding a final set back untouched, is how a reported number stays believable.

Ready when they can: Run k-fold cross-validation to choose a penalty strength; Explain what leaks when the test set is used to pick anything; Say why a time-ordered dataset must not be split at random.

https://lightmysky.com/learn/computing/cross-validation-and-honest-model-selection-mt_YG7X3HYCrT

#### Beyond Accuracy: Precision, Recall and the Cost of an Error (ages 20-22)

On imbalanced data a model that always says no can be right almost every time and be useless. The confusion matrix separates the two kinds of mistake, and precision, recall and the curves over thresholds say which model suits which cost.

Ready when they can: Build a confusion matrix and compute precision and recall from it; Show a case where high accuracy hides a model that never finds the rare class; Choose a threshold from a stated cost of a miss against a cost of a false alarm.

https://lightmysky.com/learn/computing/beyond-accuracy-precision-recall-and-the-cost-of-an-error-mt_BHGgZM7tak

#### Decision Trees and Ensembles (ages 20-22)

A tree splits the data one question at a time, choosing each split to make the resulting groups purer. One tree is easy to read and unstable; averaging many trees grown on resampled data trades that readability for accuracy.

Ready when they can: Choose the first split of a small dataset using an impurity measure; Show that a small change in the data changes a single tree's structure; Explain why averaging many trees reduces variance.

https://lightmysky.com/learn/computing/decision-trees-and-ensembles-mt_xo9EEd4R1i

#### Clustering: Structure Without Labels (ages 20-22)

With no target column, the question becomes which examples resemble each other. K-means alternates assigning points to the nearest centre and moving the centres, and the awkward parts are choosing k, choosing a distance, and deciding whether the groups mean anything.

Ready when they can: Run two rounds of k-means by hand on a small set of points; Show how different starting centres give different final groups; Say what makes a clustering result meaningful rather than merely tidy.

https://lightmysky.com/learn/computing/clustering-structure-without-labels-mt_BAMGOlWgRY

#### Principal Components and Dimensionality Reduction (ages 20-22)

When features are many and correlated, most of the variation lies along a few directions. Principal component analysis finds those directions from the covariance structure and re-expresses each example in far fewer numbers, which makes data visible and models cheaper.

Ready when they can: Project a correlated two-feature dataset onto its first component and say what was kept; Read a scree plot and choose how many components to keep, with a reason; Say why the components are hard to name in the language of the original features.

https://lightmysky.com/learn/computing/principal-components-and-dimensionality-reduction-mt_l-9XHg_ChZ

#### From Perceptron to Multilayer Network (ages 21-22)

A single artificial neuron is a linear score with a threshold, and it cannot separate patterns that are not linearly separable. Stacking layers with a non-linear function between them removes that limit, because the middle layers build features of their own.

Ready when they can: Show that a single unit cannot represent exclusive-or; Build a two-layer network by hand that does represent it; Explain why a stack of layers without a non-linearity collapses to one layer.

https://lightmysky.com/learn/computing/from-perceptron-to-multilayer-network-mt_TTa7KN1-IO

#### Backpropagation: Assigning Blame for an Error (ages 21-22)

Training a network means knowing how much each weight contributed to the error, which the chain rule gives by passing derivatives backwards through the layers. Every weight is then nudged by gradient descent, and the whole procedure is one pass forward and one pass back.

Ready when they can: Propagate an error backwards through a two-layer network by hand; Say what the chain rule contributes at each layer boundary; Explain why a squashing function with a flat tail slows learning.

https://lightmysky.com/learn/computing/backpropagation-assigning-blame-for-an-error-mt_5bwaSWfF96

#### Deep Learning: Convolution, Sequence and Scale (ages 21-22)

Deep networks work because their architecture matches the data: convolution shares weights across positions in an image, and sequence models carry information along a sentence. What changed in practice was scale, in data and in the hardware that could process it.

Ready when they can: Say what weight sharing in a convolution assumes about the input; Explain why a sequence model needs some memory of what came earlier; Name what a deep model needs that a small one does not, beyond layers.

https://lightmysky.com/learn/computing/deep-learning-convolution-sequence-and-scale-mt_karzGN5JnI

#### Attention as a Learned Lookup (ages 22-23)

Attention scores a query against every key in the sequence, turns the scores into weights, and returns a blend of the matching values. Nothing about distance is fixed in advance, so a position can read from anywhere, and the price is a comparison against everything.

Ready when they can: Compute the weights of one attention head by hand and say what the softmax did to the raw scores; Say what a fixed convolution window and a recurrent state each lose that attention keeps; Give the cost of attention in the sequence length and name what that cost rules out.

https://lightmysky.com/learn/computing/attention-as-a-learned-lookup-mt_rrdtS1lHvC

#### The Transformer Block: Heads, Residuals and Normalisation (ages 22-23)

One block stacks multi-head attention and a position-wise network around a residual path, with normalisation holding the scale steady. Attention treats a sequence as a set, so position has to be supplied explicitly or the block cannot tell an order from a shuffle.

Ready when they can: Trace a single vector through one block and name what each sub-layer changed about it; Say why several narrow heads are used instead of one wide one; Predict what fails if the residual path is cut, and what fails if position is never encoded.

https://lightmysky.com/learn/computing/the-transformer-block-heads-residuals-and-normalisation-mt_eKC2IehaDT

#### Tokenisation and What a Model Actually Reads (ages 22-23)

A model never sees letters or words. It sees ids drawn from a vocabulary built by merging frequent pieces of text, and that vocabulary decides what is cheap to express, which spellings are fragile, and why digits and rare names behave badly.

Ready when they can: Segment a sentence into subword pieces and count the tokens it costs; Show two spellings of the same thing that tokenise differently and predict the effect on the model; Say why a request is priced and limited in tokens rather than in words.

https://lightmysky.com/learn/computing/tokenisation-and-what-a-model-actually-reads-mt_PW7s8qEiJD

#### Pretraining by Predicting the Next Token (ages 22-23)

Every position in a corpus is a labelled example asking what comes next, so the text supplies its own supervision. One objective, run over enough text, forces the model to carry grammar, facts and a rough sense of the task being asked of it.

Ready when they can: State the training loss for next-token prediction and say what a low held-out value does and does not mean; Explain why the objective needs no human labelling, and where that stops being an advantage; Separate what the objective rewards from what a person asking a question actually wants.

https://lightmysky.com/learn/computing/pretraining-by-predicting-the-next-token-mt_D8b2phZJfp

#### Scaling Laws and the Compute Budget (ages 22-23)

Held-out loss falls as a smooth power of parameters, tokens and compute, which turns a training decision into arithmetic. The same curve shows where a budget is being wasted, usually on a model larger than the data it will ever see.

Ready when they can: Read a scaling curve on log axes and predict the loss at a larger budget; Split a fixed compute budget between model size and token count, and defend the split; Name two things the curve says nothing about.

https://lightmysky.com/learn/computing/scaling-laws-and-the-compute-budget-mt_tzl0sQblIM

#### Adapting a Pretrained Model: Fine-Tuning and Low-Rank Updates (ages 22-24)

Most work starts from weights someone else paid for. A full fine-tune moves every parameter and costs a whole copy to store, while a low-rank update trains a small factored correction and leaves the base weights alone.

Ready when they can: Compare parameter count and storage for a full fine-tune against a low-rank adapter; Say when adapting beats prompting for a task, and when it does not; Describe catastrophic forgetting and one measure that keeps it in check.

https://lightmysky.com/learn/computing/adapting-a-pretrained-model-fine-tuning-and-low-rank-updates-mt_NaA2iGtMPc

#### Generative Models: Learning a Distribution You Can Sample (ages 22-24)

A generative model is judged by what it produces rather than by a label it predicts. Latent-variable models put a simple distribution behind the data and learn a decoder from it, which is what makes sampling easy and the likelihood awkward.

Ready when they can: Say what separates a generative model from a discriminative one trained on the same data; Explain the job of a latent variable and why training optimises a bound rather than the likelihood; Name two ways to judge samples when there is no accuracy to report.

https://lightmysky.com/learn/computing/generative-models-learning-a-distribution-you-can-sample-mt_3CHsmpWVX5

#### Diffusion Models: Learning to Undo Noise (ages 22-24)

Training adds noise to a sample in small steps and asks the network to predict the noise that was added. Generation runs that chain backwards from pure noise, so one hard sampling problem becomes a long series of easy denoising ones.

Ready when they can: Describe the forward corruption process and say why it needs no training; State what the network predicts at each step and how repeating it yields a sample; Say what more sampling steps buy and what they cost.

https://lightmysky.com/learn/computing/diffusion-models-learning-to-undo-noise-mt_kZdQJ96iZ3

#### Markov Decision Processes: States, Actions and Return (ages 22-24)

Reinforcement learning begins by writing the problem down: states, actions, a transition rule, a reward and a discount. The return is the quantity being maximised, and the discount is the modelling choice that fixes how far ahead the agent looks.

Ready when they can: Write a small described task as an MDP and say what each part holds; Compute a discounted return along a short trajectory; Say what the Markov assumption rules out and give a task where it is wrong.

https://lightmysky.com/learn/computing/markov-decision-processes-states-actions-and-return-mt_bTCO27sgc6

#### Temporal-Difference Learning and Q-Learning (ages 23-24)

An agent that cannot see the transition probabilities can still learn a value by bootstrapping: move each estimate towards the reward plus the next estimate. Q-learning does this over state-action pairs and reaches the best policy while behaving by a different one.

Ready when they can: Perform a temporal-difference update by hand and say which estimate moved and why; Say what off-policy learning means and why exploring does not spoil the target; Give one failure mode of bootstrapping with a function approximator.

https://lightmysky.com/learn/computing/temporal-difference-learning-and-q-learning-mt_Z78E2llE0C

#### Policy Gradients and the Actor-Critic Split (ages 23-24)

Instead of learning values and reading a policy off them, the policy can be a parameterised distribution trained directly by gradient ascent on expected return. The gradient is noisy, so a learned value function serves as a baseline to hold the variance down.

Ready when they can: Say why the policy gradient works even though the reward is not differentiable in the parameters; Explain what a baseline changes about the estimator, and what it leaves alone; Name what the actor and the critic each learn and why both are kept.

https://lightmysky.com/learn/computing/policy-gradients-and-the-actor-critic-split-mt_eXm6stg8zj

#### Learning from Human Preferences: Reward Models and Policy Optimisation (ages 23-24)

When the goal cannot be written as a reward, people compare pairs of outputs and a reward model is fitted to those comparisons. The language model is then optimised as a policy against that fitted reward, with a penalty for drifting away from where it started.

Ready when they can: Describe how pairwise comparisons become a scalar reward model; Say why the policy is held near the pretrained model and what happens without that penalty; Give one way a policy scores well against a reward model while getting worse for people.

https://lightmysky.com/learn/computing/learning-from-human-preferences-reward-models-and-policy-optimisation-mt_yA1ud53Oy_

#### Training Across Many Devices: Data, Model and Pipeline Parallelism (ages 23-24)

A run stops fitting on one device well before the interesting model sizes. Data parallelism copies the model and splits the batch, model parallelism splits the tensors, and pipeline parallelism splits the layers, each paying a different communication bill.

Ready when they can: Match each parallelism strategy to what it splits and what it has to communicate; Say which strategy a memory-bound run needs and which a bandwidth-bound run needs; Explain what a pipeline bubble is and one way to shrink it.

https://lightmysky.com/learn/computing/training-across-many-devices-data-model-and-pipeline-parallelism-mt__e-JwIxHek

#### Serving a Model: Batching, the Key-Value Cache and Quantisation (ages 23-24)

Generation is memory-bandwidth bound and runs one token at a time, so serving is a different problem from training. Batching amortises the weight reads, a key-value cache stops the model recomputing the past, and lower-precision weights buy throughput against a small accuracy loss.

Ready when they can: Say why serving is bandwidth bound while training is compute bound; Explain what the key-value cache stores and how its size grows with the request; State the trade quantisation makes and one way to measure whether it was worth it.

https://lightmysky.com/learn/computing/serving-a-model-batching-the-key-value-cache-and-quantisation-mt_Nv1-WLGIO4

#### Benchmarks and the Traps in Them (ages 22-24)

A benchmark is a proxy that becomes a target and then stops measuring what it did. Test data leaks into training sets, baselines are tuned less than the proposed method, and a leaderboard everyone reports against is being overfitted by a whole field at once.

Ready when they can: Give three ways a reported score can be correct and still misleading; Say how contamination happens when a benchmark predates the pretraining corpus; Describe an evaluation that would separate a real gain from a tuning artefact.

https://lightmysky.com/learn/computing/benchmarks-and-the-traps-in-them-mt_o9zLZbkaen

#### Fairness, Accountability and the Limits of a Model (ages 21-22)

A model trained on past decisions reproduces the pattern in them, including the parts nobody would defend out loud. Several reasonable definitions of fairness cannot all hold at once, so a team has to choose one, say which, and be able to explain a decision to the person it lands on.

Ready when they can: Show how a model can be accurate overall and much worse for one group; State two fairness criteria that cannot both hold and say what forces the choice; Say what a person affected by an automated decision is owed.

https://lightmysky.com/learn/computing/fairness-accountability-and-the-limits-of-a-model-mt_tTh4WtAyk5

#### Interpretability: Probes, Features and Circuits (ages 23-24)

A trained network is a working artifact that nobody designed in detail. Probes ask whether a property is readable from an activation, feature analysis asks what a direction stands for, and circuit analysis asks which components carry a behaviour. Each answers less than it appears to.

Ready when they can: Say what a successful probe does and does not prove about how the model works; Explain why a single unit rarely stands for a single human-named concept; Describe one intervention that turns a claim about a circuit into a test.

https://lightmysky.com/learn/computing/interpretability-probes-features-and-circuits-mt_C8POKvRkq6

### Networks & Security

https://lightmysky.com/learn/computing/areas/networks-and-security

#### Layering and Encapsulation in the Protocol Stack (ages 18-19)

Each layer wraps the layer above in a header and hands it down, so a message crossing the network is a set of nested envelopes. The arrangement means a change in how a link carries bits does not reach the application, and it also means a failure at one layer is reported in that layer's terms.

Ready when they can: Follow one message down the stack, naming the header each layer adds; Say which layer a stated failure belongs to and how it would be reported; Explain what a layer boundary buys and what it hides.

https://lightmysky.com/learn/computing/layering-and-encapsulation-in-the-protocol-stack-mt_D33SEBslXH

#### Reliable Delivery over an Unreliable Network (ages 18-19)

The network below may drop, duplicate, delay and reorder. A reliable transport rebuilds order and completeness on top of it using sequence numbers, acknowledgements, timeouts and retransmission, and a window so the sender need not wait for each reply.

Ready when they can: Trace a transfer where one segment is lost and say what triggers the resend; Explain what the sequence number does when segments arrive out of order; Say why a window raises throughput on a link with long delay.

https://lightmysky.com/learn/computing/reliable-delivery-over-an-unreliable-network-mt_kCM411CSac

#### Congestion Control and Sharing a Link (ages 18-20)

Nothing tells a sender how much of the path is free, so it probes: increase the rate while packets get through, and cut it sharply when they do not. That rule is what keeps a shared network from collapsing, and it makes loss a signal rather than only a fault.

Ready when they can: Explain why a sender treats a lost packet as evidence about the path; Sketch how a sending rate rises and falls over time under this rule; Say what happens if one sender ignores the rule while others follow it.

https://lightmysky.com/learn/computing/congestion-control-and-sharing-a-link-mt_y5hPUrdKyq

#### Naming: DNS and the Resolution Path (ages 19-20)

People use names and machines use addresses, so a distributed directory translates between them by walking a hierarchy from the root down. Caching with a time to live is what keeps it fast, and it is also why a change takes a while to be seen everywhere.

Ready when they can: Walk a name resolution from the root through to the answer; Explain what the time to live decides and who honours it; Say what a stale cached answer looks like from a user's side.

https://lightmysky.com/learn/computing/naming-dns-and-the-resolution-path-mt_omttmGkEgW

#### Routing: How a Path Is Learned (ages 19-20)

No router knows the whole network. Inside one organisation routers exchange what they know until their tables agree; between organisations the choice is shaped by policy and business relationships as much as by distance.

Ready when they can: Run a distance-vector exchange on a small network until the tables settle; Explain why a link failure takes time to be reflected everywhere; Say why the path between two organisations is not always the shortest one.

https://lightmysky.com/learn/computing/routing-how-a-path-is-learned-mt_gyqPDrV6Uo

#### The Web as a Protocol: Requests, State and Caching (ages 19-21)

The web runs on a request and response protocol that remembers nothing between calls, so any sense of a session is built on top with cookies or tokens. Caching headers decide what may be reused and for how long, which is most of what makes the web feel fast.

Ready when they can: Read a request and response pair and name the parts that carry meaning; Explain how a stateless protocol supports a logged-in session; Say what a caching header changes for a browser and for an intermediate cache.

https://lightmysky.com/learn/computing/the-web-as-a-protocol-requests-state-and-caching-mt_MDiW4Vt0bo

#### Clocks, Ordering and Happens-Before (ages 20-21)

Separate machines have separate clocks that drift, so a timestamp cannot settle which of two events came first. What can be settled is causality: one event happened before another if a message carried information from the first to the second.

Ready when they can: Show two events on different machines whose order no clock can decide; Use the happens-before relation to order the events that can be ordered; Explain what a logical clock counts and what it does not measure.

https://lightmysky.com/learn/computing/clocks-ordering-and-happens-before-mt_ratia1eb_2

#### Failure Models and Replication (ages 20-21)

A distributed system has to say what kinds of failure it tolerates: a machine that stops, a message that never arrives, a machine that stops and comes back with old state. Replication is the usual answer, and it turns one copy's truth into a question about which copy to believe.

Ready when they can: Distinguish a crashed node from a slow one from the outside, and say why it is hard; Explain what a primary and its replicas each promise a client; Say what a replica that rejoins with stale state has to do before serving reads.

https://lightmysky.com/learn/computing/failure-models-and-replication-mt_aYK210-NIS

#### Consensus and Why Agreement Is Hard (ages 20-21)

Several machines have to agree on one value even though some may fail and messages may be delayed. A majority quorum plus a leader gets there in practice, and the theory says no protocol can guarantee both safety and progress when delays have no bound.

Ready when they can: Explain why a majority quorum makes two conflicting decisions impossible; Follow a leader election and say what happens if the old leader returns; State what the impossibility result rules out and what it leaves available.

https://lightmysky.com/learn/computing/consensus-and-why-agreement-is-hard-mt_cF-JiM_xRz

#### Consistency Models and the CAP Trade-off (ages 20-22)

A replicated store can behave as though there were one copy, or it can keep serving both sides of a network split and reconcile later. It cannot do both during a partition, and the choice belongs to the application rather than to the database.

Ready when they can: Say what a client can observe under strong consistency and under eventual consistency; Work out what each side of a partitioned system may do under each choice; Choose a consistency model for a stated application and defend the choice.

https://lightmysky.com/learn/computing/consistency-models-and-the-cap-trade-off-mt_j6qtpYPHsr

#### Symmetric Encryption and What a Cipher Promises (ages 20-21)

A symmetric cipher turns readable data into something unreadable using a shared key, and the promise is narrow: an eavesdropper learns nothing about the contents. It says nothing about who sent the message, whether it was altered, or how the key got to both ends.

Ready when they can: State exactly what a cipher protects and three things it does not; Explain why reusing a key stream across two messages leaks information; Say why the security has to rest on the key rather than on the method staying secret.

https://lightmysky.com/learn/computing/symmetric-encryption-and-what-a-cipher-promises-mt_egJQEiFWZA

#### Public-Key Cryptography and Key Exchange (ages 20-22)

A key pair splits the secret: one half can be published, and only the other half undoes what the first did. That solves the problem symmetric ciphers cannot, which is agreeing on a shared key with someone you have never met, over a line somebody is reading.

Ready when they can: Explain what each half of a key pair can do and what it cannot; Follow a key exchange and say what an eavesdropper has at the end of it; Say why public-key operations are used to set up a symmetric key rather than to carry the data.

https://lightmysky.com/learn/computing/public-key-cryptography-and-key-exchange-mt_AHCtrer4eh

#### Hashes, Signatures and Certificates (ages 21-22)

A cryptographic hash gives a short fingerprint that is impractical to forge a match for, which makes tampering detectable. Signing a hash with a private key proves who produced it, and a certificate is that signature applied to the claim that a key belongs to a name.

Ready when they can: Say what property of a hash makes it usable for detecting tampering; Explain what a signature proves and what it does not; Follow a certificate chain up to a root and say what trust is being placed where.

https://lightmysky.com/learn/computing/hashes-signatures-and-certificates-mt_qLHm767U87

#### TLS: Putting the Pieces Together (ages 21-22)

A secure connection is assembled from all of it: a certificate proves the server's key, a key exchange produces a fresh shared secret, and a symmetric cipher with an integrity check carries the traffic. Reading the handshake in order is how the pieces stop being separate ideas.

Ready when they can: Order the steps of a handshake and say what each one establishes; Say which step fails when a certificate does not match the name asked for; Explain what forward secrecy protects and against what later event.

https://lightmysky.com/learn/computing/tls-putting-the-pieces-together-mt_JzIwi-BYG0

#### Threat Modelling: Assets, Adversaries and Trust Boundaries (ages 21-22)

Security work starts by naming what is worth protecting, who might want it, and where data crosses from a place you control into one you do not. Without that, defences are chosen by habit, and the effort lands away from where the risk is.

Ready when they can: Draw a system's trust boundaries and mark every crossing; List assets and rank them by what their loss would cost; Match a defence to a named adversary rather than to a general worry.

https://lightmysky.com/learn/computing/threat-modelling-assets-adversaries-and-trust-boundaries-mt_VRXTkrNFvx

#### Authentication, Authorisation and Secure Defaults (ages 21-22)

Proving who someone is and deciding what they may do are two questions, and confusing them is a common source of holes. Storing credentials with a slow hash, giving each part the least access it needs, and failing closed are the defaults that hold up when something else goes wrong.

Ready when they can: Separate an authentication decision from an authorisation decision in a stated design; Say why passwords are stored with a deliberately slow hash and a per-user salt; Apply least privilege to a service and name what it no longer needs.

https://lightmysky.com/learn/computing/authentication-authorisation-and-secure-defaults-mt_ofIiD4Bbpk

#### Impossibility Under Asynchrony: What Consensus Cannot Promise (ages 22-23)

With no bound on message delay and one process allowed to fail, no algorithm is guaranteed both to agree and to finish. Real systems live with this by giving up guaranteed termination and leaning on timeouts, which are a failure detector under another name.

Ready when they can: State the two properties the impossibility result puts in conflict and the model it assumes; Say which property practical systems relax, and what a timeout is standing in for; Explain why a slow process and a failed process cannot be told apart in this model.

https://lightmysky.com/learn/computing/impossibility-under-asynchrony-what-consensus-cannot-promise-mt_le54TNOeiR

#### Raft: Leader Election and Log Replication (ages 22-23)

One consensus algorithm end to end. A term-numbered election picks a single leader, the leader appends entries to its followers, and an entry is committed once a majority holds it. Every rule in the protocol exists to stop one specific bad history.

Ready when they can: Walk an election through a term change and say why two leaders cannot both win one term; Say what commitment means here and why a majority is the threshold; Take one rule of the protocol and name the history it prevents.

https://lightmysky.com/learn/computing/raft-leader-election-and-log-replication-mt_JdHtEJSPSP

#### Quorums, Leases and Changing the Membership (ages 22-23)

A majority is one point on a curve: any read set and write set that intersect will do, and the choice moves cost between reads and writes. A lease buys a leader a bounded window of authority, and changing the member set safely needs a protocol of its own.

Ready when they can: Choose read and write quorum sizes for a stated read-heavy workload and justify them; Say what a lease assumes about clocks and what breaks when that assumption fails; Explain why adding and removing members in one step can split a cluster.

https://lightmysky.com/learn/computing/quorums-leases-and-changing-the-membership-mt_2uRmRqFutD

#### Linearizability and Checking a History (ages 22-23)

Linearizability says every operation appears to take effect at one instant between its call and its return, so a replicated store can be reasoned about as a single object. Whether a recorded history satisfies it is a decidable question, and the check is expensive.

Ready when they can: Decide whether a short recorded history is linearizable and give the ordering or the conflict; Say how linearizability differs from serializability and from a weaker consistency model; Explain why the client-observed history, not the server's internal order, is what gets checked.

https://lightmysky.com/learn/computing/linearizability-and-checking-a-history-mt_lTaHmlGtuo

#### Cryptographic Security Definitions and Proof by Reduction (ages 23-24)

A scheme is secure when a precisely stated game leaves every efficient adversary a negligible advantage. Security is then proved by reduction: an adversary that wins the game is turned into an algorithm for a problem assumed hard, so breaking the scheme would break the assumption.

Ready when they can: State a security game, name the adversary's powers, and say what advantage means in it; Sketch a reduction from an adversary against a scheme to an assumed-hard problem; Say what a proof of security does not promise about a deployed implementation.

https://lightmysky.com/learn/computing/cryptographic-security-definitions-and-proof-by-reduction-mt_qPCwxkqYY2

### Data & Databases

https://lightmysky.com/learn/computing/areas/data-and-databases

#### The Relational Model and Relational Algebra (ages 18-19)

A table is a set of tuples over named attributes, and queries are built from a handful of operations on those sets: select, project, join, union, difference. Every query language sits on top of this algebra, which is why the same question can be asked several ways and mean one thing.

Ready when they can: Write a query as a composition of relational algebra operations; Show two different algebra expressions that produce the same relation; Explain what it means that a relation is a set rather than a list.

https://lightmysky.com/learn/computing/the-relational-model-and-relational-algebra-mt_unDBd_Ug8T

#### Functional Dependencies and Boyce-Codd Normal Form (ages 18-19)

A functional dependency says one set of attributes fixes another. Computing the closure of a set of dependencies finds the candidate keys, and Boyce-Codd normal form is the condition that every dependency starts from one of those keys.

Ready when they can: List the functional dependencies of a table and compute the closure of an attribute set; Find all candidate keys from a set of dependencies; Decompose a table that violates Boyce-Codd form and check the join still recovers it.

https://lightmysky.com/learn/computing/functional-dependencies-and-boyce-codd-normal-form-mt_PfWLq1aEQz

#### SQL at Depth: Subqueries, Set Operations and Views (ages 18-20)

A query can use another query as a table, as a value, or as a test of existence, and set operations combine results that share a shape. A view names a query so the rest of the system can treat it as a table.

Ready when they can: Rewrite a correlated subquery as a join and say when the two differ; Use exists and not exists to express a question about absence; Define a view and explain what it does and does not store.

https://lightmysky.com/learn/computing/sql-at-depth-subqueries-set-operations-and-views-mt_SLKUlC-7or

#### Window Functions and Running Calculations (ages 19-20)

A window function computes over a set of neighbouring rows while keeping every row in the output, which grouping cannot do. Ranking, running totals and comparisons with the previous row all come from partitioning and ordering the window.

Ready when they can: Compute a running total per customer with a window rather than a self join; Rank rows within a partition and handle ties deliberately; Say what a window function keeps that a group by would have collapsed.

https://lightmysky.com/learn/computing/window-functions-and-running-calculations-mt_aaVxFPjWQv

#### Indexes: B-Trees and the Cost of a Lookup (ages 19-20)

An index is a second structure that makes some lookups cheap and every write more expensive. Most are B-trees, whose wide nodes suit a disk that reads a page at a time, and whose ordering also serves ranges and sorts.

Ready when they can: Say which of several queries an index on a given column would help; Explain why B-tree nodes are wide rather than binary; Name the costs an index adds to inserts, updates and storage.

https://lightmysky.com/learn/computing/indexes-b-trees-and-the-cost-of-a-lookup-mt_1Z5EQTqooI

#### Reading a Query Plan (ages 19-21)

The database chooses how to run a query: which index to use, which join method, in what order. The plan is that choice written down with estimated row counts, and reading it is how a slow query stops being a mystery.

Ready when they can: Read a plan and name the access method chosen for each table; Find the step where the estimated row count disagrees with reality; Explain why a nested loop join beats a hash join on small inputs.

https://lightmysky.com/learn/computing/reading-a-query-plan-mt_spbbzsCoBB

#### Transactions and the ACID Promise (ages 19-21)

A transaction groups statements so they take effect together or not at all, keep the database's rules true, do not see each other half-done, and survive a crash once committed. Those four promises are what let application code stay simple.

Ready when they can: State each of the four properties in terms of what a failure would otherwise leave behind; Identify a sequence of statements that has to be one transaction; Explain what rollback restores and what it cannot undo.

https://lightmysky.com/learn/computing/transactions-and-the-acid-promise-mt_8Egjmafq-L

#### Isolation Levels and the Anomalies They Allow (ages 20-21)

Full isolation is expensive, so databases offer weaker levels, each defined by which anomalies it permits: dirty reads, non-repeatable reads, phantoms. Choosing a level is choosing which wrong answers the application can tolerate.

Ready when they can: Produce an interleaving that shows a non-repeatable read; Match each named anomaly to the lowest level that forbids it; Choose an isolation level for a stated workload and justify it.

https://lightmysky.com/learn/computing/isolation-levels-and-the-anomalies-they-allow-mt_utxPNgxveB

#### Concurrency Control: Locks and Snapshots (ages 20-21)

Two-phase locking makes transactions wait for each other and can deadlock. Multi-version concurrency control gives each transaction a consistent snapshot instead, so readers never block writers, at the price of keeping old versions around.

Ready when they can: Explain what the two phases of two-phase locking are and why the order matters; Say what a transaction sees under snapshot isolation and when that view was taken; Describe a write conflict that a snapshot system has to detect at commit.

https://lightmysky.com/learn/computing/concurrency-control-locks-and-snapshots-mt_gOd17LRKel

#### Crash Recovery and Write-Ahead Logging (ages 20-22)

Durability is achieved by writing the intention to a log before touching the data pages. After a crash the system replays committed work and undoes the rest, which is how a commit can be trusted the moment it returns.

Ready when they can: Order the log write, the commit record and the page write, and say why; Walk through redo and undo for a log that ends mid-transaction; Explain what a checkpoint saves during recovery.

https://lightmysky.com/learn/computing/crash-recovery-and-write-ahead-logging-mt_JFPafSWOWF

#### Key-Value and Document Stores (ages 20-21)

Some workloads want a single key lookup and nothing else, and pay for the freedom by giving up joins and schema checks. A document store keeps whole nested objects together, which suits reading one thing at a time and makes any cross-cutting question harder.

Ready when they can: Model a small domain as documents and as normalised tables, and compare the queries; Say what duplication buys in a document design and what it costs on update; Name a workload that suits a key-value store and one that does not.

https://lightmysky.com/learn/computing/key-value-and-document-stores-mt_PfBDSgfeQX

#### Wide-Column and Graph Stores (ages 20-22)

A wide-column store arranges data by the queries it must serve, so the design starts from the access pattern rather than the entities. A graph store makes relationships first-class, which turns a chain of joins into a traversal.

Ready when they can: Design a wide-column table starting from the query it must answer; Express a friends-of-friends question as a traversal rather than repeated joins; Say which questions a graph store answers cheaply and which it does not.

https://lightmysky.com/learn/computing/wide-column-and-graph-stores-mt_4a4yDq83fy

#### Partitioning and Replication for Scale (ages 21-22)

Beyond one machine, data is split by key across nodes and copied for safety. The partition key decides which queries stay fast and which become scatter-and-gather, and the replication scheme decides what a read may return after a recent write.

Ready when they can: Choose a partition key for a stated query mix and say which queries it hurts; Explain what a hot partition is and how it arises from a skewed key; Compare synchronous and asynchronous replication on what a reader can see.

https://lightmysky.com/learn/computing/partitioning-and-replication-for-scale-mt_Xvzz5Hnuvu

#### Data Pipelines: Batch, Streaming and Doing It Twice (ages 21-22)

Data moves from where it is produced to where it is analysed through stages that extract, transform and load it. Any stage can be retried after a failure, so each one has to be safe to run twice, and late or out-of-order records have to be handled on purpose.

Ready when they can: Design a stage that gives the same result when it is run twice on the same input; Say what a batch job and a stream processor each do with a record that arrives late; Explain what a schema change upstream does to everything downstream.

https://lightmysky.com/learn/computing/data-pipelines-batch-streaming-and-doing-it-twice-mt_o0zBEPLbmF

#### The Data Science Workflow (ages 21-22)

Useful analysis runs in a loop: state the question, find and check the data, build something, look at what it says, then report it in a form someone can act on. Most of the work is in the first two stages, and skipping them is what produces confident nonsense.

Ready when they can: Turn a business question into one that the available data could answer; Say what could make a dataset unable to answer a question at all; Keep an analysis reproducible so a second person gets the same numbers.

https://lightmysky.com/learn/computing/the-data-science-workflow-mt_99QNfiyQ55

#### Cleaning Real Data: Missing, Duplicated and Wrong (ages 21-22)

Real datasets have blanks, repeats, impossible values and three spellings of the same city. Every repair is a decision that changes the result, so a cleaning step has to be written down and defended rather than done quietly.

Ready when they can: Decide between dropping, filling and flagging a column of missing values, with a reason; Find duplicates that are not exact copies and choose a matching rule; Say how a cleaning choice could change the conclusion of the analysis.

https://lightmysky.com/learn/computing/cleaning-real-data-missing-duplicated-and-wrong-mt_qIsLXA-7EC

#### Exploratory Analysis and an Honest Chart (ages 21-22)

Before modelling anything, look: distributions, outliers, relationships between pairs. Then the chart that reports it has to make the truth easy to read, which rules out a truncated axis, a misleading area, and a colour scale nobody can order.

Ready when they can: Choose the chart that suits a distribution, a comparison and a relationship; Redraw a chart with a truncated axis and say what changed in the reader's impression; Say what an outlier in an exploratory plot should prompt before it is removed.

https://lightmysky.com/learn/computing/exploratory-analysis-and-an-honest-chart-mt_Jpb78Z6Ytu

#### Distributed Transactions and the Blocking Case of Two-Phase Commit (ages 22-24)

A transaction spanning several stores needs one atomic decision. Two-phase commit gets it by making participants promise before the coordinator decides, and its known weakness is that a coordinator failure at the wrong moment leaves participants holding locks with nobody to ask.

Ready when they can: Walk both phases and say what a participant has promised once it votes yes; Identify the window where a coordinator failure blocks the participants; Say how running consensus on the commit decision removes the blocking case, and what it costs.

https://lightmysky.com/learn/computing/distributed-transactions-and-the-blocking-case-of-two-phase-commit-mt_MP_B_a_EwW

#### Conflict-Free Replicated Data Types (ages 22-24)

If every update is commutative and idempotent, replicas that receive the same set of updates in any order end in the same state, and no coordination is needed at write time. The cost is that the merge rule, not the application, decides what concurrent edits mean.

Ready when they can: Say what a merge function has to satisfy for replicas to converge; Design a counter or a set that converges, and state what its merge does with a concurrent add and remove; Name a case where automatic convergence produces a state no user intended.

https://lightmysky.com/learn/computing/conflict-free-replicated-data-types-mt_Bhf1nu-9jz

#### Log-Structured Storage and Compaction (ages 22-24)

Writing sequentially to a log and merging sorted runs in the background turns random writes into sequential ones. Reads then have to consult several runs, so the design trades read amplification and background work against write throughput.

Ready when they can: Trace a key through a memory table, a flushed run and a compaction; Say which of write, read and space amplification each compaction policy favours; Explain why a read may have to touch several runs, and what a membership filter saves.

https://lightmysky.com/learn/computing/log-structured-storage-and-compaction-mt_MDZ7MPNEhO

#### Stream Processing: Windows, Watermarks and Late Events (ages 23-24)

An unbounded stream has no end at which to compute an answer, so results are cut by windows over event time. A watermark is the system's claim that event time has passed a point, and every record arriving after it forces a choice between waiting longer and being wrong.

Ready when they can: Assign records to windows by event time and by processing time and show where the two differ; Say what a watermark asserts and what it costs to hold one back; Choose a policy for late records and defend it against the alternative.

https://lightmysky.com/learn/computing/stream-processing-windows-watermarks-and-late-events-mt_CfzXL_cL0D

### Software Engineering

https://lightmysky.com/learn/computing/areas/software-engineering

#### Version Control as a Graph of Commits (ages 18-19)

A repository is a graph: each commit is a snapshot that points at the one it came from, and a branch is a movable label on a node. Once the shape is clear, most version control commands stop being incantations and become moves on that graph.

Ready when they can: Draw the commit graph of a short history and mark where each branch label sits; Say what changes in the graph when a commit is made and when a branch is created; Explain what a detached head means in terms of the labels.

https://lightmysky.com/learn/computing/version-control-as-a-graph-of-commits-mt_oKsDRKirMy

#### Branching, Merging and Resolving a Conflict (ages 18-19)

Two branches that changed different lines merge on their own; two that changed the same lines cannot, and a person has to decide. A rebase rewrites the history into a straight line instead, which reads better and throws away what actually happened.

Ready when they can: Merge two branches and identify the common ancestor the merge used; Resolve a conflict by choosing what the combined code should mean, not by picking a side; Say when a rebase is a better choice than a merge, and when it is a worse one.

https://lightmysky.com/learn/computing/branching-merging-and-resolving-a-conflict-mt_l3vFbU7L3E

#### Code Review: Reading a Change You Did Not Write (ages 18-20)

Review reads a diff and asks whether it does what was intended, whether it breaks anything nearby, and whether the next person will understand it. The skill is separating the change that has to happen from the taste that does not.

Ready when they can: Review a small change and separate correctness comments from preference comments; Ask a question about a change instead of asserting what it should have been; Spot a change that is right in itself but breaks a caller elsewhere.

https://lightmysky.com/learn/computing/code-review-reading-a-change-you-did-not-write-mt_Hhe1Ou709s

#### Requirements: Turning a Wish into a Testable Statement (ages 19-20)

Someone asks for a system that is fast, or fair, or easy. A requirement rewrites that as something with a check attached, separating what the system must do from how well it must do it, and naming what is out of scope.

Ready when they can: Rewrite a vague request as a statement with an observable pass or fail; Separate functional requirements from qualities such as speed or availability; Write down one thing the system will not do, and why that helps.

https://lightmysky.com/learn/computing/requirements-turning-a-wish-into-a-testable-statement-mt_TFb-YNpvT1

#### Interfaces, Coupling and What a Module Promises (ages 19-20)

A module's interface is the set of promises other code may rely on, and everything else is free to change. Coupling measures how much of a neighbour's insides a caller depends on, and it is the quantity that decides how expensive the next change will be.

Ready when they can: State the promise of a module without describing how it is implemented; Find the place where one module reaches past another's interface; Predict which of two designs makes a stated future change cheaper.

https://lightmysky.com/learn/computing/interfaces-coupling-and-what-a-module-promises-mt_EUZyD26WFk

#### Design Patterns: Naming a Solution That Keeps Recurring (ages 19-21)

Some arrangements of objects appear again and again: swapping behaviour at runtime, telling listeners something happened, hiding the choice of which class to build. Naming them gives a team shared vocabulary, and the risk is reaching for a pattern where a plain function would do.

Ready when they can: Recognise the strategy arrangement in code that does not use the word; Apply the observer arrangement to decouple a producer from its listeners; Give an example where a pattern adds indirection without buying anything.

https://lightmysky.com/learn/computing/design-patterns-naming-a-solution-that-keeps-recurring-mt_bhUEk8PwBp

#### Refactoring: Changing Structure Without Changing Behaviour (ages 19-21)

Refactoring is a sequence of small edits that each keep the program doing the same thing while moving it toward a shape that is easier to change. The discipline is in the size of the step and in running the tests between steps.

Ready when they can: Extract a function from a long block without altering any observable behaviour; Rename and move a class in steps, keeping the code running throughout; Say what makes a change a refactoring rather than a rewrite.

https://lightmysky.com/learn/computing/refactoring-changing-structure-without-changing-behaviour-mt_HHZufOyTg4

#### Test Doubles and Testing at a Boundary (ages 20-21)

To test code that talks to a database, a clock or a network, the test replaces that neighbour with a stand-in it controls. The choice of where to put the seam decides whether the test survives a refactoring or breaks on every change.

Ready when they can: Replace a real dependency with a stand-in and test the logic around it; Distinguish a stub that returns canned answers from a mock that checks calls; Explain why a test that asserts on internal calls breaks during refactoring.

https://lightmysky.com/learn/computing/test-doubles-and-testing-at-a-boundary-mt_4ep3SiMYNM

#### Test Strategy: Unit, Integration and End to End (ages 20-21)

Tests trade speed against realism. Many small tests find faults fast and prove little about the assembled system; a few whole-system tests prove a lot and are slow and flaky. A strategy decides how many of each and what each level is responsible for.

Ready when they can: Assign a set of risks to the level of test that should catch each one; Explain why a suite of only end-to-end tests slows a team down; Say what an integration test proves that a unit test cannot.

https://lightmysky.com/learn/computing/test-strategy-unit-integration-and-end-to-end-mt_fdAvx1MMFE

#### Property-Based Testing (ages 20-22)

Instead of listing examples, state a property that should hold for every input and let the machine generate inputs trying to break it. Good properties are relations that must survive, such as encoding then decoding returning the original.

Ready when they can: Write a property that a sorting function must satisfy for any input list; Explain what shrinking does to a failing case and why it helps; Say which faults example tests catch that property tests usually miss.

https://lightmysky.com/learn/computing/property-based-testing-mt_QqCNKT06IY

#### Continuous Integration and the Build Pipeline (ages 20-22)

Every change is built and tested by a machine that does not have anyone's local setup, so a failure is the code's fault rather than a laptop's. The pipeline is the team's shared definition of ready, and its running time is a real constraint on how people work.

Ready when they can: Describe the stages a change passes through from push to merge; Explain why a build that passes locally and fails on the server is useful information; Say what a team loses when the pipeline takes an hour.

https://lightmysky.com/learn/computing/continuous-integration-and-the-build-pipeline-mt_z__G4nfjwh

#### Software Architecture: Layers, Services and Their Trade-offs (ages 21-22)

Architecture is the set of decisions that are expensive to reverse: what is split from what, what talks to what, and where state lives. Splitting a system into services buys independent deployment and pays for it in network calls, partial failure and versioning.

Ready when they can: Name the decisions in a design that would be costly to change later; List what a team gives up when one program becomes several services; Choose a split for a stated growth problem and defend the boundary.

https://lightmysky.com/learn/computing/software-architecture-layers-services-and-their-trade-offs-mt_uz_OkFgysJ

#### Technical Debt and the Cost of the Next Change (ages 21-22)

A shortcut taken today is borrowed time, and the interest is paid by everyone who touches that code afterwards. Some debt is worth taking deliberately; the failure is taking it without recording it or planning when it gets repaid.

Ready when they can: Identify a shortcut in a codebase and estimate what it costs per change; Argue for taking on a piece of debt deliberately, with the repayment named; Distinguish debt from code that is merely old and still fine.

https://lightmysky.com/learn/computing/technical-debt-and-the-cost-of-the-next-change-mt_iA8-0Qg4ID

#### Working in a Team: Issues, Estimates and Iterations (ages 21-22)

A team splits work into pieces small enough to finish, agrees what done means for each, and looks at what actually happened before planning the next stretch. Estimates are a planning tool rather than a promise, and treating them as promises is what makes teams stop giving honest ones.

Ready when they can: Split a feature into pieces that can each be finished and reviewed; Give an estimate with its uncertainty rather than a single number; Explain what a team learns from comparing plan to outcome.

https://lightmysky.com/learn/computing/working-in-a-team-issues-estimates-and-iterations-mt_HNNnVvADcF

#### Reading a Systems or Machine-Learning Paper (ages 22-23)

A paper is a claim, a method and evidence, in that order of importance. Reading the evaluation before the method shows what is actually being demonstrated, and the related work shows what the authors compared against and what they left out.

Ready when they can: State a paper's central claim in one sentence and name the evidence offered for it; Find the assumption the result rests on and say what changes if it fails; Name a baseline the paper should have compared against and did not.

https://lightmysky.com/learn/computing/reading-a-systems-or-machine-learning-paper-mt_4LsuT0TdxT

#### Specifying Correctness: Safety, Liveness and Invariants (ages 22-24)

Before anything can be proved, the claim has to be written down. A safety property says nothing bad ever happens and is refuted by a finite trace; a liveness property says something good eventually does and is not. An invariant is the safety property a proof actually uses.

Ready when they can: Classify stated properties as safety or liveness and say what a counterexample to each looks like; Write an invariant for a small algorithm and check that every step preserves it; Say why a specification that only forbids things can be satisfied by doing nothing.

https://lightmysky.com/learn/computing/specifying-correctness-safety-liveness-and-invariants-mt_4_KaoDSHZF

#### Model Checking and the State-Space Explosion (ages 23-24)

Given a finite model and a temporal property, a checker explores every reachable state or proves it need not. The states multiply with every component, so the whole craft is abstraction: shrink the model until the check finishes while the property still means what it did.

Ready when they can: Explain how a checker returns a counterexample trace and why that trace is the useful output; Say why the state count grows with components and name two ways to cut it; Say what an abstraction has to preserve for a passing check to say anything about the real system.

https://lightmysky.com/learn/computing/model-checking-and-the-state-space-explosion-mt__pgZ0PzEZo

#### Hoare Logic and Proving a Program Meets Its Specification (ages 23-24)

A triple states what holds before a fragment runs and what holds after. Rules compose triples along the structure of the program, loops need an invariant that a person supplies, and the leftover verification conditions are what a solver is handed.

Ready when they can: Prove a short straight-line fragment correct by composing triples; Supply a loop invariant and show it is preserved and strong enough at exit; Say why a tool computes the weakest precondition rather than the strongest postcondition.

https://lightmysky.com/learn/computing/hoare-logic-and-proving-a-program-meets-its-specification-mt_bJZnbBrUIP

#### Reproducibility: Seeds, Environments and the Ablation (ages 23-24)

A result that cannot be rerun is a claim, not a finding. Fixing seeds, pinning the environment and recording the exact command make a run repeatable, and an ablation is what shows which part of a method the gain came from.

Ready when they can: List what has to be recorded for a stranger to repeat a run; Design an ablation that isolates one component's contribution; Say why a single seed is not a result and what to report instead.

https://lightmysky.com/learn/computing/reproducibility-seeds-environments-and-the-ablation-mt_Rp__eJ-vjn

#### Scoping and Writing a Thesis-Scale Project (ages 23-24)

A year-long project fails on scope more often than on difficulty. A workable one has a question that can be answered either way, a result that stands even if the ambitious part does not land, and a written argument that survives a reader who was not there.

Ready when they can: Turn a broad interest into a question with a falsifiable answer and a stated scope; Name the smallest result worth writing up and what it depends on; Structure an argument so a reader finds the claim, the method and the evidence without being told where they are.

https://lightmysky.com/learn/computing/scoping-and-writing-a-thesis-scale-project-mt_Y46uRENRVf

#### Dependencies, Licences and the Supply Chain (ages 21-22)

Most of a shipped program was written by strangers. Pulling in a library brings its bugs, its updates and its licence terms, so a team has to know what it depends on, what those terms allow, and what happens when a dependency stops being maintained.

Ready when they can: Read a dependency tree and find a package nobody chose directly; Say what a copyleft licence asks of a project that links against it; Plan what a team does when a dependency is abandoned.

https://lightmysky.com/learn/computing/dependencies-licences-and-the-supply-chain-mt_2kilqPb0aV

## History

147 topics, ages 5 to 18. https://lightmysky.com/learn/history

### Historical Thinking

https://lightmysky.com/learn/history/areas/historical-thinking

#### Past Events and Change (ages 5-7)

Notice how everyday life has changed within living memory — homes, toys, schools, transport — and learn about famous events from long before anyone alive today, like the Great Fire of London or the first aeroplane flight

Ready when they can: Compare an everyday object from the past with its modern version (e.g., a grandparent's old phone versus a smartphone) and describe what changed; Retell a famous event from long ago (e.g., the Great Fire of London) and say it happened before their parents or grandparents were born; Sort pictures of objects or street scenes into 'then' and 'now' and explain their choices.

https://lightmysky.com/learn/history/past-events-and-change-mt_wy086IHQ0G

#### Significant Historical Figures (ages 5-7)

Learn the life stories of people from the past who changed the world — explorers, inventors, monarchs, campaigners — and compare figures from different times to see how life itself changed between their eras

Ready when they can: Retell the story of a significant person from the past (e.g., Rosa Parks or Neil Armstrong) and say what they did that mattered; Explain why a figure's achievement was hard or brave in their own time (e.g., nobody had ever flown to the Moon before); Compare two figures from different eras (e.g., a queen from Tudor times and one from Victorian times) and point out how life changed between them.

Needs first: Past Events and Change.

https://lightmysky.com/learn/history/significant-historical-figures-mt_f4W-c5trxf

#### Change and Continuity (ages 11-14)

Analyse a period for what changed and what stayed the same: classify developments as change, continuity, or both; judge how fast and how deep change ran; and notice that life can transform in one way while barely moving in another

Ready when they can: Identify, for one period, both things that changed and things that stayed the same (e.g., new machines in factories while most people's food barely changed); Describe a change as fast or slow, and as deep or surface-level, giving reasons; Explain how a single development can be change and continuity at once (e.g., new rulers keeping the old laws).

Needs first: Past Events and Change.

https://lightmysky.com/learn/history/change-and-continuity-mt_OusQE68QDs

#### Vocabulary: historical thinking (ages 6-10)

Know and use the vocabulary of historical thinking — source, evidence, primary source, secondary source, artefact, chronology, chronological order, BC/BCE, AD/CE, century, decade, era, period, timeline, excavation, archaeologist, interpretation, corroborate, bias, perspective — and apply these terms when discussing how we know about the past and how reliable our knowledge is

Ready when they can: Correctly use BC/BCE and AD/CE to place events in time and explain what the letters stand for; Distinguish between a primary source and a secondary source with an example of each; Use 'evidence', 'interpretation', and 'bias' correctly in a sentence about a historical source.

Needs first: Domain Vocabulary Across Subject Areas.

https://lightmysky.com/learn/history/vocabulary-historical-thinking-mt_VXcua6-txq

#### Evidence from the Past (ages 6-7)

Understand that everything we know about the past comes from evidence — objects, buildings, pictures, documents, and stories that have survived

Ready when they can: Wineburg historical thinking framework; Historical Thinking in the Elementary Years (ERIC).

Needs first: Thinking Before Starting, Vocabulary: historical thinking.

https://lightmysky.com/learn/history/evidence-from-the-past-mt_9REmUc8r4D

#### Asking Questions About the Past (ages 7-10)

Generate your own questions about the past — who changed things, why did people act as they did, what was life like, what stayed the same — and use those questions to steer what to find out next

Ready when they can: Ask finding-out questions when meeting a new historical topic (e.g., 'Why did the Vikings leave home?' rather than only 'What is a Viking?'); Turn curiosity about a person or event into a question that could actually be investigated; Suggest where an answer might be found (e.g., a book, a museum, or asking an older relative).

Needs first: Past Events and Change, Evidence from the Past.

https://lightmysky.com/learn/history/asking-questions-about-the-past-mt_6nTw-Ic6pC

#### Causes and Consequences in History (ages 7-10)

Work out why past events happened and what happened because of them: suggest possible reasons, notice that big events usually have more than one cause, and trace the consequences that followed

Ready when they can: Give a sensible reason why a historical event happened (e.g., 'The Great Fire spread because the houses were wooden and close together'); Name more than one cause for the same event when asked what led to it; Describe what changed as a result of an event (e.g., 'After the fire, London was rebuilt with brick').

Needs first: Asking Questions About the Past.

https://lightmysky.com/learn/history/causes-and-consequences-in-history-mt_Ev1gJOrEp1

#### Local History (ages 7-10)

Investigate the history of your own area: read old photographs, maps, street names, buildings, and memorials as clues; gather stories from older residents; and connect local changes to wider national events

Ready when they can: Spot historical clues in the local area (e.g., a street called 'Mill Lane', a war memorial, a datestone on a building); Compare an old photograph or map of their area with the same spot today and describe what changed; Ask an older relative or neighbour about the area's past and report back what they learned.

Needs first: Evidence from the Past, Asking Questions About the Past.

https://lightmysky.com/learn/history/local-history-mt_v1pzywJwvI

#### Different Accounts of the Same Event (ages 6-8)

Recognise that different people can give different accounts of the same event — and that both can be genuine while still disagreeing

Ready when they can: Wineburg corroboration heuristic; Initiating Historical Thinking in Elementary Schools.

Needs first: Evidence from the Past, Comparing Characters Across Stories, Vocabulary: historical thinking, Spotting Patterns.

https://lightmysky.com/learn/history/different-accounts-of-the-same-event-mt_2GDBmKCJxs

#### Questioning Historical Sources (ages 8-10)

Before trusting a historical source, ask: who made this, when, and why? — the answers shape how much weight the source should carry

Ready when they can: Wineburg sourcing heuristic; Teaching Historical Thinking Using Primary Sources (Library of Congress).

Needs first: Different Accounts of the Same Event, Reading between the lines, Inferring Characters' Feelings and Motives, Understanding Why.

https://lightmysky.com/learn/history/questioning-historical-sources-mt_TTzJTF-OkG

#### Checking Sources Against Each Other (ages 8-10)

Corroborate: check whether multiple sources agree on the same facts — and investigate why they might not

Ready when they can: Wineburg corroboration heuristic; Historical Thinking in the Elementary Years (ERIC).

Needs first: Different Accounts of the Same Event, Describing Rules & Patterns, Questioning Historical Sources, Vocabulary: historical thinking, Evidence-Based Writing.

https://lightmysky.com/learn/history/checking-sources-against-each-other-mt_wWlZoLQBR6

#### Understanding People in Their Own Time (ages 8-10)

Understand that people in the past saw the world very differently from us — judge their actions by the context they lived in, not only by today's values

Ready when they can: Historical Empathy: A Cognitive-Affective Theory (ERIC); Year 4-6 historical empathy research.

Needs first: Different Accounts of the Same Event, Connecting New & Old Ideas, Vocabulary: historical thinking.

https://lightmysky.com/learn/history/understanding-people-in-their-own-time-mt_IlyE-Sm8k5

#### Evidence Versus Interpretation (ages 10-11)

Distinguish between historical evidence and historical interpretation — evidence is what survived, interpretation is the argument a historian builds from it, and the same evidence can support different arguments

Ready when they can: Development of historical understanding among 9-14 year olds; Ways of Seeing: Evidence and Learning in the History Classroom (RRCHNM).

Needs first: Understanding People in Their Own Time, Analysing Your Own Errors, Questioning Historical Sources, Vocabulary: historical thinking, Checking Sources Against Each Other, Evidence-Based Writing.

https://lightmysky.com/learn/history/evidence-versus-interpretation-mt_Lu4H4mbsqO

#### Historical Significance (ages 11-14)

Understand that significance is a judgement, not a fact: analyse why some people and events are remembered — deep change, many lives affected, lasting consequences — and why the judgement can differ between viewpoints and eras

Ready when they can: Explain why a person or event counts as significant using criteria (how many lives it touched, how deep and lasting the change was); Compare how the same person is judged by different groups or eras (e.g., an explorer celebrated in one country and resented in another); Nominate someone or something overlooked as historically significant and argue the case.

Needs first: Significant Historical Figures, Evidence Versus Interpretation.

https://lightmysky.com/learn/history/historical-significance-mt_dy3l8XHcb1

#### Weighing Historical Causes (ages 11-14)

Analyse events with many causes and effects: sort causes into types (long-term and short-term, underlying and trigger), evaluate which mattered most, and defend that judgement with evidence

Ready when they can: Sort the causes of an event into long-term and short-term (e.g., tensions building for years versus the spark that set things off); Argue which cause of an event was the most important and back the claim with evidence; Explain how one event's consequences became causes of the next (e.g., a harsh peace settlement feeding a later conflict).

Needs first: Causes and Consequences in History, Evidence Versus Interpretation.

https://lightmysky.com/learn/history/weighing-historical-causes-mt_BjY92Ahl-S

#### Weighing a Source's Reliability (ages 14-16)

Judge how much weight a source can carry: who made it, when, for whom, and what they were in a position to know. Reliability is a question about one specific claim, not a label stuck on a whole document.

Ready when they can: State who made a source, when, and for which audience, and say how each of those changes its weight; Separate what a source is strong evidence for from what it is weak evidence for; Explain why a one-sided source can still be good evidence of what its author wanted believed; Say what would have to turn up for you to change your judgement about a source.

https://lightmysky.com/learn/history/weighing-a-sources-reliability-mt_24TQ9c30NI

#### Telling a Cause From a Coincidence (ages 15-16)

Two things moving together is not one causing the other. Test a causal claim about the past by checking the order of events, hunting for a third factor that could explain both, and asking what evidence would count against the claim.

Ready when they can: Give a case where two historical trends moved together without either causing the other; Check that a proposed cause actually came before the effect it is offered for; Name a third factor that could explain both of two linked changes; Say what evidence would count against a causal claim you have just made.

https://lightmysky.com/learn/history/telling-a-cause-from-a-coincidence-mt_SN1oFNj2gb

#### Why Historians Disagree (ages 15-16)

Accounts of the same past change with the questions asked, the sources available, and the time of writing. Read a historian's account as an argument: find the claim, find the evidence under it, and ask what it leaves out.

Ready when they can: Give two reasons two historians can read the same event differently; State a historian's claim in one sentence and name the evidence it rests on; Explain how a newly opened archive or a newly asked question can overturn an accepted account; Say why historians disagreeing is not the same as nobody knowing anything.

https://lightmysky.com/learn/history/why-historians-disagree-mt_qSzuXmTEJz

#### Reading a Source in the World That Made It (ages 16-18)

A document answers a question somebody was asking at the time, for an audience with its own expectations. Reading it well means reconstructing that question before judging the answer.

Ready when they can: For a given source, state who made it, for whom, and what they wanted from that audience; Identify one convention of the source's genre that would be misread as sincerity or as fact today; Say what the source's silences are, and whether each is evidence of absence or of censorship.

https://lightmysky.com/learn/history/reading-a-source-in-the-world-that-made-it-mt_S5EPefrFAi

#### How an Interpretation Changes (ages 16-18)

The same events get retold differently every generation, and the change usually says as much about the present as about new evidence. Tracking one topic across three eras of writing is how you see it happen.

Ready when they can: Take one event and summarise how accounts of it differed across three periods of writing; Separate changes driven by new evidence from changes driven by new questions; Say what a historian's own moment makes easy to see, and what it makes hard.

https://lightmysky.com/learn/history/how-an-interpretation-changes-mt_VnBjDyqCtd

#### Counting the Past (ages 16-18)

Censuses, price series, parish registers and shipping lists let you ask questions no diary can answer, such as how many and how much. They also carry the assumptions of the clerks who filled them in.

Ready when they can: Convert a historical wage or price into today's terms and state what the conversion assumes; Name two questions a serial record can answer that a single document cannot; Identify one systematic bias in a historical record, such as who was left off a census and why.

https://lightmysky.com/learn/history/counting-the-past-mt_U3Fc_UVWJ5

#### Contingency: What Almost Happened (ages 16-18)

Asking what would have followed if one thing had gone otherwise is a way of testing which causes were actually doing work. Done loosely it is a parlour game; done with constraints it is an argument.

Ready when they can: Take a decision point and state what changes if it goes the other way, holding everything else fixed; Distinguish a cause the outcome depended on from a background condition that was going to hold either way; Say why some outcomes look inevitable only because we know how they ended.

https://lightmysky.com/learn/history/contingency-what-almost-happened-mt_bTs2PTs8a-

#### Whose Past Is It: Museums, Statues and Public Memory (ages 16-18)

What a country puts in its museums and on its plinths is a claim about who it thinks it is. Arguments over removal, return and renaming are arguments about that claim, not usually about the facts.

Ready when they can: Explain the difference between what happened and what a society chooses to commemorate; Set out the strongest case for and against returning an object to where it was taken from; Say what a monument's original commissioners wanted it to do, and whether it still does that.

https://lightmysky.com/learn/history/whose-past-is-it-museums-statues-and-public-memory-mt_DFZgwFicqQ

### Ancient Egypt

https://lightmysky.com/learn/history/areas/ancient-egypt

#### Egypt, the Nile, and the Desert (ages 5-7)

Locate Egypt on a map of Africa and understand that it is a country in a very hot, dry desert, but the River Nile — the longest river in the world — flows through it, bringing water and rich soil that allowed people to grow food and build one of the earliest great civilisations

Ready when they can: Point to Egypt on a map and identify the River Nile running through it; Explain why the Nile was so important to the ancient Egyptians (water, food, transport); Describe how the desert and the river created two very different environments side by side.

https://lightmysky.com/learn/history/egypt-the-nile-and-the-desert-mt_8UL1opbJEt

#### Everyday Life in Ancient Egypt (ages 5-7)

Describe what everyday life was like for ordinary people in ancient Egypt: farmers grew wheat and barley near the Nile, families lived in mud-brick houses, children played games and had pets, and people ate bread, fish, fruit, and vegetables

Ready when they can: Describe at least two things ordinary Egyptian families did in their daily lives; Name foods that ancient Egyptians ate or crops they grew; Identify at least one similarity and one difference between life in ancient Egypt and life today.

Needs first: Egypt, the Nile, and the Desert.

https://lightmysky.com/learn/history/everyday-life-in-ancient-egypt-mt_P0HBNfp46z

#### Vocabulary: ancient egypt (ages 5-9)

Know and use the key vocabulary of ancient Egypt — pharaoh, pyramid, tomb, mummy/mummification, hieroglyphs, papyrus, sarcophagus, canopic jar, natron, archaeologist, artefact, Nile, delta, irrigation, shaduf, scribe, vizier, obelisk, sphinx, cartouche — and apply these terms accurately when describing Egyptian society, religion, and material culture

Ready when they can: Use 'pharaoh', 'pyramid', and 'hieroglyphs' correctly and naturally in a spoken or written account of ancient Egypt; Explain what mummification is and why the Egyptians did it, using 'sarcophagus', 'canopic jar', and 'natron'; Use 'archaeologist' and 'artefact' correctly when discussing how we know about ancient Egypt.

https://lightmysky.com/learn/history/vocabulary-ancient-egypt-mt_szw1Ln490b

#### Hieroglyphs and Papyrus (ages 5-7)

Know that the ancient Egyptians used a special writing system called hieroglyphs — pictures and symbols that stood for sounds and words — and that they wrote on a paper-like material called papyrus, which was made from a plant that grew along the Nile

Ready when they can: Describe hieroglyphs as a writing system that uses pictures and symbols; Explain that papyrus was a material like paper made from a river plant; Understand that only specially trained people called scribes could read and write hieroglyphs.

Needs first: Knowing all letters, Everyday Life in Ancient Egypt, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/hieroglyphs-and-papyrus-mt_iFkd0CTwlA

#### Pharaohs and Tutankhamun (ages 5-7)

Know that ancient Egypt was ruled by powerful kings and queens called pharaohs, who lived in grand palaces and made the laws — and that one of the most famous pharaohs is Tutankhamun, a boy who became pharaoh as a child and whose golden tomb was discovered thousands of years later

Ready when they can: Explain that a pharaoh was the ruler of ancient Egypt, like a king or queen; Name Tutankhamun as a famous pharaoh and describe at least one fact about him; Understand that pharaohs were very powerful and made important decisions for everyone in Egypt.

Needs first: Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/pharaohs-and-tutankhamun-mt_E7avIa-tcE

#### Egyptian Social Hierarchy (ages 7-9)

Describe the social structure of ancient Egypt as a pyramid-shaped hierarchy: the pharaoh at the top, then priests and nobles, followed by scribes and soldiers, then craftworkers and merchants, and farmers and labourers at the base — understanding that a person's position was usually inherited and determined their whole way of life

Ready when they can: Draw or describe the social pyramid with at least four levels correctly ordered; Explain that most people were farmers and had very different lives from the pharaoh; Give an example of how social position affected someone's daily life (e.g., only scribes could read).

Needs first: Pharaohs and Tutankhamun, Everyday Life in Ancient Egypt, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/egyptian-social-hierarchy-mt_bEvMBUv4eG

#### Scribes and the Rosetta Stone (ages 7-9)

Know that scribes were specially trained people who could read and write hieroglyphs, that the Rosetta Stone — a slab with the same text in three scripts — was the key to cracking the hieroglyphic code, and that Jean-François Champollion used it to decipher hieroglyphs in 1822 after centuries of mystery

Ready when they can: Explain the importance of scribes as the only people who could read and write; Describe the Rosetta Stone as having the same message in three different scripts; Name Champollion as the person who decoded hieroglyphs using the Rosetta Stone.

Needs first: Egyptian Social Hierarchy, Knowing all letters, Hieroglyphs and Papyrus.

https://lightmysky.com/learn/history/scribes-and-the-rosetta-stone-mt_V_kAitNbLN

#### Pyramids and the Great Sphinx (ages 5-7)

Know that the ancient Egyptians built enormous stone pyramids as tombs for the pharaohs, that the Great Pyramid at Giza was one of the Seven Wonders of the Ancient World and is still standing today, and that the Great Sphinx — a statue with a lion's body and a human head — guards the pyramids

Ready when they can: Explain that pyramids were built as tombs to protect the pharaoh's body for the afterlife; Describe the Great Pyramid as very large, very old, and still standing at Giza; Describe the Sphinx as a stone statue with a lion's body and a human head.

Needs first: Pharaohs and Tutankhamun, 3-D shapes, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/pyramids-and-the-great-sphinx-mt_mmudyxf7bT

#### Egyptian Gods and the Afterlife (ages 5-7)

Understand that the ancient Egyptians believed in many gods and goddesses and believed that life continued after death in a wonderful afterlife — which is why they took great care to prepare bodies and fill tombs with food, jewellery, and precious objects for the dead person to use

Ready when they can: Explain that ancient Egyptians worshipped many different gods and goddesses; Describe the basic belief that Egyptians thought life continued after death; Give a reason why tombs were filled with treasures and everyday objects.

Needs first: Pyramids and the Great Sphinx, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/egyptian-gods-and-the-afterlife-mt_bvxkT1nepy

#### Egyptian Gods and Goddesses (ages 7-9)

Name and describe key Egyptian gods and goddesses: Ra the sun god who sailed across the sky each day, Osiris the ruler of the afterlife, Isis the goddess of magic and motherhood, Anubis the jackal-headed god of mummification, Horus the falcon-headed sky god, Thoth the ibis-headed god of writing, and Bastet the cat goddess of protection

Ready when they can: Name at least four Egyptian gods/goddesses and describe their roles; Explain why many gods were shown with animal heads and what the animals represented; Understand that Egyptians built temples as homes for the gods and performed daily rituals there.

Needs first: Egyptian Gods and the Afterlife.

https://lightmysky.com/learn/history/egyptian-gods-and-goddesses-mt_B1ATUEVNPz

#### The Pharaoh as Living God (ages 9-11)

Understand that the pharaoh was not just a ruler but was believed to be a living god — the intermediary between the gods and the people — and that the concept of Ma'at (truth, justice, and cosmic order) guided Egyptian law and government, with viziers and officials administering the kingdom on the pharaoh's behalf

Ready when they can: Explain the pharaoh's dual role as both political ruler and divine figure; Describe Ma'at as the principle of truth, justice, and order that governed Egyptian society; Identify the role of viziers and officials in running the government day to day.

Needs first: Egyptian Gods and Goddesses, Egyptian Social Hierarchy.

https://lightmysky.com/learn/history/the-pharaoh-as-living-god-mt_PCX1jZZnf9

#### Egyptian Timelines and Maps (ages 9-10)

Read and construct historical timelines — place Ancient Egyptian periods, pharaohs, and key events on a timeline relative to each other and to the present day; interpret maps showing the Nile delta, trade routes, and the location of key sites

Ready when they can: Place the Old, Middle, and New Kingdoms on a timeline and calculate the number of years between them; Read a map of ancient Egypt and identify the Nile, Memphis, Thebes, and the Valley of the Kings; Compare the age of Ancient Egypt on a timeline against other civilisations studied (e.g. Ancient Greece, Roman Britain).

Needs first: Telling time to the minute (age 9+), First Quadrant Coordinates.

https://lightmysky.com/learn/history/egyptian-timelines-and-maps-mt_C3eNLQJlgt

#### Ancient Egypt on the Timeline (ages 7-9)

Place ancient Egypt on a timeline spanning over 3,000 years — from around 3100 BCE (unification under the first pharaoh) to 30 BCE (Roman conquest) — understanding that this civilisation lasted longer than the time between the Romans and today, and was divided into major periods: the Old Kingdom (pyramid age), Middle Kingdom, and New Kingdom (empire age)

Ready when they can: Place ancient Egypt on a timeline showing it lasted over 3,000 years; Name the three main periods (Old, Middle, New Kingdom) and associate one fact with each; Compare the length of ancient Egyptian civilisation with another time period the child knows.

Needs first: Days, Weeks, Months & Years, Egyptian Timelines and Maps, Pharaohs and Tutankhamun.

https://lightmysky.com/learn/history/ancient-egypt-on-the-timeline-mt_pTz6u49fQt

#### Building the Pyramids (ages 7-9)

Understand how the pyramids were built: thousands of workers moved enormous stone blocks using ramps, rollers, and sledges, the work was organised by the pharaoh's officials, and the design evolved from flat-topped mastabas to step pyramids (like Djoser's) to the smooth-sided Great Pyramid — and know that later pharaohs were buried in hidden rock-cut tombs in the Valley of the Kings

Ready when they can: Describe at least two methods used to move and raise heavy stone blocks; Explain that pyramid design changed over time from simple tombs to the Great Pyramid; Explain why later pharaohs chose hidden tombs in the Valley of the Kings instead of pyramids.

Needs first: Calculating with measurements, Pyramids and the Great Sphinx, Ancient Egypt on the Timeline.

https://lightmysky.com/learn/history/building-the-pyramids-mt_kgTN6yk4oE

#### Egyptian Maths and Engineering (ages 11-13)

Describe the Egyptian achievement in mathematics and engineering: the Rhind Mathematical Papyrus shows calculations of area, volume, and fractions; the precision of pyramid alignment (within 0.05° of true north) required sophisticated surveying; and Egyptian medical papyri describe detailed anatomical knowledge and pharmacological remedies — placing Egypt as a major contributor to the early history of science and technology

Ready when they can: Describes the Rhind Mathematical Papyrus as containing worked examples of arithmetic, geometry, and unit fractions; Explains one specific engineering achievement: pyramid alignment, ramp logistics, or the accuracy of the Great Pyramid's dimensions; Names at least one medical papyrus (e.g. Ebers Papyrus) and describes the type of medical knowledge it contains.

Needs first: Unit fractions, Building the Pyramids.

https://lightmysky.com/learn/history/egyptian-maths-and-engineering-mt_PPNDO7BUrY

#### Historical Sources on Ancient Egypt (ages 11-13)

Explain how knowledge of ancient Egypt is built from multiple source types — inscriptions, papyri, artefacts, and physical remains — and critically evaluate each: what biases, gaps, and distortions exist? Explore how Champollion’s decipherment of hieroglyphs transformed the field, and why the same artefact can be interpreted differently by different scholars

Ready when they can: Identifies at least four types of historical source (inscriptions, papyri, tomb art, physical artefacts) and explains what each type can and cannot tell us; Explains that hieroglyphic sources were created by the literate elite and therefore tend to record official versions of events, not ordinary people's experiences; Describes at least one example where the same artefact or text has been interpreted in significantly different ways by scholars, and explains why this happens.

Needs first: Evidence Versus Interpretation, Inferring Characters' Feelings and Motives, Scribes and the Rosetta Stone, Checking Sources Against Each Other.

https://lightmysky.com/learn/history/historical-sources-on-ancient-egypt-mt_bhEuF-CCuY

#### Who Really Built the Pyramids (ages 12-14)

Analyse who built the pyramids and why, evaluating the evidence against the alien-builder myth and the slave-labour myth: archaeological evidence from worker villages at Giza shows a paid, skilled, well-fed workforce; discuss the social functions of monument building as a form of state organisation, religious duty, and employment; and assess the current controversy over newly discovered construction ramps and logistics

Ready when they can: Cites at least three pieces of archaeological evidence from Giza that point to an organised, skilled, fed workforce rather than slaves or aliens (e.g. worker villages, bakery remains, graffiti tags, medical care); Explains why the alien hypothesis fails to meet the standards of historical evidence and what the burden of proof in history requires; Evaluates at least two proposed explanations for ramp logistics and describes which is currently supported by the most evidence.

Needs first: Building the Pyramids, Evidence Versus Interpretation, Persuasive Writing, Checking Sources Against Each Other, Egyptian Maths and Engineering.

https://lightmysky.com/learn/history/who-really-built-the-pyramids-mt_xAG0aMeAIN

#### Discovering Tutankhamun's Tomb (ages 5-7)

Understand that we know about ancient Egypt because archaeologists have dug up and studied objects buried in the sand for thousands of years — and that one of the most exciting discoveries ever was when Howard Carter found the hidden tomb of Tutankhamun in 1922, filled with golden treasures

Ready when they can: Explain that archaeologists find and study old objects to learn about people who lived long ago; Retell the story of Howard Carter discovering Tutankhamun's tomb; Understand that discoveries like this help us learn about how ancient Egyptians lived and what they believed.

Needs first: Fossils & Palaeontologists, Egyptian Gods and the Afterlife, Pyramids and the Great Sphinx, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/discovering-tutankhamuns-tomb-mt_IR8kIjZn_V

#### Egyptian Tomb Paintings and Artefacts (ages 7-9)

Use tomb paintings, artefacts, and objects from ancient Egypt as evidence to find out about daily life: Nebamun's tomb paintings show hunting and feasting, jewellery and furniture reveal craftsmanship, and everyday objects like pots and tools tell us what ordinary people used — understanding that these sources are how we piece together information about a civilisation that ended thousands of years ago

Ready when they can: Describe what can be learned about Egyptian life by studying a tomb painting or artefact; Explain that objects found in tombs and ruins are evidence that helps archaeologists understand the past; Give an example of something specific a painting or object reveals (e.g., what food they ate, what games they played).

Needs first: Egyptian Gods and Goddesses, Discovering Tutankhamun's Tomb, Non-Fiction Text Features.

https://lightmysky.com/learn/history/egyptian-tomb-paintings-and-artefacts-mt_yNGrY9xJ8Y

#### Egyptian Art and Architecture (ages 9-11)

Analyse Egyptian art and architecture: understand that Egyptian paintings followed strict conventions (people shown from the side with eyes from the front, size indicating importance), that tomb and temple design evolved from mastabas to step pyramids to smooth pyramids to rock-cut temples like Abu Simbel, and that obelisks, colossal statues, and temples like Karnak demonstrated the pharaoh's power and devotion to the gods

Ready when they can: Identify at least two conventions used in Egyptian painting and explain their purpose; Describe how monument design changed over the course of Egyptian history; Explain why pharaohs built such enormous structures (power, religion, afterlife).

Needs first: Building the Pyramids, Egyptian Tomb Paintings and Artefacts.

https://lightmysky.com/learn/history/egyptian-art-and-architecture-mt__qlBYNP62H

#### Upper and Lower Egypt (ages 7-9)

Understand that ancient Egypt was divided into Upper Egypt (the narrow river valley in the south) and Lower Egypt (the wide delta in the north), that the two lands were united under one pharaoh, and that Egyptians managed the Nile's water through irrigation canals and shadufs to grow crops year-round

Ready when they can: Identify Upper and Lower Egypt on a map and explain why they had different landscapes; Describe how irrigation tools like shadufs and canals helped farmers water their fields; Explain that uniting the two lands was an important achievement of the early pharaohs.

Needs first: Egypt, the Nile, and the Desert, Habitats & Basic Needs, Everyday Life in Ancient Egypt, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/upper-and-lower-egypt-mt_lSFwVU7V9g

#### Egyptian Trade and Economy (ages 9-11)

Understand that ancient Egypt had a thriving economy based on farming surplus, trade, and specialised labour: the Nile's fertile soil produced enough food to support craftworkers, priests, and officials, and Egypt traded along the Nile and across the Mediterranean — exchanging gold, papyrus, and grain for cedarwood from Lebanon, lapis lazuli from Afghanistan, and incense from Punt

Ready when they can: Explain how agricultural surplus along the Nile allowed people to specialise in non-farming jobs; Name at least two goods Egypt exported and two it imported, and where they came from; Describe how the barter system worked and why trade routes were important to Egypt's wealth.

Needs first: Egyptian Social Hierarchy, Upper and Lower Egypt, Scribes and the Rosetta Stone.

https://lightmysky.com/learn/history/egyptian-trade-and-economy-mt_5OxKnrGEMP

#### Cleopatra and the End of Egypt (ages 9-11)

Know that ancient Egypt eventually came to an end: the last pharaoh was Cleopatra VII, who allied with Rome but was defeated by Octavian (later Augustus) in 31 BCE, after which Egypt became a province of the Roman Empire — ending over 3,000 years of pharaonic rule and beginning a new chapter in Egypt's history

Ready when they can: Name Cleopatra VII as the last pharaoh of ancient Egypt; Explain that Egypt was conquered by Rome and became part of the Roman Empire; Understand that the end of pharaonic rule did not mean the end of Egyptian culture.

Needs first: Egyptian Trade and Economy, The Pharaoh as Living God, Ancient Egypt on the Timeline, Roman Republic and Empire.

https://lightmysky.com/learn/history/cleopatra-and-the-end-of-egypt-mt_HZyUwycFvf

#### Ancient Egypt's Lasting Legacy (ages 9-11)

Evaluate ancient Egypt's lasting legacy: the Egyptians developed early forms of medicine, mathematics (used to build pyramids and survey land after floods), astronomy (calendar based on star observations), and engineering that influenced later civilisations including Greece and Rome — and compare ancient Egypt with other early civilisations (Mesopotamia, Indus Valley, Shang Dynasty) to identify shared features like writing, agriculture, cities, and organised religion

Ready when they can: Name at least two Egyptian achievements that influenced later civilisations; Identify at least two features that ancient Egypt shared with other early civilisations; Explain why studying ancient Egypt helps us understand how human civilisation developed.

Needs first: Egyptian Trade and Economy, Cleopatra and the End of Egypt, The Pharaoh as Living God, Egyptian Art and Architecture.

https://lightmysky.com/learn/history/ancient-egypts-lasting-legacy-mt_JdAnBKIDnw

#### Egypt and Its Neighbours (ages 12-13)

Examine Egypt's relationships with neighbouring civilisations: trade networks reaching Nubia, the Levant, and Punt; the Hyksos invasion and the introduction of the chariot; and the New Kingdom empire and its conflict with the Hittites, culminating in the Battle of Kadesh and the world's earliest surviving peace treaty — understanding Egypt not as isolated but as part of a connected ancient world

Ready when they can: Describes the trade relationship with Nubia and Punt, naming at least two goods exchanged in each direction; Explains how the Hyksos invasion introduced new military technologies to Egypt, including the horse-drawn war chariot; Describes the Battle of Kadesh (Ramesses II vs. the Hittites) and the resulting Egypto-Hittite peace treaty as a landmark in diplomatic history.

Needs first: Egyptian Trade and Economy.

https://lightmysky.com/learn/history/egypt-and-its-neighbours-mt_NnlnxCx1DO

#### Fall of Ancient Egyptian Civilisation (ages 13-14)

Trace the end of ancient Egyptian civilisation through its successive conquests — Assyrian, Persian, Macedonian (Alexander the Great), and finally Roman — and explain how each conqueror was simultaneously shaped by Egyptian culture; examine Cleopatra VII as the last pharaoh and as a multilingual political strategist; and consider what survives of ancient Egypt in modern culture, religion, and language

Ready when they can: Names the main conquerors of Egypt in chronological order (Assyrians, Persians, Macedonians under Alexander, Romans) and gives approximate dates; Describes Cleopatra VII accurately: not as a romantic icon but as a politically sophisticated ruler who spoke multiple languages and tried to preserve Egyptian independence; Identifies at least two enduring legacies of ancient Egypt in the modern world (e.g. the Coptic language as a descendant of ancient Egyptian, obelisks in Rome and Paris, Egyptian motifs in Western art and architecture).

Needs first: Egypt and Its Neighbours, The Pharaoh as Living God.

https://lightmysky.com/learn/history/fall-of-ancient-egyptian-civilisation-mt_5qNMVZi3dQ

#### Mummification Step by Step (ages 7-9)

Describe the step-by-step process of mummification: the body was washed, internal organs were removed and placed in canopic jars, the body was dried with natron salt for 40 days, then wrapped in linen bandages with amulets tucked between the layers, and finally placed in a decorated coffin (sarcophagus)

Ready when they can: List the main steps of mummification in the correct order; Explain the purpose of canopic jars and what was stored in them; Describe why mummification was performed (to preserve the body for the afterlife).

Needs first: Egyptian Gods and Goddesses, Egyptian Gods and the Afterlife, Skeletons & Muscles, Vocabulary: ancient egypt.

https://lightmysky.com/learn/history/mummification-step-by-step-mt_cJ8CeyRKKs

#### Judgement of the Dead (ages 9-11)

Describe the Egyptian belief in the judgement of the dead: after death, the heart was weighed against the feather of Ma'at in the Hall of Judgement, with Anubis overseeing the scales and Thoth recording the result — a pure heart meant entry to the Field of Reeds (paradise), while a heavy heart was devoured by the monster Ammit, and know that the Book of the Dead contained spells to help the deceased pass this test

Ready when they can: Describe the weighing of the heart ceremony and name the gods involved; Explain the role of the Book of the Dead as a guide through the underworld; Connect the concept of the ka (life force) and ba (personality) to why Egyptians preserved the body.

Needs first: Egyptian Gods and Goddesses, Mummification Step by Step, The Pharaoh as Living God.

https://lightmysky.com/learn/history/judgement-of-the-dead-mt_8qQ2IosZZw

#### Modern Archaeology and Egyptian Ethics (ages 10-12)

Understand that modern Egyptologists use advanced technologies — CT scanning of mummies, satellite imagery to find buried structures, DNA analysis — alongside traditional excavation, and think critically about the ethics of archaeology: whether mummies should be displayed in museums, who owns ancient artefacts, and how colonial-era collecting affects how we study and present ancient Egypt today

Ready when they can: Name at least two modern technologies used in Egyptology and explain what they reveal; Discuss at least one ethical question about how ancient Egyptian artefacts are treated today; Understand that how we study ancient Egypt reflects our own values and biases, not just facts about the past.

Needs first: Changing Scientific Knowledge, Discovering Tutankhamun's Tomb, Building the Pyramids, Evidence Versus Interpretation, Persuasive Writing, Questioning Historical Sources, Egyptian Tomb Paintings and Artefacts, Judgement of the Dead.

https://lightmysky.com/learn/history/modern-archaeology-and-egyptian-ethics-mt_B1LdSGMP66

### Ancient Greece & Rome

https://lightmysky.com/learn/history/areas/ancient-greece-and-rome

#### Ancient Greece and Rome on the Map (ages 5-7)

Locate Greece and Italy on a map and know they are countries around the Mediterranean Sea where two great ancient civilisations — Ancient Greece and Ancient Rome — grew up thousands of years ago, long after the ancient Egyptians but long before our time

Ready when they can: Point to Greece and Italy on a world map or globe; Say that Ancient Greece and Ancient Rome were around the Mediterranean Sea; Place Greece and Rome on a simple timeline after Ancient Egypt and before today.

Needs first: Egypt, the Nile, and the Desert.

https://lightmysky.com/learn/history/ancient-greece-and-rome-on-the-map-mt_mMMXD4v9Sh

#### Ancient life vs today (ages 5-7)

Compare how children in ancient Greece or Rome lived with how children live today — including differences in school (writing on wax tablets, learning to fight in Sparta), food (olives, bread, grapes), games, and clothing (tunics and sandals) — and understand these civilisations existed thousands of years ago

Ready when they can: Name two ways a child's life in ancient Greece or Rome was different from today; Describe what ancient Greek or Roman children might have eaten or worn; Say that these civilisations existed thousands of years ago — long before grandparents were born.

Needs first: Ancient Greece and Rome on the Map, Everyday Life in Ancient Egypt.

https://lightmysky.com/learn/history/ancient-life-vs-today-mt_19qy2uuaKp

#### Romulus & Remus (ages 5-7)

Know the Roman founding myth of Romulus and Remus — twin brothers abandoned as babies, raised by a she-wolf, who grew up to found the city of Rome — and understand that this is a legend the Romans told about how their city began

Ready when they can: Retell the story of Romulus and Remus being raised by a wolf; Say that Romulus founded the city of Rome; Explain that this is a legend — a story people told, not necessarily true.

Needs first: Ancient Greece and Rome on the Map.

https://lightmysky.com/learn/history/romulus-and-remus-mt_zh_RyesCgZ

#### Roman soldiers & builders (ages 5-7)

Know that Roman soldiers marched across a huge empire building straight roads and strong walls, and that some Roman roads, walls, and buildings can still be seen today — showing that the Romans were powerful builders whose work has lasted thousands of years

Ready when they can: Describe Roman soldiers as part of a powerful army that marched across an empire; Name something the Romans built that we can still see today such as roads or walls; Explain that Roman buildings and roads lasted because the Romans were skilled builders.

Needs first: Ancient Greece and Rome on the Map, Romulus & Remus.

https://lightmysky.com/learn/history/roman-soldiers-and-builders-mt_VjxyJLtIbT

#### Roman Army and Conquest of Britain (ages 7-9)

Describe how the Roman army was organised into legions of highly trained soldiers, how Julius Caesar first raided Britain in 55 BC and Emperor Claudius later conquered it in AD 43, and explain why the Romans wanted to expand their empire — for land, resources, taxes, and glory

Ready when they can: Describe a Roman legion as a large unit of highly trained, disciplined soldiers; Explain that Julius Caesar raided Britain first and Claudius conquered it later; Give at least one reason why the Romans invaded Britain.

Needs first: Roman soldiers & builders.

https://lightmysky.com/learn/history/roman-army-and-conquest-of-britain-mt_MlD0gwLSw9

#### Boudicca's Revolt Against Rome (ages 7-9)

Tell the story of Boudicca, queen of the Iceni tribe, who led a fierce revolt against Roman rule in Britain — burning Colchester, London, and St Albans — before her army was defeated, and understand her significance as a symbol of resistance against a powerful empire

Ready when they can: Retell the story of Boudicca: who she was, why she revolted, what happened; Name at least one town Boudicca's army destroyed during the revolt; Explain why Boudicca is remembered as a symbol of resistance against the Romans.

Needs first: Roman Army and Conquest of Britain.

https://lightmysky.com/learn/history/boudiccas-revolt-against-rome-mt_e1Yr6rhRNW

#### Daily Life in a Roman Town (ages 7-9)

Describe daily life in a Roman town — the forum (marketplace and meeting place), public baths, amphitheatre, and villas — and explain that the Romans were brilliant engineers who built straight roads, aqueducts to carry water, underfloor heating (hypocaust), and Hadrian's Wall to mark the empire's northern frontier in Britain

Ready when they can: Describe at least three features of a Roman town such as forum, baths, or amphitheatre; Explain what an aqueduct was and why the Romans built them; Describe Hadrian's Wall and say why it was built.

Needs first: Roman Army and Conquest of Britain.

https://lightmysky.com/learn/history/daily-life-in-a-roman-town-mt_6nqVnVdexe

#### Greek gods & Mount Olympus (ages 5-7)

Know that the ancient Greeks believed in many gods and goddesses who lived on Mount Olympus — including Zeus (king of the gods, thunder), Athena (wisdom), Poseidon (the sea), Hermes (messages), and Aphrodite (love) — and that each god had special powers and a role in the world

Ready when they can: Name at least three Greek gods and say what each one was god of; Say that the Greek gods were believed to live on Mount Olympus; Explain that the ancient Greeks prayed to different gods for different things.

Needs first: Egyptian Gods and the Afterlife, Ancient Greece and Rome on the Map.

https://lightmysky.com/learn/history/greek-gods-and-mount-olympus-mt_H1pAi4F_Oh

#### Greek Myths and Heroes (ages 5-7)

Retell at least one Greek myth involving a hero and a monster — such as Theseus and the Minotaur in the labyrinth, Heracles (Hercules) and the lion, or Perseus and Medusa — and understand that these were stories ancient Greeks told to explain the world and teach lessons

Ready when they can: Retell a Greek myth naming the hero, the monster, and what happened; Explain that myths were stories the ancient Greeks told to make sense of the world; Describe what made a Greek hero brave or clever in the story.

Needs first: Greek gods & Mount Olympus.

https://lightmysky.com/learn/history/greek-myths-and-heroes-mt_PhIZNl2230

#### The first Olympics (ages 5-7)

Know that the Olympic Games began in ancient Greece at a place called Olympia as athletic competitions held in honour of Zeus, and that the modern Olympic Games we watch today were inspired by those ancient games

Ready when they can: Say that the Olympic Games started in ancient Greece at Olympia; Name at least one sport or event from the ancient Olympics such as running or wrestling; Explain that today's Olympic Games got the idea from the ancient Greek ones.

Needs first: Greek gods & Mount Olympus, Ancient Greece and Rome on the Map.

https://lightmysky.com/learn/history/the-first-olympics-mt_bKV2JYNwf7

#### Athens Versus Sparta (ages 7-9)

Compare Athens and Sparta as two very different Greek city-states: Athens focused on learning, arts, debate, and democracy, while Sparta focused on military training, discipline, and obedience — and understand that a city-state was a city that ruled itself like a small country

Ready when they can: Name at least two differences between life in Athens and life in Sparta; Explain what a city-state was and why Greek city-states were independent from each other; Describe what was valued most in Athens (learning, arts) versus Sparta (military strength).

Needs first: Ancient life vs today, Ancient Greece and Rome on the Map, The first Olympics.

https://lightmysky.com/learn/history/athens-versus-sparta-mt_CSGqz245rV

#### Athenian Democracy (ages 7-9)

Understand that Athens invented democracy — a system where free male citizens gathered in an Assembly to debate and vote on important decisions for the city — but that women, enslaved people, and foreigners were not allowed to vote

Ready when they can: Explain what democracy meant in Athens: citizens voted on decisions together; Identify who could vote in Athenian democracy (free men born in Athens) and who could not; Say that the idea of people voting on decisions started in Athens and still influences us today.

Needs first: Athens Versus Sparta.

https://lightmysky.com/learn/history/athenian-democracy-mt_8ad4U6msea

#### Gods & the Parthenon (ages 7-9)

Name the major Greek gods and their roles — Zeus (king, thunder), Hera (queen, marriage), Athena (wisdom, warfare), Poseidon (sea), Apollo (sun, music), Artemis (hunting, moon), Ares (war), Aphrodite (love), Hermes (messengers), Hephaestus (fire, crafts), Hades (underworld) — and know that the Parthenon in Athens was a grand temple built to honour Athena

Ready when they can: Name at least five Greek gods and say what each was responsible for; Describe the Parthenon as a temple to Athena built on the acropolis in Athens; Explain that Greeks built temples to honour their gods and held festivals and sacrifices.

Needs first: Greek gods & Mount Olympus.

https://lightmysky.com/learn/history/gods-and-the-parthenon-mt_W_CNRTBgYR

#### Greek Gods with Roman Names (ages 7-9)

Understand that the Romans adopted the Greek gods but gave them new names — Zeus became Jupiter, Hera became Juno, Ares became Mars, Athena became Minerva, Poseidon became Neptune, Aphrodite became Venus — and that this shows how deeply Rome was influenced by Greek culture

Ready when they can: Match at least four Greek gods to their Roman names; Explain that the Romans took Greek gods and gave them Latin names; Say that this borrowing shows Rome was strongly influenced by Greek culture.

Needs first: Roman Army and Conquest of Britain, Gods & the Parthenon.

https://lightmysky.com/learn/history/greek-gods-with-roman-names-mt_FDKd7I79JZ

#### Greek theatre (ages 7-9)

Know that the ancient Greeks invented theatre, performing tragedies and comedies in large open-air amphitheatres with actors wearing masks — and that plays were performed as part of religious festivals honouring the god Dionysus, with audiences of thousands

Ready when they can: Explain that the Greeks invented theatre with two types of plays: tragedies and comedies; Describe how Greek actors wore masks and performed in open-air amphitheatres; Say that plays were part of festivals honouring the god Dionysus.

Needs first: Athens Versus Sparta, Gods & the Parthenon.

https://lightmysky.com/learn/history/greek-theatre-mt_f4O__f3OU4

#### Marathon and Thermopylae (ages 7-9)

Describe the battles of Marathon and Thermopylae as moments when Greek city-states united against the invading Persian Empire — the runner Pheidippides bringing news of victory at Marathon (origin of the marathon race), and the heroic stand of 300 Spartans at Thermopylae — and understand these wars were fought to defend Greek independence

Ready when they can: Retell the story of the Battle of Marathon and the runner Pheidippides; Describe the Spartan stand at Thermopylae against a much larger Persian army; Explain that the Persian Wars were about Greek city-states defending their freedom.

Needs first: Athens Versus Sparta.

https://lightmysky.com/learn/history/marathon-and-thermopylae-mt_14F_x1Xwwp

#### Greek and Roman Architecture (ages 9-11)

Identify Greek column styles — Doric (plain and sturdy), Ionic (scroll-shaped capitals), and Corinthian (ornate leafy capitals) — and Roman architectural innovations — the arch, the dome, and concrete — and spot their influence in modern public buildings such as courthouses, museums, government buildings, and monuments

Ready when they can: Identify the three Greek column orders (Doric, Ionic, Corinthian) from pictures; Name Roman architectural innovations: the arch, the dome, and concrete; Point out Greek or Roman architectural features in a modern public building.

Needs first: Daily Life in a Roman Town, Gods & the Parthenon.

https://lightmysky.com/learn/history/greek-and-roman-architecture-mt_lzCcQzPJZi

#### Greek Philosophers and Medicine (ages 9-11)

Know that Greek thinkers called philosophers developed ways of understanding the world that still influence us today — Socrates asked challenging questions to test ideas (the Socratic method), Plato imagined the ideal society, Aristotle observed and classified the natural world — and that Hippocrates is called the father of medicine for insisting on natural causes of illness rather than blaming the gods

Ready when they can: Describe what Socrates, Plato, and Aristotle each contributed to thinking and learning; Explain the Socratic method as learning by asking questions rather than just being told answers; Say why Hippocrates is called the father of medicine.

Needs first: Athenian Democracy, Athens Versus Sparta.

https://lightmysky.com/learn/history/greek-philosophers-and-medicine-mt_cUMUYkDqZp

#### Alexander the Great's Empire (ages 9-11)

Describe how Alexander the Great of Macedon conquered a vast empire stretching from Greece to Egypt to India, spreading Greek language, culture, and ideas across the ancient world — creating a period known as the Hellenistic Age where Greek and Eastern cultures blended

Ready when they can: Describe the extent of Alexander's empire on a map (Greece to Egypt to India); Explain that Alexander spread Greek culture and language across the lands he conquered; Say what the Hellenistic Age was — a blending of Greek and Eastern cultures.

Needs first: Marathon and Thermopylae, Greek Philosophers and Medicine.

https://lightmysky.com/learn/history/alexander-the-greats-empire-mt_XMz_ohNjYO

#### Roman Republic and Empire (ages 9-11)

Explain how Rome was first governed as a republic — with elected consuls, a powerful Senate, and a distinction between patricians and plebeians — before becoming an empire ruled by emperors like Augustus (who brought peace, the Pax Romana) and Nero, and compare republican government with Athenian direct democracy

Ready when they can: Describe the Roman Republic's structure: consuls, Senate, patricians, and plebeians; Explain how Rome changed from a republic to an empire under Augustus; Compare Athenian direct democracy (citizens vote on decisions) with Roman republican government (citizens elect representatives).

Needs first: Daily Life in a Roman Town, Athenian Democracy.

https://lightmysky.com/learn/history/roman-republic-and-empire-mt_vFYFvgrPgD

#### Fall of the Western Roman Empire (ages 9-11)

Describe how the Western Roman Empire gradually declined due to a combination of factors — military pressure from invading peoples, political instability, economic problems, and an overstretched empire — and finally fell in AD 476, while the Eastern Roman (Byzantine) Empire continued for nearly a thousand more years

Ready when they can: Name at least two reasons why the Western Roman Empire declined and fell; State the date AD 476 as when the last Western Roman emperor was removed; Explain that the Eastern (Byzantine) Empire survived for nearly 1,000 years after the West fell.

Needs first: Roman Republic and Empire.

https://lightmysky.com/learn/history/fall-of-the-western-roman-empire-mt_H4bLNkDrGJ

#### Roman Law, Latin, and Christianity (ages 9-11)

Understand that Roman law became the basis for legal systems across Europe and beyond, that Latin is the root of French, Spanish, Italian, Portuguese, and Romanian and gave English hundreds of words (e.g. exit, video, annual, education), and that Christianity spread throughout the Roman Empire, eventually becoming its official religion under Emperor Constantine

Ready when they can: Give examples of English words that come from Latin; Explain that Roman law influenced modern legal systems in Europe and beyond; Describe how Christianity spread through the Roman Empire and became its official religion.

Needs first: Greek Gods with Roman Names, Roman Republic and Empire.

https://lightmysky.com/learn/history/roman-law-latin-and-christianity-mt_uzk7qs4KxE

#### Inclusion and Exclusion in Athens (ages 11-13)

Analyse who was included and excluded from Athenian democracy — only free adult male citizens (roughly 30% of adults) could participate, while women, enslaved people (who may have made up a third of the population), and foreign residents (metics) were excluded — and evaluate whether Athens truly deserves the title 'birthplace of democracy' by comparing it with modern representative democracies

Ready when they can: Calculate approximately what fraction of the Athenian population could participate in democracy; List the groups excluded from Athenian democracy and explain why each was excluded; Construct an argument for or against calling Athens a true democracy, using evidence.

Needs first: Athenian Democracy, Roman Republic and Empire.

https://lightmysky.com/learn/history/inclusion-and-exclusion-in-athens-mt_EHiM4_qg1R

#### Gladiators & Pompeii (ages 7-9)

Know that Romans watched gladiators fight in huge arenas like the Colosseum in Rome, that gladiators were usually enslaved people or prisoners trained to fight, and that the city of Pompeii was buried by the eruption of Mount Vesuvius in AD 79, preserving an extraordinary snapshot of Roman daily life

Ready when they can: Describe what gladiators were and where they fought; Explain that the Colosseum in Rome was a giant arena for public entertainment; Retell what happened to Pompeii and why it is important for understanding Roman life.

Needs first: Daily Life in a Roman Town, Roman Army and Conquest of Britain, What Is a Volcano.

https://lightmysky.com/learn/history/gladiators-and-pompeii-mt_VP9yZJ1xeP

#### Evidence for Greek and Roman Life (ages 9-11)

Understand that historians and archaeologists piece together ancient Greek and Roman life from evidence — pottery paintings, coins, inscriptions, ruins like Pompeii, and written texts by authors such as Homer and Pliny — and that the same evidence can be interpreted in different ways by different historians

Ready when they can: Name at least three types of evidence historians use to learn about ancient Greece and Rome; Explain why Pompeii is especially valuable as a source of evidence about Roman life; Give an example of how the same piece of evidence could be interpreted in more than one way.

Needs first: Evidence from the Past, Questioning Historical Sources, Gladiators & Pompeii, Gods & the Parthenon.

https://lightmysky.com/learn/history/evidence-for-greek-and-roman-life-mt_N1744276Zu

#### Hidden Voices of Greece and Rome (ages 11-13)

Examine the lives of people usually left out of the Greek and Roman story — enslaved people who made up roughly 30% of Athens and powered Rome's economy, women whose lives varied dramatically between Athens (largely confined to the home) and Sparta (physical training, property ownership), and conquered peoples across both empires — and evaluate whose voices are missing from the historical record and why

Ready when they can: Describe the daily life of an enslaved person in Athens or Rome using available evidence; Compare the lives of women in Athens and Sparta, explaining key differences; Explain why the historical record favours elite men and what this means for our understanding.

Needs first: Athens Versus Sparta, Understanding People in Their Own Time, Evidence for Greek and Roman Life, Roman Republic and Empire.

https://lightmysky.com/learn/history/hidden-voices-of-greece-and-rome-mt_c-F__Qe23X

#### Troy: Myth or History? (ages 11-13)

Explore how Heinrich Schliemann's excavation at Hisarlik in modern Turkey raised questions about whether the Trojan War described in Homer's Iliad was historical, partly historical, or entirely mythical — understanding that archaeology and literary sources can support or contradict each other, and that the line between myth and history in the ancient world is often blurred

Ready when they can: Describe Schliemann's excavation at Hisarlik and what he claimed to have found; Explain how archaeological evidence at Troy both supports and complicates Homer's story; Discuss why the boundary between myth and history is difficult to draw for the ancient world.

Needs first: Evidence for Greek and Roman Life, Greek Myths and Heroes.

https://lightmysky.com/learn/history/troy-myth-or-history-mt_aXNlkbAeIk

#### Fall of the Roman Republic (ages 12-14)

Trace how Roman political violence — the murder of the Gracchi brothers, civil wars between Marius and Sulla, Caesar's crossing of the Rubicon and assassination on the Ides of March, and the final war between Octavian and Antony — destroyed the Republic and led to one-man rule under Augustus, and debate whether the fall of the Republic was inevitable or a series of choices

Ready when they can: Describe at least three key events in the collapse of the Roman Republic in chronological order; Explain what 'crossing the Rubicon' meant and why it was a point of no return; Construct an argument about whether the Republic's fall was inevitable or could have been prevented.

Needs first: Evidence for Greek and Roman Life, Roman Republic and Empire.

https://lightmysky.com/learn/history/fall-of-the-roman-republic-mt__o3TCmfomv

#### Greek and Roman Legacy Today (ages 9-11)

Evaluate the lasting contributions of Greek and Roman civilisations to modern life — democracy, law, language (Latin roots), architecture (columns, arches, domes), sport (Olympics), philosophy, literature, and theatre — and understand that Greek ideas reached us through Rome, and then through later European civilisations, in a chain of cultural transmission

Ready when they can: List at least five ways ancient Greece and Rome still influence modern life; Explain how Greek culture spread to Rome and then from Rome across Europe; Give a specific modern example of a Greek or Roman legacy such as democratic voting or architectural columns.

Needs first: Greek Philosophers and Medicine, Ancient Egypt's Lasting Legacy, Greek and Roman Architecture, Roman Law, Latin, and Christianity, Alexander the Great's Empire, Greek theatre.

https://lightmysky.com/learn/history/greek-and-roman-legacy-today-mt_Nj32xtOhno

### Medieval Times

https://lightmysky.com/learn/history/areas/medieval-times

#### The Vikings (ages 5-7)

Who the Vikings were: seafaring warriors and traders from Scandinavia; longships; Viking raids on Britain; that Vikings also settled and farmed

Ready when they can: Describe who the Vikings were and where they came from; Explain what made longships special (fast, could sail in shallow water, dragon prows); State that Vikings were not just raiders but also farmers, traders, and settlers.

https://lightmysky.com/learn/history/the-vikings-mt_X5fdB4haHf

#### What Is a Castle? (ages 5-7)

What a castle is: a fortified building used as both a home and a defence; key parts including towers, moat, drawbridge, and thick walls; why castles were built

Ready when they can: Name at least four parts of a castle (tower, moat, drawbridge, walls, gatehouse); Explain that castles were both homes and defences; Describe why someone in medieval times would need a castle.

https://lightmysky.com/learn/history/what-is-a-castle-mt_oN7fI4d_kU

#### Knights & Armour (ages 5-7)

What knights were: trained warriors who served a lord; armour, shields, swords, and lances; the code of chivalry as rules for how knights should behave

Ready when they can: Describe what a knight wore and carried (armour, helmet, shield, sword, lance); Explain that knights trained from a young age and served a lord; Name one rule of the code of chivalry (be brave, be honest, protect the weak).

Needs first: What Is a Castle?.

https://lightmysky.com/learn/history/knights-and-armour-mt_M_xcaRcvSo

#### Kings & Queens (ages 5-7)

What medieval kings and queens did: ruling the land, making laws, collecting taxes; the crown and throne as symbols of power; the Tower of London

Ready when they can: Explain what a medieval king or queen did (ruled, made laws, led armies, collected taxes); Describe at least one symbol of royal power (crown, throne, sceptre); Name one famous medieval monarch or describe the Tower of London's role.

Needs first: Knights & Armour, What Is a Castle?.

https://lightmysky.com/learn/history/kings-and-queens-mt_2DBPJ38iWl

#### Robin Hood & King Arthur (ages 5-7)

The legends of Robin Hood (Sherwood Forest, stealing from the rich, Merry Men) and King Arthur (Round Table, Excalibur, Camelot); that these are stories, not proven history, but reflect medieval values

Ready when they can: Retell the basic story of Robin Hood or King Arthur; Name at least two characters from one of these legends; Explain that these are legends (stories) rather than proven facts.

Needs first: Kings & Queens, Knights & Armour.

https://lightmysky.com/learn/history/robin-hood-and-king-arthur-mt_0FYFiLTqx4

#### Village Life (ages 5-7)

Daily life for ordinary people in a medieval village: thatched houses, farming, baking bread, fetching water; how different life was from today

Ready when they can: Describe what a typical medieval village looked like (thatched cottages, fields, church); Name at least three daily tasks a medieval villager would do; Give two differences between life in a medieval village and life today.

Needs first: What Is a Castle?.

https://lightmysky.com/learn/history/village-life-mt_PThM5P7Umd

#### Medieval Clothing (ages 5-7)

What people wore in medieval times: peasant clothes (wool, linen) vs noble clothes (silk, fur, bright colours); no zippers or buttons; how clothes showed your place in society

Ready when they can: Describe what a medieval peasant would typically wear; Explain how noble clothing was different from peasant clothing; Give one way that what you wore showed your place in society.

Needs first: Village Life.

https://lightmysky.com/learn/history/medieval-clothing-mt_R1xLS1c2Pg

#### Medieval Food & Feasts (ages 5-7)

What people ate in medieval times: bread and pottage for ordinary people, grand feasts for the rich; no forks, eating with hands; the great hall as the centre of castle life

Ready when they can: Describe what ordinary people ate most days (bread, pottage, vegetables, ale); Explain how a feast in a great hall was different from everyday meals; Name one surprising table manner from medieval times (no forks, shared cups, food thrown on the floor).

Needs first: Village Life.

https://lightmysky.com/learn/history/medieval-food-and-feasts-mt_2NKzPeLzIm

#### Anglo-Saxon Britain (ages 7-9)

Who the Anglo-Saxons were: Germanic peoples who settled in Britain after the Romans left; their kingdoms, villages, place names, art, and eventual conversion to Christianity

Ready when they can: Explain who the Anglo-Saxons were and when they came to Britain (after the Romans left); Name at least two Anglo-Saxon kingdoms (e.g. Wessex, Mercia, Northumbria); Give an example of Anglo-Saxon influence still visible today (place names ending in -ton, -ham, -bury).

Needs first: Village Life, The Vikings.

https://lightmysky.com/learn/history/anglo-saxon-britain-mt_26OJ9MetR9

#### Vikings vs Anglo-Saxons (ages 7-9)

The conflict between Vikings and Anglo-Saxons for control of England: Viking raids, Alfred the Great's resistance, the Danelaw, Athelstan as first king of all England, Edward the Confessor

Ready when they can: Describe the Viking raids on Anglo-Saxon England and their impact; Explain who Alfred the Great was and why he was important; Describe what the Danelaw was (the area of England under Viking control).

Needs first: Anglo-Saxon Britain, The Vikings.

https://lightmysky.com/learn/history/vikings-vs-anglo-saxons-mt_6XnezHOcM3

#### Battle of Hastings and 1066 (ages 7-9)

The events of 1066: the death of Edward the Confessor, three claimants to the throne, the Battle of Hastings, William the Conqueror, and the Bayeux Tapestry as a historical source

Ready when they can: Explain why there was a crisis when Edward the Confessor died in 1066; Describe the Battle of Hastings and its outcome; Explain what the Bayeux Tapestry is and why it is important as a historical source.

Needs first: Kings & Queens, Vikings vs Anglo-Saxons, Evidence from the Past.

https://lightmysky.com/learn/history/battle-of-hastings-and-1066-mt_OiDHqtLoln

#### Castle Design Through the Ages (ages 7-9)

How castles were built and evolved: from wooden motte-and-bailey to stone keeps to concentric castles; rooms and their uses; how castle design responded to new attack methods

Ready when they can: Describe the difference between an early motte-and-bailey castle and a later stone castle; Name at least three rooms or areas in a medieval castle and their purpose; Explain one way castle design changed to resist new attack methods.

Needs first: Battle of Hastings and 1066, What Is a Castle?.

https://lightmysky.com/learn/history/castle-design-through-the-ages-mt_doVAdMqfJg

#### Medieval Pyramid of Power (ages 7-9)

How medieval society was organised: king at the top, then lords, then knights, then peasants/serfs; who owed what to whom; the pyramid of power and mutual obligations

Ready when they can: Draw or describe the feudal pyramid showing king, lords, knights, and peasants; Explain what each level owed to the level above (loyalty, military service, labour); Describe what a serf's life was like and why they couldn't easily leave.

Needs first: Kings & Queens, Knights & Armour, Battle of Hastings and 1066, Village Life, Medieval Clothing.

https://lightmysky.com/learn/history/medieval-pyramid-of-power-mt_bjlY5TE1y-

#### Siege Warfare (ages 7-9)

How castles were attacked and defended: siege weapons (trebuchets, battering rams, siege towers), boiling liquids, arrow slits, murder holes; the drama of a medieval siege

Ready when they can: Name at least three siege weapons or attack methods; Describe at least two ways a castle was designed to resist attack; Explain what a siege was and why it could last weeks or months.

Needs first: Castle Design Through the Ages, Knights & Armour.

https://lightmysky.com/learn/history/siege-warfare-mt_CqzsM0BDFP

#### The Black Death (ages 7-9)

The Black Death of 1348-49: what the plague was, how it spread, its devastating death toll; how it changed society by giving surviving workers more power and higher wages

Ready when they can: Describe what the Black Death was and at least two symptoms; Explain how the plague spread (fleas on rats, person to person); Describe one major way the Black Death changed society (fewer workers led to higher wages, peasants gained power).

Needs first: Medieval Pyramid of Power, Village Life.

https://lightmysky.com/learn/history/the-black-death-mt_8oAzr0WxRb

#### The Medieval Church (ages 7-9)

The enormous power of the medieval Church: monasteries and the daily life of monks and nuns; building great cathedrals; pilgrimage as a religious journey; the Church's influence over everyday life

Ready when they can: Explain why the Church was so powerful in medieval times (owned land, controlled education, people feared God's punishment); Describe what daily life was like for a monk or nun; Explain what a pilgrimage was and give one reason people went on them.

Needs first: Medieval Pyramid of Power, Village Life.

https://lightmysky.com/learn/history/the-medieval-church-mt_LuwHnQItF_

#### The Crusades (ages 7-9)

A simplified account of the Crusades: why Europeans travelled to the Holy Land, what they found there, the cultural exchange between Christian Europe and the Islamic world

Ready when they can: Explain in simple terms why European armies travelled to the Holy Land; Describe at least one thing Europeans learned from the Islamic world during the Crusades; Acknowledge that the Crusades involved violence and suffering on both sides.

Needs first: The Medieval Church, Knights & Armour.

https://lightmysky.com/learn/history/the-crusades-mt_Zy-CKUkq34

#### Crime & Punishment (ages 9-11)

How justice worked in medieval times: trial by ordeal, trial by combat, the role of the sheriff; punishments including stocks, pillory, and dungeons; how different it was from modern justice

Ready when they can: Describe at least two medieval methods of deciding guilt (trial by ordeal, trial by combat); Name at least two medieval punishments and explain what they involved; Compare one aspect of medieval justice to how justice works today.

Needs first: Medieval Pyramid of Power, The Medieval Church, Robin Hood & King Arthur.

https://lightmysky.com/learn/history/crime-and-punishment-mt_3tQXH9GwIa

#### Towns & Trade (ages 9-11)

The growth of medieval towns: markets, guilds, the merchant class; how towns won charters of self-governance; the shift from purely rural to partly urban life

Ready when they can: Describe how medieval towns were different from villages (markets, walls, guilds, more people); Explain what a guild was and why it mattered for tradespeople; Describe one way towns changed medieval society (new merchant class, more freedom for townspeople).

Needs first: Medieval Pyramid of Power, The Crusades, Medieval Food & Feasts.

https://lightmysky.com/learn/history/towns-and-trade-mt_UMOjbmLcbM

#### Women in the Middle Ages (ages 9-11)

The lives of medieval women: noblewomen managing estates, peasant women's hard daily work, nuns and abbesses, notable figures like Eleanor of Aquitaine and Joan of Arc

Ready when they can: Describe the different lives of noblewomen, peasant women, and nuns; Name at least one notable medieval woman and explain what she did; Explain one way women's lives in medieval times were more restricted than today.

Needs first: Medieval Pyramid of Power, The Medieval Church.

https://lightmysky.com/learn/history/women-in-the-middle-ages-mt_uuB3owTqNY

#### Art & Architecture (ages 9-11)

Medieval cultural achievements: illuminated manuscripts, Gothic cathedrals (flying buttresses, stained glass), Gregorian chant, the Bayeux Tapestry; art and architecture as expressions of faith and power

Ready when they can: Describe what an illuminated manuscript is and who made them; Name at least two features of Gothic cathedral architecture (pointed arches, flying buttresses, stained glass); Explain how medieval art and buildings were connected to the Church and religious belief.

Needs first: Castle Design Through the Ages, The Medieval Church, Greek and Roman Architecture.

https://lightmysky.com/learn/history/art-and-architecture-mt_pitjUcaAdy

#### Magna Carta and Limiting Royal Power (ages 9-11)

King John, the barons' revolt, and the sealing of the Magna Carta in 1215; what the Magna Carta said about limiting the king's power; its lasting importance for democracy and rights

Ready when they can: Explain why the barons rebelled against King John; Describe what the Magna Carta said (the king must follow the law too, fair trial rights); Explain why the Magna Carta still matters today (foundation of democracy and human rights).

Needs first: Athenian Democracy, Medieval Pyramid of Power, Siege Warfare.

https://lightmysky.com/learn/history/magna-carta-and-limiting-royal-power-mt_8ShghTx0jd

#### Printing Press & Renaissance (ages 9-11)

The invention of the printing press by Gutenberg and its arrival in England with William Caxton; how printed books changed everything; the transition from the Middle Ages to the Renaissance

Ready when they can: Explain what the printing press was and why it was revolutionary; Describe William Caxton's role in bringing printing to England; Give at least one way printed books changed society (more people could read, ideas spread faster).

Needs first: Art & Architecture, Towns & Trade.

https://lightmysky.com/learn/history/printing-press-and-renaissance-mt_rf23aL6KwH

#### Medieval Legacy in Modern Life (ages 9-11)

What the Middle Ages gave us: Parliament, universities, common law, Gothic architecture, the English language (Anglo-Saxon + Norman French), place names, surnames; why we are still fascinated by the medieval world

Ready when they can: Name at least three things from the Middle Ages that still affect our lives today; Explain how the English language was shaped by Anglo-Saxon and Norman French; Give a reason why people today are still fascinated by the medieval period (castles, knights, fantasy literature, games).

Needs first: Anglo-Saxon Britain, Magna Carta and Limiting Royal Power, Greek and Roman Legacy Today, Art & Architecture, Printing Press & Renaissance.

https://lightmysky.com/learn/history/medieval-legacy-in-modern-life-mt_Ik-WC2ARPf

#### Medieval Worlds Beyond Europe (ages 9-11)

The medieval world beyond Europe: the Islamic Golden Age (maths, medicine, architecture), the Mali Empire and Mansa Musa, Song Dynasty China; how the medieval world was connected through trade routes like the Silk Road

Ready when they can: Name at least two achievements of the Islamic Golden Age (algebra, hospitals, architecture); Describe who Mansa Musa was and why he is remembered; Explain how the Silk Road connected distant parts of the medieval world through trade.

Needs first: Greek and Roman Legacy Today, Towns & Trade, The Crusades.

https://lightmysky.com/learn/history/medieval-worlds-beyond-europe-mt_eosO26KE-Z

### Britain Through Time

https://lightmysky.com/learn/history/areas/britain-through-time

#### Prehistoric Britain (ages 7-11)

How life in Britain changed from the Stone Age to the Iron Age: hunter-gatherers becoming the first farmers, stone tools giving way to bronze and then iron, hillforts and trade — all pieced together from archaeology, because nobody wrote anything down

Ready when they can: Place the Stone Age, Bronze Age, and Iron Age in order and describe one big change across them (e.g., from hunting to farming); Explain what a site like Skara Brae or Stonehenge tells us about how prehistoric people lived; Explain why we depend on objects and sites rather than writing to learn about prehistoric Britain.

Needs first: Evidence from the Past, Past Events and Change.

https://lightmysky.com/learn/history/prehistoric-britain-mt_XdvTpVdWIk

#### Britain After 1066 (ages 8-11)

Follow one thread of British life across the centuries after 1066 — how homes, crime and punishment, medicine, or childhood changed from castles and plague to the present day — spotting turning points and things that barely moved

Ready when they can: Trace one theme (e.g., medicine or childhood) across several periods of British history and describe how it changed; Place the major periods after 1066 in order (medieval, Tudor, Victorian, modern) when telling the story of their theme; Point out a turning point in their theme and explain why things changed then (e.g., Victorian laws ending children's factory work).

Needs first: Battle of Hastings and 1066.

https://lightmysky.com/learn/history/britain-after-1066-mt_q9nvf5GuED

#### Roman Britain and What It Left (ages 9-11)

Four centuries of Roman rule left roads, walls, towns and Latin place names, and then the province was let go. What survived the Romans leaving says as much as what they built.

Ready when they can: Name two things the Romans built in Britain that can still be traced today; Say what happened to British towns after the legions left, and give one reason; Find one Roman trace in your own region: a road line, a name ending, a museum object.

https://lightmysky.com/learn/history/roman-britain-and-what-it-left-mt_tPhLD6HhjL

#### Tudor England and the Break With Rome (ages 10-12)

Henry VIII's quarrel with the Pope ended with the crown taking over the church, its land and its money. The argument that followed ran for a century and cost a great many people their lives.

Ready when they can: Say what Henry VIII wanted from the Pope and what he did when refused; Name one thing the crown gained when the monasteries were dissolved; Explain why a change of religion at the top was dangerous for ordinary people.

https://lightmysky.com/learn/history/tudor-england-and-the-break-with-rome-mt_RUPYnRkH7i

#### The King, Parliament and the Civil War (ages 11-13)

A quarrel over who could raise money and command an army ended with a king tried and executed by his own subjects. The republic that followed did not last, but the question of who is above the law never went back in the box.

Ready when they can: Say what Parliament and the king each claimed the right to do; Explain why executing a king in 1649 was different from killing one in a battle; Name one thing that changed for good after the monarchy came back.

https://lightmysky.com/learn/history/the-king-parliament-and-the-civil-war-mt_OGW1jWquJn

#### Britain, the Slave Trade and Abolition (ages 11-13)

For over a century British ships carried more enslaved Africans across the Atlantic than any other nation's, and British ports and banks grew on the profits. Abolition took decades of campaigning, and the enslaved themselves forced the pace with revolt.

Ready when they can: Explain what British ships carried on each leg of the Atlantic route; Name two things abolitionists did to change public opinion; Say why the 1807 ban on the trade did not end slavery in the empire.

https://lightmysky.com/learn/history/britain-the-slave-trade-and-abolition-mt_va8IlbmszO

#### The Victorian City (ages 11-13)

Within two generations Britain went from mostly rural to mostly urban, and the new cities were built faster than anyone could drain them. Cholera, and the surveys that followed it, are what produced sewers, clean water and the first public health law.

Ready when they can: Say why people moved into the industrial cities despite the conditions there; Name one disease that spread in those cities and one public works answer to it; Explain how counting and mapping deaths changed what governments thought they should pay for.

https://lightmysky.com/learn/history/the-victorian-city-mt__vBvBBi8cO

#### Votes for Women and the Long Fight for the Ballot (ages 12-13)

Britain went from a vote held by a small minority of men to a vote held by nearly every adult in about a century, and no stage of it was given freely. The campaign for women's suffrage split over whether to petition or to break windows.

Ready when they can: Say roughly who could vote in 1830 and who could vote in 1930; Describe one peaceful and one militant tactic used by suffrage campaigners; Give one argument used against extending the vote, and how campaigners answered it.

https://lightmysky.com/learn/history/votes-for-women-and-the-long-fight-for-the-ballot-mt_7Cr6IwxFFv

#### Britain After the War (ages 12-13)

Out of a bankrupt, bombed country came a health service free at the point of use, mass council housing and an invitation to workers from the Caribbean and south Asia. The Britain most people now live in was largely built between 1945 and 1975.

Ready when they can: Name two things the post-war governments built or founded that still exist; Say why Britain recruited workers from abroad in the 1940s and 1950s; Describe one way the country looked different in 1975 from 1945.

https://lightmysky.com/learn/history/britain-after-the-war-mt_mLUFonfZlC

### The Modern World

https://lightmysky.com/learn/history/areas/the-modern-world

#### The Industrial Revolution (ages 14-16)

How coal, steam and the factory changed where people worked, where they lived and how fast goods could be made, first in Britain and then across much of the world. The same century that raised output also produced the factory town and its costs.

Ready when they can: Say what changed when work moved out of homes and fields and into factories driven by coal and steam; Name two machines that raised output sharply and say what human work each one replaced; Describe one cost paid by the people who lived through it, such as child labour, twelve-hour shifts, or crowded towns without drains; Explain why railways changed prices and not only journey times.

https://lightmysky.com/learn/history/the-industrial-revolution-mt_tiftXKn0P6

#### Empire and Its Costs (ages 14-16)

How a handful of states came to rule much of the world, and what that took: the Atlantic slave trade, forced and cheap labour, land, and raw materials shipped home. Enslaved and colonised people resisted throughout, and abolition was won, not granted.

Ready when they can: Explain what the Atlantic slave trade was and describe the three legs it is usually drawn as; Name two things empires took from the places they ruled, such as raw materials, land, taxes, or forced labour; Name one form of resistance, from a revolt to an abolition campaign, and say what it demanded; Say why banning the trade in enslaved people did not end slavery everywhere at once.

https://lightmysky.com/learn/history/empire-and-its-costs-mt_i3Yw06vg5I

#### The First World War (ages 14-16)

Why an alliance system turned one assassination into a war across continents, what industrial weapons did to the men who fought it, and how the settlement of 1919 left the next twenty years loaded.

Ready when they can: Name the trigger of 1914 and explain how alliances turned a regional crisis into a war between empires; Describe trench warfare and say why attacks so often failed to move the line; Say what a home front looked like: rationing, conscription, and women moving into factory work; Explain one way the 1919 settlement stored up trouble for later.

https://lightmysky.com/learn/history/the-first-world-war-mt_9-0GTkTf6b

#### The Second World War (ages 15-16)

How depression, grievance and dictatorship produced a second and wider war within a generation, why it was fought on every ocean and continent, and what stood where when it ended in 1945.

Ready when they can: Explain how the 1930s depression and the 1919 settlement helped dictators take power; Name the main sides and say roughly when the fighting began and ended in Europe and in Asia; Give one reason civilians died in far greater numbers than in the previous war; Say what the war changed about the map and about who held power in 1945.

https://lightmysky.com/learn/history/the-second-world-war-mt_BKXKdNc51v

#### The Holocaust (ages 15-16)

How a state organised the murder of six million Jews, along with Roma, disabled people, and others it classed as enemies. It happened in steps, from law and propaganda to exclusion, ghettos and killing centres, and the record of those steps survives.

Ready when they can: Describe the sequence from law and propaganda through exclusion and ghettos to mass murder; Say roughly how many Jewish people were murdered and name other groups that were targeted; Name a kind of evidence historians work from, such as survivor testimony, camp records, or the perpetrators' own paperwork; Give one example of resistance or of rescue.

https://lightmysky.com/learn/history/the-holocaust-mt_HeDd-GMdo-

#### The Cold War (ages 15-16)

How two victors of 1945 split the world into armed camps and competed for forty years without ever fighting each other directly. The fighting happened elsewhere, and the arms race set the ceiling on how far either side would push.

Ready when they can: Explain what cold means here: two blocs armed against each other but never at direct war; Name the two sides and one place where the rivalry turned into real fighting; Say what nuclear weapons added to the standoff; Describe one moment the rivalry nearly turned hot, and how it was pulled back.

https://lightmysky.com/learn/history/the-cold-war-mt_vod9wscQjU

#### Decolonisation and New Nations (ages 15-16)

Between 1945 and the 1970s dozens of colonies became independent countries, by negotiation, by mass campaign, and by armed struggle. Independence settled who governed, and left borders, economies and old obligations still to argue about.

Ready when they can: Name two routes to independence and say what each demanded of the colonial power; Explain why a border drawn by an empire can cause trouble after independence; Give one country's independence date and say which power it became independent from; Say why political independence did not automatically bring economic independence.

https://lightmysky.com/learn/history/decolonisation-and-new-nations-mt_VWuBm6iRmI

#### Civil Rights and Equal Citizenship (ages 15-16)

How people denied equal rights inside their own country organised to win them, from the United States civil rights movement to the campaign against apartheid in South Africa. Boycotts, marches and court cases turned moral claims into law, and the law then had to be enforced.

Ready when they can: Explain the difference between a right written into law and a right people actually have; Name two methods campaigners used and say what each was meant to force; Give one law or court ruling that changed after a campaign; Say why campaigning continued after the law changed.

https://lightmysky.com/learn/history/civil-rights-and-equal-citizenship-mt_t4C-tlQd04

#### The Digital Age (ages 15-16)

In fifty years computers moved from air-conditioned rooms to pockets, and networks made copying information almost free. That one change rearranged work, money, news and privacy, and the arguments about it are still open.

Ready when they can: Put early computers, personal computers, the web and smartphones in order and say roughly when each arrived; Name one kind of work the network created and one it removed; Explain what changed once copying information cost almost nothing; Give one cost people argue about now, such as privacy, misinformation, or a few firms holding most of the traffic.

https://lightmysky.com/learn/history/the-digital-age-mt_9aQnMPk7y-

### World History

https://lightmysky.com/learn/history/areas/world-history

#### China's First Empires (ages 11-13)

How Qin and then Han rulers turned a set of warring states into one empire with a shared script, shared weights and a road system. The Han governed more people than Rome did, and did it with written exams and paperwork rather than only with soldiers.

Ready when they can: Say what the Qin unification standardised, and why one script and one set of weights makes a large state easier to run; Name one Han invention or method that spread far beyond China, such as paper or the seismoscope; Compare the Han empire with Rome on one point: size, how officials were chosen, or how the frontier was defended.

https://lightmysky.com/learn/history/chinas-first-empires-mt_l1uAV1oGid

#### The Silk Roads (ages 11-13)

The overland and sea routes that carried silk, horses, paper and glass between China, India, Persia and the Mediterranean. They carried more than goods: religions, technologies and diseases travelled the same way.

Ready when they can: Trace one route on a map and name two goods that moved in each direction along it; Give an example of something other than goods that travelled the roads, such as a faith, a technique or an illness; Explain why few traders travelled the whole distance, and what that meant for prices at each end.

https://lightmysky.com/learn/history/the-silk-roads-mt_Ud5GTBfVTz

#### India From the Vedas to the Gupta (ages 11-13)

The long story of the Indian subcontinent from the Vedic period through Ashoka's Mauryan empire to the Gupta courts. It is where the numerals we write with, and a great deal of early mathematics and astronomy, were worked out.

Ready when they can: Say who Ashoka was and what changed in how he ruled after the Kalinga war; Name two things worked out in India that the rest of the world later took up, such as the decimal numerals or the idea of zero as a number; Describe one way the subcontinent was connected outward, by sea trade or by the spread of a religion.

https://lightmysky.com/learn/history/india-from-the-vedas-to-the-gupta-mt_WylqxfbwwJ

#### Belief Systems That Travelled (ages 11-13)

Why some religions and philosophies moved far beyond where they began while others stayed local. Buddhism, Christianity, Islam and Confucian ideas all crossed borders, and each changed as it went.

Ready when they can: Name two belief systems that spread far from their birthplace, and say roughly where each reached; Give one reason a set of ideas travels well: traders carry it, rulers adopt it, or it does not require you to be born into it; Describe one way a belief system changed as it settled in a new place.

https://lightmysky.com/learn/history/belief-systems-that-travelled-mt_1RVIe0k2AU

#### The Rise of Islam and Its First Empires (ages 11-13)

How a movement that began in seventh-century Arabia came within a century to rule from Spain to the Indus. The new states taxed rather than converted at first, and much of the population they governed stayed Christian, Jewish or Zoroastrian for generations.

Ready when they can: Say roughly when and where Islam began, and name two regions it reached within a hundred years; Explain one reason the early conquests moved fast, such as exhausted rival empires or terms offered to cities that surrendered; Say why conquest and conversion are not the same thing, using this case.

https://lightmysky.com/learn/history/the-rise-of-islam-and-its-first-empires-mt_kgkvNTMNCD

#### Baghdad, Cordoba and the Work of Translation (ages 12-13)

For several centuries the busiest centres of medicine, astronomy and mathematics were in the Islamic world. Greek works that Europe had lost survived because scholars in Baghdad translated them into Arabic and argued with them.

Ready when they can: Name one field, such as medicine, optics or algebra, that was carried forward in this period and say by whom; Explain how a Greek text could reach medieval Europe by way of Arabic; Give one reason cities like Baghdad and Cordoba attracted scholars: patronage, paper, libraries, or a mix of languages in one street.

https://lightmysky.com/learn/history/baghdad-cordoba-and-the-work-of-translation-mt_ZkjqYHk0cN

#### Gold, Salt and the Kingdoms of the Sahel (ages 12-13)

Ghana, Mali and Songhai grew rich controlling the trade that crossed the Sahara: gold going north, salt coming south. Timbuktu had libraries and a university while the trade was running.

Ready when they can: Explain why salt was worth trading for gold, given where each was found; Name one Sahelian kingdom and one thing it is remembered for; Say what a caravan crossing needed, and why control of the wells mattered more than control of the sand.

https://lightmysky.com/learn/history/gold-salt-and-the-kingdoms-of-the-sahel-mt_EUkNLax9Yz

#### The Indian Ocean and the Swahili Coast (ages 12-13)

Monsoon winds that reverse twice a year made the Indian Ocean a predictable highway between Africa, Arabia, India and China. The stone towns of the Swahili coast, and inland Great Zimbabwe, were built on that traffic.

Ready when they can: Explain how a wind that changes direction with the season made long voyages practical; Name one port or site on this network and say what it traded; Give one piece of evidence that these places were connected far afield, such as Chinese pottery found on an African coast.

https://lightmysky.com/learn/history/the-indian-ocean-and-the-swahili-coast-mt_0hVCaCE7QL

#### The Mongol Century (ages 12-13)

In two generations the Mongols built the largest connected land empire there has been, from Korea to Hungary. What they destroyed is well recorded; what they connected, from postal relays to safe roads for merchants, is easier to miss.

Ready when they can: Say roughly how far the empire reached at its height and name two regions it took in; Give one military advantage the Mongol armies had over settled states; Name one thing that moved more easily because the roads were under one authority.

https://lightmysky.com/learn/history/the-mongol-century-mt_9dNatkNqRt

#### When Plague Crossed a Continent (ages 12-13)

The plague of the 1340s was not a European event. It moved along the same roads and sea lanes that carried silk and silver, and it changed wages, land and belief everywhere it landed.

Ready when they can: Trace the plague's route from central Asia to western Europe and name one place it hit on the way; Explain why the trade network that made everyone richer also made this spread faster; Name one lasting change that followed in a region outside Europe.

https://lightmysky.com/learn/history/when-plague-crossed-a-continent-mt_852vI5oN6Y

#### Cities of the Americas Before 1500 (ages 12-13)

Tenochtitlan was larger than any city in Europe when the Spanish first saw it, and the Inca ran a mountain state of millions without wheels, money or writing as Europe knew it. Maya astronomers had a calendar more accurate than the one Spain arrived with.

Ready when they can: Name two American civilisations before 1500 and say roughly where each was; Give one engineering or record-keeping method they used, such as terraces, causeways or the quipu; Say one thing that is often assumed about the Americas before 1500 and why the evidence contradicts it.

https://lightmysky.com/learn/history/cities-of-the-americas-before-1500-mt_KMAiatbUp8

#### Why Empires Fall (ages 12-13)

Rome, Han China, the Maya cities and the Egyptian New Kingdom all ended, and the explanations repeat: overstretch, disease, climate, a broken succession, a frontier that stops paying. Comparing cases is how you tell a cause from a story.

Ready when they can: Name three causes that turn up in more than one collapse; Take two empires and say what their endings had in common and where they differ; Explain why a single dramatic event is rarely enough on its own to explain a collapse.

https://lightmysky.com/learn/history/why-empires-fall-mt_ofR2rPlIkQ

#### The Ottoman, Safavid and Mughal Empires (ages 16-18)

Three large Muslim states ran most of the land between the Danube and the Bay of Bengal from the sixteenth century, each built on cannon, cavalry and a paid bureaucracy. They were the powers European traders had to negotiate with, not around.

Ready when they can: Place all three empires on a map and give the approximate century each was at its height; Explain what gunpowder artillery changed about who could hold a fortified city, and therefore about the size of states; Describe how one of the three managed a population of several religions, and judge how well it worked.

https://lightmysky.com/learn/history/the-ottoman-safavid-and-mughal-empires-mt_CviwlUVthF

#### Ming and Qing China (ages 16-18)

China under the Ming and early Qing was the largest economy on Earth and the destination for most of the silver mined in the Americas. It traded on its own terms, which is a different story from the one that starts with European ships.

Ready when they can: Explain why so much American silver ended up in China, using what China taxed and what it sold; Say what Zheng He's voyages showed about Chinese capability, and what the decision to stop them tells you about priorities; Assess the claim that China was closed to the outside world before 1800.

https://lightmysky.com/learn/history/ming-and-qing-china-mt_-WC-wSZr7f

#### The Columbian Exchange (ages 16-18)

After 1492 crops, animals and diseases crossed the Atlantic in both directions and rearranged diets and populations everywhere. Potatoes and maize fed Europe and China; smallpox and measles emptied much of the Americas before most Europeans arrived.

Ready when they can: Name two crops that moved each way and say where each became a staple; Explain why disease hit the Americas so much harder than it hit Europe; Argue whether the exchange is better described as a trade or as a catastrophe, and say for whom.

https://lightmysky.com/learn/history/the-columbian-exchange-mt_R6zh3S5dha

#### Silver, Sugar and the First World Economy (ages 16-18)

By 1700 a market in one continent set prices in another, and states ran trade policy to keep bullion at home. Mercantilism is the name for that policy and for the wars it produced.

Ready when they can: State what mercantilist policy tried to achieve and name two instruments it used; Trace one commodity, silver or sugar, from where it was produced to where it was consumed and say who took the profit at each stage; Explain why a chartered company could act like a state, with its own soldiers and treaties.

https://lightmysky.com/learn/history/silver-sugar-and-the-first-world-economy-mt_uFhCt_GXgN

#### The Plantation Atlantic (ages 16-18)

Sugar, tobacco and cotton were grown by enslaved people on a scale no earlier slavery had reached, and the societies built on that work invented the racial law that justified it. Resistance ran from sabotage to the revolution that founded Haiti.

Ready when they can: Explain why plantation crops in particular drove demand for forced labour rather than wage labour; Describe how law in these colonies came to define status by ancestry, and say what that was for; Give three forms resistance took, and explain why the Haitian revolution frightened every slave-holding state.

https://lightmysky.com/learn/history/the-plantation-atlantic-mt_yPFkuKzale

#### The Enlightenment and the Age of Revolutions (ages 16-18)

A set of arguments about reason, rights and consent moved from coffee houses into constitutions, in America, France and Haiti within twenty-five years. Each revolution had to decide who counted as the people, and gave a different answer.

Ready when they can: State two Enlightenment claims about government and name a thinker associated with each; Compare what the American, French and Haitian revolutions each meant by equality; Explain why the Haitian revolution was the one that took the stated principles furthest, and why it was punished for it.

https://lightmysky.com/learn/history/the-enlightenment-and-the-age-of-revolutions-mt_6lJ0wjVsig

#### Independence in Latin America (ages 16-18)

Between 1810 and 1825 most of Spanish and Portuguese America became independent, led largely by locally born elites. Independence changed who governed without changing much about who owned the land.

Ready when they can: Explain how Napoleon's invasion of Spain created the opening these movements used; Say who led the independence movements and whose position barely changed afterwards; Compare one Latin American independence with decolonisation in Africa a century later on one clear point.

https://lightmysky.com/learn/history/independence-in-latin-america-mt_pQVJQQrKvm

#### Industrialising Outside Europe: Japan and Egypt (ages 16-18)

Two states tried to industrialise deliberately in the nineteenth century, and one kept its independence while the other lost it. Comparing them is the cleanest test of what industrialisation actually required.

Ready when they can: Describe what Meiji Japan changed about its government, army and schools, and over roughly how long; Say what Muhammad Ali's Egypt built, and how it ended up under British control anyway; Give two conditions that seem to matter for industrialisation from below rather than for a state programme.

https://lightmysky.com/learn/history/industrialising-outside-europe-japan-and-egypt-mt_DFhpNwT4Rq

#### Resisting Colonial Rule (ages 16-18)

Colonised people fought back throughout, and sometimes won: at Adwa an African army defeated a European one and kept its independence. The forms ranged from open war to strikes, boycotts, newspapers and courts.

Ready when they can: Name three distinct forms resistance took and give one example of each; Explain why Ethiopia's victory at Adwa mattered beyond Ethiopia; Assess why armed resistance usually failed in the nineteenth century and more often succeeded after 1945.

https://lightmysky.com/learn/history/resisting-colonial-rule-mt_7Y5kKzxsBv

#### The Non-Aligned World (ages 16-18)

After 1955 a group of newly independent states refused to line up behind either superpower and tried to act together on trade, aid and racism. The Cold War read from Bandung or Belgrade looks nothing like the Cold War read from Washington or Moscow.

Ready when they can: Say what the Bandung conference set out to do and name two states involved; Explain what non-alignment offered a new state that picking a side did not; Give one thing the movement achieved and one reason it lost force.

https://lightmysky.com/learn/history/the-non-aligned-world-mt_aHyHeLXH20

#### Globalisation and Who It Left Out (ages 16-18)

Since 1980 goods, money and information have moved with less friction than ever, and the gains have been very unevenly shared. Deciding whether that counts as progress means choosing what to measure.

Ready when they can: Name two things that made cross-border movement of goods and money cheaper after 1970; Give one measure on which global inequality fell and one on which it rose over the same period; State the strongest case for and the strongest case against, and say which evidence would change your mind.

https://lightmysky.com/learn/history/globalisation-and-who-it-left-out-mt_O008yD5Jwa

## Personal & Social Development

116 topics, ages 4 to 18. https://lightmysky.com/learn/personal-and-social-development

### Emotional Literacy

https://lightmysky.com/learn/personal-and-social-development/areas/emotional-literacy

#### Naming Basic Emotions (ages 5-7)

Name and recognise basic emotions — happy, sad, angry, scared, excited, and surprised — in themselves and in others by looking at facial expressions and body language

Ready when they can: Label at least five basic emotions from pictures or real situations; Match facial expressions to emotion words in a sorting activity; Say 'I feel ___' using a correct emotion word when asked about their own day.

https://lightmysky.com/learn/personal-and-social-development/naming-basic-emotions-mt_LhkP_KKIRS

#### Feelings Change and Differ (ages 5-7)

Understand that everyone has feelings, that feelings change throughout the day, and that the same event can make different people feel different things

Ready when they can: Give an example of a time their feelings changed during a single day; Explain why two children might feel differently about the same event; Recognise that feelings are temporary and can change.

Needs first: Naming Basic Emotions.

https://lightmysky.com/learn/personal-and-social-development/feelings-change-and-differ-mt_ggcamLzXAy

#### Triggers and Causes of Feelings (ages 5-7)

Understand that feelings have causes — something happens (a trigger) and that makes us feel a certain way — and begin to identify what triggers their own emotions

Ready when they can: Describe a trigger for at least three different emotions from their own experience; Complete 'I felt ___ because ___' sentences accurately; Identify what made a character in a story feel a particular way.

Needs first: Feelings Change and Differ.

https://lightmysky.com/learn/personal-and-social-development/triggers-and-causes-of-feelings-mt_9Y5-GjF2B0

#### Emotion Vocabulary (ages 7-9)

Use a wider vocabulary of emotion words beyond the basics — including frustrated, worried, anxious, embarrassed, jealous, proud, disappointed, grateful, and lonely — and distinguish between similar emotions

Ready when they can: Use at least five emotion words beyond the basic six in everyday conversation; Explain the difference between two similar emotions such as angry and frustrated; Choose a precise emotion word that fits a described scenario.

Needs first: Naming Basic Emotions.

https://lightmysky.com/learn/personal-and-social-development/emotion-vocabulary-mt_MOY_2Cqalz

#### How Emotions Feel in Your Body (ages 7-9)

Understand the connection between emotions and the body — recognising physical signals like butterflies in the stomach (nervous), clenched fists (angry), racing heart (scared or excited), and tight shoulders (stressed)

Ready when they can: Name at least three body sensations and match them to the emotions they signal; Notice a physical feeling in their own body and identify the emotion behind it; Explain why the body reacts physically when we have strong emotions.

Needs first: Triggers and Causes of Feelings.

https://lightmysky.com/learn/personal-and-social-development/how-emotions-feel-in-your-body-mt_Ytd8XC3eQr

#### Mild to Strong Emotions (ages 7-9)

Understand that emotions come in different intensities — from mild to strong — and that the same emotion can feel very different depending on how intense it is (e.g., annoyed → angry → furious, or nervous → anxious → panicked)

Ready when they can: Place three related emotion words in order from mild to strong; Rate their own emotion on a simple scale (e.g., 1-5) in a real situation; Explain why recognising intensity matters for choosing how to respond.

Needs first: Naming Basic Emotions.

https://lightmysky.com/learn/personal-and-social-development/mild-to-strong-emotions-mt_rymBfJmvFl

#### Mixed and Conflicting Emotions (ages 9-11)

Understand that people can experience mixed or conflicting emotions at the same time — feeling excited and nervous about starting a new school, or happy for a friend who won but disappointed for yourself

Ready when they can: Describe a personal situation where they felt two emotions simultaneously; Explain why mixed feelings are normal and not something to worry about; Identify mixed emotions in a character from a book or film.

Needs first: Emotion Vocabulary, Mild to Strong Emotions.

https://lightmysky.com/learn/personal-and-social-development/mixed-and-conflicting-emotions-mt_dlm3NspUyy

#### Emotions and Decision-Making (ages 9-11)

Understand how emotions influence thinking and decision-making — that strong feelings can cloud judgement, that we often make different choices when calm versus when upset, and that recognising this gives us more control

Ready when they can: Give an example of a time a strong emotion led them or someone else to a poor decision; Explain the idea of 'cooling off' before making an important choice; Describe how the same situation looks different when you're calm versus upset.

Needs first: Stop, Think, Then Choose, How Emotions Feel in Your Body.

https://lightmysky.com/learn/personal-and-social-development/emotions-and-decision-making-mt_KA5j5OeGvw

#### Expressing Feelings with Words (ages 5-7)

Express their own feelings appropriately using words rather than actions — saying 'I feel angry because...' instead of hitting, shouting, or withdrawing

Ready when they can: Use an 'I feel ___ when ___' statement during a disagreement; Choose to tell an adult how they feel instead of acting out physically; Describe their feelings about a difficult situation using at least two emotion words.

Needs first: Triggers and Causes of Feelings, Simple Calming Strategies.

https://lightmysky.com/learn/personal-and-social-development/expressing-feelings-with-words-mt_kvrvpQris4

#### Hidden and Masked Feelings (ages 7-9)

Recognise that people sometimes hide or mask their true feelings — smiling when they're actually sad, or saying 'I'm fine' when they're not — and understand why someone might do this

Ready when they can: Give an example of a time someone might hide their feelings and explain why; Identify mismatches between someone's words and their body language; Explain that hiding feelings is common but that it's usually better to share with someone trusted.

Needs first: Expressing Feelings with Words, Mild to Strong Emotions.

https://lightmysky.com/learn/personal-and-social-development/hidden-and-masked-feelings-mt_E5ju6kQSu3

#### Culture and Experience Shape Emotions (ages 9-11)

Understand that emotional responses are shaped by personal experiences, culture, and context — the same situation triggers different emotions in different people because of their backgrounds and past experiences

Ready when they can: Explain why two people might have very different emotional reactions to the same event; Give an example of how a past experience shaped someone's emotional response; Describe how cultural background might influence what makes someone feel proud or embarrassed.

Needs first: Hidden and Masked Feelings.

https://lightmysky.com/learn/personal-and-social-development/culture-and-experience-shape-emotions-mt_nIl1kKZHsk

#### Emotional Patterns Over Time (ages 9-11)

Reflect on their own emotional patterns over time — noticing recurring triggers, understanding their typical responses, and recognising how their emotional awareness has grown

Ready when they can: Identify a recurring emotional trigger and their typical response to it; Describe how their emotional understanding has changed compared to when they were younger; Set a personal goal related to emotional awareness, such as noticing when stress is building.

Needs first: Personal Growth Over Time, Patterns in Your Own Reactions, Personal Coping Toolkit, Emotions and Decision-Making, Culture and Experience Shape Emotions.

https://lightmysky.com/learn/personal-and-social-development/emotional-patterns-over-time-mt_cEQqskOaoo

#### Brain Science of Emotions (ages 11-12)

Understand how the amygdala triggers emotional responses and how the prefrontal cortex (still developing in adolescence) regulates them; explain why stress hormones (cortisol, adrenaline) affect thinking and memory; understand that the adolescent brain's dopamine system makes feelings more intense; distinguish between emotion regulation (managing feelings effectively) and emotion suppression (pushing feelings down, which is counterproductive); introduce cognitive reappraisal as a research-backed technique for changing how we interpret a situation

Needs first: Good Stress and Bad Stress, Emotions and Decision-Making.

https://lightmysky.com/learn/personal-and-social-development/brain-science-of-emotions-mt_gf4RUcACLg

#### Identity and Belonging in Adolescence (ages 12-13)

Understand that adolescence involves active construction of identity, leading to emotional complexity around questions of 'who am I?'; explore the emotional dynamics of belonging to multiple groups simultaneously (family, peer group, cultural or religious identity); understand social comparison and its intensification through social media; recognise that identity is not fixed and that uncertainty about identity is normal, not a sign of failure; develop language for navigating emotions tied to group membership and personal values

Needs first: Mixed and Conflicting Emotions, Brain Science of Emotions, Culture and Experience Shape Emotions.

https://lightmysky.com/learn/personal-and-social-development/identity-and-belonging-in-adolescence-mt_p-8Hlf6_9k

#### Emotional Intelligence (ages 13-14)

Introduce Goleman's emotional intelligence model (self-awareness, self-regulation, motivation, empathy, social skills); develop vocabulary for complex emotional states (ambivalence, ennui, schadenfreude, awe, nostalgia, cognitive dissonance); understand the evidence linking emotional intelligence to wellbeing, relationship quality, and long-term life outcomes; reflect on personal emotional growth over the secondary school years; explore the relationship between emotional literacy and mental health, and know when to seek professional support

Needs first: Emotional Patterns Over Time, Identity and Belonging in Adolescence.

https://lightmysky.com/learn/personal-and-social-development/emotional-intelligence-mt_mydcMoa8gN

#### Body Image and the Pictures You Scroll Past (ages 12-13)

Most images of bodies that reach a teenager are selected, posed, edited or generated, and comparing yourself with them is comparing with something that does not exist. Covers what filters and editing actually change, why a feed shows more of what you linger on, and what changes when you notice the comparison happening.

Ready when they can: Name three things routinely edited in an image of a person and say how each would be visible if undone; Explain why a feed shows more of the bodies you stopped to look at; Describe one thing to do when you notice a comparison starting, other than scrolling on.

https://lightmysky.com/learn/personal-and-social-development/body-image-and-the-pictures-you-scroll-past-mt_OyBLI3T0jX

### Self-Awareness

https://lightmysky.com/learn/personal-and-social-development/areas/self-awareness

#### Who I Am: Self-Concept and Strengths (ages 4-6)

Describe who you are: your name, family, likes and dislikes, things you are good at and things you find hard — and notice that you are growing and can already do things you couldn't do before

Ready when they can: Describe themselves in simple terms (e.g., 'I'm good at climbing, I love drawing dinosaurs, I find sitting still hard'); Name something they are proud of being able to do and something they are still learning; Point to a way they have grown (e.g., 'I couldn't zip my coat when I was little, now I can').

https://lightmysky.com/learn/personal-and-social-development/who-i-am-self-concept-and-strengths-mt_j8rBUMPEuD

#### Vocabulary: self (ages 5-10)

Know and use the vocabulary of self-reflection — self-awareness, reflect, pattern, trigger, assumption, impact, perspective, and notice — and understand that having precise words for these inner experiences makes them easier to understand and talk about

Ready when they can: Use words like 'reflect', 'pattern', and 'trigger' accurately when describing their own behaviour — e.g. 'I notice a pattern: I get frustrated when I rush'; Explain what 'self-awareness' means in their own words and give a personal example; Use the word 'perspective' correctly — e.g. 'From my perspective it felt unfair, but I can see theirs too'.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-self-mt_H4YZ1rSKP3

#### Naming Your Feelings (ages 5-6)

Notice what you are feeling and put a name to it — being able to label an emotion is the first step to understanding and managing it

Ready when they can: emotional literacy research; Fostering Emotional Literacy in Young Children (HeadStart.gov); emotion vocabulary development 4-11 years (PMC).

Needs first: Vocabulary: self, Feeling of not understanding.

https://lightmysky.com/learn/personal-and-social-development/naming-your-feelings-mt_69hFD2NgGe

#### Feelings Versus Actions (ages 6-8)

Understand that feelings and actions are separate — you can feel something strongly without having to act on it straight away

Ready when they can: emotion regulation development research; Effects of Age and Gender in Emotion Regulation (PMC 2020); expressive control to emotion regulation (PMC).

Needs first: Naming Your Feelings.

https://lightmysky.com/learn/personal-and-social-development/feelings-versus-actions-mt_TU3BcLOgiV

#### My Strengths and How I Grow (ages 7-9)

Take an honest look at your own strengths, preferences and limitations: name what you do well with evidence, admit what you find difficult without giving up on it, and notice how effort and practice have already changed what you can do

Ready when they can: Name a personal strength and back it up with an example (e.g., 'I'm good at explaining games — I taught my cousin chess'); Talk about a limitation calmly and pair it with a plan (e.g., 'I'm not fast at spelling yet, so I practise the tricky words'); Describe how practice changed one of their skills over time (e.g., swimming, times tables, riding a bike).

Needs first: Who I Am: Self-Concept and Strengths, Vocabulary: self.

https://lightmysky.com/learn/personal-and-social-development/my-strengths-and-how-i-grow-mt_UDdTHnxv4Q

#### Patterns in Your Own Reactions (ages 7-9)

Notice patterns in your own reactions — 'I tend to respond like this when I'm tired, left out, or put on the spot'

Ready when they can: middle childhood self-reliance in emotion regulation; 7-year developmental shift in self-understanding research.

Needs first: Vocabulary: self, Feelings Versus Actions, Spotting Patterns.

https://lightmysky.com/learn/personal-and-social-development/patterns-in-your-own-reactions-mt_H8dEMH_wik

#### Your Impact on Others (ages 8-9)

Reflect on how your behaviour lands on others — consider not just what you intended but what the actual impact was on the other person

Ready when they can: Describe how something they said or did affected someone else — e.g. 'When I didn't include them, they looked upset'; Predict what might happen before acting — e.g. 'If I take the last one without asking, they'll feel it's unfair'; After a conflict, explain what they could have done differently and what effect that would have had.

Needs first: Teaching It Back, Patterns in Your Own Reactions, Feelings Versus Actions.

https://lightmysky.com/learn/personal-and-social-development/your-impact-on-others-mt_rpug2tkYhb

#### Questioning First Impressions (ages 9-10)

Notice when your first reading of a social situation might be wrong — your assumptions about why someone acted a certain way are not always facts

Ready when they can: Pause before reacting to a classmate's behaviour and consider an alternative explanation — e.g. 'Maybe they bumped me by accident, not on purpose'; Describe a time they assumed the worst about someone's intention and later found out they were wrong; When told about an ambiguous social situation, suggest at least two possible reasons for the other person's behaviour instead of jumping to one conclusion.

Needs first: Patterns in Your Own Reactions, Your Impact on Others, Understanding Why.

https://lightmysky.com/learn/personal-and-social-development/questioning-first-impressions-mt_Mb1JUJmnbX

#### Personal Growth Over Time (ages 10-11)

Reflect on your own growth over time — the things that challenge you now are not fixed, and noticing how you have already changed builds genuine self-knowledge

Ready when they can: emotion vocabulary development continues to age 11 (PMC); self-reflection importance in children research.

Needs first: Patterns in Your Own Reactions, Questioning First Impressions, Reflecting After Learning.

https://lightmysky.com/learn/personal-and-social-development/personal-growth-over-time-mt_bkMDDstwwG

#### Naming and Ranking Your Own Values (ages 14-15)

Write down the handful of things you actually care about, then force a ranking by testing them against a situation where two of them cannot both win. The ranking is the useful part, not the list.

Ready when they can: List five values in their own words and give a real example of each from the past year; Take a situation where two of their values pull against each other (loyalty to a friend against telling the truth) and say which one wins for them, with a reason; Point at a past choice that went against their stated ranking and say what that tells them about the ranking.

https://lightmysky.com/learn/personal-and-social-development/naming-and-ranking-your-own-values-mt_SRNX36_g65

#### Choosing What Comes Next (ages 16-18)

The choice between study, training and work is usually made on other people's expectations and a vague sense of prestige. Made properly it is a comparison of what each path costs, what it opens, and what it closes.

Ready when they can: Set out two paths side by side on cost, time, and what each leaves open afterwards; Separate what you want from what somebody else wants for you, in writing; Name the reversible and irreversible parts of the decision.

https://lightmysky.com/learn/personal-and-social-development/choosing-what-comes-next-mt_kDhdTK2H9s

### Empathy & Social Awareness

https://lightmysky.com/learn/personal-and-social-development/areas/empathy-and-social-awareness

#### Vocabulary: understanding others (ages 5-8)

Know and use the key vocabulary for understanding others — empathy, perspective, kind, fair, community, similar, different, and care — and understand that these words describe real habits of thinking and feeling

Ready when they can: Use the word 'empathy' correctly and distinguish it from 'sympathy' — e.g. 'Empathy means I try to feel what they feel'; Explain what 'perspective' and 'point of view' mean and demonstrate by describing how two people might see the same event differently; Use words like 'community', 'belonging', and 'inclusion' accurately when talking about their school or neighbourhood.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-understanding-others-mt_wRlf0g2MbB

#### Other People's Feelings and Thoughts (ages 5-7)

Understand that other people have their own feelings and thoughts, and that these might be different from your own — a foundational awareness that not everyone sees or feels things the same way

Ready when they can: State that other people can feel differently about the same thing; Give an example of a time someone felt differently from them about the same situation; Accept another child's feeling as valid even when it differs from their own.

Needs first: Vocabulary: understanding others.

https://lightmysky.com/learn/personal-and-social-development/other-peoples-feelings-and-thoughts-mt_wzUzVEBqJb

#### Everyday Kindness and Care (ages 5-7)

Show kindness and care towards others in simple everyday ways — comforting a friend who is upset, helping someone who has dropped their things, sharing without being asked, and saying kind words

Ready when they can: Spontaneously offer comfort to someone who is visibly upset; Help another person with a practical task without being asked; Use kind words to encourage or cheer up someone who is struggling.

Needs first: Naming Basic Emotions, Vocabulary: understanding others, Other People's Feelings and Thoughts.

https://lightmysky.com/learn/personal-and-social-development/everyday-kindness-and-care-mt_lAvS72LOUO

#### Similarities & Differences (ages 5-7)

Notice and appreciate ways that people are similar to and different from each other — including appearance, family structures, languages spoken, foods eaten, and celebrations observed — and understand that differences make communities interesting

Ready when they can: Name several ways people in their class or community are different from each other; Describe at least one thing they have learned from someone who is different from them; Express a positive attitude about differences rather than judging them.

Needs first: Vocabulary: understanding others.

https://lightmysky.com/learn/personal-and-social-development/similarities-and-differences-mt_OJVkWvIaM_

#### Vocabulary: social awareness (ages 7-11)

Know and use the vocabulary of social awareness — including stereotype, prejudice, discrimination, equality, equity, bias, compassion, and fairness — and understand what distinguishes these closely related concepts

Ready when they can: Explain what 'stereotype' and 'prejudice' mean and give an example of each from everyday life; Use words like 'equality', 'equity', and 'bias' correctly when discussing a scenario — e.g. 'That's not equity because not everyone got what they needed'; Identify an example of discrimination in a story or news article and explain why it is unfair using the correct vocabulary.

Needs first: Vocabulary: understanding others.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-social-awareness-mt_a6AYrbb7x4

#### Seeing Someone Else's Point of View (ages 7-9)

Practise perspective-taking by imagining how someone else might feel in a given situation — using prompts like 'How would you feel if that happened to you?' and applying this when reading stories or during real interactions

Ready when they can: Describe how a character in a story feels and give reasons based on the plot; Predict how another child would feel in a described scenario; Use perspective-taking during a real disagreement to understand the other person's view.

Needs first: Vocabulary: social awareness, Emotion Vocabulary, Other People's Feelings and Thoughts.

https://lightmysky.com/learn/personal-and-social-development/seeing-someone-elses-point-of-view-mt_9NQEiYLQA3

#### Different Lives and Experiences (ages 7-9)

Understand that people's lives and experiences can be very different from their own — that some children face challenges like disability, poverty, family difficulties, or being new to a country — and develop compassion rather than judgement

Ready when they can: Describe at least two ways another child's life experience might differ significantly from their own; Explain why it's important not to judge someone based on their circumstances; Suggest a kind action they could take to help someone facing a difficult situation.

Needs first: Seeing Someone Else's Point of View, Vocabulary: social awareness, Similarities & Differences.

https://lightmysky.com/learn/personal-and-social-development/different-lives-and-experiences-mt_S7UTAhptLi

#### Fairness, Equality and Equity (ages 7-9)

Understand what fairness means and why it matters — recognising that fair doesn't always mean equal (everyone getting the same) but can mean equitable (everyone getting what they need), and applying this understanding in group situations

Ready when they can: Explain the difference between treating everyone the same and treating everyone fairly; Give an example of a situation where equal treatment wouldn't be fair; Apply fairness thinking when sharing resources or making group decisions.

Needs first: Seeing Someone Else's Point of View, Vocabulary: social awareness.

https://lightmysky.com/learn/personal-and-social-development/fairness-equality-and-equity-mt_mDp-1vlL3R

#### Stereotypes and Individual Differences (ages 9-11)

Recognise stereotypes — oversimplified beliefs about groups of people based on gender, race, age, or other characteristics — and understand that stereotypes are unfair because they ignore individual differences

Ready when they can: Define what a stereotype is in their own words; Identify a common stereotype and explain why it is inaccurate; Challenge a stereotype they encounter by giving a counter-example.

Needs first: Vocabulary: social awareness, Different Lives and Experiences.

https://lightmysky.com/learn/personal-and-social-development/stereotypes-and-individual-differences-mt_2oswCNuapH

#### The world contains many cultures, traditions (ages 9-11)

Understand that the world contains many cultures, traditions, and belief systems, and that learning about others' perspectives enriches our own understanding — developing genuine curiosity about and respect for cultural diversity

Ready when they can: Describe a cultural practice different from their own and explain what they find interesting about it; Ask respectful questions to learn about someone else's traditions or beliefs; Explain why understanding different cultures makes communities stronger.

Needs first: Fairness, Equality and Equity, Different Lives and Experiences.

https://lightmysky.com/learn/personal-and-social-development/the-world-contains-many-cultures-traditions-mt_DkzsZdyaL2

#### Prejudice and Discrimination (ages 9-11)

Understand the impact of prejudice and discrimination on individuals and communities — that treating people unfairly because of their identity causes real harm — and recognise their own responsibility to stand against it

Ready when they can: Define prejudice and discrimination in their own words with examples; Describe the emotional and social impact of discrimination on the person experiencing it; Identify at least one action they can personally take to challenge unfair treatment.

Needs first: Stereotypes and Individual Differences, Vocabulary: social awareness, Bystanders and Upstanders.

https://lightmysky.com/learn/personal-and-social-development/prejudice-and-discrimination-mt_HFN1pGASpZ

#### Questioning Your Own Biases (ages 9-11)

Reflect on their own assumptions and biases — recognising that everyone carries unconscious assumptions about others, and that actively questioning these assumptions is an ongoing practice that leads to greater fairness and empathy

Ready when they can: Describe a time they made an assumption about someone that turned out to be wrong; Explain what unconscious bias means in simple terms; Describe a strategy for checking their own assumptions, such as asking questions before judging.

Needs first: Stereotypes and Individual Differences, Prejudice and Discrimination, Questioning First Impressions.

https://lightmysky.com/learn/personal-and-social-development/questioning-your-own-biases-mt_cOknxrYhwL

#### Systemic Inequality and Allyship (ages 11-12)

Move beyond 'treating everyone the same' to understand that structural advantages and disadvantages exist regardless of individual effort or intention; explore concrete examples of systemic inequality (educational attainment gaps, gender pay gap, representation in leadership); distinguish between individual prejudice and structural discrimination; understand intersectionality — how multiple aspects of identity interact; develop informed compassion rooted in evidence rather than pity; explore what being a genuine ally means in practice

Needs first: Prejudice and Discrimination, Fairness, Equality and Equity.

https://lightmysky.com/learn/personal-and-social-development/systemic-inequality-and-allyship-mt_oqvJJKCJXw

#### Sympathy Versus Empathy (ages 12-13)

Distinguish sympathy ('I feel sorry for you') from empathy ('I understand what you're experiencing'); develop active listening skills: reflecting, paraphrasing, asking open questions, resisting the urge to problem-solve too quickly; understand empathic curiosity as genuine interest in another person's inner world; practise being present for someone in distress without trying to fix or minimise their experience; understand vicarious trauma and compassion fatigue, and how empathetic people can protect their own wellbeing while staying present for others

Needs first: Questioning Your Own Biases, Systemic Inequality and Allyship.

https://lightmysky.com/learn/personal-and-social-development/sympathy-versus-empathy-mt_VA126P6Wp5

#### Global Citizenship (ages 13-14)

Understand what it means to be a citizen in an interconnected world where decisions in one place affect people elsewhere; explore global issues (climate justice, forced migration, global health, poverty) through an empathy lens, distinguishing facts from value judgements; engage with the ethical tension between obligations to those close to us and obligations to distant strangers; introduce evidence-based giving and effective altruism as one framework for thinking about global responsibility; develop a personal, reasoned stance on global citizenship that acknowledges complexity

Needs first: The world contains many cultures, traditions, Sympathy Versus Empathy.

https://lightmysky.com/learn/personal-and-social-development/global-citizenship-mt_5XLhiqmocP

#### Disagreeing Without Losing the Person (ages 16-18)

Most serious disagreements are not settled, they are survived. Keeping the relationship means arguing about the claim rather than about who the other person is.

Ready when they can: Restate someone's position well enough that they would accept your version before answering it; Name three moves that turn a disagreement about a claim into one about a person; Say what to do when you find you were wrong halfway through.

https://lightmysky.com/learn/personal-and-social-development/disagreeing-without-losing-the-person-mt_iKY-2SzngN

### Friendship & Cooperation

https://lightmysky.com/learn/personal-and-social-development/areas/friendship-and-cooperation

#### Vocabulary: working with others (ages 5-8)

Know and use the vocabulary of working with others — cooperate, share, take turns, team, listen, agree, disagree respectfully, and include — and understand that these words describe habits that friendships and group work depend on

Ready when they can: Use 'cooperate' and 'compromise' correctly — e.g. 'We cooperated by taking turns choosing the game'; Explain what 'active listening' means and demonstrate it: facing the speaker, not interrupting, responding to what was said; Use 'share', 'take turns', and 'include' to describe how they work with others in a group activity.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-working-with-others-mt_NS5t-Jzlh8

#### Listening to Others (ages 5-7)

Listen to others when they are speaking — looking at the speaker, waiting until they finish, and showing they have heard by responding to what was said rather than just talking about their own ideas

Ready when they can: Face the speaker and maintain attention while someone else is talking; Wait until the other person has finished before responding; Respond to what was actually said rather than changing the subject to their own idea.

Needs first: Listening and responding, Vocabulary: working with others.

https://lightmysky.com/learn/personal-and-social-development/listening-to-others-mt_YbX3LD0Eca

#### Asking for Help (ages 5-7)

Ask for help when they need it — from a friend, teacher, or family member — and understand that asking for help is a sign of strength, not weakness

Ready when they can: Approach an appropriate person and ask for help clearly; Identify who to go to for different kinds of help (academic, emotional, practical); Explain why asking for help is sensible rather than something to be embarrassed about.

Needs first: Asking Questions, Vocabulary: working with others, Listening to Others.

https://lightmysky.com/learn/personal-and-social-development/asking-for-help-mt_PdYlsA33jB

#### Makes someone a good friend (ages 5-7)

Understand what makes someone a good friend — being kind, honest, reliable, and including others — and recognise behaviours that are not friendly, such as being bossy, leaving people out, or saying mean things

Ready when they can: List at least four qualities of a good friend; Identify unfriendly behaviour in a story or real situation; Reflect on a time they were a good friend and explain what they did.

Needs first: Vocabulary: working with others.

https://lightmysky.com/learn/personal-and-social-development/makes-someone-a-good-friend-mt_HBcvu0UxYe

#### Taking Turns and Sharing (ages 5-7)

Take turns, share materials, and play cooperatively with others — understanding that group activities work better when everyone gets a fair go and that waiting for your turn is part of being a good friend

Ready when they can: Take turns in a game or group activity without needing adult reminders; Share materials willingly during a shared task or playtime; Explain why taking turns makes games and group work more fun for everyone.

Needs first: Vocabulary: working with others.

https://lightmysky.com/learn/personal-and-social-development/taking-turns-and-sharing-mt_FwI7q7DSIx

#### Communication Vocabulary (ages 7-11)

Know and use the vocabulary of healthy communication and conflict — assertive, passive, aggressive, compromise, conflict, resolution, mediate, bystander, upstander, and peer pressure — and understand the difference between these contrasting approaches

Ready when they can: Use 'assertive' correctly and distinguish it from 'aggressive' — e.g. 'Being assertive means saying what I need calmly'; Explain what 'conflict resolution' means and describe one strategy such as using 'I feel...' statements; Use words like 'negotiate', 'boundary', and 'respect' accurately in a discussion about friendships.

Needs first: Vocabulary: working with others.

https://lightmysky.com/learn/personal-and-social-development/communication-vocabulary-mt_Ag9NSWJu-X

#### Working Well in a Group (ages 7-9)

Work effectively as part of a small group — contributing their own ideas, listening to others' ideas, taking on a fair share of the work, and supporting the group to reach a shared goal

Ready when they can: Contribute at least one idea during a group discussion; Listen to and build on another group member's idea; Complete their assigned part of a group task on time.

Needs first: Communication Vocabulary, Taking Turns and Sharing, Listening and responding, Group discussions, Listening to Others.

https://lightmysky.com/learn/personal-and-social-development/working-well-in-a-group-mt_QxsoqVUt6u

#### Roles in a Group (ages 7-9)

Understand different roles people play in groups — leader, supporter, mediator, idea-generator — and recognise that effective groups need a mix of roles, not everyone trying to be the leader

Ready when they can: Name at least three different roles people can play in a group; Identify their own preferred role and describe its strengths; Explain why groups work better when different people take different roles.

Needs first: Communication Vocabulary, Working Well in a Group.

https://lightmysky.com/learn/personal-and-social-development/roles-in-a-group-mt_w4nSIDhIgC

#### Resolving Disagreements with Friends (ages 7-9)

Resolve simple disagreements with peers by talking it through — explaining how they feel, listening to the other person's side, and finding a compromise or solution that both can accept

Ready when they can: Explain their own point of view calmly during a disagreement; Listen to the other person's perspective without interrupting; Suggest a compromise or solution that addresses both sides.

Needs first: Communication Vocabulary, Makes someone a good friend, Expressing Feelings with Words, Group discussions, Listening to Others.

https://lightmysky.com/learn/personal-and-social-development/resolving-disagreements-with-friends-mt_iWGnyUyN2j

#### Friendships change over time (ages 7-9)

Understand that friendships change over time — that it's normal for friends to drift apart or for new friendships to form — and develop strategies for making new friends and handling friendship changes without feeling like something is wrong with them

Ready when they can: Explain that friendships changing is normal and doesn't mean something is wrong; Describe a strategy for making new friends, such as joining a club or inviting someone to play; Talk about a friendship that changed and how they handled it.

Needs first: Makes someone a good friend, Resolving Disagreements with Friends.

https://lightmysky.com/learn/personal-and-social-development/friendships-change-over-time-mt_X7Tu94-a2m

#### Helping Others Resolve Conflicts (ages 9-11)

Mediate conflicts between others — helping two friends who are arguing by listening to both sides, helping them see each other's perspective, and guiding them toward a fair resolution

Ready when they can: Listen to both sides of a conflict without taking sides initially; Help each person articulate their perspective to the other; Suggest a fair resolution or compromise that both parties can accept.

Needs first: Seeing Someone Else's Point of View, Resolving Disagreements with Friends, Roles in a Group.

https://lightmysky.com/learn/personal-and-social-development/helping-others-resolve-conflicts-mt_AbnwmKD8oe

#### Assertive Communication (ages 9-11)

Use assertive communication — expressing needs, opinions, and boundaries clearly and respectfully without being aggressive (pushy/demanding) or passive (giving in/staying silent) — including saying no when something doesn't feel right

Ready when they can: Explain the difference between assertive, aggressive, and passive responses; Role-play saying no in a peer pressure scenario; Express a personal boundary clearly and respectfully in a real situation.

Needs first: Positive Self-Talk, Communication Vocabulary, Resolving Disagreements with Friends, Asking for Help.

https://lightmysky.com/learn/personal-and-social-development/assertive-communication-mt_rqLMfiw61L

#### Giving and Receiving Feedback (ages 9-11)

Give and receive constructive feedback — telling someone what they did well and what could be improved in a way that is helpful rather than hurtful, and receiving feedback about their own work without becoming defensive

Ready when they can: Give feedback that includes both a specific positive point and a constructive suggestion; Receive feedback about their own work without getting upset or dismissive; Explain why constructive feedback helps people improve.

Needs first: Communication Vocabulary, Working Well in a Group, Assertive Communication, Engaging Listeners and Valuing Viewpoints.

https://lightmysky.com/learn/personal-and-social-development/giving-and-receiving-feedback-mt_33zncDHC3N

#### Self-Reflection in Relationships (ages 9-11)

Reflect on their own role and behaviour in relationships — recognising patterns in how they interact with others, understanding what they contribute to friendships, and identifying areas where they could improve as a friend or team member

Ready when they can: Identify a pattern in their own social behaviour, such as always wanting to lead or avoiding confrontation; Describe what they do well in relationships and one area they'd like to improve; Set a specific social goal, such as 'I will ask others for their ideas before sharing mine'.

Needs first: Giving and Receiving Feedback, Patterns in Your Own Reactions, Your Impact on Others, Assertive Communication.

https://lightmysky.com/learn/personal-and-social-development/self-reflection-in-relationships-mt_z98J_Zg2L3

#### Social Cues and Group Dynamics (ages 11-12)

Understand subtext, indirect communication, and social cues in adolescent peer groups; analyse the psychology of in-group and out-group dynamics and why belonging can come at the cost of exclusion; understand gossip as a social bonding and status mechanism, and its costs; develop strategies for navigating social hierarchies without compromising values; distinguish between assertiveness and aggression in peer settings; understand how to respond to exclusion — whether experiencing it or witnessing it

Needs first: Self-Reflection in Relationships.

https://lightmysky.com/learn/personal-and-social-development/social-cues-and-group-dynamics-mt_nqM2OW0Qlm

#### Honest Conversations and Conflict Repair (ages 12-13)

Understand how to have honest, direct conversations that address problems without attacking the person; apply the principles of non-violent communication (observation, feeling, need, request); understand the repair process after significant conflicts: taking responsibility without defensiveness, offering a genuine apology (without blame-shifting), and rebuilding trust through consistent behaviour over time; distinguish between a real apology and a face-saving 'sorry'; understand how friendships survive and deepen through navigated conflict rather than avoidance

Needs first: Helping Others Resolve Conflicts, Social Cues and Group Dynamics.

https://lightmysky.com/learn/personal-and-social-development/honest-conversations-and-conflict-repair-mt_NCrbQe0LdB

#### Leadership Styles and Influence (ages 13-14)

Distinguish different leadership styles (directive, democratic, servant, transformational) and understand when each is appropriate; understand that influence in a group comes with responsibility, and explore the difference between leading through inspiration versus coercion; practise inclusive leadership: actively creating space for quieter voices and diverse perspectives; understand the ethics of influence and the boundary between persuasion and manipulation; explore concepts of consent and coercion in peer relationships; reflect on what kind of influence they want to have in their communities

Needs first: Giving and Receiving Feedback, Honest Conversations and Conflict Repair.

https://lightmysky.com/learn/personal-and-social-development/leadership-styles-and-influence-mt_8StiXnYq1u

#### Setting a Boundary and Holding It (ages 14-15)

State a limit in one sentence, give one reason, and offer what you will do instead. Then hold it when the other person pushes, using the same words rather than new excuses.

Ready when they can: Write a one-sentence limit for a real situation (lending money, late-night messages, being volunteered for someone else's work) with one reason and one alternative; Repeat the limit after a push-back without adding excuses or dropping it; Tell apart a limit that is theirs to set from a request that is really someone else's decision.

https://lightmysky.com/learn/personal-and-social-development/setting-a-boundary-and-holding-it-mt_JpJ4qi-SP8

#### Repair, Distance, or Let Go (ages 15-16)

After a serious rift, three options stay open: repair the friendship, keep it at a smaller size, or end it. Choose by what actually changed, whether it repeats, and what the other person did afterwards.

Ready when they can: Name the three options for a real rift and give one condition that points to each; Separate a one-off from a pattern by citing what happened before, not by how bad the last time felt; Describe how they would keep a friendship at a smaller size without a public fallout.

https://lightmysky.com/learn/personal-and-social-development/repair-distance-or-let-go-mt_eeWpCYQG1Z

#### Being New: Your First Weeks Somewhere (ages 16-18)

Every workplace and course has rules nobody writes down about how to ask, when to interrupt and what counts as done. Learning them fast is mostly about asking early rather than guessing for a month.

Ready when they can: Name three unwritten rules worth working out in a first week and how you would find each; Explain why asking a question early costs less than asking it after a mistake; Describe how to take a correction from someone senior without either arguing or collapsing.

https://lightmysky.com/learn/personal-and-social-development/being-new-your-first-weeks-somewhere-mt_JaM-XwOLjP

#### Building a Circle From Scratch (ages 16-18)

School supplies friends by accident, and after it nobody does. Adult friendship needs repeated unplanned contact, which has to be arranged on purpose.

Ready when they can: Explain why repeated contact in the same place matters more than any single meeting; Name two ways to create that repetition when it does not happen by itself; Say what a loose acquaintance is good for that a close friend is not.

https://lightmysky.com/learn/personal-and-social-development/building-a-circle-from-scratch-mt_ZfaDiWtn1o

### Responsible Decision-Making

https://lightmysky.com/learn/personal-and-social-development/areas/responsible-decision-making

#### Vocabulary: making decisions and keeping safe (ages 5-8)

Know and use the vocabulary of making decisions and keeping safe — choice, consequence, rule, safe, fair, honest, trusted adult, and right and wrong — and understand that naming these ideas clearly helps make better choices

Ready when they can: Explain what 'consequence' means and give an example of a positive and a negative consequence of a choice; Use 'responsible' and 'safe' correctly when talking about everyday decisions — e.g. 'The responsible choice is to tell an adult'; Define 'rule' and 'fairness' and explain why rules exist using their own examples from school or home.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-making-decisions-and-keeping-safe-mt_uTKgmWqSoI

#### Actions and Their Consequences (ages 5-7)

Understand that actions have consequences — that what you choose to do affects both yourself and other people — and begin to think about what might happen before they act

Ready when they can: Describe what happened as a consequence of a specific action they took; Predict what might happen if they choose a particular action before doing it; Explain that actions can have good or bad consequences for themselves and others.

Needs first: Vocabulary: making decisions and keeping safe.

https://lightmysky.com/learn/personal-and-social-development/actions-and-their-consequences-mt_UHQfb-n-w3

#### Everyday Safety Awareness (ages 5-7)

Keep themselves safe in everyday situations — knowing basic safety rules about roads, strangers, water, and the internet — and understanding who their trusted adults are and when to tell them something

Ready when they can: State at least three basic safety rules and explain why each matters; Name their trusted adults and describe when they should tell them something; Demonstrate safe behaviour in a familiar everyday situation without being reminded.

Needs first: Vocabulary: making decisions and keeping safe.

https://lightmysky.com/learn/personal-and-social-development/everyday-safety-awareness-mt_q3vRl4dddK

#### Right and Wrong Choices (ages 5-7)

Know the difference between right and wrong in familiar everyday situations — understanding basic rules about honesty, not hurting others, respecting others' property, and being fair — and choose to do the right thing even when it's harder

Ready when they can: Identify the right and wrong choice in a simple moral scenario; Choose to be honest even when lying would avoid trouble; Explain why rules about not hurting others and being honest matter.

Needs first: Actions and Their Consequences, Vocabulary: making decisions and keeping safe.

https://lightmysky.com/learn/personal-and-social-development/right-and-wrong-choices-mt_Wc6cOTQ1bA

#### Roads, Pavements and Crossing Safely (ages 5-7)

Where to walk, where to stop, and how to cross: find a safe place, stop at the kerb, look and listen both ways, and keep looking while you cross. Includes what a driver can and cannot see, and why a parked car is the worst place to step out from.

Ready when they can: Name three places that are safer to cross than the middle of a parked row; Say the order of the steps at the kerb and why looking continues while crossing; Explain why a driver may not see a small child standing between two cars.

https://lightmysky.com/learn/personal-and-social-development/roads-pavements-and-crossing-safely-mt_xAX6ilyS-N

#### Rules and agreements exist (ages 5-7)

Understand why rules and agreements exist — that they help keep people safe, make things fair, and help groups work well together — and follow agreed rules willingly rather than only when being watched

Ready when they can: Explain the reason behind at least two rules at home or school; Follow a rule consistently without needing to be reminded or monitored; Describe what would happen if nobody followed the rules in a specific context.

Needs first: Vocabulary: making decisions and keeping safe, Right and Wrong Choices.

https://lightmysky.com/learn/personal-and-social-development/rules-and-agreements-exist-mt_rkrG2w7WXI

#### Water Safety (ages 5-9)

Stay safe in and around water: recognise dangers at pools, beaches, rivers and ponds, follow the rules of each place (flags, signs, lifeguards, staying with an adult), and know what to do in trouble — float on your back, signal and shout

Ready when they can: State the water safety rules for a place they visit (e.g., swim between the flags, never swim alone, walk not run at the pool); Show or describe safe self-rescue: stop, float on their back, stay calm, signal and call for help; Explain what to do if someone else is struggling in water: shout for an adult or lifeguard and reach or throw something that floats, never jump in.

Needs first: Everyday Safety Awareness.

https://lightmysky.com/learn/personal-and-social-development/water-safety-mt_klF_Y8DraZ

#### Vocabulary: ethics and citizenship (ages 7-11)

Know and use the vocabulary of ethics and citizenship — bullying, cyberbullying, bystander, upstander, peer pressure, digital citizenship, rights, responsibility, and ethical — and understand the distinctions between these closely related terms

Ready when they can: Explain what 'ethics' means in their own words and give an example of an ethical dilemma; Use 'citizen', 'rights', and 'responsibilities' correctly — e.g. 'A citizen has the right to vote and the responsibility to follow laws'; Define 'consent' and 'integrity' and explain why they matter in relationships and online behaviour.

Needs first: Vocabulary: making decisions and keeping safe.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-ethics-and-citizenship-mt_h-z88yf9Pn

#### Stop, Think, Then Choose (ages 7-9)

Use a simple decision-making process when faced with a choice — stopping to think, identifying the options, considering the consequences of each option, and then choosing — rather than acting impulsively

Ready when they can: Describe at least two options when facing a decision; Predict a likely consequence for each option; Explain which option they chose and why, showing they considered the consequences.

Needs first: Vocabulary: ethics and citizenship, Choosing a Strategy, Planning a Task, Actions and Their Consequences.

https://lightmysky.com/learn/personal-and-social-development/stop-think-then-choose-mt_RhntJz7p_6

#### Understanding Bullying (ages 7-9)

Understand what bullying is — repeated behaviour intended to hurt someone, including physical, verbal, social (exclusion, spreading rumours), and cyberbullying — and know that it is always wrong and what to do if they experience or witness it

Ready when they can: Define bullying and distinguish it from a one-off conflict; Name at least three forms of bullying including cyberbullying; Describe the steps they should take if they experience or witness bullying.

Needs first: Seeing Someone Else's Point of View, Vocabulary: ethics and citizenship, Right and Wrong Choices.

https://lightmysky.com/learn/personal-and-social-development/understanding-bullying-mt_I9iSzpGRn5

#### Basic digital citizenship (ages 7-9)

Understand basic digital citizenship — being kind online, protecting personal information, recognising that people behind screens are real people with real feelings, and knowing what to do if something online makes them uncomfortable

Ready when they can: State at least three rules for staying safe and being kind online; Explain why hurtful messages online are just as harmful as saying them in person; Describe what they should do if someone online makes them feel uncomfortable or asks for personal information.

Needs first: Vocabulary: ethics and citizenship, Understanding Bullying, Everyday Safety Awareness.

https://lightmysky.com/learn/personal-and-social-development/basic-digital-citizenship-mt_zIzJGkaj0Q

#### Bystanders and Upstanders (ages 7-9)

Understand the bystander role — that when someone witnesses unkind or unfair behaviour, they have a choice: they can be a passive bystander (doing nothing), join in, or be an upstander (speaking up or getting help) — and develop the confidence to be an upstander

Ready when they can: Explain the difference between a bystander and an upstander; Describe at least two safe actions an upstander can take; Give an example of a time they or someone they know stood up for someone else.

Needs first: Vocabulary: ethics and citizenship, Understanding Bullying, Everyday Kindness and Care.

https://lightmysky.com/learn/personal-and-social-development/bystanders-and-upstanders-mt_yCmYV9ruQu

#### Community Rights and Responsibilities (ages 9-11)

Understand their rights and responsibilities as a member of a community — that everyone has a right to be treated with respect and to feel safe, and that with rights come responsibilities to treat others the same way

Ready when they can: Name at least three rights that every child has (e.g., safety, education, respect); Describe the responsibilities that go along with those rights; Give an example of how exercising their own rights responsibly supports the community.

Needs first: Vocabulary: ethics and citizenship, Rules and agreements exist.

https://lightmysky.com/learn/personal-and-social-development/community-rights-and-responsibilities-mt_h_shhH-6DC

#### First Aid You Can Actually Do (ages 9-11)

What a child can usefully do before an adult arrives: get help, keep the person still, press on a bleed with something clean, cool a burn under running water, and give an address on the phone. Includes what not to do, such as moving someone who has fallen badly.

Ready when they can: Say the emergency number for their country and what information the call handler will ask for; Demonstrate pressing on a bleeding wound and explain why pressure helps; Explain why a burn goes under cool running water and for how long; Name two situations where the right action is to fetch an adult and not to move the person.

https://lightmysky.com/learn/personal-and-social-development/first-aid-you-can-actually-do-mt_dlq0FtJVVi

#### Peer Pressure and Resisting It (ages 9-11)

Understand peer pressure — the influence friends and peers can have on your choices and behaviour — and develop strategies for resisting pressure to do something they know is wrong or that makes them uncomfortable

Ready when they can: Define peer pressure in their own words and give a real-world example; Describe at least two strategies for resisting peer pressure, such as walking away or using humour; Explain why going along with something wrong to fit in usually makes things worse.

Needs first: Vocabulary: ethics and citizenship, Stop, Think, Then Choose, Assertive Communication, Bystanders and Upstanders, Water Safety.

https://lightmysky.com/learn/personal-and-social-development/peer-pressure-and-resisting-it-mt_JivEBTD_KV

#### CPR and the Recovery Position (ages 14-16)

What to do when someone is unresponsive: check breathing, call for help and a defibrillator, start chest compressions at the right depth and rate, and use the recovery position when they are breathing. Includes why bystanders hesitate and what removes the hesitation.

Ready when they can: Check responsiveness and breathing in the right order and say what each check rules out; Give chest compressions on a manikin at roughly the right depth and rate for two minutes; Put a breathing casualty into the recovery position and say what it protects against; Name what a defibrillator does and why using one does not require training.

https://lightmysky.com/learn/personal-and-social-development/cpr-and-the-recovery-position-mt_ahwfva-o1j

#### Difficult Ethical Choices (ages 9-11)

Understand that ethical decisions are not always black and white — that sometimes there is no perfect answer and reasonable people can disagree — and practise weighing up competing values when making difficult choices

Ready when they can: Describe a moral dilemma where both sides have valid points; Explain the values in tension (e.g., loyalty vs safety, honesty vs kindness); Describe how they would make a decision in such a situation and justify their reasoning.

Needs first: Using evidence to answer questions, Mixed and Conflicting Emotions, Community Rights and Responsibilities, Stop, Think, Then Choose.

https://lightmysky.com/learn/personal-and-social-development/difficult-ethical-choices-mt_6xj94tmpi-

#### Ethics in Real-World Issues (ages 9-11)

Evaluate the ethical dimensions of real-world issues they encounter — such as environmental responsibility, fairness in sport, digital ethics, or social justice — considering multiple perspectives and forming a reasoned personal position

Ready when they can: Identify an ethical issue and describe at least two different perspectives on it; Explain which perspective they agree with most and give reasons for their position; Acknowledge that the other perspective has some validity even if they disagree.

Needs first: Difficult Ethical Choices, Questioning Your Own Biases, Community Rights and Responsibilities, Identifying Reasons Behind a Speaker's Points, Questioning First Impressions.

https://lightmysky.com/learn/personal-and-social-development/ethics-in-real-world-issues-mt_RNeEF1JU4J

#### Risk, Uncertainty, and Cognitive Bias (ages 11-12)

Distinguish between risk (decisions with known probabilities) and uncertainty (decisions with unknown outcomes); identify cognitive biases that distort risk assessment: availability heuristic (judging likelihood by how easily examples come to mind), present bias (overvaluing the immediate over the future), optimism bias (underestimating personal risk), and groupthink; understand why adolescent brains are biologically calibrated toward higher risk tolerance; apply a structured decision-making framework to real choices; understand the role of personal values in decisions where facts alone cannot determine the answer

Needs first: Ethics in Real-World Issues.

https://lightmysky.com/learn/personal-and-social-development/risk-uncertainty-and-cognitive-bias-mt_JiZ3H90Xg8

#### Online Identity and Misinformation (ages 12-13)

Understand the ethics of online identity and the importance of consistency between who you are online and offline; explain how recommendation algorithms and filter bubbles narrow information exposure; evaluate the psychology of misinformation: why it spreads, why smart people believe it, and how to apply source evaluation (lateral reading, checking evidence, recognising emotional manipulation); understand digital consent around sharing images or personal information; explore the ethics of AI, surveillance, and data privacy as they affect everyday life; reflect on responsible content creation and online influence

Needs first: Risk, Uncertainty, and Cognitive Bias, Basic digital citizenship.

https://lightmysky.com/learn/personal-and-social-development/online-identity-and-misinformation-mt_WtO50EZQkf

#### Ethical Frameworks and Moral Reasoning (ages 13-14)

Introduce the three main ethical frameworks: consequentialism (judge actions by outcomes and overall welfare), deontology (judge actions by adherence to rules and duties regardless of consequences), and virtue ethics (judge actions by the character they reflect); apply each framework to real-world moral dilemmas: climate responsibility, AI ethics, civil disobedience, wealth inequality, healthcare rationing; understand the strengths and limitations of each framework; develop the capacity for careful moral reasoning — the ability to think through ethical questions systematically rather than relying only on intuition or group opinion

Needs first: Community Rights and Responsibilities, Peer Pressure and Resisting It, Online Identity and Misinformation.

https://lightmysky.com/learn/personal-and-social-development/ethical-frameworks-and-moral-reasoning-mt_LPYPuSaxv_

#### Consent, Pressure, and the Right to Change Your Mind (ages 15-16)

Agreement counts only when it is freely given, informed, specific, and still current. Learn the marks of pressure (urgency, guilt, secrecy, an imbalance of power) and treat a withdrawn yes as final.

Ready when they can: State the four conditions that make an agreement real: freely given, informed, specific, and open to being withdrawn at any point; Read a short scenario and name which pressure move is running (urgency, guilt, secrecy, seniority); Describe how they would check that someone still agrees, and what they do the moment the answer changes.

https://lightmysky.com/learn/personal-and-social-development/consent-pressure-and-the-right-to-change-your-mind-mt_TSD3HB_ZS7

#### What a Feed Is Optimised For (ages 15-16)

A feed is ranked to hold attention, not to inform you, so posts that provoke travel further than posts that are careful. Work out who pays the platform, then read your own feed against that.

Ready when they can: Explain who pays a free platform and what the platform sells them; Give two reasons an angry post outranks a careful one when the ranking counts engagement; Change one setting or habit (notifications, follow list, time of day) and describe what it changed over a week.

https://lightmysky.com/learn/personal-and-social-development/what-a-feed-is-optimised-for-mt_kzhPakduam

#### The Version of You a Stranger Can Find (ages 15-16)

Search your own name the way an admissions tutor or an employer would, and read what the first page implies about you. Then decide what stays public on purpose rather than by accident.

Ready when they can: Search their own name and list what a stranger could conclude from the first page of results; Explain why a deleted post is not gone (screenshots, caches, other people's copies); Set one thing to private and publish one thing on purpose, and give the reason for each.

https://lightmysky.com/learn/personal-and-social-development/the-version-of-you-a-stranger-can-find-mt_VImLKlfgy4

#### Vaping, Smoking and the Decision in the Moment (ages 14-16)

The decision is rarely made in the abstract; it is made once, quickly, with people watching. Covers what nicotine does to a developing brain, why dependence forms faster than expected, what is and is not known about vaping, and how to have an answer ready before the moment arrives.

Ready when they can: Explain what nicotine does to reward and attention, and why an adolescent brain forms dependence faster; Separate what is established about vaping from what is still being measured; Say what you would actually reply in a specific situation, and why a prepared answer works better than a reason.

https://lightmysky.com/learn/personal-and-social-development/vaping-smoking-and-the-decision-in-the-moment-mt_0D_HAYKu7K

### Self-Regulation & Resilience

https://lightmysky.com/learn/personal-and-social-development/areas/self-regulation-and-resilience

#### Words for Big Feelings (ages 5-8)

Know and use the key words for managing big feelings — calm, strategy, cope, settle, patience, overwhelmed, and breathe — and understand that having words for these ideas is the first step to using them

Ready when they can: Use words like 'frustrated', 'anxious', 'overwhelmed', and 'disappointed' accurately to describe how they feel in difficult moments; Explain what 'calm down' strategies are in their own words and name at least two they have tried (e.g. deep breaths, counting, walking away); Distinguish between similar feelings — e.g. explain the difference between being angry and being disappointed.

https://lightmysky.com/learn/personal-and-social-development/words-for-big-feelings-mt_SeNxOZTHCN

#### Coping with Life Changes (ages 5-7)

Understand that change is a normal part of life — such as starting school, getting a new teacher, a new baby arriving, or moving house — and identify simple strategies that help them cope with changes

Ready when they can: Name at least two changes they have experienced and how they felt; Identify a person they can talk to when a change feels hard; Describe one strategy that helps them cope with change, such as keeping a familiar routine.

Needs first: Words for Big Feelings.

https://lightmysky.com/learn/personal-and-social-development/coping-with-life-changes-mt_aS-Gdh-MHx

#### Learning from Mistakes (ages 5-7)

Understand that making mistakes is a normal part of learning and that everyone — including adults — makes mistakes, and begin to see mistakes as opportunities to learn rather than reasons to give up

Ready when they can: Describe a time they made a mistake and what they learned from it; Respond to a mistake by trying again rather than giving up; Explain why mistakes help people learn.

Needs first: Words for Big Feelings.

https://lightmysky.com/learn/personal-and-social-development/learning-from-mistakes-mt_UGf6jICEhs

#### Simple Calming Strategies (ages 5-7)

Use simple calming strategies when feeling upset or overwhelmed — such as taking deep breaths, counting to ten, or going to a quiet space — and understand that these help the body and mind settle down

Ready when they can: Demonstrate at least two calming strategies when prompted; Choose to use a calming strategy independently during a real upset; Explain in simple terms why calming down helps them think better.

Needs first: Naming Basic Emotions, Words for Big Feelings.

https://lightmysky.com/learn/personal-and-social-development/simple-calming-strategies-mt_Iwg2diBSyW

#### Patience and Delayed Gratification (ages 5-7)

Wait for things they want without becoming very distressed — practising patience and delayed gratification in everyday situations like waiting their turn, waiting for a treat, or waiting for help

Ready when they can: Wait for their turn in a game or activity without constant complaints; Describe what they do to help themselves wait, such as thinking about something else; Explain why sometimes we have to wait and that it is a skill they can practise.

Needs first: Simple Calming Strategies, Words for Big Feelings.

https://lightmysky.com/learn/personal-and-social-development/patience-and-delayed-gratification-mt_nNDX_jZ-cb

#### Vocabulary: resilience and self (ages 7-10)

Know and use the vocabulary of resilience and self-management — including regulate, resilience, growth mindset, fixed mindset, self-talk, trigger, setback, persevere, and distress — and understand what each word means in practice

Ready when they can: Explain what 'resilience' means in their own words and give an example of a time they kept going when something was hard; Use 'growth mindset' correctly — e.g. 'I can't do it yet, but I can improve with practice'; Define 'self-regulation' and describe a strategy they use to manage frustration or setbacks.

Needs first: Words for Big Feelings.

https://lightmysky.com/learn/personal-and-social-development/vocabulary-resilience-and-self-mt_i1kk9HDctI

#### Choosing the Right Coping Strategy (ages 7-9)

Understand that different situations require different coping strategies — what works for anger might not work for sadness, and what helps at school might be different from what helps at home

Ready when they can: Name at least two different coping strategies and explain when each one is most useful; Choose an appropriate strategy based on the specific situation and emotion; Reflect on a time a strategy didn't work and explain what they might try instead.

Needs first: Vocabulary: resilience and self, Simple Calming Strategies, How Emotions Feel in Your Body.

https://lightmysky.com/learn/personal-and-social-development/choosing-the-right-coping-strategy-mt_j8Pv3s7TZR

#### Growth Mindset (ages 7-9)

Understand the concept of a growth mindset — that abilities and intelligence can grow with effort, practice, and good strategies — as opposed to a fixed mindset where you believe you're either good at something or you're not

Ready when they can: Explain the difference between growth mindset and fixed mindset in their own words; Use 'yet' language when describing something they find difficult; Give an example of something they got better at through practice and effort.

Needs first: Vocabulary: resilience and self, Learning from Mistakes, Making Sense of Problems.

https://lightmysky.com/learn/personal-and-social-development/growth-mindset-mt_pAuo9Op89t

#### Breaking Tasks into Steps (ages 7-9)

Break a challenging task into smaller, manageable steps rather than feeling overwhelmed by the whole thing — and celebrate progress along the way

Ready when they can: Take a challenging task and list at least three smaller steps to complete it; Start with the first step rather than procrastinating on the whole task; Acknowledge progress after completing each step.

Needs first: Vocabulary: resilience and self, Guided Multi-Step Problem Solving, Growth Mindset.

https://lightmysky.com/learn/personal-and-social-development/breaking-tasks-into-steps-mt_miGrca8zaS

#### Positive Self-Talk (ages 7-9)

Use positive self-talk to manage difficult situations — replacing unhelpful thoughts like 'I'm stupid' or 'I'll never be able to do this' with encouraging ones like 'This is hard but I can keep trying' or 'I've done hard things before'

Ready when they can: Give an example of an unhelpful thought and rephrase it as a helpful one; Use positive self-talk aloud or in writing when facing a challenge; Explain how the words we say to ourselves affect how we feel and perform.

Needs first: Vocabulary: resilience and self, Simple Calming Strategies, Emotion Vocabulary, Growth Mindset.

https://lightmysky.com/learn/personal-and-social-development/positive-self-talk-mt_35-DhMh_Yr

#### Personal Goal-Setting (ages 9-11)

Set realistic personal goals, create a simple plan to achieve them, monitor their own progress, and adjust their approach when things aren't working

Ready when they can: Write or state a specific, achievable personal goal with a timeframe; Describe the steps they will take to reach the goal; Review their progress and adjust their plan when something isn't working.

Needs first: Vocabulary: resilience and self, Setting Learning Goals, Breaking Tasks into Steps.

https://lightmysky.com/learn/personal-and-social-development/personal-goal-setting-mt_cJjnPjuvCU

#### Resilience and Bouncing Back (ages 9-11)

Understand resilience as the ability to recover from setbacks, adapt to difficult circumstances, and keep going — recognising that resilience is a skill that develops through experience, not a trait you either have or don't

Ready when they can: Define resilience in their own words and explain why it matters; Describe a time they bounced back from a setback and what helped them recover; Explain that resilience grows through experience and that struggling doesn't mean you're weak.

Needs first: Coping with Life Changes, Choosing the Right Coping Strategy, Emotions and Decision-Making.

https://lightmysky.com/learn/personal-and-social-development/resilience-and-bouncing-back-mt_Amw5ikSSQI

#### Personal Coping Toolkit (ages 9-11)

Reflect on which self-regulation and coping strategies work best for them personally, building a 'toolkit' of approaches they can draw on in different situations and sharing what works with others

Ready when they can: Describe at least three personal coping strategies and when each is most effective; Recommend a strategy to a friend based on the friend's specific situation; Evaluate whether a strategy they tried worked well and explain their reasoning.

Needs first: Resilience and Bouncing Back, Personal Goal-Setting, Patterns in Your Own Reactions, Choosing a Strategy.

https://lightmysky.com/learn/personal-and-social-development/personal-coping-toolkit-mt_Jd2aWEUJ9G

#### Time and Attention Management (ages 9-11)

Manage their own time and attention effectively — prioritising tasks, minimising distractions, and maintaining focus on important work even when it's not the most exciting option

Ready when they can: Create a simple plan for completing multiple tasks in a sensible order; Identify their own common distractions and describe strategies to manage them; Complete a less enjoyable task before a more enjoyable one without constant reminders.

Needs first: Breaking Tasks into Steps.

https://lightmysky.com/learn/personal-and-social-development/time-and-attention-management-mt_HoJGVsMO7H

#### Good Stress and Bad Stress (ages 11-12)

Distinguish between eustress (the productive, motivating kind of stress) and distress (harmful, overwhelming stress); explain the physiological stress response (fight-flight-freeze, HPA axis) and how chronic stress affects the body and mind; identify common adolescent stressors (academic pressure, social comparison, physical change, uncertainty about the future); evaluate evidence-based coping strategies (exercise, sleep, mindfulness, social support, expressive writing); recognise warning signs that stress has crossed into anxiety or depression and know where to get help

Needs first: Resilience and Bouncing Back.

https://lightmysky.com/learn/personal-and-social-development/good-stress-and-bad-stress-mt_0VOZSVjo6c

#### Habits and Motivation (ages 12-13)

Understand habit formation through the cue-routine-reward loop and how to design new habits intentionally; distinguish intrinsic motivation (doing something for its own value) from extrinsic motivation (rewards/punishments) and understand when each is more effective; understand procrastination as primarily an emotion regulation problem (avoiding discomfort) rather than a time management failure; apply self-determination theory (autonomy, competence, relatedness) to boost intrinsic motivation; design environments that reduce friction for desired behaviours

Needs first: Good Stress and Bad Stress, Personal Goal-Setting, Patience and Delayed Gratification.

https://lightmysky.com/learn/personal-and-social-development/habits-and-motivation-mt_0ewYhTSHtP

#### Growth Through Adversity (ages 13-14)

Understand that facing serious challenges can lead to genuine growth in three domains: new perspectives on life, improved relationships, and a strengthened sense of personal capability (post-traumatic growth); distinguish genuine growth from toxic positivity ('everything happens for a reason') and from denial; understand that resilience does not mean being unaffected by adversity but recovering and growing through it; develop a personal philosophy for handling setbacks based on meaning-making; explore how to support others going through serious difficulty without minimising their experience

Needs first: Habits and Motivation, Personal Coping Toolkit.

https://lightmysky.com/learn/personal-and-social-development/growth-through-adversity-mt__J2BO4V95l

#### How Short Nights Change Your Judgement (ages 15-16)

Missed sleep adds up, and it shows first in judgement, patience, and recall rather than in feeling sleepy. Track a week, then time your hardest decisions for the hours you are rested.

Ready when they can: Log a week of sleep and match the shortest nights against how the next day went; Name three effects of a short night that are not tiredness (thinner patience, weaker recall, faster risk-taking); Move one real decision to a rested hour and say why the timing mattered.

https://lightmysky.com/learn/personal-and-social-development/how-short-nights-change-your-judgement-mt_YvDXYIiyAb

#### Asking for Help Beyond Your Friends (ages 15-16)

Some rough patches are bigger than a friend can carry. Decide by how long it has run, whether ordinary life still works, and whether anyone is at risk, then pick who to tell and what to say first.

Ready when they can: State their own rule for when a rough patch stops being an ordinary bad week (how long it has run, whether school and eating and sleep still work, whether anyone is at risk); Name three people or services they could go to and what each one is actually for; Write the first two sentences they would say, in plain words, without making it sound smaller than it is.

https://lightmysky.com/learn/personal-and-social-development/asking-for-help-beyond-your-friends-mt_IBCfPurkXk

#### Knowing When a Feeling Needs Help (ages 16-18)

Low mood and anxiety are ordinary until they stop you doing things you care about for weeks. Telling the difference, and knowing what help actually looks like, is information most people get too late.

Ready when they can: Name the signals that a low patch has become something worth getting help with; Describe what happens at a first appointment, so the unknown stops being a reason not to go; Say one thing you can do for a friend in that position and one thing that is not yours to carry.

https://lightmysky.com/learn/personal-and-social-development/knowing-when-a-feeling-needs-help-mt_dbQHbKNTZP

### Ethics & Philosophy

https://lightmysky.com/learn/personal-and-social-development/areas/ethics-and-philosophy

#### What Makes an Argument Valid (ages 16-18)

An argument can be valid and still have a false conclusion, and it can reach a true conclusion by luck. Separating the shape of the reasoning from the truth of the parts is the first move in philosophy and in every argument after it.

Ready when they can: Set out an argument as premises and a conclusion, in your own words; Give an example of a valid argument with a false conclusion and explain why it is still valid; Say what has to be added to validity to get soundness.

https://lightmysky.com/learn/personal-and-social-development/what-makes-an-argument-valid-mt_W72nTJmeOI

#### Facts, Values and the Gap Between Them (ages 16-18)

No list of facts about the world adds up on its own to a claim about what should happen. Every moral argument therefore smuggles in a value somewhere, and finding where is the useful skill.

Ready when they can: Separate the factual claims from the value claims in a short argument; Explain why an argument that runs only on facts cannot reach a should; Identify the hidden value premise in an argument that pretends to be purely practical.

https://lightmysky.com/learn/personal-and-social-development/facts-values-and-the-gap-between-them-mt_cvgg2UNDzv

#### Consequences: The Greatest Good and Its Problems (ages 16-18)

One family of moral theories says the right act is the one with the best results, counting everyone equally. It is used in every public health decision, and it also produces conclusions most people refuse to accept.

Ready when they can: State the core claim of consequentialism and apply it to a public spending choice; Give a case where it recommends something that feels clearly wrong, and say what the objection is; Explain one repair consequentialists offer, such as judging rules rather than single acts.

https://lightmysky.com/learn/personal-and-social-development/consequences-the-greatest-good-and-its-problems-mt_XD8-rBho01

#### Duties and Rights: What You Owe Regardless of Outcome (ages 16-18)

A second family says some acts are forbidden whatever the results, because people are owed treatment they cannot be traded away from. This is where the language of rights, consent and dignity comes from.

Ready when they can: State the duty-based claim and apply it to the same case used for consequences; Explain what it means to treat someone only as a means, with an example; Give a case where two duties conflict and say how the theory handles it.

https://lightmysky.com/learn/personal-and-social-development/duties-and-rights-what-you-owe-regardless-of-outcome-mt_Mwtr4NwfUE

#### Character: The Kind of Person You Are Becoming (ages 16-18)

A third family asks not what to do in this case but what habits make a life go well, an approach shared by Aristotle, Confucius and the Daoists. It handles the ordinary parts of a life that rules and calculations both miss.

Ready when they can: Explain what a virtue is and why it sits between two failings rather than at one end; Say what this approach offers that rule-based and outcome-based accounts do not; Name a habit you are currently building and say what it is training you to become.

https://lightmysky.com/learn/personal-and-social-development/character-the-kind-of-person-you-are-becoming-mt_7GCNpcZGku

#### Justice: Who Deserves What, and Why (ages 16-18)

Arguments about tax, inheritance, university places and healthcare are all arguments about what people are owed and on what grounds: need, effort, contribution, or simply being a person. Asking what rules you would pick without knowing your own position is one honest way in.

Ready when they can: State three different bases for distributing something scarce and give a case where each seems right; Explain what changes when you have to choose the rules before knowing which position you will hold; Take one real policy and say which conception of justice it assumes.

https://lightmysky.com/learn/personal-and-social-development/justice-who-deserves-what-and-why-mt_umi3pKeHa1

#### The Ethics of the Tools We Build (ages 16-18)

Systems that rank, predict and decide about people distribute harm without anyone choosing to harm anyone. Applied ethics is where the frameworks meet a specific technology and have to say something concrete.

Ready when they can: Take one automated decision system and say who bears the cost when it is wrong; Apply two of the three moral frameworks to the same technology case and compare their verdicts; Explain why a duty owed to future people or to a species is harder to argue for than a duty to a neighbour.

https://lightmysky.com/learn/personal-and-social-development/the-ethics-of-the-tools-we-build-mt_eZh-vIoluR

## Life Skills

70 topics, ages 5 to 18. https://lightmysky.com/learn/life-skills

### Money & Finance

https://lightmysky.com/learn/life-skills/areas/money-and-finance

#### What Money Is (ages 5-7)

What money is and why we use it; that money is exchanged for goods and services; brief history from barter to coins to digital payments

Ready when they can: Explain that people use money to pay for things they need or want; Give an example of how buying worked before money existed (swapping or bartering); Name at least two forms money can take (coins, notes, card, phone payment).

https://lightmysky.com/learn/life-skills/what-money-is-mt_SsS7GptD_o

#### Jobs People Do (ages 5-7)

Different kinds of work people do; that people earn money by working; how jobs help the community; linking personal interests to possible jobs

Ready when they can: Name at least five different jobs and describe what each person does; Explain that people get paid money for the work they do; Connect a personal interest to a job (e.g. 'I like animals so I could be a vet').

Needs first: What Money Is.

https://lightmysky.com/learn/life-skills/jobs-people-do-mt_asRwlPZXC3

#### Needs & Wants (ages 5-7)

The difference between things we need (food, shelter, clothing) and things we want (toys, treats); that we sometimes have to choose because money is limited

Ready when they can: Sort a set of pictures into 'need' and 'want' categories and explain their choices; Give an example of something everyone needs and something that is a want; Explain why a family might choose to buy a need before a want.

Needs first: What Money Is.

https://lightmysky.com/learn/life-skills/needs-and-wants-mt__ab4knIaSL

#### Saving Money (ages 5-7)

Why people save money; piggy banks and saving jars; setting a savings goal; the idea that not spending now means having more later

Ready when they can: Explain why someone might save money instead of spending it straight away; Describe a savings goal they could set and how they would work towards it; Tell you what delayed gratification means in their own words (waiting to get something better).

Needs first: Needs & Wants, What Money Is.

https://lightmysky.com/learn/life-skills/saving-money-mt_zrCyqhngYm

#### Earning Money (ages 7-9)

Ways that children and adults earn money; the connection between work, skills and pay; that harder or more skilled work often pays more

Ready when they can: Name at least three different ways people can earn money; Explain why a doctor might earn more than a shop assistant (training, skills, responsibility); Describe a way a child could earn money (chores, car wash, selling crafts).

Needs first: Jobs People Do.

https://lightmysky.com/learn/life-skills/earning-money-mt_uP9faJlnRq

#### Coins & Notes (ages 5-7)

Recognising common coins and notes, knowing their values, and understanding that different combinations can make the same amount

Ready when they can: Sort a handful of mixed coins into groups by value; State the value of common coins and notes when shown them; Find two different ways to make the same amount using different coins.

Needs first: Coin Values, What Money Is.

https://lightmysky.com/learn/life-skills/coins-and-notes-mt_FIkqA0qhnj

#### Buying Things (ages 5-7)

How buying and selling works: prices, paying for items, receiving change; the basic transaction process in shops and markets

Ready when they can: Explain what happens when you buy something in a shop (choose, pay, get change); Read a price label and say whether they have enough money to buy the item; Act out a simple buying scenario using real or play coins.

Needs first: Coins & Notes.

https://lightmysky.com/learn/life-skills/buying-things-mt_RNRymbz5SO

#### Looking After Money (ages 5-7)

Keeping money safe; not losing coins or notes; understanding that money has real value and should be treated carefully; basic money responsibility

Ready when they can: Describe at least two ways to keep money safe (purse, wallet, money box, giving to a grown-up); Explain why it matters if you lose money; Show that they treat real coins and notes carefully rather than leaving them lying around.

Needs first: Coins & Notes.

https://lightmysky.com/learn/life-skills/looking-after-money-mt_FNSeo9_T2Z

#### Advertising & Spending (ages 7-9)

How advertising tries to influence what we buy; being a critical consumer; understanding 'value for money'; the difference between emotional and rational spending

Ready when they can: Spot at least two persuasion techniques in a real advert (bright colours, celebrity, special offer); Explain what 'value for money' means and compare two similar products at different prices; Describe a time when advertising made them want something they didn't really need.

Needs first: Needs & Wants, Buying Things.

https://lightmysky.com/learn/life-skills/advertising-and-spending-mt_My0OL6fhGL

#### Banks & Saving (ages 7-9)

What banks do and why people use them; bank accounts as safe places for money; that savings in a bank can earn interest; children's savings accounts

Ready when they can: Explain what a bank does in simple terms (keeps money safe, lets you save); Describe what interest means (the bank pays you a little extra for keeping money there); Name one reason a bank account is safer than keeping all your money at home.

Needs first: Looking After Money, Saving Money.

https://lightmysky.com/learn/life-skills/banks-and-saving-mt_uSUqTjOl8m

#### Budgeting Pocket Money (ages 7-9)

What a budget is; planning how to spend a fixed amount of pocket money or allowance; making trade-offs between different things you want to buy

Ready when they can: Create a simple spending plan for £10 showing what they would buy and how much is left; Explain what a budget is and why it helps to plan spending; Identify a trade-off (choosing one thing means not having enough for another).

Needs first: Needs & Wants, Buying Things, Saving Money.

https://lightmysky.com/learn/life-skills/budgeting-pocket-money-mt_Qzbh-_v0Gq

#### Fair Trade & Ethics (ages 7-9)

Where products come from and who makes them; that people around the world produce what we buy; fair pay for workers; making ethical choices as consumers

Ready when they can: Explain that the things we buy are made by real people, sometimes in other countries; Describe what 'fair trade' means in simple terms (workers get paid fairly); Give an example of a kind choice a shopper could make (buying fair trade chocolate, choosing less packaging).

Needs first: Needs & Wants, Buying Things.

https://lightmysky.com/learn/life-skills/fair-trade-and-ethics-mt_HPf-dVtA3p

#### Ways to Pay (ages 7-9)

Different ways to pay: cash, debit cards, contactless, online payments, mobile payments; that digital payments still use real money; keeping payment details safe

Ready when they can: Name at least four different ways people can pay for things; Explain that tapping a card or phone still spends real money from a bank account; Give one reason why you should keep card numbers and passwords private.

Needs first: Looking After Money, Buying Things.

https://lightmysky.com/learn/life-skills/ways-to-pay-mt_K8_RYIvrTV

#### Borrowing & Debt (ages 9-11)

What borrowing money means; that loans must be repaid with interest; what credit is; why too much debt can be risky; responsible borrowing

Ready when they can: Explain what a loan is and that borrowed money must be paid back with extra (interest); Give an example of when borrowing might be sensible (buying a house) versus risky (buying luxuries you can't afford); Describe what happens if someone borrows too much money and can't repay it.

Needs first: Budgeting Pocket Money, Banks & Saving.

https://lightmysky.com/learn/life-skills/borrowing-and-debt-mt_bAy4dmP1-A

#### Financial Planning (ages 9-11)

Setting longer-term financial goals; planning and prioritising spending; how saving regularly adds up over time; the value of thinking ahead with money

Ready when they can: Set a realistic savings goal and calculate how long it would take saving a fixed amount each week; Create a simple financial plan for a specific purpose (birthday party, school trip, gift); Explain why planning ahead with money is better than spending everything as it comes in.

Needs first: Budgeting Pocket Money, Banks & Saving.

https://lightmysky.com/learn/life-skills/financial-planning-mt_r1hw-KenpK

#### How the Economy Works (ages 9-11)

What an economy is; producers and consumers; supply and demand; why prices change; the basics of how markets work

Ready when they can: Explain what 'supply and demand' means using a simple example (ice cream on a hot day); Describe the difference between a producer and a consumer; Give a reason why the price of something might go up or down.

Needs first: Jobs People Do, Advertising & Spending, Buying Things.

https://lightmysky.com/learn/life-skills/how-the-economy-works-mt_udgPy5oAvR

#### Global Trade (ages 9-11)

Why countries trade with each other; imports and exports; how goods travel around the world; that different countries use different currencies

Ready when they can: Explain why countries buy goods from other countries (they can't make everything themselves); Give examples of imported and exported products from their own country; Explain that different countries use different currencies and you need to exchange money when travelling.

Needs first: Fair Trade & Ethics, How the Economy Works.

https://lightmysky.com/learn/life-skills/global-trade-mt_0Rx1ISxXFE

#### Scams & Online Safety (ages 9-11)

Recognising financial scams and tricks; phishing emails and fake websites; protecting personal and financial information online; 'if it seems too good to be true, it probably is'

Ready when they can: Identify at least two warning signs of a scam (asking for personal details, too-good-to-be-true offers, urgency); Explain why you should never share passwords or bank details online; Describe what to do if they receive a suspicious message or email (don't click, tell an adult).

Needs first: Looking After Money, Ways to Pay, Deepfakes and AI-Generated Content.

https://lightmysky.com/learn/life-skills/scams-and-online-safety-mt_W5euSyU2sO

#### Taxes & Public Services (ages 9-11)

What taxes are and why people pay them; how taxes fund schools, hospitals, roads, and emergency services; that governments decide how to spend tax money

Ready when they can: Explain what tax is and that most working adults pay it; Name at least three things that taxes pay for (schools, hospitals, roads, police, fire service); Describe why taxes are needed (everyone chips in so everyone benefits).

Needs first: How the Economy Works, Earning Money.

https://lightmysky.com/learn/life-skills/taxes-and-public-services-mt_cSz7XTxVAx

#### Your First Bank Account and Card (ages 12-13)

A current account turns money into a balance you check on a screen, which is easier to spend and harder to feel. Knowing what each part of the app is telling you is the first defence.

Ready when they can: Explain the difference between the balance and the money actually available to spend; Say what a direct debit is and how it differs from a one-off payment; Describe what to do first if a card is lost or a payment looks wrong.

https://lightmysky.com/learn/life-skills/your-first-bank-account-and-card-mt_YoV2gRHaLS

#### Making Change (ages 7-9)

Calculating change from a purchase; working confidently with pounds and pence together; solving practical money problems involving addition and subtraction

Ready when they can: Calculate the change from £5 when buying items costing pounds and pence; Add two or three prices together to find a total cost; Check whether they have been given the correct change in a role-play scenario.

Needs first: Money Addition & Subtraction, Adding money and giving change, Buying Things.

https://lightmysky.com/learn/life-skills/making-change-mt_aWOK1npO5s

#### Comparing Prices Properly (ages 12-13)

The cheaper item is often the one that costs more per use, per gram or per month. Working out the right unit before comparing is the whole skill.

Ready when they can: Compare two products by unit price rather than by shelf price; Work out the cost per wear or per use for something bought once and used often; Spot one offer where buying more does not lower the unit price.

https://lightmysky.com/learn/life-skills/comparing-prices-properly-mt_v3i0WMP-Sl

#### A Budget That Survives a Real Month (ages 14-15)

Split spending into fixed and variable, leave a buffer for the thing you did not predict, then track a month and compare it against the plan. The gap between plan and actual is the number that teaches you something.

Ready when they can: Build a one-month budget that separates fixed commitments from variable spending and carries a buffer line; Track actual spending for a month and say where the plan was wrong; Adjust the next month using that gap instead of writing a fresh plan from scratch.

https://lightmysky.com/learn/life-skills/a-budget-that-survives-a-real-month-mt_tFRHTFelNG

#### What Comes Out of a First Payslip (ages 15-16)

Gross pay is the rate times the hours. Net pay is what lands after income tax, national insurance, and any pension. Read a payslip line by line and check it against the hours you worked.

Ready when they can: Work out gross pay from an hourly rate and hours, then explain each deduction between gross and net; Check a payslip against their own record of hours and say what to do when the two do not match; Explain why two people on the same hourly rate can take home different amounts.

https://lightmysky.com/learn/life-skills/what-comes-out-of-a-first-payslip-mt_L4Ygz5CNjP

#### Reading What You Agree To (ages 15-16)

An agreement binds you to the terms, not to what you assumed. Find the four that usually bite: how long it runs, how much notice you owe, whether it renews itself, and what leaving early costs.

Ready when they can: Locate the length, notice period, renewal, and exit terms in a short real agreement; Say what each side is entitled to do under the terms, separately from what feels fair; Name one term they would ask about or want changed before signing.

https://lightmysky.com/learn/life-skills/reading-what-you-agree-to-mt_HIrPCOAxYt

#### Subscriptions and the Default to Renew (ages 15-16)

A subscription keeps charging until you stop it, so forgetting is the default setting. Annualise the monthly price, list everything running, and compare cost per use against buying the thing once.

Ready when they can: List every recurring charge on an account and total what they cost over a year; Convert a monthly price to a yearly one and compare it against a one-off purchase of the same thing; Explain how a free trial becomes a charge and what they would set so it does not arrive as a surprise.

https://lightmysky.com/learn/life-skills/subscriptions-and-the-default-to-renew-mt_jvVqDwwHIj

#### The Real Cost of Buying Now and Paying Later (ages 15-16)

Credit turns one price into a stream of payments plus interest. Work out the total repaid rather than the monthly figure, and see what paying only the minimum does to a balance over a year.

Ready when they can: Work out the total repaid under a credit offer and compare it against the cash price; Explain what an annual interest rate means for a balance that is not cleared each month; Show what happens to a balance when only the minimum payment is made each month.

https://lightmysky.com/learn/life-skills/the-real-cost-of-buying-now-and-paying-later-mt_VidrDsqJqA

#### The Four Moves Behind a Scam (ages 15-16)

Most scams run the same four moves: a reason to hurry, a borrowed authority, a request to keep it quiet, and a payment route that cannot be reversed. Verify through a channel you looked up yourself.

Ready when they can: Name the four moves in a scam message and point at each one in a real example; Explain why letting someone else move money through your account makes you the person the bank comes to; Verify a request by contacting the organisation through a number or address they found themselves, not one in the message.

https://lightmysky.com/learn/life-skills/the-four-moves-behind-a-scam-mt_0H9a6qv2XL

#### Saving for Something Months Away (ages 12-13)

A goal that takes four months needs a number per week and a place to keep the money where it is awkward to reach. Most saving fails on the second part, not the first.

Ready when they can: Turn a target amount and a date into a weekly amount to put aside; Name two ways to make saved money harder to spend by accident; Say what to do when one week's contribution is missed, other than giving up.

https://lightmysky.com/learn/life-skills/saving-for-something-months-away-mt_NFZG8bDa5o

#### The True Cost of a Phone (ages 12-13)

A phone on a contract is a loan for the handset plus a rental for the network, wrapped so the two are hard to separate. Adding up the whole term is usually a surprise.

Ready when they can: Multiply a monthly cost by the contract length and compare it with buying outright plus a cheap plan; Explain what a contract locks you into and what an early exit costs; Name two extras that are easy to miss, such as insurance or data overage.

https://lightmysky.com/learn/life-skills/the-true-cost-of-a-phone-mt_L_o7NzVuh5

#### Spending Inside Games and Apps (ages 12-13)

Free games make money from a small share of players, so the design is built to make spending feel like progress. Recognising the moves is what turns a nudge back into a decision.

Ready when they can: Name three design moves that encourage spending, such as timers, streaks or a currency that hides the real price; Convert an in-game currency purchase back into real money per item; Say what a random-reward purchase is actually selling, and why the odds matter.

https://lightmysky.com/learn/life-skills/spending-inside-games-and-apps-mt_DCmLETXmjd

#### Protecting Money and Identity (ages 16-18)

Once there is real money in an account, you become worth attacking. Most of the defence is a handful of habits set up once, before anything goes wrong.

Ready when they can: Name what a bank will never ask for, and what to do when someone asks anyway; Set up the account protections that matter and say what each one blocks; Describe the first three steps after discovering a fraudulent payment.

https://lightmysky.com/learn/life-skills/protecting-money-and-identity-mt_h1OSxzjD2T

#### Tax: What You File and Why (ages 16-18)

Most employees never file anything, and then one year they have a second job, a side income or an overpayment and suddenly they do. Knowing which situation you are in is most of the work.

Ready when they can: Say which circumstances turn an employee into someone who has to file a return; Explain what an allowance or threshold is and what happens to income above it; Describe what records to keep during the year so filing takes an hour rather than a weekend.

https://lightmysky.com/learn/life-skills/tax-what-you-file-and-why-mt_ukXzPycdh0

#### Renting a Place and What It Really Costs (ages 16-18)

The rent is the advertised number and rarely the real one: deposit, bills, council charges and travel all land on top. The contract also decides who pays when something breaks.

Ready when they can: Build a monthly total from rent, bills, and travel for a specific place; Name three clauses in a tenancy agreement worth reading before signing; Say what a deposit protects, who holds it, and on what grounds it can be kept.

https://lightmysky.com/learn/life-skills/renting-a-place-and-what-it-really-costs-mt_jxyHZEprXc

#### Credit Files and What Lenders See (ages 16-18)

Every borrowing decision made about you rests on a file you did not write and can inspect. Small habits build it, and a few specific events damage it for years.

Ready when they can: Name three things that appear on a credit file and how long each stays; Explain why having no history can be treated much like a bad history; Describe how to check your own file and what to do about an error on it.

https://lightmysky.com/learn/life-skills/credit-files-and-what-lenders-see-mt_SfwNy9cOjb

#### Applying for a Job: The Application, the CV and the Interview (ages 16-18)

An application is read for about a minute by someone with a stack of them, so it has to answer what they are checking for. Covers matching a CV to a specific advert, what a reference actually is, preparing for the two or three questions that always appear, and following up.

Ready when they can: Rewrite one CV for two different adverts and say what changed and why; Name what an employer is checking in the first minute and where on the page they find it; Answer the question about a time something went wrong, with a structure that ends on what changed; Say who to ask for a reference and what to give them before asking.

https://lightmysky.com/learn/life-skills/applying-for-a-job-the-application-the-cv-and-the-interview-mt_H4fIhsLvEV

#### Insurance: Paying Not to Be Ruined (ages 16-18)

Insurance is a bad deal on average and a good deal against the losses you could not absorb. That single rule decides which policies are worth buying and which are sold on fear.

Ready when they can: State the rule for which risks are worth insuring and apply it to three examples; Explain what an excess does to a premium and to your own incentives; Name one common policy that fails the rule and say why it is still sold.

https://lightmysky.com/learn/life-skills/insurance-paying-not-to-be-ruined-mt_JrCLZCH881

#### Starting a Pension at Eighteen (ages 16-18)

Money put aside at eighteen has four decades to compound, which makes early contributions worth several times later ones. It is the only financial decision where being young is the whole advantage.

Ready when they can: Compare the final value of the same contribution started at twenty and at forty; Explain what an employer match is and why declining it is turning down pay; Say what a fee of one percent a year does over forty years.

https://lightmysky.com/learn/life-skills/starting-a-pension-at-eighteen-mt_mGfpMq2IAW

#### Paying for What Comes After School (ages 16-18)

Courses, apprenticeships and training all have a price and a payoff, and both vary far more by subject and provider than by prestige. Comparing them honestly needs the repayment terms, not just the sticker price.

Ready when they can: Compare two post-school paths on total cost, earnings foregone, and what is repaid and when; Explain how a repayment threshold changes who actually pays the full amount; Name two forms of support that do not have to be repaid and how to find them.

https://lightmysky.com/learn/life-skills/paying-for-what-comes-after-school-mt_Zarsb85RH9

### Entrepreneurship

https://lightmysky.com/learn/life-skills/areas/entrepreneurship

#### Goods & Services (ages 5-7)

Some people make things (goods) and some people do things for others (services); recognising both in everyday life and understanding that both have value

Ready when they can: Sort a set of pictures into goods (things you can touch) and services (things people do for you); Give three examples of goods and three examples of services from their everyday life; Explain that both making things and helping people are valuable kinds of work.

https://lightmysky.com/learn/life-skills/goods-and-services-mt_RgQxPddV8v

#### Buyers & Sellers (ages 5-7)

When someone makes or has something, they can sell it; when someone wants something, they can buy it; introduction to the concept of exchange and transactions

Ready when they can: Explain what a buyer does and what a seller does; Act out a simple buying and selling transaction with a partner; Describe a time they or a family member bought something from a person (market stall, car boot sale, bake sale).

Needs first: Goods & Services, What Money Is.

https://lightmysky.com/learn/life-skills/buyers-and-sellers-mt_SbEaQnMQoD

#### Making Something to Sell (ages 5-7)

The experience of creating a product to sell — a craft, a drawing, baked goods; what makes something worth buying; pride in making something others want

Ready when they can: Create a simple product (craft, drawing, baked item) that could be sold; Explain what makes their product good enough for someone to want to buy it; Suggest a fair price for their product and give a reason.

Needs first: Needs & Wants, Buyers & Sellers.

https://lightmysky.com/learn/life-skills/making-something-to-sell-mt_CrGnpVjnk8

#### Who Is a Customer? (ages 5-7)

Understanding that a customer is someone who buys what you make or do; thinking about what customers want and need; the idea that businesses serve people

Ready when they can: Define what a customer is in their own words; Suggest what a customer might look for when deciding whether to buy something (quality, price, looks nice); Explain why it matters to think about what the customer wants, not just what you want to make.

Needs first: Making Something to Sell, Buyers & Sellers.

https://lightmysky.com/learn/life-skills/who-is-a-customer-mt_vpMDMbx4pc

#### Being a Good Seller (ages 7-9)

Customer service, fairness, and honesty in business; keeping promises to customers; why being trustworthy matters for repeat business and reputation

Ready when they can: Explain why being honest about what you're selling matters; Describe what good customer service looks like (being polite, helpful, keeping promises); Give an example of how being unfair or dishonest could hurt a business.

Needs first: Making Something to Sell, Who Is a Customer?.

https://lightmysky.com/learn/life-skills/being-a-good-seller-mt_cq711F7ruL

#### Having a Business Idea (ages 7-9)

Where business ideas come from; spotting everyday problems and thinking of solutions; the difference between inventing something new and improving something that exists

Ready when they can: Identify a simple everyday problem and suggest a product or service that could solve it; Explain the difference between an invention (something new) and an innovation (making something better); Describe where one real entrepreneur got their business idea from.

Needs first: Making Something to Sell, Who Is a Customer?.

https://lightmysky.com/learn/life-skills/having-a-business-idea-mt_RTwmvr9R7V

#### Marketing Basics (ages 7-9)

How people find out about what you're selling; signs, posters, social media, word of mouth; being persuasive; the basics of advertising and promotion

Ready when they can: Design a simple poster or advert for a product or service; Name at least three ways to let people know about something you're selling; Explain why a catchy name or eye-catching design helps sell more.

Needs first: Having a Business Idea, Who Is a Customer?.

https://lightmysky.com/learn/life-skills/marketing-basics-mt_M2Gou3O6qT

#### Social Enterprise (ages 9-11)

Using business skills to help others or solve social and environmental problems; making money AND making a difference; examples of social enterprises

Ready when they can: Explain what a social enterprise is in their own words (a business that helps people or the planet); Give an example of a real social enterprise or charity shop; Suggest a social enterprise idea that could help their school or community.

Needs first: Being a Good Seller, Having a Business Idea.

https://lightmysky.com/learn/life-skills/social-enterprise-mt_QepALf3bin

#### Making a Simple Plan (ages 7-9)

Before starting a business, making a simple plan: what will I make or do, who will buy it, what do I need, how much will it cost, and what price will I charge?

Ready when they can: Write or draw a simple business plan covering: product, customer, materials needed, and price; Identify at least three things they would need before they could start selling; Explain why planning ahead is better than just starting without thinking.

Needs first: Budgeting Pocket Money, Having a Business Idea.

https://lightmysky.com/learn/life-skills/making-a-simple-plan-mt_phpn6KhCAv

#### Learning from Failure (ages 7-9)

Not every business idea works; entrepreneurs try, fail, learn, and try again; iteration and resilience as core entrepreneurial skills; famous failure-to-success stories

Ready when they can: Give an example of a famous entrepreneur who failed before succeeding; Explain what they would do differently if a business idea didn't work the first time; Describe why failing and trying again is better than giving up.

Needs first: Making a Simple Plan, Having a Business Idea.

https://lightmysky.com/learn/life-skills/learning-from-failure-mt_dknMcCqvoY

#### Teamwork in Business (ages 7-9)

Most businesses need more than one person; working together, dividing tasks, and using different people's strengths; the value of teamwork in business

Ready when they can: Describe how they would divide tasks in a team business project (one person makes, one sells, one designs); Explain why using people's different strengths makes a business better; Give an example of a problem that could happen if a team doesn't work well together.

Needs first: Making a Simple Plan.

https://lightmysky.com/learn/life-skills/teamwork-in-business-mt_pOstrrS763

#### Pitching an Idea (ages 9-11)

Presenting a business idea to others convincingly; explaining what makes it good and why people should support it; building confidence in public speaking about ideas

Ready when they can: Deliver a 1-2 minute pitch for a business idea covering: what it is, who it helps, and why it's good; Answer at least two questions about their idea from an audience; Explain why being able to explain your idea clearly matters for getting support.

Needs first: Marketing Basics, Making a Simple Plan.

https://lightmysky.com/learn/life-skills/pitching-an-idea-mt_bAYy0ytbfC

#### Real Entrepreneurs (ages 9-11)

Stories of real entrepreneurs who started young: Mikaila Ulmer (Me & the Bees), Moziah Bridges (Mo's Bows), Cory Nieves (Mr. Cory's Cookies); what makes someone an entrepreneur

Ready when they can: Retell the story of at least one real entrepreneur who started as a child; Identify three qualities that helped that entrepreneur succeed (creativity, persistence, passion); Explain what the word 'entrepreneur' means in their own words.

Needs first: Learning from Failure, Having a Business Idea.

https://lightmysky.com/learn/life-skills/real-entrepreneurs-mt_rxJ2O_9Lkr

#### Finding Out If Anyone Wants It (ages 12-13)

The cheapest way to learn an idea is wrong is to ask the people it is for before building anything. Asking well means not leading them to the answer you want.

Ready when they can: Write three questions that could get a no, rather than three that fish for a yes; Explain why what people say they would buy is weaker evidence than what they have already bought; Say what result would make you drop the idea.

https://lightmysky.com/learn/life-skills/finding-out-if-anyone-wants-it-mt_99X6saJ6Kt

#### Costs & Revenue (ages 7-9)

It costs money to make things (costs/expenses); you earn money by selling them (revenue); if revenue is more than costs, that's profit; if costs are more, that's a loss

Ready when they can: Explain what costs, revenue, and profit mean using a simple example; Calculate profit from a given scenario (e.g. spent £3 on ingredients, sold cakes for £8, profit = £5); Explain what happens if costs are higher than revenue (you make a loss).

Needs first: Making Change, Making a Simple Plan, Buyers & Sellers.

https://lightmysky.com/learn/life-skills/costs-and-revenue-mt_9gpUHWVKMR

#### Scaling Up (ages 9-11)

What happens when a small business grows; making more products, hiring people, reaching more customers; the challenges and opportunities of scaling

Ready when they can: Describe what 'scaling up' means for a business; Identify at least two challenges of growing a business (need more money, more people, more materials); Explain how a lemonade stand could grow into a bigger business step by step.

Needs first: Costs & Revenue, Teamwork in Business, Financial Planning.

https://lightmysky.com/learn/life-skills/scaling-up-mt_7SsduPB2tP

#### Pricing So the Numbers Work (ages 12-13)

A price has to cover what each item costs to make and leave something over, and it has to be one people will pay. Break-even is where those two facts meet.

Ready when they can: Work out the cost of making one unit, including the parts people forget; Calculate how many units must sell to cover a fixed setup cost; Explain why cutting the price to sell more can leave you worse off.

https://lightmysky.com/learn/life-skills/pricing-so-the-numbers-work-mt_m4DGdFIm5h

#### Unit Economics: Does Each Sale Make Money? (ages 16-18)

A business can grow fast and lose more with every customer it wins. The test is what one more sale costs to win and to serve, against what it brings in.

Ready when they can: Work out the contribution from one sale after the costs that vary with it; Explain why acquisition cost has to be counted per customer, not per month; Say what growing faster does to a business whose unit economics are negative.

https://lightmysky.com/learn/life-skills/unit-economics-does-each-sale-make-money-mt_NUoV6LB-o4

#### Supply Chains (ages 9-11)

Where products come from before they reach the customer; raw materials, making, transporting, and selling; the journey of a product from start to finish

Ready when they can: Trace the journey of a familiar product (e.g. chocolate bar) from raw material to shop shelf; Identify at least three stages in a supply chain; Explain why a long supply chain can make a product more expensive.

Needs first: Global Trade, Costs & Revenue, Goods & Services, Where Things Come From.

https://lightmysky.com/learn/life-skills/supply-chains-mt_tqgZH11cP5

#### Ethics in Business (ages 9-11)

Being honest, being fair, treating workers well, not harming the environment; what makes a 'good' business; whether businesses should care about more than profit

Ready when they can: Name at least two things that make a business ethical (fair wages, honest advertising, environmentally responsible); Explain why a business that only cares about profit might cause problems; Describe a situation where a business owner faces an ethical choice and suggest what they should do.

Needs first: Being a Good Seller, Fair Trade & Ethics, Social Enterprise, Supply Chains.

https://lightmysky.com/learn/life-skills/ethics-in-business-mt_b0sXYFblDL

#### Doing It Right When Nobody Is Watching (ages 12-13)

A small business runs on promises kept when breaking them would be easier and cheaper. Reputation is the only asset a young venture actually has.

Ready when they can: Describe a case where the profitable choice and the honest one differ, and say what you would do; Explain why exaggerating what a product does costs more than it gains over a year; Name one thing a small seller owes a customer even without a written contract.

https://lightmysky.com/learn/life-skills/doing-it-right-when-nobody-is-watching-mt_MViH0gLbvQ

#### The Smallest Version Worth Testing (ages 16-18)

Building the whole thing before anyone has paid for it is the standard way to waste a year. The useful question is what is the least you could put in front of a real customer that would still teach you something.

Ready when they can: Reduce an idea to the smallest version that still tests the risky assumption; Name the one assumption whose failure would kill the whole idea, and design the test for it; Explain why a test that cannot fail teaches nothing.

https://lightmysky.com/learn/life-skills/the-smallest-version-worth-testing-mt_q7e_4e7BoN

#### Knowing When to Stop (ages 16-18)

Persisting is a virtue right up to the point where the evidence has arrived and been ignored. Deciding in advance what result would make you stop is how you tell one from the other later.

Ready when they can: Write down in advance what result would make you close the venture; Explain how money and time already spent should not affect the decision, and why they usually do; Say what is worth keeping from a project that ends.

https://lightmysky.com/learn/life-skills/knowing-when-to-stop-mt_Xh61d76aET

### First aid for kids

https://lightmysky.com/learn/life-skills/areas/first-aid-for-kids

#### Get a grown-up first (ages 5-11)

The most important step for any hurt: stay calm and get a grown-up.

Ready when they can: Can explain Get a grown-up first.

https://lightmysky.com/learn/life-skills/get-a-grown-up-first-ct_R-WpL3cayxk

#### Calling for help (ages 6-11)

Know your emergency number, then say who you are, where you are, and what happened.

Ready when they can: Can explain Calling for help.

https://lightmysky.com/learn/life-skills/calling-for-help-ct_4XVW6U6eHX8

#### Small cuts and scrapes (ages 5-10)

Tell a grown-up, rinse with clean water, pat dry, and cover it.

Ready when they can: Can explain Small cuts and scrapes.

https://lightmysky.com/learn/life-skills/small-cuts-and-scrapes-ct_rWV_10I5NnM

#### Bumps and bruises (ages 5-10)

Rest the sore spot and use something cold wrapped in a cloth, never ice straight on skin.

Ready when they can: Can explain Bumps and bruises.

https://lightmysky.com/learn/life-skills/bumps-and-bruises-ct_L8iRzjpFt0M

#### Nosebleeds (ages 6-11)

Sit, lean a little forward, and pinch the soft part of your nose. Do not lean back.

Ready when they can: Can explain Nosebleeds.

https://lightmysky.com/learn/life-skills/nosebleeds-ct_jpz3gOtC0rM

#### Burns from hot things (ages 6-11)

Tell a grown-up and cool it with running water for a long time. Never butter, never ice.

Ready when they can: Can explain Burns from hot things.

https://lightmysky.com/learn/life-skills/burns-from-hot-things-ct_e1P8bgtTI6w

#### Sun and heat (ages 5-10)

On hot days, drink water, rest in the shade, and wear a hat and sunscreen.

Ready when they can: Can explain Sun and heat.

https://lightmysky.com/learn/life-skills/sun-and-heat-ct__NhpX8AUu-0

#### What you can and cannot do (ages 7-11)

Kids help by staying calm, fetching things, and telling adults. Grown-ups do the treating.

Ready when they can: Can explain What you can and cannot do.

https://lightmysky.com/learn/life-skills/what-you-can-and-cannot-do-ct_bDSSnbf8KbM

## Civics & Economics

55 topics, ages 5 to 18. https://lightmysky.com/learn/civics-and-economics

### Citizenship in Action

https://lightmysky.com/learn/civics-and-economics/areas/citizenship-in-action

#### Deciding Together (ages 5-8)

Make decisions as a group and act on them: listen to each person's idea, look for an option most people can accept, and vote when the group can't agree; then help carry out what was decided, even if you voted differently

Ready when they can: Listen to others' suggestions before pushing their own (e.g., waits to hear three ideas before the group picks); Take part in a fair vote and accept the result (e.g., 'the class voted for the story I didn't pick, and that's okay'); Help carry out a group decision (e.g., joins the tidy-up plan the group chose).

Needs first: Listening to Others, Taking Turns and Sharing.

https://lightmysky.com/learn/civics-and-economics/deciding-together-mt_GduE5KnI1e

#### How Groups Make Decisions (ages 8-11)

Different ways groups decide: one person in charge, a vote, or talking until everyone agrees; where each is used, from families and classrooms to councils and courts, and the trade-offs in speed and fairness

Ready when they can: Name the decision method used in a real setting (e.g., 'the referee decides alone; our class votes'); Explain a trade-off between methods (e.g., consensus is fair but slow; one leader deciding is fast but can ignore people); Suggest a decision method that fits a situation and say why (e.g., a fire drill needs one person deciding, not a vote).

Needs first: Deciding Together.

https://lightmysky.com/learn/civics-and-economics/how-groups-make-decisions-mt_nW4AxgWheP

#### Deliberation and Democratic Decision-Making (ages 11-14)

Deliberate before deciding: state a position with reasons, listen seriously to opposing views, separate personal interest from the common good, then use debate, voting, consensus or representatives to reach a decision the group can accept

Ready when they can: Give reasons for a position and respond to the strongest counter-argument, not the weakest; Follow a fair procedure in a group decision (e.g., timed speaking turns, a vote taken after all sides are heard); Notice when self-interest is steering a debate (e.g., 'I want the late bedtime, but is it good for everyone?').

Needs first: How Groups Make Decisions, Seeing Someone Else's Point of View.

https://lightmysky.com/learn/civics-and-economics/deliberation-and-democratic-decision-making-mt_0U9eaCtm5u

#### Taking Action on Community Problems (ages 8-11)

Tackle a real problem in the community step by step: name the problem, find out who it affects and who can fix it, weigh ways to act alone or with others, predict what each action might change, then try one and see

Ready when they can: Identify a specific local problem and who it affects (e.g., 'litter in the park spoils it for everyone'); Propose more than one way to act and predict the results (e.g., 'a sign might help; a clean-up day would help more'); Take part in an action and reflect on what changed (e.g., wrote to the council, joined a collection drive).

Needs first: Deciding Together, Community Helpers and Leaders.

https://lightmysky.com/learn/civics-and-economics/taking-action-on-community-problems-mt_8tFS0k82bU

#### How People Change Society (ages 9-12)

How ordinary people have changed unfair situations, past and present: petitions, peaceful protest, boycotts, forming movements, and voting; why change often takes many people, many methods and a long time

Ready when they can: Give a historical example of people changing society (e.g., the movement for women's right to vote); Match a method to a movement (e.g., boycotts, marches, petitions) and explain how it applied pressure; Explain why lasting change usually needs many people acting together over time, not one dramatic moment.

Needs first: Taking Action on Community Problems, Laws and How They Change.

https://lightmysky.com/learn/civics-and-economics/how-people-change-society-mt_Wx2pvpg4QP

#### Public Policy and Public Problems (ages 11-14)

Weigh policies as solutions to public problems: define the problem, compare alternatives, and ask who each option helps, who it burdens, and what it costs, since almost every policy has winners, losers and side effects

Ready when they can: Restate a public problem precisely before jumping to solutions (e.g., 'too much traffic near school at 8:30'); Compare two policy options by benefits and costs (e.g., a new bus lane versus a car ban: who gains, who pays?); Predict a side effect of a proposed rule (e.g., 'banning plastic bags might increase paper waste').

Needs first: Laws and How They Change, Incentives and Choices, Taxes & Public Services.

https://lightmysky.com/learn/civics-and-economics/public-policy-and-public-problems-mt_5vYuvjkprY

#### Citizens in Public Life (ages 11-14)

The roles people play in public life: voter, juror, taxpayer, petitioner, volunteer, protester, office-holder; what each role can and can't achieve, and how individuals and groups size up their power to change things

Ready when they can: Describe what several civic roles involve (e.g., a juror weighs evidence; a petitioner gathers support); Match a goal to an effective lever (e.g., changing a national law needs more than a local petition); Assess what one person versus an organised group can realistically achieve on an issue.

Needs first: Levels and Branches of Government, How People Change Society.

https://lightmysky.com/learn/civics-and-economics/citizens-in-public-life-mt_G6PCjvFUCO

### Economics

https://lightmysky.com/learn/civics-and-economics/areas/economics

#### Where Things Come From (ages 5-7)

Some things are made or grown nearby and others come from far away; bananas, toys and clothes travel by ship, truck and plane; places trade with each other because no place can make everything it needs

Ready when they can: Sort familiar items into 'made or grown near here' and 'comes from far away' (e.g., local bread vs. bananas); Explain simply why we get some things from other places (e.g., 'bananas need hot weather to grow'); Trace how an item reached them (e.g., 'the toy was made in a factory, went on a ship, then to the shop').

Needs first: Goods & Services.

https://lightmysky.com/learn/civics-and-economics/where-things-come-from-mt_9v5-1k236E

#### Incentives and Choices (ages 8-11)

Rewards and penalties steer choices: sales, pocket-money deals, prizes, fines and late fees all change what people do; spotting the incentive behind a choice, including who set it up and why

Ready when they can: Point out the incentive in an everyday situation (e.g., 'the loyalty card makes people come back to that shop'); Predict how behaviour changes when an incentive changes (e.g., 'if the fine doubles, fewer people will park there'); Explain why someone created an incentive (e.g., the library drops fines so people return books without fear).

Needs first: Needs & Wants.

https://lightmysky.com/learn/civics-and-economics/incentives-and-choices-mt_KxkoDkbjPy

#### Productivity, Skills and Tools (ages 9-12)

Why some work produces more: better tools and machines (capital goods) and better-trained people (human capital); how learning a skill raises what a person can earn, and how rising productivity lifts living standards

Ready when they can: Explain how a tool raises output (e.g., 'a dishwasher washes more dishes per hour than hands can'); Connect training to earning (e.g., 'a qualified electrician can charge more than an untrained helper'); Give an example of investing now to produce more later (e.g., a farmer buying a tractor, a student learning to code).

Needs first: Earning Money.

https://lightmysky.com/learn/civics-and-economics/productivity-skills-and-tools-mt_q9wqRR_1Vk

#### Externalities and Spillovers (ages 10-13)

Choices spill over onto people who had no say: a factory's smoke, a neighbour's loud music, a planted garden, a vaccination; why harmful spillovers get overproduced and helpful ones underproduced when nobody pays or is paid for them

Ready when they can: Identify the third party affected by a choice (e.g., 'the whole street breathes the barbecue smoke'); Sort spillovers into helpful and harmful (e.g., a flower garden on the street vs. litter left at the park); Suggest a way to handle a spillover (e.g., a rule, a fine or a reward, like a tax on pollution or a subsidy for bee-keeping).

Needs first: Incentives and Choices, How the Economy Works.

https://lightmysky.com/learn/civics-and-economics/externalities-and-spillovers-mt_F4SQsGpZk9

#### How Markets Work (ages 11-14)

Buyers and sellers meet in markets for products, work and money; competition pushes prices and wages up or down; supply and demand shifts explain shortages, sales and price spikes; firms, non-profits and unions each play a part

Ready when they can: Explain a price change using supply and demand (e.g., 'umbrella prices rise in a sudden storm because demand jumps'); Describe the labour market as a market (employers buy work, workers sell it, and the wage is the price); Distinguish the roles of institutions (e.g., a corporation seeks profit, a union bargains for workers, a charity serves a mission).

Needs first: How the Economy Works, Incentives and Choices.

https://lightmysky.com/learn/civics-and-economics/how-markets-work-mt_IWiQW8Sq2R

#### Money, Banking and Interest Rates (ages 11-14)

Why money beats barter: it makes trading fast and lets value be stored and compared; how banks connect savers and borrowers, and how a change in interest rates ripples out to loans, savings, spending and big purchases

Ready when they can: Explain why money makes exchanges easier than barter (no need to find someone who wants exactly what you have); Describe how a bank uses savers' deposits to make loans, paying interest to one side and charging it to the other; Predict an effect of an interest-rate change (e.g., 'if rates rise, mortgages cost more, so fewer people buy houses').

Needs first: Banks & Saving, Borrowing & Debt.

https://lightmysky.com/learn/civics-and-economics/money-banking-and-interest-rates-mt__aqBHw2wZM

#### Inflation, Unemployment and Growth (ages 12-14)

Reading an economy's vital signs: inflation as rising prices, unemployment as people seeking work, growth as more being produced; who gains and who is hurt when prices climb or fall or jobs disappear

Ready when they can: Explain inflation in their own words and its effect on savings and wages (money buys less than before); Interpret a simple chart of unemployment or prices over time and describe the trend; Identify who is hit hardest by a change (e.g., inflation hurts savers and people on fixed incomes; deflation hurts borrowers).

Needs first: How Markets Work, Money, Banking and Interest Rates.

https://lightmysky.com/learn/civics-and-economics/inflation-unemployment-and-growth-mt_Zr0YyQwtKy

#### Trade Policy and Barriers (ages 12-14)

Governments shape trade with tariffs, quotas and subsidies; a tariff can protect local factories yet raise prices for everyone; weighing who wins and who loses when trade is made freer or more restricted

Ready when they can: Explain what a tariff is and trace its effects (imported goods cost more; local makers face less competition); Argue both sides of a trade barrier (e.g., protecting jobs at home versus cheaper goods for families); Identify winners and losers from a specific policy (e.g., a steel tariff helps steel towns, hurts carmakers and buyers).

Needs first: Global Trade, How Markets Work.

https://lightmysky.com/learn/civics-and-economics/trade-policy-and-barriers-mt_l_l6qXfRle

#### Scarcity, Opportunity Cost and the Production Frontier (ages 14-15)

Wants run ahead of what the available time, money and land can make, so every choice gives up the next best use of the same resources. A production frontier draws that trade-off for a whole economy: points inside waste resources, points outside are out of reach, and moving along the curve costs some of the other good.

Ready when they can: State the opportunity cost of a decision as the single best alternative given up, not the whole list of things not chosen; Read a production frontier: name a point that wastes resources, a point that is unreachable, and the cost of moving along the curve; Explain why the frontier bends instead of running straight (resources are not equally suited to both jobs).

https://lightmysky.com/learn/civics-and-economics/scarcity-opportunity-cost-and-the-production-frontier-mt_p_c7nNzHEw

#### Demand and Supply as Curves (ages 14-15)

A demand schedule and a supply schedule become two curves on the same axes: quantity demanded falls as price rises, quantity supplied rises with it. Reading a quantity off a price, and a price off a quantity, is the basic move the rest of the model is built from.

Ready when they can: Plot a demand curve and a supply curve from a table of prices and quantities; State the law of demand and the law of supply and give a reason for each, not just the direction; Read both quantities at a stated price and say which one is larger.

https://lightmysky.com/learn/civics-and-economics/demand-and-supply-as-curves-mt_FyYrlvzXct

#### Market Equilibrium, Shortage and Surplus (ages 14-16)

Where the two curves cross, the amount buyers want matches the amount sellers offer and the market clears. Away from that price a shortage or a surplus builds up, and what disappointed buyers and stuck sellers do next is the pressure that pushes the price back.

Ready when they can: Find the equilibrium price and quantity on a diagram and check that the two quantities match there; Predict a shortage or a surplus from a price set below or above equilibrium and say who is left disappointed; Explain the pressure that returns the price to equilibrium in terms of what buyers and sellers actually do.

https://lightmysky.com/learn/civics-and-economics/market-equilibrium-shortage-and-surplus-mt_SarFx2o1IM

#### Shifts in Demand and Supply (ages 14-16)

Income, tastes, the price of a substitute, a new technology or a ruined harvest move a whole curve rather than sliding along it. A fixed routine follows any event through: decide which curve moves, decide which way, then read the new crossing point.

Ready when they can: Sort an event into a shift of demand, a shift of supply, or a movement along a curve; Work a news story through the steps and state the new price and the new quantity; Explain the 'other things equal' assumption and why the model needs it.

https://lightmysky.com/learn/civics-and-economics/shifts-in-demand-and-supply-mt_z7FcJ9BAz3

#### Price Elasticity of Demand (ages 15-16)

Elasticity puts a number on how strongly quantity answers a price change: the percentage change in quantity divided by the percentage change in price. Whether that number lands above or below one decides whether a price rise raises or lowers what the seller takes in.

Ready when they can: Compute price elasticity of demand from two points and label it elastic, inelastic or unit elastic; Predict what happens to total revenue when an elastic good and an inelastic good each rise in price; Give reasons a good comes out inelastic (few substitutes, small share of a budget, habit or medical need) and apply one to a real product.

https://lightmysky.com/learn/civics-and-economics/price-elasticity-of-demand-mt_4ktSwG3D5q

#### Price Ceilings and Price Floors (ages 15-16)

A ceiling holds a price below equilibrium and a floor holds it above, and each leaves the two quantities unequal on purpose. The side effects follow: queues, waiting lists and resale markets under a ceiling, unsold stock under a floor.

Ready when they can: Draw a binding price ceiling and mark the shortage it creates on the diagram; Name who gains and who loses under rent control, including the people who never get a flat and so never appear in the argument; Explain why elasticity decides how large the shortage or surplus turns out to be.

https://lightmysky.com/learn/civics-and-economics/price-ceilings-and-price-floors-mt_ycfT-gkRVy

#### Competition, Market Power and Barriers to Entry (ages 15-16)

Where many sellers offer the same thing, no one of them holds a price above the rest for long, because a rival takes the sale. Market power comes from barriers to entry such as a patent, a network or control of a resource, and a firm that has it can charge more and sell less than competition would allow.

Ready when they can: Contrast a firm that has to take the market price with one that sets its own, and say what makes the difference; Name three barriers to entry and give a real example of each; Explain why a monopoly's price sits above the competitive one and who pays for the gap.

https://lightmysky.com/learn/civics-and-economics/competition-market-power-and-barriers-to-entry-mt_7rSbpD7hJ1

#### Market Failure: Externalities and Public Goods (ages 15-16)

Some costs and benefits land on people outside the deal, so a market makes too much of what pollutes and too little of what spills over as a benefit. Public goods sit further out still: nobody can be shut out and one person's use does not use them up, so no seller can charge for them and taxes fund them instead.

Ready when they can: Compare private cost with social cost for a polluting factory and show why the market quantity is too high; Choose a tool for a stated failure (a tax, a subsidy, a tradable permit, a rule) and justify the choice; Explain free riding and why street lighting is not sold lamp by lamp.

https://lightmysky.com/learn/civics-and-economics/market-failure-externalities-and-public-goods-mt_TvBDQJqv1R

#### Wages and the Labour Market (ages 15-16)

Work is traded in a market where firms buy and workers sell, and the wage is the price. Demand for a skill comes from what it earns the employer, supply from how many people can and will do the job, which is what pay gaps between jobs are made of.

Ready when they can: Explain a pay gap between two jobs using demand for the skill and supply of people who hold it; Predict the effect of a minimum wage set above the market wage, naming both the gain and the risk; Describe how a union, or a town with one dominant employer, changes the bargain.

https://lightmysky.com/learn/civics-and-economics/wages-and-the-labour-market-mt_GhsftwhrYS

#### Money and How Banks Create It (ages 15-16)

Money is whatever does three jobs at once: settles a payment, stores value until later, and gives prices a common scale. Banks hold deposits and lend most of them out, and because each loan becomes somebody else's deposit, lending itself enlarges the quantity of money in circulation.

Ready when they can: Name the three functions of money and test an awkward candidate against them (gold, air miles, a crypto coin); Trace a deposit through a bank's lending and show why the total amount of money grows; Explain what a reserve is for and why a rush of withdrawals threatens a bank that is not insolvent.

https://lightmysky.com/learn/civics-and-economics/money-and-how-banks-create-it-mt_ytmJOgw66I

#### Interest, Compound Growth and the Cost of Borrowing (ages 15-16)

Interest is the price of using money before you have it, quoted as a rate per year. Because each year's interest earns interest of its own, the same rate turns a long-running debt into a repayment far above the sum borrowed, and a long-held saving into far more than the deposits put in.

Ready when they can: Compute a balance after several years of compound interest and compare it against simple interest at the same rate; Compare two loans by their yearly rate and total repaid rather than by the monthly payment; Explain why the same rate feels mild over one year and severe over twenty.

https://lightmysky.com/learn/civics-and-economics/interest-compound-growth-and-the-cost-of-borrowing-mt_Zzl9SWMgvQ

#### Risk, Insurance and Pooling (ages 15-16)

A loss that would ruin one household is affordable once thousands share it, which is what an insurance premium buys: the expected cost of the claim plus the cost of running the pool. The pool only holds while premiums track risk, because the people most likely to claim are the keenest to buy.

Ready when they can: Estimate an expected cost from a probability and a size of loss, and compare it with a quoted premium; Explain why pooling many independent risks makes each one bearable; Describe adverse selection in a case: who signs up first, and what that does to the price everyone pays.

https://lightmysky.com/learn/civics-and-economics/risk-insurance-and-pooling-mt_zrMeXUHV4Y

#### Inflation, Price Indexes and Real Values (ages 15-16)

Inflation is measured by pricing the same basket of goods year after year and turning each total into an index against a base year. Dividing a money amount by that index converts a nominal figure into a real one, which is the only fair way to compare wages or prices across years.

Ready when they can: Build a simple index from a basket of prices and read the inflation rate between two years off it; Convert a wage from twenty years ago into today's money and say whether it rose in real terms; Name a reason the published index misses what a particular household actually feels.

https://lightmysky.com/learn/civics-and-economics/inflation-price-indexes-and-real-values-mt_58FeRqSjYh

#### GDP: Measuring an Economy and What It Misses (ages 15-16)

GDP adds up the value of final goods and services produced inside a country in a year, counting output only once so that parts are not double counted. It is the standard measure of an economy's size and a weak measure of life in it, because unpaid work, damage to the environment and how the income is shared all sit outside the total.

Ready when they can: Explain why intermediate goods are left out and give a case of double counting avoided; Compare two countries on GDP per head and state what the comparison hides; Name three things GDP leaves out and one decision that should not rest on GDP alone.

https://lightmysky.com/learn/civics-and-economics/gdp-measuring-an-economy-and-what-it-misses-mt_JFm9bVs0_n

#### Taxes, Public Spending and the Government Budget (ages 15-16)

Governments raise most revenue from taxes on income, spending and profits, and a tax rarely stays where it is placed: the side of the market that can walk away pays less of it. Spending above revenue means borrowing, and the debt that builds up is judged against the size of the economy rather than in pounds.

Ready when they can: Classify a tax as progressive, proportional or regressive and justify it with worked figures; Explain who really bears a tax on a good when demand for it is inelastic; Distinguish a deficit from debt and say why debt is quoted as a share of GDP.

https://lightmysky.com/learn/civics-and-economics/taxes-public-spending-and-the-government-budget-mt_OEjK6v1-F0

#### Comparative Advantage and the Gains from Trade (ages 15-16)

A country gains by making whatever it gives up least to make, even when its trading partner is better at making everything. Comparing opportunity costs rather than raw output is what explains the extra production trade creates, and what a tariff redistributes at a cost.

Ready when they can: Work out each country's opportunity cost from an output table and say who should specialise in what; Show with figures that both countries can end up with more of both goods than before trade; Explain why being better at everything does not remove the case for trading.

https://lightmysky.com/learn/civics-and-economics/comparative-advantage-and-the-gains-from-trade-mt_gcGxu7E2Y8

#### Fiscal Policy: Spending, Taxing and the Deficit (ages 16-18)

Governments can spend more than they take, and whether that helps depends on where the economy is in its cycle. A deficit is a flow, a debt is a stock, and confusing the two produces most bad arguments about both.

Ready when they can: Distinguish deficit from debt and state which one a single year's budget changes; Explain what a government is trying to do when it spends into a downturn; Give one argument that borrowing is a burden on the future and one that it is not.

https://lightmysky.com/learn/civics-and-economics/fiscal-policy-spending-taxing-and-the-deficit-mt_TC8A2ecFFL

#### Monetary Policy and What a Central Bank Can Do (ages 16-18)

A central bank sets a short-term interest rate and hopes it reaches mortgages, wages and prices some quarters later. Its tools are blunt, slow and mostly about what people expect will happen.

Ready when they can: Trace the path from a change in the policy rate to a change in what households spend; Explain why expectations about future inflation affect present prices; Name one thing monetary policy cannot fix and say why.

https://lightmysky.com/learn/civics-and-economics/monetary-policy-and-what-a-central-bank-can-do-mt_w0xvI0iouQ

#### Growth, Productivity and Why Some Countries Got Rich (ages 16-18)

Living standards over decades are almost entirely a story about output per hour worked, which comes from tools, skills and institutions. Explaining why a few countries pulled ahead is still an open argument, and the bad answers are easy to spot.

Ready when they can: Explain why output per hour, not hours worked, drives long-run living standards; Name three things that raise productivity and give an example of each; State one serious explanation for the divergence between countries and one explanation that does not survive the evidence.

https://lightmysky.com/learn/civics-and-economics/growth-productivity-and-why-some-countries-got-rich-mt_n6KY-0vlw_

#### Measuring Inequality and Arguing About It (ages 16-18)

How unequal a country is depends on whether you measure income or wealth, before or after tax, and per person or per household. Once the measurement is settled the argument about what is fair can actually begin.

Ready when they can: Read a Lorenz curve and say what a Gini coefficient of 0.3 versus 0.5 looks like; Explain why wealth is usually more unequally held than income; Give the strongest argument that some inequality is useful and the strongest that a given level is too high.

https://lightmysky.com/learn/civics-and-economics/measuring-inequality-and-arguing-about-it-mt_oQhtuk8b8T

### Government

https://lightmysky.com/learn/civics-and-economics/areas/government

#### What Is Government? (ages 5-7)

What a government is and what it does: making rules for everyone, keeping people safe, and providing things families use every day, like schools, roads, parks, libraries and firefighters

Ready when they can: Name things a government provides that families use (e.g., schools, roads, the park, the fire service); Explain in simple terms what a government does (makes rules, keeps people safe, helps the community); Point out a rule that applies to everyone and say who made it (e.g., 'cars must stop at red lights').

Needs first: Rules and agreements exist.

https://lightmysky.com/learn/civics-and-economics/what-is-government-mt_5JieIg_5_L

#### Community Helpers and Leaders (ages 5-7)

Who holds authority in a community and why: mayors, judges, police officers, teachers and principals; how each role helps, how everyone plays a part, and how people work together to fix local problems

Ready when they can: Match community roles to what they do (e.g., 'a judge decides if a rule was broken', 'a mayor leads the town'); Explain why a person in authority gets to make certain decisions (e.g., the principal decides school rules); Give an example of people working together to improve their community (e.g., a park clean-up, a food drive).

Needs first: What Is Government?.

https://lightmysky.com/learn/civics-and-economics/community-helpers-and-leaders-mt_8akvgAO8Dr

#### Laws and How They Change (ages 8-11)

Why communities have laws: to keep people safe, protect freedoms and settle disputes fairly; where laws come from, and how citizens change a law that isn't working, by voting, petitioning or campaigning

Ready when they can: Explain the purpose behind a specific law (e.g., seatbelt laws protect people in crashes); Describe one way an unfair or outdated law can be changed (e.g., people petition, vote, or campaign); Give an example of a law that protects a freedom (e.g., laws that let people speak or worship freely).

Needs first: What Is Government?, Rules and agreements exist.

https://lightmysky.com/learn/civics-and-economics/laws-and-how-they-change-mt_5gxLuo0u_V

#### Levels and Branches of Government (ages 8-11)

Government works at different levels: local, regional and national; in many countries power is also split between those who make laws, those who carry them out, and those who judge disputes

Ready when they can: Sort decisions by level of government (e.g., 'fixing our street is local; printing money is national'); Explain why power is often split between branches (so no one person or group decides everything); Name an official at each level and one thing they are responsible for (e.g., mayor, governor, president or prime minister).

Needs first: What Is Government?.

https://lightmysky.com/learn/civics-and-economics/levels-and-branches-of-government-mt_kbdfkqinc_

#### Constitutions and Separation of Powers (ages 11-14)

How constitutions set up and limit government: why countries write down the rules for rule-making; how power is divided between branches and levels so each can check the others; how systems differ across countries

Ready when they can: Explain what a constitution is and why it is harder to change than an ordinary law; Describe how one branch can check another (e.g., courts can strike down a law; a legislature can remove a leader); Compare two systems of government (e.g., a presidential and a parliamentary system, or a monarchy and a republic).

Needs first: Levels and Branches of Government, Laws and How They Change.

https://lightmysky.com/learn/civics-and-economics/constitutions-and-separation-of-powers-mt_kxIAbYuR5i

#### Democratic Ideals and Founding Documents (ages 11-14)

The ideas behind the United States' founding documents: liberty, equality and consent of the governed in the Declaration of Independence, the Constitution and the Bill of Rights; how these ideals shaped, and still test, American life

Ready when they can: Identify a core ideal in a founding document (e.g., 'all men are created equal' in the Declaration of Independence); Explain 'consent of the governed' in their own words (government gets its power from the people); Point to a gap between the ideals and reality at the founding (e.g., people who could not vote) and how it narrowed over time.

Needs first: Constitutions and Separation of Powers.

https://lightmysky.com/learn/civics-and-economics/democratic-ideals-and-founding-documents-mt_dK8hcP-1tS

#### Parties, Interest Groups and the Media (ages 11-14)

Who tries to shape public decisions besides officials: political parties bundle ideas and candidates; interest groups and charities push causes; journalists inform and scrutinise; citizens weigh what each says and wants

Ready when they can: Explain what a political party is and why candidates join one (shared ideas, shared support); Identify who is trying to persuade in a news story or campaign ad, and what they want; Describe how the media can hold powerful people to account (e.g., reporting on a broken promise).

Needs first: Levels and Branches of Government.

https://lightmysky.com/learn/civics-and-economics/parties-interest-groups-and-the-media-mt_Eb9SeGnavc

#### How a Law Actually Gets Made (ages 14-16)

Between somebody's idea and a rule the police can enforce there are drafts, committees, amendments and at least two chambers or their equivalent. Most proposals die somewhere in the middle, and knowing where is how you know who really decides.

Ready when they can: List the stages a proposal passes through in your country's system, in order; Say at which stage a proposal is most often changed and at which it is most often killed; Name one way a small group can stop a bill that a majority supports.

https://lightmysky.com/learn/civics-and-economics/how-a-law-actually-gets-made-mt_G6NfTNWnbR

#### Courts, Judges and a Fair Trial (ages 14-16)

Courts decide what a law means when people disagree, and in most systems they can strike down a government action. What makes a trial fair is a short list, and every item on it was fought for.

Ready when they can: Name four protections a defendant has, and say what abuse each one exists to prevent; Explain what judicial independence means and one thing that protects it; Say what a court can do when a government acts beyond its powers.

https://lightmysky.com/learn/civics-and-economics/courts-judges-and-a-fair-trial-mt_jJF6pQc7a6

#### Rights and Their Limits (ages 14-16)

Almost no right is absolute: speech, privacy, assembly and property all run into other people's rights and into public safety. The interesting work is in where the line is drawn and who draws it.

Ready when they can: State one right and give a case where it is legitimately restricted, with the reason; Explain the difference between a right against the state and a duty the state owes you; Take one hard case where two rights conflict and set out both sides fairly.

https://lightmysky.com/learn/civics-and-economics/rights-and-their-limits-mt_FLOs4KxTlj

#### Who Gets to Vote, and How Votes Become Seats (ages 14-16)

The franchise was widened in stages, each one contested, and it is still narrower than it looks. How votes are counted then decides how much a vote is worth, and different counting rules give different governments from identical ballots.

Ready when they can: Sketch how the franchise widened in one country and name two groups added late; Work the same set of votes through first-past-the-post and a proportional rule and compare the seat counts; Name one thing other than the rules that suppresses turnout.

https://lightmysky.com/learn/civics-and-economics/who-gets-to-vote-and-how-votes-become-seats-mt_nteHv_swOv

#### Campaigns, Money and the Media (ages 14-16)

Getting elected costs money, and where the money comes from shapes what candidates say and who they answer to afterwards. Coverage and targeted advertising then decide which of those messages anyone hears.

Ready when they can: Name two sources of campaign money and say what each donor might expect; Explain how targeting lets a campaign tell different groups different things; Give one rule countries use to limit the effect of money, and one way around it.

https://lightmysky.com/learn/civics-and-economics/campaigns-money-and-the-media-mt_uBWxmdMU2d

#### Civil Servants, Councils and Everyday Government (ages 15-16)

Almost everything government does to you day to day is done by permanent officials and local councils, not by ministers. They apply rules they did not write, which is both why the state works and why it can be maddening.

Ready when they can: Name three services delivered locally rather than nationally and say who pays for them; Explain what discretion an official has when applying a rule, and what limits it; Describe how a citizen challenges a decision made about them by an official body.

https://lightmysky.com/learn/civics-and-economics/civil-servants-councils-and-everyday-government-mt_oCh-n1NG7P

#### Where the Money Goes (ages 15-16)

A budget is the only document that shows what a government actually values, because it is the one where the promises have to add up. Most of it is already committed before anyone debates anything.

Ready when they can: Name the three or four largest items in a national budget and give rough shares; Explain why most spending is hard to cut in any one year; Take one proposed new programme and say what would have to give way for it.

https://lightmysky.com/learn/civics-and-economics/where-the-money-goes-mt_eMsYs94O9Z

#### When Democracies Fail (ages 15-16)

Democracies rarely fall to a single coup. They are more often hollowed out step by step, with courts packed, election rules rewritten and the press bought or bullied, each move defended as legal.

Ready when they can: Name four warning signs that appear across cases of democratic decline; Explain why each step is usually legal, and why that makes it harder to resist; Take one historical case and say what a different decision at one point might have changed.

https://lightmysky.com/learn/civics-and-economics/when-democracies-fail-mt_DdZ1wfg8yC

#### How a Policy Actually Gets Made (ages 16-18)

A law is the middle of the story, not the end. A policy has to get onto the agenda, be drafted by people with their own interests, survive implementation by an agency, and then be evaluated by somebody who may or may not want it to work.

Ready when they can: Name the stages of a policy cycle and say who holds power at each; Explain why a well-drafted policy can still fail at implementation; Take one policy and say what evidence would show whether it met its stated aim.

https://lightmysky.com/learn/civics-and-economics/how-a-policy-actually-gets-made-mt_TMkaYc1MIg

#### Forms of Government Compared (ages 16-18)

Presidential and parliamentary systems, federal and unitary states, one-party and multi-party regimes each distribute power differently and fail differently. Comparing them is how you tell a constitutional problem from a national character.

Ready when they can: State the main difference between presidential and parliamentary systems and one consequence of it; Explain what federalism gives a large or diverse country, and what it costs; Name a failure mode each system is prone to.

https://lightmysky.com/learn/civics-and-economics/forms-of-government-compared-mt_6itblQG2R6

#### Political Ideas and What They Actually Claim (ages 16-18)

Liberal, conservative, socialist and nationalist are not insults but positions, each with a claim about human nature, freedom and what the state is for. Stating each in its strongest form is the only honest way to disagree with it.

Ready when they can: State the core claim of three ideologies in a sentence each, in terms their supporters would accept; Explain why left and right mean different things in different countries; Take a live issue and show how two traditions would each argue their case.

https://lightmysky.com/learn/civics-and-economics/political-ideas-and-what-they-actually-claim-mt_NhqCoZs875

#### Where International Rules Come From (ages 16-18)

There is no world government, so international rules rest on treaties states chose to sign and on the cost of breaking them. That makes international law weaker than domestic law and stronger than nothing.

Ready when they can: Explain how a treaty becomes binding on a state and how a state can leave one; Name two international bodies and say what each can and cannot compel; Give one case where international rules changed a state's behaviour and one where they did not.

https://lightmysky.com/learn/civics-and-economics/where-international-rules-come-from-mt_prBdcYuLoY

#### Judging a Political Claim (ages 16-18)

Manifestos, campaign figures and government statistics are all written to persuade. Checking one means finding the baseline, the denominator and the time window somebody chose.

Ready when they can: Take a political statistic and identify the baseline and the time window it depends on; Explain how the same policy can be reported as a cut and as an increase; Say what you would need to know before believing a costed promise.

https://lightmysky.com/learn/civics-and-economics/judging-a-political-claim-mt_pGwJVkz8L1

## Languages

45 topics, ages 5 to 18. https://lightmysky.com/learn/languages

### Language Learning

https://lightmysky.com/learn/languages/areas/language-learning

#### Many Languages, One World (ages 5-7)

The language spoken at home is one of thousands, and each one names the same world in its own way. A word is a label a group of people settled on, not the thing itself.

Ready when they can: Name a language other than the one spoken at home and say where people speak it; Recognise that another language has its own word for a familiar thing such as water or dog; Listen to speech in an unknown language with interest instead of deciding it is nonsense.

https://lightmysky.com/learn/languages/many-languages-one-world-mt_XETW8tM2MC

#### Listening and Speaking in a New Language (ages 7-11)

Listen attentively to a new language and join in: hold simple conversations, ask and answer questions, speak in sentences using familiar phrases, and build pronunciation and intonation through songs, rhymes and presenting aloud

Ready when they can: Join in with songs and rhymes in the new language, copying its sounds and rhythm (e.g. singing along to a counting song); Ask and answer simple questions in a short conversation (e.g. exchanging names, ages and likes with a partner); Say short sentences from memory with pronunciation a listener can follow (e.g. introducing themselves to the class).

Needs first: Listening and responding.

https://lightmysky.com/learn/languages/listening-and-speaking-in-a-new-language-mt_iXtqoIfjHb

#### Reading and Vocabulary in a New Language (ages 7-11)

Read and understand words, phrases and short passages in a new language; enjoy its stories, songs and poems; and broaden vocabulary by working out new words from familiar material and checking them in a dictionary

Ready when they can: Read short familiar sentences in the new language and show understanding (e.g. matching captions to the right pictures); Work out an unfamiliar word from surrounding words or a lookalike English word (e.g. guessing 'chocolat' means chocolate); Use a bilingual dictionary to find or check a word (e.g. looking up an animal name for a poster).

Needs first: Listening and Speaking in a New Language, Reading fluently, Using a Dictionary to Check Spellings.

https://lightmysky.com/learn/languages/reading-and-vocabulary-in-a-new-language-mt_chlXo6jI0U

#### Grammar Patterns Across Languages (ages 8-11)

Understand how a new language is built: gendered nouns, verb endings that change with the speaker, and word-order patterns; use these patterns to build new sentences and compare how the new language and English do things differently

Ready when they can: Spot that nouns in the new language have gender and choose the matching article (e.g. 'le chat' but 'la table'); Change a verb ending to match who is doing the action (e.g. 'je joue' vs 'nous jouons'); Point out a pattern that works differently from English (e.g. adjectives coming after the noun).

Needs first: Listening and Speaking in a New Language, Grammar Terms: Nouns, Verbs and Tense, Agreement in sentences.

https://lightmysky.com/learn/languages/grammar-patterns-across-languages-mt_McU78DkGy_

#### Writing in a New Language (ages 8-11)

Write phrases from memory in a new language and adapt them to make new sentences; describe people, places, things and actions in writing, using familiar vocabulary and simple structures to express ideas clearly

Ready when they can: Write memorised phrases correctly without copying (e.g. writing 'me gusta el fútbol' from memory); Swap words in a known sentence pattern to say something new (e.g. turning 'I have a dog' into 'I have two cats'); Write a few sentences describing a person or place (e.g. a short description of their family for a pen pal).

Needs first: Listening and Speaking in a New Language, Reading and Vocabulary in a New Language, Grammar Patterns Across Languages.

https://lightmysky.com/learn/languages/writing-in-a-new-language-mt_aq8JZdKD3m

#### First Words: Greetings, Numbers and Colours (ages 6-8)

Build a small stock of words you can use straight away: hello and goodbye, please and thank you, the first numbers, the colours, and the names of everyday things. These are the first words a learner owns rather than recognises.

Ready when they can: Greet someone and say goodbye in the new language without being prompted; Count to ten in the new language from memory; Name five everyday objects or colours in the new language without help.

https://lightmysky.com/learn/languages/first-words-greetings-numbers-and-colours-mt_Ow32SJmrgN

#### Cognates and False Friends (ages 8-10)

Many words look or sound like words you already know, because languages borrow from each other and share ancestors. Some of those lookalikes mean something else entirely, so a resemblance is a first guess and not an answer.

Ready when they can: Guess an unfamiliar word from its likeness to a known one, then check the guess against the sentence; Give an example of a lookalike word that means something different in the two languages; Say why a guess from a lookalike still needs checking.

https://lightmysky.com/learn/languages/cognates-and-false-friends-mt_5UdrDnwYCD

#### Building a Word Bank That Sticks (ages 9-11)

Keep your own store of words and phrases, and bring them back on purpose: write each one in a sentence you would actually say, test yourself from memory, and return to the ones that keep slipping. Meeting a word once is not learning it.

Ready when they can: Record a new word inside a sentence of their own rather than as a bare translation; Test themselves from memory instead of rereading the list; Go back to words forgotten last time before adding new ones.

https://lightmysky.com/learn/languages/building-a-word-bank-that-sticks-mt_gGV99k0ZpI

#### Writing More Than One Sentence (ages 10-12)

Put sentences together into a paragraph that holds: link them with the connecting words the language uses, keep the tense steady, and adapt a model text instead of translating out of your head.

Ready when they can: Write a short paragraph in the new language that stays in one tense; Join two sentences with a connecting word from the new language; Adapt a model text into their own version rather than translating word by word.

https://lightmysky.com/learn/languages/writing-more-than-one-sentence-mt_o-mglXOz-_

#### Practising a Language Week by Week (ages 10-12)

A language grows on regular contact, not on one long session before a test. Plan short contact on most days, cover all four skills across a week, and go back over old material on purpose.

Ready when they can: Keep a short practice slot on most days across several weeks; Include listening and speaking in the week, not only written exercises; Revisit material from earlier weeks instead of only moving forward.

https://lightmysky.com/learn/languages/practising-a-language-week-by-week-mt_VIIT69dTyI

#### Writing to Someone Who Will Reply (ages 12-14)

Write a message, letter or post that a real reader answers: use the openings and sign-offs the language uses, say something worth replying to, and check the parts you know you get wrong.

Ready when they can: Write a message with the opening and closing conventions of the new language; Reply to what the other person actually wrote rather than sending a prepared text; Check their own draft for the two or three errors they know they repeat.

https://lightmysky.com/learn/languages/writing-to-someone-who-will-reply-mt_9l0fpUo3x0

#### Knowing Where You Are and What to Fix (ages 12-14)

Judge your own level honestly, skill by skill: what you can do in listening, speaking, reading and writing, and which one is holding the others back. Public level descriptions give the yardstick.

Ready when they can: Say what they can and cannot yet do in the language, skill by skill; Name the weakest of the four skills and give evidence for the judgement; Choose what to work on next from that judgement rather than from preference.

https://lightmysky.com/learn/languages/knowing-where-you-are-and-what-to-fix-mt_4qpc9U7hWx

#### Growing Vocabulary by the Thousand (ages 14-16)

At this level progress is mostly words. Work with word families and word parts, learn a word with the company it keeps, and take most of the intake from reading and listening volume rather than from lists.

Ready when they can: Derive related words from one stem using the language's prefixes and endings; Record a word together with the words it usually appears with; Take a real share of new words from reading or listening rather than from lists.

https://lightmysky.com/learn/languages/growing-vocabulary-by-the-thousand-mt_2kBaoqZimP

#### Working Through the Plateau (ages 15-16)

Progress slows once you can get by, and errors nobody corrects settle in for good. Ask for correction, work on the mistake you keep making, and pick material a little beyond comfortable.

Ready when they can: Name one error they repeat and show a plan for it; Ask a speaker for correction and use what comes back; Choose material that is slightly too hard on purpose.

https://lightmysky.com/learn/languages/working-through-the-plateau-mt_AVRXCiZD1S

#### Writing for an Academic or Professional Reader (ages 17-18)

Write something the language's own institutions would accept: an application, a report, or an essay, following that language's conventions rather than English structure in translation.

Ready when they can: Produce a structured piece of several hundred words in the new language; Follow that language's conventions for openings, references and closings; Edit their own draft for the errors that survive at this level.

https://lightmysky.com/learn/languages/writing-for-an-academic-or-professional-reader-mt_Yt0K5UuNSK

#### Learning the Next Language Faster (ages 17-18)

The second language teaches you how you learn. Language families, shared word stock and transferable habits make a third one quicker, and the same relationships show where transfer will mislead you.

Ready when they can: Say which of their study habits transferred and which did not; Use a known language's word stock to get a start in a related one; Name a place where a known language interferes rather than helps.

https://lightmysky.com/learn/languages/learning-the-next-language-faster-mt_cB5FEznW7h

#### Keeping a Language for Life (ages 17-18)

An unused language fades. Decide how contact continues once nobody sets homework: input you would consume anyway, people to speak with, and an honest level check every so often.

Ready when they can: Name the contact with the language they will keep after formal study ends; Say what fades first when a language goes unused, and what stays; Check their level against public descriptors and record the result.

https://lightmysky.com/learn/languages/keeping-a-language-for-life-mt_eIKA2JyNVb

### Sounds & Conversation

https://lightmysky.com/learn/languages/areas/sounds-and-conversation

#### Hearing the Sounds of Another Language (ages 5-7)

Tell apart sounds your own language does not use, and hear where one word ends and the next begins. This is ear work, and it comes before any speaking.

Ready when they can: Say whether two spoken words in the new language are the same or different; Clap once per word in a short spoken phrase in the new language; Point out a sound in the new language that the home language does not have.

https://lightmysky.com/learn/languages/hearing-the-sounds-of-another-language-mt_BNrRACypmh

#### Copying Sounds, Rhythm and Tune (ages 5-7)

Say back what you hear: the sounds, the beat of the phrase, and the way the voice rises and falls. Songs, chants and rhymes carry all three at once.

Ready when they can: Repeat a short phrase closely enough that a speaker of the language recognises it; Join in with a song or chant in the new language and keep its rhythm; Copy the rise or fall of the voice in a question the way it was said.

https://lightmysky.com/learn/languages/copying-sounds-rhythm-and-tune-mt_v7Vd-VlVdA

#### Following Spoken Instructions in a New Language (ages 6-8)

Act on what you hear before you can say it back. Simple commands and questions, understood from the few words you know plus gesture and situation.

Ready when they can: Carry out a two-part instruction given in the new language; Answer a yes or no question in the new language correctly; Show which part of an instruction was missed instead of freezing.

https://lightmysky.com/learn/languages/following-spoken-instructions-in-a-new-language-mt_sP3xxDGINc

#### Sound and Spelling in a New Language (ages 8-10)

Learn how the new language writes its sounds: which letters and marks make which sound, which letters stay silent, and where the stress falls. With the map in hand a written word can be said aloud and a heard word can be written down.

Ready when they can: Read aloud an unfamiliar written word in the new language with sounds a speaker recognises; Write down a short spoken word using the new language's spelling rules; Explain what a mark above or below a letter does to the sound.

https://lightmysky.com/learn/languages/sound-and-spelling-in-a-new-language-mt_aLRdIL4V2_

#### Asking For What You Need (ages 9-11)

Get through a real exchange on a small stock of words: ask for something, ask a price or a direction, and say you did not follow and need it again. The phrases that keep an exchange alive matter more here than correct grammar.

Ready when they can: Ask for something they need in the new language and act on the answer; Say they did not understand and ask for repetition or slower speech; Keep going with a gesture or a simpler word when the exact word is missing.

https://lightmysky.com/learn/languages/asking-for-what-you-need-mt_Dn4GKSRgKd

#### Listening to Real Speech (ages 11-13)

Follow speech meant for speakers of the language: fast, run together, and full of shortcuts. Get the gist first and the detail second, and accept that some words will go past you.

Ready when they can: State the main point of an unscripted clip after one listening; Pick out a named detail on a second listening; Carry on following after missing a word instead of stalling on it.

https://lightmysky.com/learn/languages/listening-to-real-speech-mt_QC3x14zrgx

#### Keeping a Conversation Going (ages 11-13)

Hold your end of a conversation: take turns, buy time while you think, ask for a repeat, and repair a sentence that went wrong halfway. These moves keep a conversation alive, not perfect sentences.

Ready when they can: Use a holding phrase instead of falling silent while thinking; Ask a follow-up question that keeps the other person talking; Restart a sentence that went wrong and finish it.

https://lightmysky.com/learn/languages/keeping-a-conversation-going-mt_SZsWbcNJIv

#### Telling a Story About Yourself (ages 11-13)

Speak for a minute without help: what you did, in order, with times and reasons. Extended speaking is where past forms and connecting words stop being exercises.

Ready when they can: Recount something that happened in the right order, using past forms; Speak for about a minute without switching to their first language; Add a reason or an opinion instead of listing events.

https://lightmysky.com/learn/languages/telling-a-story-about-yourself-mt_Y03mNSjNK9

#### Sound Systems, Stress and Accent (ages 14-16)

Work on pronunciation on purpose: the handful of sounds that mark a learner out, where the stress falls, and how words run together in speech. A few targeted changes buy more than general practice.

Ready when they can: Identify two or three sounds in their own speech that a speaker of the language notices; Place stress correctly in longer words of the new language; Hear and produce the way words join together in connected speech.

https://lightmysky.com/learn/languages/sound-systems-stress-and-accent-mt_dGUiCiHhEP

#### Speaking at Length With Reasons (ages 14-16)

Say what you think and why, for several minutes, in the new language. An opinion needs connectives, an example, and a way to concede a point without abandoning it.

Ready when they can: Give an opinion and support it with a reason and an example; Link points across sentences with the language's own connecting words; Answer an unexpected follow-up question without having prepared it.

https://lightmysky.com/learn/languages/speaking-at-length-with-reasons-mt_eIQfZ5tswq

#### Speaking Without Rehearsing (ages 16-18)

Speak at something near your own pace: assemble the sentence while talking, repair it without stopping, and drop the habit of composing in your first language first. Fluency here is a question of what has become automatic.

Ready when they can: Hold a long conversation without building sentences in the first language first; Repair a wrong start mid-sentence and keep the turn; Keep a workable pace when the topic changes without warning.

https://lightmysky.com/learn/languages/speaking-without-rehearsing-mt_Pf2HXXUnW-

#### Arguing a Case in Another Language (ages 16-18)

Disagree well in the new language: concede a point, qualify a claim, and press an objection without losing the room. The moves are the same as in a first language, and each one has its own wording here.

Ready when they can: Concede a point and then qualify it, in the new language; Object to a claim using the language's own softening rather than a blunt contradiction; Hold a position under pressure without dropping into the first language.

https://lightmysky.com/learn/languages/arguing-a-case-in-another-language-mt_mOXW08EFdW

### Grammar Across Languages

https://lightmysky.com/learn/languages/areas/grammar-across-languages

#### Word Order and Question Forms (ages 9-11)

Languages put the parts of a sentence in different orders, and each has its own way of turning a statement into a question. Learn the order the new language uses and how it marks a question, and you can build sentences you have never heard.

Ready when they can: State the usual order of subject, verb and object in the new language; Turn a statement into a question in the new language; Show one ordering the new language uses that English does not.

https://lightmysky.com/learn/languages/word-order-and-question-forms-mt_aY-pVRzyEz

#### Talking About Time: First Tenses (ages 10-12)

Say when something happened. A language can mark time by changing the verb, by adding a helper word, or by leaving it to a time word, and the new language does it in its own way.

Ready when they can: Say the same short sentence about now and about yesterday in the new language; Point to the part of the sentence carrying the time; Describe one way the new language marks time differently from English.

https://lightmysky.com/learn/languages/talking-about-time-first-tenses-mt_6526HcZG0R

#### Gender, Case and Noun Classes (ages 11-13)

Many languages sort nouns into classes and make the words around them agree, or change a noun's ending to show its job in the sentence. Learn what the new language sorts, and what has to match what.

Ready when they can: Choose the article and adjective forms that match a noun's class; Explain what a change to a noun's ending signals in the new language; Name a sorting or ending system the new language has and English does not.

https://lightmysky.com/learn/languages/gender-case-and-noun-classes-mt_NavTs37V06

#### Joining Ideas: Clauses in Another Language (ages 14-16)

Move past short sentences: relative clauses, reported speech, and the words that hang one idea off another. Every language has its own rules about what joining does to word order.

Ready when they can: Combine two short sentences into one using a relative clause; Report what someone said, making the changes the language requires; Show what subordination does to word order in the new language.

https://lightmysky.com/learn/languages/joining-ideas-clauses-in-another-language-mt_Vf6M9DJmW7

#### How Languages Cut Up Time (ages 14-16)

Tense is not the whole story. Languages also mark whether an action was finished, repeated, or going on at the time, and choosing between two past forms is usually a decision about that rather than about when.

Ready when they can: Choose between two past forms and justify the choice by what the action was like; Explain the difference between when something happened and how it unfolded; Point to a distinction the new language forces that English leaves open.

https://lightmysky.com/learn/languages/how-languages-cut-up-time-mt_lCx2JzFUeD

#### Saying What Might Be: Mood and Modality (ages 15-16)

Talk about what is possible, wished for, or required rather than what is the case. A language carries this with modal verbs, with conditional forms, or with a separate mood that has its own endings.

Ready when they can: Build a conditional sentence in the new language and say what it commits the speaker to; Soften a request using the form that language uses for politeness; Explain where the language requires a form that English handles with a helper verb.

https://lightmysky.com/learn/languages/saying-what-might-be-mood-and-modality-mt_IIgSDzD2a9

### Texts, Media & Translation

https://lightmysky.com/learn/languages/areas/texts-media-and-translation

#### Writing Systems: Sound, Syllable and Symbol (ages 8-10)

Not every language writes the way English does. Some spell out sounds, some give a symbol per syllable, some a symbol per word, and some leave the vowels for the reader to supply. Which kind you face decides what learning to read it will take.

Ready when they can: Say whether the language they are learning writes sounds, syllables or whole words; Name a script that does not run left to right, or that leaves vowels unwritten; Explain what has to be learned first in a script that does not spell sounds out.

https://lightmysky.com/learn/languages/writing-systems-sound-syllable-and-symbol-mt_kUaS9WiVY0

#### Reading a Whole Story in a New Language (ages 10-12)

Read something longer than a caption: a short book or story written for learners, from start to finish. The skill is holding the thread while some words stay unknown.

Ready when they can: Finish a short book in the new language and retell what happened; Read past an unknown word and pick up its sense from the story; Choose material at a level where most of the words are already known.

https://lightmysky.com/learn/languages/reading-a-whole-story-in-a-new-language-mt__TM_JDJS1F

#### Reading Material Written for Native Speakers (ages 12-14)

Read what the language's own readers read: a menu, a website, a news piece. Decide what to look up and what to leave, and use the surrounding text before reaching for a dictionary.

Ready when they can: Get the point of a real article without looking up every unknown word; Decide which words are worth looking up and which can be skipped; Use a dictionary entry with several senses and pick the one that fits.

https://lightmysky.com/learn/languages/reading-material-written-for-native-speakers-mt_R2M7Qh2Rai

#### Politeness and Everyday Culture (ages 12-14)

Languages carry rules about who is addressed how: formal and familiar forms, titles, greetings, and what counts as rude. Getting the words right and the manner wrong still misfires.

Ready when they can: Choose the formal or familiar form of address that fits the person being spoken to; Name one custom around greeting, eating or thanking that differs from home; Explain what an over-familiar form would signal to a listener.

https://lightmysky.com/learn/languages/politeness-and-everyday-culture-mt_p44544zHZH

#### Following Media Without Subtitles (ages 15-16)

Watch and listen to what speakers of the language watch and listen to: long unscripted input, several voices, background noise, and no help on screen.

Ready when they can: Follow the plot of an episode or the point of a podcast without subtitles; Pick the thread back up after a stretch that was not understood; Choose material where enough is understood to stay with it for half an hour.

https://lightmysky.com/learn/languages/following-media-without-subtitles-mt_gibt6RSHpo

#### Formal and Informal: Choosing Register (ages 15-16)

One language holds several ways of saying the same thing, and the wrong one lands as rude or as stiff. Learn what the new language marks: forms of address, verb forms, word choice, and how much can be left out.

Ready when they can: Rewrite a message in the new language from familiar to formal; Say which register a text is in and point at what signals it; Choose a register for an unfamiliar situation and justify the choice.

https://lightmysky.com/learn/languages/formal-and-informal-choosing-register-mt_pfuaayT8UF

#### Reading an Argument in Another Language (ages 15-16)

Read opinion writing in the new language and get the case, not only the topic: what is claimed, what is offered as support, and where the writer hedges.

Ready when they can: State the writer's claim in one sentence, in the new language; Separate the evidence given from the opinion asserted; Notice hedging or loaded wording and say what it does for the writer.

https://lightmysky.com/learn/languages/reading-an-argument-in-another-language-mt_2QSUNppH7a

#### Literature and Film in the Original (ages 16-18)

Read a whole book or watch a whole film as its first audience did, older and literary registers included. What the original gives you is what no translation carries.

Ready when they can: Finish a full-length work in the new language and discuss it in that language; Handle older or literary wording without abandoning the text; Point to something in the original that a translation cannot carry over.

https://lightmysky.com/learn/languages/literature-and-film-in-the-original-mt_S4LLM2SAiw

#### Translation as a Craft (ages 16-18)

Move a passage between languages and account for every choice: what stays literal, what goes idiomatic, what is lost, and who the translation is for. Also the live version, where there is no time to revise.

Ready when they can: Produce two defensible translations of one passage for different readers; Name what was lost in a translation and why it could not be kept; Interpret a short exchange live, holding the sense while the speaker continues.

https://lightmysky.com/learn/languages/translation-as-a-craft-mt_sWG0qzlY5Y

#### Variation Inside One Language (ages 17-18)

One language is many: regional standards, dialects, slang, and forms that carry status. What counts as correct is a judgement about people as much as about grammar.

Ready when they can: Name two regional varieties of the language and a difference between them; Explain who decides what counts as the standard form, and how; Adjust their own usage towards the variety of the place they are in.

https://lightmysky.com/learn/languages/variation-inside-one-language-mt_H8tghWQO59

## Geography

42 topics, ages 5 to 18. https://lightmysky.com/learn/geography

### Maps & Globes

https://lightmysky.com/learn/geography/areas/maps-and-globes

#### First Maps and Globes (ages 5-7)

Draw simple maps of familiar places (a bedroom, the route to school) and use maps, globes and photographs to describe places: finding land and water on a globe, spotting buildings and roads in a photo, saying what a place is like

Ready when they can: Draw a simple map of a familiar place with key features roughly in the right spots (e.g., their bedroom or the walk to school); Point out land and water on a globe or world map; Use a photograph or map to describe a place's features (e.g., 'this town is by the sea and has a harbour').

https://lightmysky.com/learn/geography/first-maps-and-globes-mt_wwNUtlTw7m

#### Reading Maps: Symbols and Grids (ages 8-11)

Read and draw maps using symbols, a key, the eight compass points and four- and six-figure grid references; use atlases, globes and digital maps to locate countries and features, and use scale to judge real distances

Ready when they can: Use a key to decode map symbols (e.g., finding the campsite, church or railway on an Ordnance Survey-style map); Give directions with the eight compass points and find a location from a four-figure grid reference; Locate a country or feature in an atlas or digital map and estimate a real distance using the map's scale.

Needs first: First Maps and Globes, First Quadrant Coordinates.

https://lightmysky.com/learn/geography/reading-maps-symbols-and-grids-mt__Xl9qT-B20

#### Latitude, Longitude and Time Zones (ages 9-12)

Use the global grid: latitude and longitude, the Equator, the hemispheres, the Tropics of Cancer and Capricorn, the Arctic and Antarctic Circles and the Prime Meridian; and time zones, including why day and night differ around the world

Ready when they can: Locate the Equator, Prime Meridian, tropics and polar circles on a globe or world map; Find a place from its latitude and longitude, and give the rough coordinates of a place (e.g., 'London is about 51 degrees north'); Explain why it is night in Sydney when it is morning in London, using time zones and Earth's rotation.

Needs first: Reading Maps: Symbols and Grids, Earth's rotation and day/night.

https://lightmysky.com/learn/geography/latitude-longitude-and-time-zones-mt_3LBzy7Jbxv

#### Thematic Maps and GIS (ages 11-14)

Make and interpret thematic maps: choropleth, dot and flow maps of population, rainfall or trade; use GIS layers and satellite imagery to spot spatial patterns and ask why they occur

Ready when they can: Interpret a choropleth map (e.g., reading a population-density map and naming the most and least crowded regions); Choose a sensible map type for a data set (e.g., a flow map for exports, a dot map for earthquakes); Overlay layers in a digital mapping or GIS tool to explore a pattern (e.g., comparing rainfall and farmland layers).

Needs first: Latitude, Longitude and Time Zones, Reading and Comparing Bar Graphs.

https://lightmysky.com/learn/geography/thematic-maps-and-gis-mt_khsAUcwLke

### People & Environments

https://lightmysky.com/learn/geography/areas/people-and-environments

#### Moving People, Goods and Ideas (ages 5-8)

People, goods and ideas travel from place to place: why families move, how food and toys reach the shops by ship, lorry, train and plane, and how ideas spread through letters, books, calls and the internet

Ready when they can: Give a reason a family might move to a new place (e.g., a new job, to be near grandparents); Trace how something reaches them (e.g., 'the banana came on a ship, then a lorry, then to our shop'); Give an example of an idea travelling (e.g., a recipe, game or song from another country).

https://lightmysky.com/learn/geography/moving-people-goods-and-ideas-mt_MJ4amGf5DN

#### Geographical Fieldwork (ages 8-11)

Study real places first-hand: observe, measure, record and present the human and physical features of the local area using sketch maps, plans, tallies, graphs, photographs and digital tools

Ready when they can: Draw a labelled sketch map or plan of a local area (e.g., mapping the park with its paths, trees and benches); Collect fieldwork data with a simple method (e.g., tallying traffic outside school, measuring rainfall over a week); Present findings with a graph, annotated photo or map and say what they show.

Needs first: Reading Maps: Symbols and Grids, Measuring accurately.

https://lightmysky.com/learn/geography/geographical-fieldwork-mt_RT-RAZ0SRX

#### Types of Communities (ages 5-8)

Communities come in different types: cities, towns, suburbs, villages and farms; each uses its environment to meet daily needs for food, water, shelter and work, and different kinds of jobs are found in each

Ready when they can: Name types of communities and how they differ (e.g., 'a city has tall buildings and buses; a village is small and quiet'); Give examples of how a community uses its environment to meet needs (e.g., farms grow food, ports use the sea); Match jobs to community types (e.g., farmer in the countryside, office worker in a city, fisher by the coast).

Needs first: Places Near and Far.

https://lightmysky.com/learn/geography/types-of-communities-mt_AAUExZ1Swj

#### Adapting to Environments (ages 8-11)

How culture shapes the way people adapt to and modify their environments: housing built for heat, cold or floods; irrigation and terracing that make farming possible; clothing and daily rhythms suited to the local climate

Ready when they can: Give examples of housing adapted to place (e.g., stilt houses in flood zones, thick-walled houses in hot deserts); Explain how people modify land for farming (e.g., terracing hillsides, irrigating dry fields, draining wetlands); Link clothing or daily routines to climate (e.g., loose light clothing in desert heat, a midday rest in hot countries).

Needs first: Types of Communities, Weather vs Climate.

https://lightmysky.com/learn/geography/adapting-to-environments-mt_jMDYpyZo6w

#### Human and Economic Geography (ages 8-11)

Human features of places: cities, towns, villages, ports, factories and farms; types of settlement and land use; economic activity and trade links; how natural resources such as energy, food, minerals and water are spread around the world

Ready when they can: Use terms for human features correctly when describing places (e.g., port, harbour, factory, office); Describe land use in an area from a map or a walk (e.g., housing, farming, industry, shops); Explain a trade link or resource pattern (e.g., 'oil comes from a few places, so tankers carry it around the world').

Needs first: Types of Communities.

https://lightmysky.com/learn/geography/human-and-economic-geography-mt_Q-Px2v3Cd_

#### Where People Live and Why (ages 8-11)

Why people cluster in some places and not others: settlements grow near rivers, coasts, fertile land and resources; climate, water and culture shape where populations concentrate and how settlements change

Ready when they can: Explain why many settlements grew near rivers or coasts (e.g., fresh water, fishing, trade by boat); Point out crowded and empty regions on a population map and suggest reasons (e.g., deserts and high mountains hold few people); Explain how a resource drew people to a place (e.g., coalfields, gold rushes, fertile floodplains).

Needs first: Types of Communities, Weather vs Climate.

https://lightmysky.com/learn/geography/where-people-live-and-why-mt_r1SD8eMOxU

#### Migration and Movement (ages 9-12)

Why people migrate: push factors (drought, conflict, scarce work) and pull factors (jobs, safety, family); how environments and cultures drive the movement of people, goods and ideas, and how migration changes places

Ready when they can: Distinguish push and pull factors with examples (e.g., 'drought pushed farmers out; city jobs pulled them in'); Describe a real migration and its causes (e.g., people moving from countryside to city for work); Explain how migration changes both places (e.g., new foods and festivals arrive; villages lose young workers).

Needs first: Moving People, Goods and Ideas, Where People Live and Why.

https://lightmysky.com/learn/geography/migration-and-movement-mt_kTmHn_iAZ_

#### Environmental Change and Conflict (ages 11-14)

How long-term human-caused environmental change (deforestation, water scarcity, a warming climate) puts pressure on land, water and food, and how that pressure drives both conflict and cooperation between communities and countries

Ready when they can: Give an example of environmental change creating tension (e.g., a shared river running low, herders and farmers competing for shrinking land); Give an example of cooperation over environments (e.g., treaties sharing river water, international climate agreements); Explain a chain from cause to conflict (e.g., drought shrinking harvests, prices rising, people migrating).

Needs first: Adapting to Environments, Human impact on environments.

https://lightmysky.com/learn/geography/environmental-change-and-conflict-mt_Vlp61dF3KL

#### Settlements, Movement and Connections (ages 11-14)

How transport and communication networks link settlements and spread people, goods and ideas; how human-environment relationships shape settlement patterns; how global population shifts change land use in particular places

Ready when they can: Explain how a transport or communication link changed a settlement (e.g., a railway or fibre-optic cable bringing growth); Relate a settlement pattern to the environment (e.g., towns strung along a valley, ribbon development along roads); Describe how population shifts change land use (e.g., farmland turning into suburbs as a city grows).

Needs first: Where People Live and Why, Migration and Movement.

https://lightmysky.com/learn/geography/settlements-movement-and-connections-mt_Kq3quvrn63

#### Population Growth and Age Structure (ages 14-16)

A country's population changes through births, deaths and migration, and the balance between those three leaves an age structure behind: some countries mostly young, others mostly old. The structure decides what the country has to plan for.

Ready when they can: Name the three things that change a population's size: births, deaths and migration; Read an age-structure chart and say whether the country is mostly young or mostly ageing; Give one thing a young population has to plan for and one thing an ageing population has to plan for; Explain why birth rates usually fall as incomes and schooling rise.

https://lightmysky.com/learn/geography/population-growth-and-age-structure-mt_0X30bM1Hox

#### Migration at World Scale (ages 14-16)

Follow one migration route end to end: what pushed people out, what pulled them to a destination, what the journey cost, and what changed at both ends. The place people leave changes as much as the place they reach.

Ready when they can: Separate a push factor from a pull factor for one real route; Explain the difference between a refugee and someone moving for work, and why the difference matters in law; Name one effect on the place people left, such as money sent home or missing workers; Name one effect on the place people arrived, such as filled jobs or pressure on housing.

https://lightmysky.com/learn/geography/migration-at-world-scale-mt_xZ-ZHtIrvF

#### Urbanisation and the Growth of Cities (ages 14-16)

More than half the world now lives in urban areas, and most of the growth is in Asia and Africa. Cities grow both from people arriving and from births inside them, and housing and services usually arrive late.

Ready when they can: Say what urbanisation means and roughly what share of the world now lives in urban areas; Name the two ways a city's population grows: people arriving, and births inside the city; Describe what an informal settlement is and why it forms; Give one thing a city does better than scattered settlement, such as transport, services, or jobs per hectare.

https://lightmysky.com/learn/geography/urbanisation-and-the-growth-of-cities-mt_EF-n2IXJ3-

#### Geography of World Trade (ages 11-14)

Why world trade flows the way it does: environments and resources decide where things can be grown, mined or made; location, transport routes and chokepoints shape the spatial pattern of imports and exports

Ready when they can: Explain why a product is made or grown where it is (e.g., coffee near the equator, microchips in a few specialised regions); Trace a supply chain across a map (e.g., cotton grown, spun, sewn and sold on different continents); Identify a major trade route or chokepoint and why it matters (e.g., the Suez Canal, the Strait of Malacca).

Needs first: Human and Economic Geography, Countries of the World.

https://lightmysky.com/learn/geography/geography-of-world-trade-mt_Vpbi5Z4ypw

#### Water, Food and Energy Futures (ages 15-16)

Three resources decide how liveable a place is, and all three are under pressure from more people, higher incomes and a shifting climate. A shortage can be met by finding more supply or by using less, and the choice is rarely free.

Ready when they can: Name a region under water stress and say what causes the stress there; Explain why rising incomes usually raise energy and meat demand; Give one supply-side response and one demand-side response to a shortage; Say why a resource can be plentiful worldwide and still scarce in one place.

https://lightmysky.com/learn/geography/water-food-and-energy-futures-mt_nEcLm4RkSK

#### Living With Climate Risk (ages 15-16)

Climate risk is the hazard, plus who and what is exposed to it, plus how well a place can cope. Two coasts can take the same storm and lose very different amounts, and most of that difference is defences, warning and money.

Ready when they can: Break one disaster into hazard, exposure and ability to cope; Explain why the same flood does far more damage in one country than another; Name one way to cut exposure and one way to cut the hazard itself; Say why the countries emitting least are often among the most exposed.

https://lightmysky.com/learn/geography/living-with-climate-risk-mt_B4xy4Bs3DR

#### Fieldwork That Answers a Question (ages 14-16)

Good fieldwork starts with a question you could be wrong about, and a plan for where and how often to measure. Everything after that is deciding what would count as an answer.

Ready when they can: Turn a vague interest into a question that data could settle; Choose a sampling method and justify it against the alternatives for that site; Identify two things about your method that could bias the result, and say how you would reduce each.

https://lightmysky.com/learn/geography/fieldwork-that-answers-a-question-mt_ejnJbK_swN

#### Turning Field Data Into an Argument (ages 14-16)

Numbers collected in the field only become geography when they are put in a form that answers the question, and when their limits are stated. A chart that hides the sample size is not an answer.

Ready when they can: Choose a graph or map form that fits the data type and defend the choice; State a conclusion with the uncertainty attached, rather than as a flat fact; Say what a small or unrepresentative sample lets you claim and what it does not.

https://lightmysky.com/learn/geography/turning-field-data-into-an-argument-mt_A1qZ6jJ472

#### Why Biomes Sit Where They Do (ages 15-16)

Rainforest, desert, grassland and tundra are not scattered at random: they follow bands of temperature and rainfall set by how the atmosphere circulates. Once you know the pattern, you can predict roughly what grows at a given latitude before looking.

Ready when they can: Explain why deserts cluster around thirty degrees north and south; Match three biomes to their temperature and rainfall conditions; Give one place where the simple latitude rule fails and say what overrides it.

https://lightmysky.com/learn/geography/why-biomes-sit-where-they-do-mt_zQLshCSJh8

#### Places Change, and Not for Everyone (ages 16-18)

Regeneration rebuilds a neighbourhood and usually changes who can afford to live in it. Whether that counts as success depends on which residents you ask and when you ask them.

Ready when they can: Name three measures used to say a place has improved, and state what each misses; Explain how rising rents can follow investment and who that displaces; Take one regeneration scheme and argue whether it met its stated aim, using evidence.

https://lightmysky.com/learn/geography/places-change-and-not-for-everyone-mt_Irdf-DD3OQ

#### Where Your Things Are Actually Made (ages 16-18)

A single product is usually assembled from parts made in a dozen countries, chosen for wage rates, tariffs and shipping times. Following one object backwards is the fastest way to see the world economy as a map.

Ready when they can: Trace one manufactured product back through at least three countries and say what each stage contributed; Explain why firms split production across borders instead of making everything in one place; Name two things that make a long supply chain fragile, and give a recent example of one breaking.

https://lightmysky.com/learn/geography/where-your-things-are-actually-made-mt_d1ovR3Nk3S

#### Where Illness Spreads and Why (ages 16-18)

Disease follows water, crowding, travel routes and money, which makes its map a geography question as much as a medical one. The same infection kills at very different rates depending on where it lands.

Ready when they can: Name three geographical factors that shape how far an infection spreads; Explain why the same disease has very different death rates in two countries; Say what a map of cases can and cannot tell you about where transmission happened.

https://lightmysky.com/learn/geography/where-illness-spreads-and-why-mt_U2Hkw5FbiV

#### What Extraction Costs the Place It Happens (ages 16-18)

Metals for batteries, sand for concrete and water for crops all come from somewhere specific, and the bill for the damage is usually paid locally. Recycling and substitution change the arithmetic but do not remove it.

Ready when they can: Take one resource and describe the local effects of getting it out of the ground or the river; Explain why the costs of extraction and the benefits of use usually fall in different places; Assess one proposal to reduce demand for a resource, and say what it shifts rather than solves.

https://lightmysky.com/learn/geography/what-extraction-costs-the-place-it-happens-mt_diS2vBXcV4

#### Cities That Work (ages 16-18)

Density, transport and land use decide how long a city's residents spend travelling and how much energy the whole place burns. Most of the choices that fix that were made decades before anyone noticed.

Ready when they can: Explain how density and transport choices reinforce each other in a growing city; Compare two cities on how people get to work and say what in the layout explains the difference; Name one planning decision that is hard to undo later and say why.

https://lightmysky.com/learn/geography/cities-that-work-mt_AXiZ8RDe4Z

### Places & Regions

https://lightmysky.com/learn/geography/areas/places-and-regions

#### Places Near and Far (ages 5-7)

Every place has its own character: weather, land, plants, buildings and how people live; some places are near (our street, our town) and some are far away, and far-off places can be very different from home

Ready when they can: Describe features of their own street or town (e.g., 'our town has a market and a river'); Describe a faraway place from photos or stories (e.g., a desert village or a snowy city) and say how it differs from home; Name something people do differently in another place because of where it is (e.g., clothes for hot or cold places).

Needs first: First Maps and Globes.

https://lightmysky.com/learn/geography/places-near-and-far-mt_zbCartJJ2j

#### Comparing Places (ages 6-9)

Compare the human and physical geography of one small area with a contrasting area far away (a UK area and one in another country or continent): what is similar, what differs, and how land, weather and daily life go together

Ready when they can: Name similarities and differences between their own area and a contrasting place (e.g., 'both have farms, but their houses stand on stilts because of floods'); Compare physical features of two places (e.g., flat coast vs mountains, hot and dry vs cold and wet); Compare how people live in two places (jobs, homes, travel) and link a difference to the land or weather.

Needs first: Places Near and Far.

https://lightmysky.com/learn/geography/comparing-places-mt_SvEBb2xVzt

#### Continents and Oceans (ages 6-8)

Name and locate the world's seven continents and five oceans on a globe and world map; know which continent home is on, and begin placing familiar countries within their continents

Ready when they can: Name the seven continents and five oceans; Point to each continent and ocean on a globe or world map; Say which continent they live on and place a familiar country on the right continent (e.g., 'Brazil is in South America').

Needs first: First Maps and Globes.

https://lightmysky.com/learn/geography/continents-and-oceans-mt_aNGHn8yqR8

#### The United Kingdom (ages 7-10)

The four countries of the United Kingdom and their capitals; the surrounding seas; counties, major cities and regions; key features such as hills, mountains, coasts and rivers, and how land use has changed over time

Ready when they can: Name the four countries of the UK, their capital cities and the surrounding seas; Locate major UK cities, counties or regions on a map (e.g., Manchester, Cornwall, the Highlands); Describe a key UK physical feature and where it is (e.g., 'the Pennines run down the middle of northern England').

Needs first: Continents and Oceans.

https://lightmysky.com/learn/geography/the-united-kingdom-mt_Da-EAL3BvB

#### Countries of the World (ages 8-11)

Locate the world's countries and major cities using maps and atlases, with a focus on Europe (including Russia) and North and South America; know key physical and human features of the countries studied

Ready when they can: Locate major countries of Europe and the Americas on a map (e.g., finding France, Russia, Brazil, the USA); Name capital or major cities of countries studied (e.g., Paris, Moscow, Buenos Aires); Describe a key feature of a country studied (e.g., 'the Andes run down the west side of South America').

Needs first: Continents and Oceans, Reading Maps: Symbols and Grids.

https://lightmysky.com/learn/geography/countries-of-the-world-mt_xLEoqfmGFo

#### Comparing World Regions (ages 11-14)

How cultural and environmental characteristics vary across world regions; how cultural patterns and economic decisions shape landscapes and daily life; and how the character of a place feeds into people's sense of identity

Ready when they can: Compare the environments and cultures of two world regions (e.g., the Sahel and Scandinavia: climate, farming, cities, traditions); Explain how an economic decision shaped a place (e.g., tourism transforming a coastline, mining creating towns); Describe how a place shapes identity (e.g., how island life or a megacity shapes how people see themselves).

Needs first: Comparing Places, Countries of the World, Climate Zones, The United Kingdom.

https://lightmysky.com/learn/geography/comparing-world-regions-mt_cY5D2gWt0Y

#### Measuring Development Gaps (ages 15-16)

Countries differ in income, health and schooling, and each measure tells a different story about the same place. Compare what income per person, life expectancy and years of schooling each capture, and what a national average hides.

Ready when they can: Explain what income per person measures and name one thing it misses; Say why life expectancy and schooling sit alongside income in a development index; Give an example of a national average hiding a gap inside the country; Name one reason a development gap can narrow over time.

https://lightmysky.com/learn/geography/measuring-development-gaps-mt_bboR-ofYrR

#### Borders, Territory and the Sea (ages 16-18)

Most borders were drawn by someone who was not living there, and a good many are still argued over. At sea the claims reach two hundred miles out, which is why uninhabited rocks get fought over.

Ready when they can: Explain the difference between a border drawn along a physical feature and one drawn on a grid, and give a consequence of each; Say what an exclusive economic zone gives a state and why a small island can be worth claiming; Take one contested border and set out what each side claims and on what basis.

https://lightmysky.com/learn/geography/borders-territory-and-the-sea-mt_vsZWx6C8fM

### Physical Geography

https://lightmysky.com/learn/geography/areas/physical-geography

#### How a River Shapes Its Valley (ages 11-13)

A river carries energy, and it spends that energy cutting down, sideways, or dropping what it carries. Waterfalls, meanders and floodplains are all the same three actions in different proportions.

Ready when they can: Name the three things a river does with the material it moves: erode, transport, deposit; Explain why a waterfall retreats upstream over time; Say why the outside of a meander bend is deeper and the inside is shallow.

https://lightmysky.com/learn/geography/how-a-river-shapes-its-valley-mt_v6D9mgcf0P

#### From Source to Sea (ages 11-13)

Follow one river the whole way and the changes are systematic: steeper and rockier near the source, wider and slower near the mouth. That pattern is why upland and lowland landscapes look so different.

Ready when they can: Describe how width, depth, gradient and load change between source and mouth; Match three landforms to the part of the course where each is usually found; Explain why a river usually gets faster downstream even though the slope gets gentler.

https://lightmysky.com/learn/geography/from-source-to-sea-mt_VuUB9PiYan

#### Coasts on the Move (ages 11-13)

Waves take material from one part of a coast and put it down further along, so beaches, spits and bars are all sediment in transit. A coastline is a balance sheet that never quite settles.

Ready when they can: Explain how waves arriving at an angle move sediment along a beach; Say how a headland and a bay form on a coast made of alternating hard and soft rock; Name one coastal landform made by erosion and one made by deposition.

https://lightmysky.com/learn/geography/coasts-on-the-move-mt_IVnXDRpfqE

#### What the Ice Left Behind (ages 12-13)

Ice does not flow around obstacles the way water does, so glaciers gouge straight, steep-sided valleys and dump unsorted rubble where they stop. Much of northern Europe and North America is still wearing the shape of ice that melted ten thousand years ago.

Ready when they can: Say how a glacial valley differs in cross-section from a river valley, and why; Name two things a glacier leaves behind when it melts; Explain why lakes are common in landscapes that were once under ice.

https://lightmysky.com/learn/geography/what-the-ice-left-behind-mt_D-aB1k0K73

#### Reading a Landscape Off a Map (ages 12-13)

Contour lines carry the shape of the ground, and once you can read them a map tells you where a valley is steep, where a floodplain is, and where a spit is growing. Drawing a cross-section is how you check you have read it right.

Ready when they can: Say what closely spaced contours mean, and what a V pointing upstream tells you; Draw a cross-section between two grid references from contour values; Find one river landform and one coastal landform on a map extract and name each.

https://lightmysky.com/learn/geography/reading-a-landscape-off-a-map-mt_MWlY_e59Rg

#### Drainage Basins and Why Rivers Flood (ages 14-16)

Everything that falls on a basin has to leave it, and how fast it gets to the channel decides whether the river rises gently or all at once. Concrete, drains and cleared hillsides all shorten that journey.

Ready when they can: Explain what a drainage basin is and name three routes water takes to reach the channel; Read a flood hydrograph and say what a short lag time tells you about the basin; Give two human changes that raise flood risk downstream and say why each does.

https://lightmysky.com/learn/geography/drainage-basins-and-why-rivers-flood-mt_Vu4fTs7goJ

#### Choosing How to Defend a Coast (ages 14-16)

Sea walls, groynes, beach nourishment and doing nothing are all real options, and each moves the problem somewhere or someone else. Defending one town often starves the beach of the next one along.

Ready when they can: Compare one hard and one soft engineering method on cost, lifespan and effect further along the coast; Explain what managed retreat means and when a council might choose it; Say who gains and who loses from a defence scheme, and how that decision is usually made.

https://lightmysky.com/learn/geography/choosing-how-to-defend-a-coast-mt_3Px4N4va3o

## Arts & Music

39 topics, ages 5 to 16. https://lightmysky.com/learn/arts-and-music

### Music

https://lightmysky.com/learn/arts-and-music/areas/music

#### Exploring and Making Sounds (ages 5-7)

Experiment with sounds from voices, objects and instruments: make them louder or quieter, higher or lower, faster or slower; choose and combine sounds to match a mood, a story or a picture

Ready when they can: Change a sound deliberately and describe how (e.g. tapping a glass harder to make it louder); Choose sounds to match a mood or story moment (e.g. slow low notes for a giant's footsteps); Combine two or more sounds and say what they were trying to make (e.g. shakers and tapping for rain).

https://lightmysky.com/learn/arts-and-music/exploring-and-making-sounds-mt_HkEHXVCzRe

#### Listening to Music (ages 5-9)

Listen with concentration to a wide range of music: pick out instruments and voices, describe how pieces change (faster, slower, louder, quieter) and recall sounds and short patterns from memory with growing accuracy

Ready when they can: Listen to a piece of music all the way through and describe what they noticed (e.g. 'the drums came in halfway'); Identify familiar instruments or voices by sound alone (e.g. piano vs guitar, one singer vs many); Recall and describe a short rhythm or tune after hearing it (e.g. spotting when a melody comes back).

https://lightmysky.com/learn/arts-and-music/listening-to-music-mt_sVUxOvaDOO

#### Reading Musical Notation (ages 7-11)

Read staff notation and other ways of writing music down: note names on the stave, note and rest lengths (crotchets, quavers, minims), and graphic scores; follow a written melody and match notation to what is heard

Ready when they can: Name notes on the treble stave and explain that higher positions mean higher sounds; Identify note and rest lengths (e.g. a minim lasts twice as long as a crotchet); Follow a simple score while listening and point to where the music has got to, or match a short rhythm they hear to the right notation.

Needs first: Listening to Music.

https://lightmysky.com/learn/arts-and-music/reading-musical-notation-mt_YrnMXGEnk-

#### Composing Music (ages 8-11)

Improvise and compose short pieces for a purpose: build and layer patterns of pitch, rhythm, tempo and dynamics; repeat, vary and order ideas into a shape, and explain the choices behind the finished piece

Ready when they can: Create a short piece with a clear beginning, middle and end (e.g. layering loops in a music app); Use musical elements deliberately (e.g. getting louder towards the ending, a low repeated pattern under a tune); Explain the choices in their piece (e.g. 'I made it slow and low because it's the sad part').

Needs first: Exploring and Making Sounds, Listening to Music.

https://lightmysky.com/learn/arts-and-music/composing-music-mt_QzScsMn9fX

#### Music Through History (ages 8-11)

Get to know great composers and musicians and music from different times, places and traditions; describe what makes each style distinctive and how music has changed from early and classical eras to recorded and popular music

Ready when they can: Name several composers or musicians from different eras and something distinctive about their music (e.g. Beethoven's stormy symphonies); Recognise broad styles by ear (e.g. telling a classical orchestra from jazz or gamelan); Describe one way music changed over time (e.g. how recording let people hear music without live players).

Needs first: Listening to Music.

https://lightmysky.com/learn/arts-and-music/music-through-history-mt__1i5N9PywE

#### Scales, Keys and Why a Tune Sounds Happy or Sad (ages 11-13)

The notes of a tune are picked from a small set called a scale, and the scale a piece sits in gives it a mood before a single word is sung. Major and minor are the two sets a listener meets first.

Ready when they can: Say that a tune uses notes from a scale rather than any note at all; Hear a short piece and say whether it sounds major or minor, and give the word for the mood it carries; Point out on a keyboard or a stave that a scale is a fixed pattern of steps, some larger than others; Explain what it means that a song is in a key, and why two singers might want it moved.

https://lightmysky.com/learn/arts-and-music/scales-keys-and-why-a-tune-sounds-happy-or-sad-mt_9XMu4MF7_t

#### The Families of the Orchestra (ages 11-13)

Orchestral instruments group into four families by how they are made to sound: strings, woodwind, brass and percussion. Knowing the families is what lets a listener name what they are hearing.

Ready when they can: Name the four families and give two instruments in each; Say how each family starts a vibration: a bowed or plucked string, air split or reed, buzzing lips, something struck; Pick out one family in a recording and say what gave it away; Explain why a longer or larger instrument in the same family sounds lower.

https://lightmysky.com/learn/arts-and-music/the-families-of-the-orchestra-mt_5asOXH89es

#### Chords and Harmony (ages 12-14)

Notes sounded together make a chord, and a run of chords underneath a tune is what most songs are built on. A few chords, repeated in an order, carry a whole song.

Ready when they can: Say what a chord is and how it differs from a melody; Hear when the chord under a song changes, even without naming it; Explain that many songs run on three or four chords in a repeating order; Give one example of a chord change that sounds like an ending and one that sounds unfinished.

https://lightmysky.com/learn/arts-and-music/chords-and-harmony-mt_SWhLE91u-E

#### Music Traditions Around the World (ages 12-14)

Not every tradition organises music the way European classical music does. Javanese gamelan, Indian raga and West African drumming each set up pitch, rhythm and the role of the players differently.

Ready when they can: Name three traditions from different parts of the world and one instrument or sound from each; Give one way a tradition differs from Western classical music, such as tuning, rhythm layers, or who improvises; Say that a scale is a choice a tradition makes, not a law of sound; Describe one occasion a named tradition is played for, such as a ceremony or a dance.

https://lightmysky.com/learn/arts-and-music/music-traditions-around-the-world-mt_FObFf1o8rL

#### The Shape of a Piece (ages 12-14)

Music is arranged in sections that repeat, contrast and return, which is why a listener can follow a piece that lasts ten minutes. Verse and chorus, theme and variations, and movements are three of the shapes.

Ready when they can: Label the sections of a pop song as verse, chorus and bridge while it plays; Say what repetition and contrast each do for a listener; Recognise a theme coming back changed, and describe one thing that changed about it; Explain what a movement is in a longer classical piece.

https://lightmysky.com/learn/arts-and-music/the-shape-of-a-piece-mt_sSoi-W_vs-

#### Four Eras of Western Classical Music (ages 14-16)

Baroque, classical, romantic and modern name four stretches of European music, each with its own habits about size, tune and feeling. Knowing the four gives a listener somewhere to put a piece they have never heard.

Ready when they can: Put the four eras in order and give rough dates for each; Name a composer per era and one thing that composer is known for; Hear an unfamiliar piece and place it in an era with a reason drawn from the sound; Describe one change between eras, such as the orchestra growing or the tune getting freer.

https://lightmysky.com/learn/arts-and-music/four-eras-of-western-classical-music-mt_qD4DNod70-

#### From Work Songs to Hip Hop (ages 14-16)

Blues, jazz, rock, soul and hip hop are one connected line, carried mostly by Black American musicians and borrowed from everywhere. Each style kept something from the last and threw something away.

Ready when they can: Put blues, jazz, rock and hip hop in rough order and name what each took from the one before; Say where the blues came from and why that history matters to the music; Name one thing hip hop does that no earlier style did, such as building a track from existing records; Give an example of a style crossing from one community to a much wider audience, and one question that raises.

https://lightmysky.com/learn/arts-and-music/from-work-songs-to-hip-hop-mt_6cNI4oKzCA

#### Listening to a Whole Piece and Saying What Happens (ages 14-16)

Given six minutes of unfamiliar music, a listener can track what enters, what returns and where the piece turns. Saying it out loud is the whole skill.

Ready when they can: Describe a piece in order: what starts it, what enters next, where it changes; Use the right words for tempo, dynamics, texture and instrumentation; Name the moment a piece turns, and say what turned it; Give a judgement about the piece backed by something that actually happens in it.

https://lightmysky.com/learn/arts-and-music/listening-to-a-whole-piece-and-saying-what-happens-mt_rtquCTEn0v

#### How Recording Changed Music (ages 15-16)

Before recording, music existed only while someone played it. Microphones, multitrack tape, sampling and streaming each changed what could be made and who got to hear it.

Ready when they can: Explain what a microphone turns sound into and what a speaker turns it back into; Say what multitrack recording made possible that a live take cannot do; Describe what sampling is and one argument it starts about credit or payment; Name one effect of streaming on what music gets made, such as shorter intros.

https://lightmysky.com/learn/arts-and-music/how-recording-changed-music-mt_CP9uGPaeez

### Visual Art

https://lightmysky.com/learn/arts-and-music/areas/visual-art

#### Art Materials and Techniques (ages 5-7)

Explore drawing, painting and simple sculpture to share ideas and experiences; try out colour, pattern, texture, line and shape with different materials (pencils, paint, clay, collage) and talk about the effects

Ready when they can: Make pictures and models using a range of materials (e.g. thick and thin pencil lines, mixing paint colours, rolling and pinching clay); Use words like colour, pattern, texture, line and shape when talking about their own artwork (e.g. 'I used wavy lines for the sea'); Choose a material or technique to match an idea (e.g. picking bumpy collage paper for a dragon's skin).

https://lightmysky.com/learn/arts-and-music/art-materials-and-techniques-mt_FQa-W9aXrg

#### Great Artists and Designers (ages 7-11)

Learn about the work of artists, architects, craft makers and designers past and present; describe similarities and differences between their styles and methods, and make links to your own artwork

Ready when they can: Name several artists or designers and describe what their work looks like (e.g. Van Gogh's swirling brushstrokes, Kusama's dots); Compare two artworks or buildings, pointing out similarities and differences in style, materials or purpose; Try an idea borrowed from an artist in their own work and say where it came from.

Needs first: Art Materials and Techniques.

https://lightmysky.com/learn/arts-and-music/great-artists-and-designers-mt_RdVEVrWmGZ

#### Developing Art Techniques (ages 8-11)

Improve control of drawing, painting and sculpture: shading and tone with pencil and charcoal, mixing and layering paint, building forms in clay; keep a sketchbook to record observations, test ideas and revisit them

Ready when they can: Use shading, hatching or blending to show light and shadow in a drawing; Keep a sketchbook of observations and ideas, and return to earlier pages to improve a piece (e.g. redrawing a hand study); Explain which technique or material they chose for a piece and why (e.g. charcoal for soft smoky edges).

Needs first: Art Materials and Techniques.

https://lightmysky.com/learn/arts-and-music/developing-art-techniques-mt_WHP0beHTl1

#### Looking at a Picture: What to Notice First (ages 11-13)

There is a method for looking at a painting: find where the eye lands, follow how it is led around, then ask what the artist did to arrange that. Composition, light and colour are the levers.

Ready when they can: Say where the eye lands first in a picture and name one thing that put it there; Use composition words correctly: foreground and background, focal point, balance; Describe what the light in a picture is doing, such as picking out one figure or flattening everything; Give an opinion about a picture with a reason drawn from what is actually in it.

https://lightmysky.com/learn/arts-and-music/looking-at-a-picture-what-to-notice-first-mt_jJxX9-kw1V

#### Perspective and the Illusion of Depth (ages 12-14)

A flat surface can be made to look deep using rules that were worked out and then taught: lines that converge, things that shrink with distance, colours that fade. Not every tradition wanted that illusion.

Ready when they can: Find the horizon line and a vanishing point in a picture that uses them; Name two tricks besides converging lines that make depth, such as overlap or paler distant colour; Compare a picture built on perspective with one that stacks figures flat, and say what each is for; Explain that linear perspective was invented at a time and place, not always used.

https://lightmysky.com/learn/arts-and-music/perspective-and-the-illusion-of-depth-mt_viqsbnnXt5

#### The Camera as an Art Tool (ages 12-14)

A camera records light through a lens, and the photographer still chooses framing, moment and focus. Once photographs could be made, painters stopped needing to be the only record of what things looked like.

Ready when they can: Say what the lens does and what the sensor or film does; Name three choices a photographer makes: what is in frame, when to press, what is sharp; Explain one way photography changed what painters chose to paint; Look at a photograph and say whether it is a record, an argument or a composition, with a reason.

https://lightmysky.com/learn/arts-and-music/the-camera-as-an-art-tool-mt_TIdod5lPOl

#### Movements: Why Painting Kept Changing (ages 14-16)

Renaissance, impressionism, cubism and abstraction are labels for groups of artists who agreed about what a picture was for. Each movement is a reaction to what came before it and to what was happening around it.

Ready when they can: Name four movements in rough order with one visual giveaway each; Explain what the impressionists were reacting against, and what let them paint outdoors; Say what cubism was trying to solve about showing a solid thing on a flat surface; Argue why abstraction is still painting, using one work as evidence.

https://lightmysky.com/learn/arts-and-music/movements-why-painting-kept-changing-mt_HRX2JsxDEY

#### Art Traditions Beyond Europe (ages 14-16)

Chinese ink painting, West African sculpture, Islamic geometry and Japanese woodblock prints each set their own standards for what good work is. Judging them by European rules misses what they were made to do.

Ready when they can: Name four traditions from different regions and one material or technique each is known for; Say what one tradition values that European painting has not, such as brushwork, pattern or ancestral function; Give an example of a European artist borrowing from another tradition, and say what was taken; Explain why calling non-European work primitive was a judgement, not a description.

https://lightmysky.com/learn/arts-and-music/art-traditions-beyond-europe-mt_hg9B9DnGt8

#### Digital Images as an Art Medium (ages 15-16)

An image made of pixels can be copied perfectly, edited without trace and generated by a model. That changes what an original is and what the artist's decision actually was.

Ready when they can: Say what a digital image is made of and why it can be copied with no loss; Name two things editing software makes easy that were hard or impossible on paper; Explain what is left of the artist's choice when a model generates the image; Give one argument about credit or consent that generated images raise, and one answer to it.

https://lightmysky.com/learn/arts-and-music/digital-images-as-an-art-medium-mt_UwgfEOMPk5

#### What Galleries Keep and Who Decided (ages 15-16)

The art a person grows up seeing was selected: bought, donated, looted or left out. Museums, collectors and critics made those calls, and some of them are being argued over now.

Ready when they can: Explain how a work ends up in a national museum, naming at least two routes; Give one reason whole groups of artists were left out of the standard story; State the case for returning an object to where it was taken from, and the case against; Say what a curator does and how that job shapes what the public sees.

https://lightmysky.com/learn/arts-and-music/what-galleries-keep-and-who-decided-mt_xT1-Eojyb5

### Performing Arts

https://lightmysky.com/learn/arts-and-music/areas/performing-arts

#### Dance: Telling a Story Without Words (ages 7-9)

Dance carries meaning through the body: how big a movement is, how fast, how high, and whether it repeats. A dance can tell a story or show a feeling with no words at all.

Ready when they can: Describe a movement using size, speed, level and direction; Match a movement to a mood in the music and say why it fits; Spot a movement that repeats in a dance and say what the repeat does; Watch a short dance and say what it seemed to be about.

https://lightmysky.com/learn/arts-and-music/dance-telling-a-story-without-words-mt_JCmUH5GmE9

#### Playing a Part: Voice, Face and Body (ages 7-9)

An actor shows who a character is with three tools: how they say the words, what their face does, and how they hold and move their body. The same line can be made kind or cruel by voice alone.

Ready when they can: Say one line two ways and name what changed, such as louder, slower, or a different feeling; Show a feeling with face and body without speaking, and have someone else name it; Explain that an actor is pretending to be someone else on purpose, not being themselves; Watch a short scene and say what the actor's voice told you about the character.

https://lightmysky.com/learn/arts-and-music/playing-a-part-voice-face-and-body-mt_uN2l8k1-Oi

#### Building a Scene: Who Wants What (ages 9-11)

A scene works when each character wants something and something is in the way. Change what one of them wants and the scene changes, which is why actors and writers start there.

Ready when they can: State what each character in a short scene wants; Name the obstacle between a character and what they want; Predict how a scene changes if one character's want is swapped; Explain why a scene with nobody wanting anything is boring to watch.

https://lightmysky.com/learn/arts-and-music/building-a-scene-who-wants-what-mt_CZbWK5gf0v

#### Dances People Do: Folk, Social and Stage (ages 10-12)

Some dances are done in a village or a club with everyone joining in, and some are made to be watched from seats. The difference decides who the dance is for and how it is learned.

Ready when they can: Sort named dances into ones people join and ones people watch; Name two folk or social dance traditions and where they come from; Say one thing ballet asks of a dancer that a social dance does not; Explain how a street or social dance spreads without anyone writing it down.

https://lightmysky.com/learn/arts-and-music/dances-people-do-folk-social-and-stage-mt_8i89DDjT_v

#### How a Play Gets Made (ages 11-13)

Between a script and an audience sit a director, a cast, a designer and weeks of rehearsal. Set, lighting, sound and costume are decisions someone made, and each one can be read.

Ready when they can: Name four jobs behind a production and say what each decides; Explain what happens in rehearsal that is not in the script; Point at one staging choice in a production and say what it told the audience; Give one reason two productions of the same play can feel completely different.

https://lightmysky.com/learn/arts-and-music/how-a-play-gets-made-mt_vuaFvRSoi2

#### Theatre Traditions Around the World (ages 14-16)

Greek amphitheatres, Japanese noh, Indian kathakali and European realism each answer the same question differently: how do you show a story to a crowd. Masks, distance and convention do the work.

Ready when they can: Name four traditions and one convention each uses, such as masks, chorus or a bare stage; Explain why a large open-air theatre pushes actors towards big gesture and strong voice; Say what an audience has to agree to accept for a convention to work; Compare a realistic set with a bare stage and say what each gains.

https://lightmysky.com/learn/arts-and-music/theatre-traditions-around-the-world-mt_g9NGWncIy6

#### Watching a Live Performance and Saying Why It Worked (ages 15-16)

A play, a gig or a dance can be described the way a picture can: what the makers chose, what it did to the room, and whether it held. Live work also carries risk, which is part of what an audience comes for.

Ready when they can: Describe a performance in terms of choices made, not only whether it was enjoyed; Name one thing that only works live, such as an audience reacting or a mistake being absorbed; Write or say a short response that quotes a specific moment as evidence; Separate a judgement about the work from a judgement about the performers.

https://lightmysky.com/learn/arts-and-music/watching-a-live-performance-and-saying-why-it-worked-mt_jmRc5JDGTd

### Music theory first steps

https://lightmysky.com/learn/arts-and-music/areas/music-theory-first-steps

#### Finding the steady beat (ages 5-7)

Feel and keep the even beat that runs through a song.

Ready when they can: Can explain Finding the steady beat.

https://lightmysky.com/learn/arts-and-music/finding-the-steady-beat-ct_ebGLHfzz27o

#### Long and short sounds (ages 5-8)

Say ta and ti-ti for long and short sounds on the beat.

Ready when they can: Can explain Long and short sounds.

https://lightmysky.com/learn/arts-and-music/long-and-short-sounds-ct_x6T1ummvCdc

#### Loud and quiet (ages 5-7)

Forte means loud and piano means quiet.

Ready when they can: Can explain Loud and quiet.

https://lightmysky.com/learn/arts-and-music/loud-and-quiet-ct_NoBGDceitaw

#### Fast and slow (ages 5-7)

Tempo is the speed of the beat. Allegro is fast and adagio is slow.

Ready when they can: Can explain Fast and slow.

https://lightmysky.com/learn/arts-and-music/fast-and-slow-ct_3D2KcLXr2bk

#### High and low sounds (ages 5-8)

Pitch is how high or low a sound is.

Ready when they can: Can explain High and low sounds.

https://lightmysky.com/learn/arts-and-music/high-and-low-sounds-ct_jV8R937gcGI

#### The staff and where notes sit (ages 6-9)

The staff has five lines and four spaces, and notes sit on them.

Ready when they can: Can explain The staff and where notes sit.

https://lightmysky.com/learn/arts-and-music/the-staff-and-where-notes-sit-ct_nPkxk0ezxeY

#### Note names A to G (ages 7-10)

The musical alphabet and the treble clef landmarks E G B D F and FACE.

Ready when they can: Can explain Note names A to G.

https://lightmysky.com/learn/arts-and-music/note-names-a-to-g-ct_hb_IpciuWGg

#### Reading and clapping simple rhythms (ages 7-10)

Quarter notes, eighth-note pairs, a quarter rest, and four beats in a bar.

Ready when they can: Can explain Reading and clapping simple rhythms.

https://lightmysky.com/learn/arts-and-music/reading-and-clapping-simple-rhythms-ct_OK5jHg1Uw3o

## Learning to Learn

30 topics, ages 5 to 18. https://lightmysky.com/learn/learning-to-learn

### Learning to Learn

https://lightmysky.com/learn/learning-to-learn/areas/learning-to-learn

#### Asking for Help with Learning (ages 5-6)

Ask for help when you've had a go yourself and are still stuck — knowing when to ask is a skill in itself

Ready when they can: Hattie visible learning; self-regulated learning research.

https://lightmysky.com/learn/learning-to-learn/asking-for-help-with-learning-mt_mvXufozy2s

#### Checking Your Own Work (ages 5-6)

After finishing a task, look back at what you did and ask yourself: does this seem right?

Ready when they can: After finishing a piece of work, re-read or review it without being asked to; Spot and correct at least one error in their own work by checking back through it; Describe what they checked for — e.g. 'I re-read each line to make sure my answers matched the question'.

https://lightmysky.com/learn/learning-to-learn/checking-your-own-work-mt_8dstvf-KKb

#### Persisting When It's Hard (ages 5-6)

Keep trying when something feels hard — making mistakes and trying again is how learning happens

Ready when they can: Keep working on a difficult task for a sustained period without giving up or asking someone else to do it; After making a mistake, try again with a different approach rather than saying 'I can't do it'; Talk about difficulty positively — e.g. 'This is hard but I'm getting better' rather than 'I'm no good at this'.

https://lightmysky.com/learn/learning-to-learn/persisting-when-its-hard-mt_S4G6GLKr1-

#### Feeling of not understanding (ages 6-7)

Notice the feeling of not understanding — recognise when something is confusing rather than reading or listening past it

Ready when they can: comprehension monitoring research; Flavell metacognitive monitoring.

Needs first: Asking for Help with Learning.

https://lightmysky.com/learn/learning-to-learn/feeling-of-not-understanding-mt_klyw-tdlhP

#### Planning a Task (ages 6-7)

Make a simple plan before starting a task: what do I need to do, and what should I do first?

Ready when they can: Before starting a task, describe what they need to do and what order to do it in; Break a larger task into smaller steps without being prompted — e.g. 'First I'll read the question, then I'll draw a diagram'; Gather the materials or information they need before beginning, rather than starting and then stopping to find things.

Needs first: Checking Your Own Work.

https://lightmysky.com/learn/learning-to-learn/planning-a-task-mt_QR3vxbN1o4

#### Thinking Before Starting (ages 6-7)

Before starting something new, stop and think: what do I already know about this topic?

Ready when they can: prior knowledge activation research; Ausubel meaningful learning.

Needs first: Persisting When It's Hard.

https://lightmysky.com/learn/learning-to-learn/thinking-before-starting-mt_LE7nFEwS12

#### Big Questions and Supporting Questions (ages 7-10)

Know what makes a question big and worth investigating — no single quick answer, more than one possible view — and break it into smaller supporting questions whose answers build up towards answering the big one

Ready when they can: Tell apart a big question ('Why do people move to new places?') from a quick-lookup one ('What is the capital of France?'); Break a big question into two or three smaller questions that would each help answer it; Explain how the answer to a small question feeds the bigger one (e.g., 'Knowing what jobs there were tells us why families moved here').

Needs first: Planning a Task.

https://lightmysky.com/learn/learning-to-learn/big-questions-and-supporting-questions-mt_JUHStYGUel

#### Connecting New & Old Ideas (ages 7-8)

Look for connections between new ideas and things you already know — how does this fit with what I've learned before?

Ready when they can: elaborative encoding; schema theory (Bartlett, Rumelhart).

Needs first: Thinking Before Starting.

https://lightmysky.com/learn/learning-to-learn/connecting-new-and-old-ideas-mt_32B7xjUPwF

#### Spotting Patterns (ages 7-8)

Spot patterns and recurring structures — in numbers, words, nature, sounds, or events — and use them to make sense of new information

Ready when they can: Spot a pattern in a set of numbers, shapes, or facts without being told to look for one; Use a pattern they noticed to make a prediction — e.g. 'The next one should be 16 because it's doubling each time'; Explain the pattern they found and why they think it works.

Needs first: Connecting New & Old Ideas.

https://lightmysky.com/learn/learning-to-learn/spotting-patterns-mt_wvcFlwOrDl

#### Trying a New Approach (ages 7-8)

When your first approach isn't working, try a different one — being flexible about strategies is part of being a good learner

Ready when they can: When stuck on a problem, try a completely different approach rather than repeating the same method — e.g. drawing a picture instead of writing equations; Describe a time they changed strategy mid-task and explain why the new approach worked better; Accept that their first idea might not work and show willingness to start over with a fresh plan.

Needs first: Feeling of not understanding, Planning a Task.

https://lightmysky.com/learn/learning-to-learn/trying-a-new-approach-mt_95zxYqpP7m

#### Analysing Your Own Errors (ages 8-9)

When you get something wrong, investigate why — what did you misunderstand or overlook? Analysing errors is one of the most powerful ways to learn

Ready when they can: error analysis research; Hattie feedback effect size.

Needs first: Checking Your Own Work, Trying a New Approach.

https://lightmysky.com/learn/learning-to-learn/analysing-your-own-errors-mt_TDUpy57QVM

#### Describing Rules & Patterns (ages 8-9)

When you notice a pattern repeating, describe it as a rule that works every time — then test whether the rule holds in new cases

Ready when they can: Describe a pattern or rule they've noticed in their own words — e.g. 'Every time you add 0 to a number, it stays the same'; Test whether a rule they've described holds for new examples they haven't seen before; Explain the difference between noticing a pattern and proving it always works.

Needs first: Spotting Patterns.

https://lightmysky.com/learn/learning-to-learn/describing-rules-and-patterns-mt_hbe_kdE_7C

#### Transferring Skills (ages 8-9)

Recognise when a skill or strategy learned in one subject or situation can be applied in a completely different one

Ready when they can: transfer of learning research; Perkins & Salomon transfer taxonomy.

Needs first: Connecting New & Old Ideas, Spotting Patterns.

https://lightmysky.com/learn/learning-to-learn/transferring-skills-mt_99G6Msdzw-

#### Teaching It Back (ages 7-8)

After learning something new, explain it in your own words — to yourself, a family member, or even a toy

Ready when they can: Explain a concept they've learned to someone else in their own words, not just repeating what the teacher said; After teaching something to a friend or sibling, identify a gap in their own understanding that they only noticed through explaining; Summarise a lesson by pretending to teach it back, using examples they made up themselves.

Needs first: Explaining Mathematical Reasoning, Thinking Before Starting.

https://lightmysky.com/learn/learning-to-learn/teaching-it-back-mt_6eTZUwKQZr

#### Understanding Why (ages 8-9)

Go beyond knowing *that* something is true — ask *why* it is true and *how* it works

Ready when they can: Ask 'why?' or 'how does that work?' about something they've been told, rather than just accepting it; Explain the reason behind a rule or method — e.g. 'We carry the ten because 13 ones is the same as 1 ten and 3 ones'; Show deeper understanding by connecting a new idea to something they already know — e.g. 'Oh, that's like when we...'.

Needs first: Teaching It Back.

https://lightmysky.com/learn/learning-to-learn/understanding-why-mt_Y6P9y1Rz-u

#### Reflecting After Learning (ages 9-10)

After completing a piece of learning, reflect on the process: what helped most, what was confusing, and what would you do differently next time?

Ready when they can: Kolb reflective learning cycle; Hattie & Timperley feedback model.

Needs first: Teaching It Back, Analysing Your Own Errors.

https://lightmysky.com/learn/learning-to-learn/reflecting-after-learning-mt_v5yDTWEiyQ

#### Choosing a Strategy (ages 9-10)

Before starting a study task, choose a deliberate strategy; after finishing, evaluate honestly whether that strategy actually helped

Ready when they can: Before starting a task, name the strategy they plan to use and explain why — e.g. 'I'll make a mind map first because there's a lot to organise'; After finishing, honestly evaluate whether their chosen strategy helped or whether a different one would have been better; Describe at least three different learning strategies and explain when each works best.

Needs first: Guided Multi-Step Problem Solving, Multi-Step Problem Solving, Analysing Your Own Errors.

https://lightmysky.com/learn/learning-to-learn/choosing-a-strategy-mt_q7zxOloj_L

#### Finding Knowledge Gaps (ages 10-11)

Survey your own understanding of a whole topic — identify where your knowledge is solid, where it is shaky, and what still needs work

Ready when they can: metacognitive monitoring research; Flavell metacognition framework.

Needs first: Choosing a Strategy, Reflecting After Learning.

https://lightmysky.com/learn/learning-to-learn/finding-knowledge-gaps-mt_2uHYdoxD0H

#### Setting Learning Goals (ages 10-11)

Set a specific learning goal, work towards it with a deliberate plan, then honestly assess whether you achieved it and what you would change

Ready when they can: Set a specific, achievable learning goal for themselves — e.g. 'By Friday I want to know all my 7-times tables' rather than just 'get better at maths'; Make a simple plan for how to reach their goal and follow through on it over several days; After the deadline, honestly assess whether they achieved the goal and describe what they would do differently next time.

Needs first: Finding Knowledge Gaps, Planning a Task.

https://lightmysky.com/learn/learning-to-learn/setting-learning-goals-mt_jIszRCO2ij

#### Framing Research Questions (ages 11-13)

Frame a compelling research question around the important ideas of a field: judge whether it can be answered with available evidence, sharpen it when it is too broad or too narrow, and design supporting questions that carry the inquiry forward

Ready when they can: Draft a research question, judge it too broad, too narrow, or unanswerable, and revise it (e.g., 'Was the Industrial Revolution good?' becomes 'How did factory work change family life in one town?'); Explain why a question matters — what bigger idea in the subject it connects to; Plan a set of supporting questions and say what evidence would be needed to answer each one.

Needs first: Big Questions and Supporting Questions, Finding Knowledge Gaps.

https://lightmysky.com/learn/learning-to-learn/framing-research-questions-mt_ngkBCLLMYu

#### Retrieval Practice Instead of Rereading (ages 14-15)

Close the book and write down what you remember, then check it against the notes. Pulling the answer out is what builds the memory; rereading mostly builds the feeling that you already know it.

Ready when they can: Run a blank-page recall on a topic, mark it against the notes, and list what was missing; Explain why a page that feels familiar is not evidence they could answer a question on it; Turn a set of notes into questions they can test themselves with a week later.

https://lightmysky.com/learn/learning-to-learn/retrieval-practice-instead-of-rereading-mt_Pj5Au-ztqs

#### Spacing Revision Across Weeks (ages 14-15)

Come back to a topic after a gap, and let the gap grow each time the recall goes well. Two short sessions a week apart beat one long session, even though the spaced one feels harder at the time.

Ready when they can: Turn one topic into a schedule of repeats at growing gaps and say why the gaps grow; Explain why the session that felt harder is usually the one that lasts; Rebuild the schedule after a missed week without starting the topic from the beginning.

https://lightmysky.com/learn/learning-to-learn/spacing-revision-across-weeks-mt_cuBD3LE88f

#### Mixing Topics Instead of Blocking Them (ages 14-16)

Practise a mixed set rather than twenty questions of the same kind. Mixing makes you choose the method before you apply it, which is the step an exam actually tests.

Ready when they can: Build a mixed practice set from three topics and say what each question is testing; Explain why a blocked set feels easier during the session and scores worse later; Name the step mixing trains: choosing the method, not running it.

https://lightmysky.com/learn/learning-to-learn/mixing-topics-instead-of-blocking-them-mt_C28PN50zwX

#### Working Backwards From a Deadline (ages 15-16)

Start at the exam date and lay the sessions backwards to today, counting the hours you really have rather than the ones you meant to have. Then cut the plan until it fits.

Ready when they can: Build a backwards plan from a real deadline with dated sessions and a named topic for each; Count the hours actually free in a week (school, travel, sleep, commitments) before filling any of them; Cut a plan that does not fit and say what was dropped and why that was the right thing to drop.

https://lightmysky.com/learn/learning-to-learn/working-backwards-from-a-deadline-mt_DrdBx9c0pf

#### Protecting One Block of Attention (ages 15-16)

A plan works only if the blocks in it are real. Cut the interruptions before the block starts, run one task for a set time, and have a rule ready for the moment you get stuck.

Ready when they can: Set up a block by naming the one task, the length, and what gets switched off; Explain the cost of switching tasks: the minutes spent getting back to where they were; State their own stuck rule (try for a set time, write the question down, move on, come back to it).

https://lightmysky.com/learn/learning-to-learn/protecting-one-block-of-attention-mt_KMarG52Ab7

#### Notes That Are Worth Rereading (ages 16-18)

Notes that transcribe are notes nobody reads again. Notes that pose questions, mark what was confusing and connect to what came before are the ones that repay the effort.

Ready when they can: Turn a page of transcribed notes into questions and answers; Mark the parts you did not understand rather than skipping them silently; Explain why writing less can leave you knowing more.

https://lightmysky.com/learn/learning-to-learn/notes-that-are-worth-rereading-mt_u95SIfc8iI

#### Getting Through a Text That Is Too Hard (ages 16-18)

A hard chapter is not read once, it is passed over three times at increasing depth. Knowing that in advance is the difference between struggling and giving up.

Ready when they can: Describe a three-pass approach and say what each pass is for; Say what to do with a term you do not know, and when to look it up rather than push on; Explain why rereading the same sentence five times rarely works.

https://lightmysky.com/learn/learning-to-learn/getting-through-a-text-that-is-too-hard-mt_9QadnOEb-t

#### Running a Long Project Without Losing the Thread (ages 16-18)

A project measured in months fails in the middle, where there is no deadline and no obvious next step. The fix is a working question, a visible next action, and a record of what you already decided.

Ready when they can: State a working question narrow enough to answer and wide enough to be worth answering; Keep a decision log so past-you does not have to be re-argued with; Say what to do in the middle stretch when nothing feels urgent.

https://lightmysky.com/learn/learning-to-learn/running-a-long-project-without-losing-the-thread-mt_73LjxFuEul

#### Judging How Well You Actually Know It (ages 16-18)

Feeling fluent while reading is not the same as being able to produce it later, and the gap between them is where most revision is wasted. Calibration is checking that your confidence tracks your actual performance.

Ready when they can: Predict a score before a self-test and compare it with the result; Explain why material that feels easy while reading is often the least well learned; Name two checks that give an honest signal rather than a comfortable one.

https://lightmysky.com/learn/learning-to-learn/judging-how-well-you-actually-know-it-mt_xYl6rMw-op

#### Learning With an AI Without Handing Over the Thinking (ages 16-18)

A model will explain anything at any level, which makes it the best tutor available and the fastest way to feel you understand something you cannot do. The useful discipline is to attempt first, ask second, and always verify.

Ready when they can: Describe a workflow that attempts before asking, and say why the order matters; Name two ways to check an answer that does not rely on the same model; Explain the difference between using it to get unstuck and using it to skip the work.

https://lightmysky.com/learn/learning-to-learn/learning-with-an-ai-without-handing-over-the-thinking-mt_cw3agzDhxN

## Design & Technology

22 topics, ages 5 to 16. https://lightmysky.com/learn/design-and-technology

### Designing & Making

https://lightmysky.com/learn/design-and-technology/areas/designing-and-making

#### Designing Products (ages 5-8)

Design purposeful products for yourself and other users: say who a product is for and what it must do, gather ideas from looking and asking, set simple design criteria, and describe or draw a design that meets them

Ready when they can: State who a design is for and what it needs to do before making it (e.g. 'a boat for my teddy, so it has to float'); Set simple criteria and check a design against them (e.g. 'the card had to stand up on its own'); Draw or describe a design idea clearly enough for someone else to picture it.

Needs first: Describing Material Properties.

https://lightmysky.com/learn/design-and-technology/designing-products-mt_fZo-OWjM-T

#### Using Tools Safely (ages 5-9)

Choose and use tools and equipment for cutting, shaping, joining and finishing (scissors, hole punches, saws, sandpaper, glue): match the tool to the material and the job, and explain the safety rules for each

Ready when they can: Pick a sensible tool for a job and say why (e.g. a junior hacksaw for a wooden dowel, scissors for card); Describe the safety rules for a tool before using it (e.g. cutting away from fingers, clamping wood first); Name ways of joining and finishing materials and when each works best (e.g. glue vs tape vs split pins).

Needs first: Naming Everyday Materials.

https://lightmysky.com/learn/design-and-technology/using-tools-safely-mt_8_IFOc79VA

#### Strengthening Structures (ages 7-11)

How structures stand up and how to make them stronger, stiffer and more stable: wide bases, triangles, tubes, folds and cross-bracing; why some shapes resist pushing and pulling, and how real bridges and towers use these tricks

Ready when they can: Explain why a triangle or a folded sheet is stiffer than a flat one (e.g. corrugated card vs plain card); Suggest ways to stop a model tower falling over (e.g. widening the base, adding diagonal braces); Point out strengthening features in real structures (e.g. triangles in a bridge truss or a crane).

Needs first: Choosing the Right Material, Pushes & Pulls.

https://lightmysky.com/learn/design-and-technology/strengthening-structures-mt_QnYDI3itJY

#### Design Briefs and Better Products (ages 8-11)

Investigate and analyse existing products: work out who a product is for, what it does well and badly, how it works and what it is made from; use the analysis to write a design brief and criteria for a better version

Ready when they can: Take a product (e.g. a lunchbox or a torch) and explain who it is for, how it works and what it is made from; Point out strengths and weaknesses of a product against its purpose (e.g. 'the zip is fiddly for small hands'); Turn findings into a brief and criteria for an improved design (e.g. 'must open one-handed').

Needs first: Designing Products, Comparing Design Solutions.

https://lightmysky.com/learn/design-and-technology/design-briefs-and-better-products-mt_QeNClHE0EG

#### Design That Changed the World (ages 8-11)

How key designers, engineers and inventions have shaped everyday life: stories such as the printing press, the safety bicycle, flight and the telephone; what problem each design solved and how it changed the way people live

Ready when they can: Name several inventions or designers and the problem each design solved (e.g. the printing press making books cheap enough for many people); Describe how one invention changed daily life (e.g. how washing machines changed household work); Explain that designs improve over time as people spot problems (e.g. early cars vs modern ones).

Needs first: Designing Products.

https://lightmysky.com/learn/design-and-technology/design-that-changed-the-world-mt_6PWs6Qp8V6

#### Mechanisms That Make Things Move (ages 9-11)

A mechanism turns one movement into another: a push into a lift, a turn into a wobble, a small force into a big one. Levers, linkages, cams and cranks are the pieces a maker reaches for.

Ready when they can: Name the mechanism inside a moving toy or a pop-up card and say what it converts; Explain what a cam does to a follower and why the cam's shape decides the movement; Pick a mechanism for a stated job, such as making a puppet's arm wave; Say why a linkage can reverse a direction of movement.

https://lightmysky.com/learn/design-and-technology/mechanisms-that-make-things-move-mt_i6Je5hnxJz

#### Drawing a Design So Someone Else Can Build It (ages 10-12)

A design drawing is not a picture, it is an instruction. Views from more than one side, real dimensions and a stated scale are what let someone else make the thing without asking.

Ready when they can: Draw an object from front, side and above and label which view is which; Put dimensions on a drawing with units, and state the scale used; Say what an exploded view shows that a single outside view cannot; Look at someone else's drawing and name the one thing missing that would stop you building it.

https://lightmysky.com/learn/design-and-technology/drawing-a-design-so-someone-else-can-build-it-mt_8ezErqUhZw

#### Electronics in a Product: Switch, Sensor, Output (ages 11-13)

Most electrical products are the same three parts: something that decides, something that senses, and something that happens. A switch is a person deciding, a sensor is the product deciding for itself.

Ready when they can: Sort the parts of a simple product into input, control and output; Explain the difference between a switch and a sensor in what triggers them; Name two sensors and what each measures, such as light or temperature; Sketch a circuit for a stated behaviour, such as a light that comes on when it gets dark.

https://lightmysky.com/learn/design-and-technology/electronics-in-a-product-switch-sensor-output-mt_KNLW4qke5J

#### Iterative Design and Prototyping (ages 11-14)

Develop a design through repeated cycles: build a model or prototype, test it against criteria, use the results to find weaknesses, and modify the design; run the loop several times so each version measurably beats the last

Ready when they can: Build a rough prototype or model to test an idea before making a final version; Test a prototype against criteria, record the results, and identify the main weakness (e.g. 'the bridge failed at the joints, not the beams'); Explain how each version changed and what test evidence prompted the change.

Needs first: Design Briefs and Better Products, Fair testing (age 8+), Strengthening Structures, Using Tools Safely.

https://lightmysky.com/learn/design-and-technology/iterative-design-and-prototyping-mt_fYD3KaViOZ

#### Systems: Input, Process, Output (ages 12-14)

Any made thing can be drawn as a block diagram: what goes in, what is done to it, what comes out. Drawing it that way shows where a fault must be before anything is opened up.

Ready when they can: Draw a block diagram for an everyday product with the three stages labelled; Use a block diagram to say which stage a described fault must be in; Explain what feedback adds to a system, using a thermostat or a cruise control; Say why the same diagram fits a kettle and a phone app.

https://lightmysky.com/learn/design-and-technology/systems-input-process-output-mt_bMNTQ-3a_u

#### CAD and Making by Machine (ages 14-16)

A design drawn on a computer can be sent straight to a machine that cuts, prints or mills it. What the machine can and cannot do reaches back into the design, which is why the drawing changes once you know how it will be made.

Ready when they can: Say what a CAD model holds that a paper drawing does not; Name three machines that take a digital file and what each is good at, such as 3D printing, laser cutting or CNC milling; Give one constraint a 3D printer imposes on a shape, such as overhangs needing support; Explain why a part is redesigned once the making method is chosen.

https://lightmysky.com/learn/design-and-technology/cad-and-making-by-machine-mt_jNf8g85YbY

#### Designing for the People Who Use It (ages 14-16)

Bodies vary, and a product sized for an average nobody actually is will fail most people. Measured body data, reach and grip, and the needs of people with limited sight or movement all belong in the brief.

Ready when they can: Explain why designing to the average measurement excludes most users; Name two body measurements that decide a real product's dimensions, such as grip width or seat height; Redesign one feature of a product so it works one-handed or without sight; Say what a designer learns from watching someone use a product that they cannot learn from asking.

https://lightmysky.com/learn/design-and-technology/designing-for-the-people-who-use-it-mt_QPznzhuBNI

#### Making One, Making Thousands (ages 14-16)

The cheapest way to make one of something is almost never the cheapest way to make ten thousand. Tooling, jigs and tolerances are the price of repeating a design exactly.

Ready when they can: Explain why a mould is worth paying for at high volume and not at low volume; Say what a tolerance is and why parts that must fit together need one; Name what a jig or a template does for repeatability; Compare one-off, batch and mass production on cost per item and on flexibility.

https://lightmysky.com/learn/design-and-technology/making-one-making-thousands-mt_0wbzsY10cQ

#### The Whole Life of a Product (ages 15-16)

A product's cost to the world runs from digging up the material to whatever happens after it is thrown away. Designers decide most of that at the drawing stage, including whether the thing can be opened and repaired.

Ready when they can: List the stages of a product's life from raw material to disposal; Name one design decision that decides whether a product can be repaired; Explain why recycling a mixed-material product is harder than recycling a single-material one; Give one argument that a product was designed to be replaced rather than fixed, and what evidence would settle it.

https://lightmysky.com/learn/design-and-technology/the-whole-life-of-a-product-mt_hyBZiDvDoX

### Food & Cooking

https://lightmysky.com/learn/design-and-technology/areas/food-and-cooking

#### Where Food Comes From (ages 5-8)

Where food comes from: which foods are grown, reared or caught (wheat, apples, milk, fish); how ingredients travel from farms and seas to shops; seasonality, and why some fruits and vegetables are only picked at certain times of year

Ready when they can: Say whether familiar foods are grown, reared or caught (e.g. bread starts as wheat, fish fingers as fish); Describe the steps between farm and plate for one food (e.g. milk goes from cow to dairy to bottle); Name fruits or vegetables that are in season at different times of year (e.g. strawberries in summer).

Needs first: Wild, Farm & Pet Animals.

https://lightmysky.com/learn/design-and-technology/where-food-comes-from-mt_HTJsTS1XzU

#### Cooking and Food Preparation (ages 8-11)

Prepare and cook mostly savoury dishes using a range of techniques: washing, peeling, chopping, mixing, boiling, frying and baking; follow a recipe in order, and know the hygiene and safety rules for handling food

Ready when they can: Describe the steps and techniques a recipe needs (e.g. dice the onion, simmer the sauce, drain the pasta); Explain food hygiene and safety rules (e.g. washing hands, separate boards for raw meat, oven gloves); Help cook a simple savoury dish and say which technique each stage used (e.g. frying vs boiling).

Needs first: Where Food Comes From, Using Tools Safely, Heating & Cooling Changes.

https://lightmysky.com/learn/design-and-technology/cooking-and-food-preparation-mt_rEYrcOo7Vu

#### Reading a Food Label (ages 11-13)

The back of a packet states what is in it, in order of how much, and what a portion gives you. Reading it is how a shopper compares two products that both claim to be healthy.

Ready when they can: Say what the ingredient order tells you and use it to spot what a product is mostly made of; Read energy, sugar, fat and salt per 100 g and compare two products fairly; Explain the difference between per portion and per 100 g, and why packets prefer one; Find the allergen information and say who needs it.

https://lightmysky.com/learn/design-and-technology/reading-a-food-label-mt_1oQ_cPb_-T

#### Why Food Goes Bad and How to Stop It (ages 12-14)

Food spoils because microbes grow in it, and every preserving method is an attack on one of the things they need: warmth, water, air or time. Cooking, chilling, drying, salting and canning are the same idea applied differently.

Ready when they can: Name what microbes need to grow and match each preserving method to the thing it removes; Explain why the fridge slows spoiling but does not stop it; Say what cross-contamination is and give one habit that prevents it; Explain the difference between a use-by date and a best-before date, and which one matters for safety.

https://lightmysky.com/learn/design-and-technology/why-food-goes-bad-and-how-to-stop-it-mt_Nw5F4g18lY

#### Planning Meals for a Whole Week (ages 12-14)

Planning a week is a design problem with real constraints: what is in the cupboard, who is home, how long each evening allows, and what has to be used before it spoils. A plan that ignores any of those falls apart by Wednesday.

Ready when they can: Build a week of meals and show where a leftover from one becomes part of another; Check a plan against a stated constraint, such as twenty minutes on a school night; Order the shopping list so that the things that spoil fastest get eaten first; Say what makes a set of meals balanced across the week rather than at every meal.

https://lightmysky.com/learn/design-and-technology/planning-meals-for-a-whole-week-mt_T_GY879Oa7

#### Cooking Methods That Carry Across Recipes (ages 14-16)

There are only a few things heat can do to food, and every recipe is a combination of them. Someone who understands frying, boiling, roasting and baking as methods can cook without a recipe in front of them.

Ready when they can: Match each method to what heat is doing: dry heat, water, fat, or steam; Say why browning changes flavour and which methods produce it; Substitute an ingredient in a dish and predict what it changes; Cook something and explain what would have gone wrong at a higher or lower heat.

https://lightmysky.com/learn/design-and-technology/cooking-methods-that-carry-across-recipes-mt_-fGuaw1mON

#### Feeding Yourself on a Budget (ages 14-16)

Eating well on a fixed amount of money is a planning problem, not a willpower problem. Unit price, batch cooking, and what actually gets eaten before it spoils decide the outcome.

Ready when they can: Compare two package sizes by price per unit and say when the bigger one is not the better deal; Build a week of meals to a stated spend and show the arithmetic; Name two cheap ingredients that carry protein and say what to do with them; Explain why food thrown away is the most expensive food in the shop.

https://lightmysky.com/learn/design-and-technology/feeding-yourself-on-a-budget-mt_C1XoXVJlgA

#### Processing, Packaging and Food Miles (ages 15-16)

Between a field and a shelf sit processing, packaging and transport, and each one shows up in the price, the shelf life and the environmental cost. Ultra-processed is a claim about that route, not about taste.

Ready when they can: Trace one product from raw ingredient to shelf and name each step that was added; Say what packaging is actually doing besides looking good, such as extending shelf life; Explain why food miles alone is a poor measure of environmental cost; Give one reason heavily processed food is cheap and one reason that is a problem.

https://lightmysky.com/learn/design-and-technology/processing-packaging-and-food-miles-mt_MOrYB3f7qg

## French

12 topics, ages 4 to 10. https://lightmysky.com/learn/french

### French for immersion kids

https://lightmysky.com/learn/french/areas/french-for-immersion-kids

#### Greetings (ages 4-7)

First French hellos and goodbyes: bonjour, salut, au revoir.

Ready when they can: Can explain Greetings.

https://lightmysky.com/learn/french/greetings-ct_f8suouOlTuY

#### Being polite (ages 4-7)

Polite French words: s'il vous plaît, merci, de rien, pardon.

Ready when they can: Can explain Being polite.

https://lightmysky.com/learn/french/being-polite-ct_6-rtrCl-i_0

#### Classroom phrases (ages 4-8)

The French your teacher says all day: asseyez-vous, écoutez, levez la main.

Ready when they can: Can explain Classroom phrases.

https://lightmysky.com/learn/french/classroom-phrases-ct_M8Rn43GV6-0

#### Counting one to ten (ages 4-8)

The French numbers from un to dix.

Ready when they can: Can explain Counting one to ten.

https://lightmysky.com/learn/french/counting-one-to-ten-ct_4tbNL6R5BZE

#### Counting eleven to twenty (ages 5-9)

The French numbers from onze to vingt.

Ready when they can: Can explain Counting eleven to twenty.

https://lightmysky.com/learn/french/counting-eleven-to-twenty-ct_8HklNYP1ciM

#### Colors (ages 4-8)

French color words: rouge, bleu, vert, jaune, and more.

Ready when they can: Can explain Colors.

https://lightmysky.com/learn/french/colors-ct_Jo54cFtvunQ

#### Family words (ages 4-7)

French names for the family: maman, papa, frère, sœur.

Ready when they can: Can explain Family words.

https://lightmysky.com/learn/french/family-words-ct_JFs4XP40nCA

#### Animals (ages 5-8)

French animal words: chat, chien, oiseau, poisson, and more.

Ready when they can: Can explain Animals.

https://lightmysky.com/learn/french/animals-ct_rZ_Qea18A1s

#### Food and snack time (ages 4-8)

French words for snack time: pomme, pain, lait, eau, collation.

Ready when they can: Can explain Food and snack time.

https://lightmysky.com/learn/french/food-and-snack-time-ct_mrE-oK64nZU

#### Days of the week (ages 5-9)

The French days: lundi to dimanche, plus aujourd'hui and demain.

Ready when they can: Can explain Days of the week.

https://lightmysky.com/learn/french/days-of-the-week-ct_mPv10Z4XvjI

#### My body (ages 4-8)

French body words: tête, épaules, genoux, pieds, and the song.

Ready when they can: Can explain My body.

https://lightmysky.com/learn/french/my-body-ct_FMpBAD2dNBU

#### Saying who I am (ages 5-10)

First French sentences about yourself: je m'appelle, j'ai six ans.

Ready when they can: Can explain Saying who I am.

https://lightmysky.com/learn/french/saying-who-i-am-ct_gvykZ_dESs0

## Chess

9 topics, ages 6 to 11. https://lightmysky.com/learn/chess

### Chess basics

https://lightmysky.com/learn/chess/areas/chess-basics

#### The board and setting it up (ages 6-8)

The 64 squares and where every piece starts.

Ready when they can: Can explain The board and setting it up.

https://lightmysky.com/learn/chess/the-board-and-setting-it-up-ct_yl8BQGr-zn4

#### How rooks and bishops move (ages 6-9)

Straight lines for the rook, diagonals for the bishop.

Ready when they can: Can explain How rooks and bishops move.

https://lightmysky.com/learn/chess/how-rooks-and-bishops-move-ct_1zmskuQE6TE

#### How the queen and king move (ages 6-9)

The strongest piece and the most important one.

Ready when they can: Can explain How the queen and king move.

https://lightmysky.com/learn/chess/how-the-queen-and-king-move-ct_1mQxRof2KO8

#### The knight's jump (ages 7-10)

The L-shaped move and the only piece that jumps.

Ready when they can: Can explain The knight's jump.

https://lightmysky.com/learn/chess/the-knights-jump-ct_mPGl83Ay3OU

#### Pawns, capturing, and promotion (ages 6-10)

How pawns move, take, and turn into a stronger piece.

Ready when they can: Can explain Pawns, capturing, and promotion.

https://lightmysky.com/learn/chess/pawns-capturing-and-promotion-ct_4XOtOIhTbws

#### Check and getting out of it (ages 7-10)

When the king is attacked and the three ways to escape.

Ready when they can: Can explain Check and getting out of it.

https://lightmysky.com/learn/chess/check-and-getting-out-of-it-ct_yFf5pURph_s

#### Simple checkmates (ages 8-11)

Back-rank mate and the two-rook ladder.

Ready when they can: Can explain Simple checkmates.

https://lightmysky.com/learn/chess/simple-checkmates-ct_JP-fgSJrY6U

#### Making good trades (ages 8-11)

Piece values and how to come out ahead.

Ready when they can: Can explain Making good trades.

https://lightmysky.com/learn/chess/making-good-trades-ct_z4y-wLtcoTY

#### First opening ideas (ages 9-11)

Take the center, develop your pieces, and castle.

Ready when they can: Can explain First opening ideas.

https://lightmysky.com/learn/chess/first-opening-ideas-ct_hHjgl2wQAZI

## Persian

8 topics, ages 4 to 9. https://lightmysky.com/learn/persian

### Persian for kids

https://lightmysky.com/learn/persian/areas/persian-for-kids

#### Hello and goodbye (ages 4-6)

First Persian greetings: salâm and khodâhâfez.

Ready when they can: Can explain Hello and goodbye.

https://lightmysky.com/learn/persian/hello-and-goodbye-ct_XGeoi5x5XHc

#### How are you (ages 4-7)

Asking and answering: chetori, khubam, merci.

Ready when they can: Can explain How are you.

https://lightmysky.com/learn/persian/how-are-you-ct_y02aTz96_So

#### Counting one to ten (ages 5-8)

The Persian numbers from yek to dah.

Ready when they can: Can explain Counting one to ten.

https://lightmysky.com/learn/persian/counting-one-to-ten-ct_METwG4FlCVo

#### Family words (ages 4-7)

Names for the family: mâmân, bâbâ, and more.

Ready when they can: Can explain Family words.

https://lightmysky.com/learn/persian/family-words-ct_DrZltlQAu64

#### Colors (ages 5-8)

Persian color words: ghermez, âbi, sabz, and more.

Ready when they can: Can explain Colors.

https://lightmysky.com/learn/persian/colors-ct_8YUCTVWbe5c

#### Animals (ages 5-8)

Persian animal words: gorbeh, sag, mâhi, and more.

Ready when they can: Can explain Animals.

https://lightmysky.com/learn/persian/animals-ct_9tZg_T0Cg0w

#### Food and drink (ages 5-8)

Everyday Persian food words: nân, âb, shir, sib, berenj.

Ready when they can: Can explain Food and drink.

https://lightmysky.com/learn/persian/food-and-drink-ct_dcEoiBcG1lE

#### Putting words together (ages 6-9)

First small sentences: man ... hastam and in ... ast.

Ready when they can: Can explain Putting words together.

https://lightmysky.com/learn/persian/putting-words-together-ct_C4g0WOO5_5M

## Add-on packs

### Chess basics

https://lightmysky.com/learn/packs/pk_B5ZKc7wcp5Y

Learn the board, how every piece moves, and how to give your first checkmates.

#### The board and setting it up (ages 6-8)

The 64 squares and where every piece starts.

https://lightmysky.com/learn/chess/the-board-and-setting-it-up-ct_yl8BQGr-zn4

#### How rooks and bishops move (ages 6-9)

Straight lines for the rook, diagonals for the bishop.

https://lightmysky.com/learn/chess/how-rooks-and-bishops-move-ct_1zmskuQE6TE

#### How the queen and king move (ages 6-9)

The strongest piece and the most important one.

https://lightmysky.com/learn/chess/how-the-queen-and-king-move-ct_1mQxRof2KO8

#### The knight's jump (ages 7-10)

The L-shaped move and the only piece that jumps.

https://lightmysky.com/learn/chess/the-knights-jump-ct_mPGl83Ay3OU

#### Pawns, capturing, and promotion (ages 6-10)

How pawns move, take, and turn into a stronger piece.

https://lightmysky.com/learn/chess/pawns-capturing-and-promotion-ct_4XOtOIhTbws

#### Check and getting out of it (ages 7-10)

When the king is attacked and the three ways to escape.

https://lightmysky.com/learn/chess/check-and-getting-out-of-it-ct_yFf5pURph_s

#### Simple checkmates (ages 8-11)

Back-rank mate and the two-rook ladder.

https://lightmysky.com/learn/chess/simple-checkmates-ct_JP-fgSJrY6U

#### Making good trades (ages 8-11)

Piece values and how to come out ahead.

https://lightmysky.com/learn/chess/making-good-trades-ct_z4y-wLtcoTY

#### First opening ideas (ages 9-11)

Take the center, develop your pieces, and castle.

https://lightmysky.com/learn/chess/first-opening-ideas-ct_hHjgl2wQAZI

### First aid for kids

https://lightmysky.com/learn/packs/pk_tEK_3gVKa88

What to do for small hurts, and when to get a grown-up. Calm, safe steps for kids ages 5 to 11.

#### Get a grown-up first (ages 5-11)

The most important step for any hurt: stay calm and get a grown-up.

https://lightmysky.com/learn/life-skills/get-a-grown-up-first-ct_R-WpL3cayxk

#### Calling for help (ages 6-11)

Know your emergency number, then say who you are, where you are, and what happened.

https://lightmysky.com/learn/life-skills/calling-for-help-ct_4XVW6U6eHX8

#### Small cuts and scrapes (ages 5-10)

Tell a grown-up, rinse with clean water, pat dry, and cover it.

https://lightmysky.com/learn/life-skills/small-cuts-and-scrapes-ct_rWV_10I5NnM

#### Bumps and bruises (ages 5-10)

Rest the sore spot and use something cold wrapped in a cloth, never ice straight on skin.

https://lightmysky.com/learn/life-skills/bumps-and-bruises-ct_L8iRzjpFt0M

#### Nosebleeds (ages 6-11)

Sit, lean a little forward, and pinch the soft part of your nose. Do not lean back.

https://lightmysky.com/learn/life-skills/nosebleeds-ct_jpz3gOtC0rM

#### Burns from hot things (ages 6-11)

Tell a grown-up and cool it with running water for a long time. Never butter, never ice.

https://lightmysky.com/learn/life-skills/burns-from-hot-things-ct_e1P8bgtTI6w

#### Sun and heat (ages 5-10)

On hot days, drink water, rest in the shade, and wear a hat and sunscreen.

https://lightmysky.com/learn/life-skills/sun-and-heat-ct__NhpX8AUu-0

#### What you can and cannot do (ages 7-11)

Kids help by staying calm, fetching things, and telling adults. Grown-ups do the treating.

https://lightmysky.com/learn/life-skills/what-you-can-and-cannot-do-ct_bDSSnbf8KbM

### Music theory first steps

https://lightmysky.com/learn/packs/pk_B1kBYNtjs84

Learn about beat, rhythm, pitch, and reading your first notes.

#### Finding the steady beat (ages 5-7)

Feel and keep the even beat that runs through a song.

https://lightmysky.com/learn/arts-and-music/finding-the-steady-beat-ct_ebGLHfzz27o

#### Long and short sounds (ages 5-8)

Say ta and ti-ti for long and short sounds on the beat.

https://lightmysky.com/learn/arts-and-music/long-and-short-sounds-ct_x6T1ummvCdc

#### Loud and quiet (ages 5-7)

Forte means loud and piano means quiet.

https://lightmysky.com/learn/arts-and-music/loud-and-quiet-ct_NoBGDceitaw

#### Fast and slow (ages 5-7)

Tempo is the speed of the beat. Allegro is fast and adagio is slow.

https://lightmysky.com/learn/arts-and-music/fast-and-slow-ct_3D2KcLXr2bk

#### High and low sounds (ages 5-8)

Pitch is how high or low a sound is.

https://lightmysky.com/learn/arts-and-music/high-and-low-sounds-ct_jV8R937gcGI

#### The staff and where notes sit (ages 6-9)

The staff has five lines and four spaces, and notes sit on them.

https://lightmysky.com/learn/arts-and-music/the-staff-and-where-notes-sit-ct_nPkxk0ezxeY

#### Note names A to G (ages 7-10)

The musical alphabet and the treble clef landmarks E G B D F and FACE.

https://lightmysky.com/learn/arts-and-music/note-names-a-to-g-ct_hb_IpciuWGg

#### Reading and clapping simple rhythms (ages 7-10)

Quarter notes, eighth-note pairs, a quarter rest, and four beats in a bar.

https://lightmysky.com/learn/arts-and-music/reading-and-clapping-simple-rhythms-ct_OK5jHg1Uw3o

### Persian for kids

https://lightmysky.com/learn/packs/pk_6qkLEB7rAYI

First Farsi words for greetings, counting, family, colors, animals, food, and everyday sentences.

#### Hello and goodbye (ages 4-6)

First Persian greetings: salâm and khodâhâfez.

https://lightmysky.com/learn/persian/hello-and-goodbye-ct_XGeoi5x5XHc

#### How are you (ages 4-7)

Asking and answering: chetori, khubam, merci.

https://lightmysky.com/learn/persian/how-are-you-ct_y02aTz96_So

#### Counting one to ten (ages 5-8)

The Persian numbers from yek to dah.

https://lightmysky.com/learn/persian/counting-one-to-ten-ct_METwG4FlCVo

#### Family words (ages 4-7)

Names for the family: mâmân, bâbâ, and more.

https://lightmysky.com/learn/persian/family-words-ct_DrZltlQAu64

#### Colors (ages 5-8)

Persian color words: ghermez, âbi, sabz, and more.

https://lightmysky.com/learn/persian/colors-ct_8YUCTVWbe5c

#### Animals (ages 5-8)

Persian animal words: gorbeh, sag, mâhi, and more.

https://lightmysky.com/learn/persian/animals-ct_9tZg_T0Cg0w

#### Food and drink (ages 5-8)

Everyday Persian food words: nân, âb, shir, sib, berenj.

https://lightmysky.com/learn/persian/food-and-drink-ct_dcEoiBcG1lE

#### Putting words together (ages 6-9)

First small sentences: man ... hastam and in ... ast.

https://lightmysky.com/learn/persian/putting-words-together-ct_C4g0WOO5_5M

### French for immersion kids

https://lightmysky.com/learn/packs/pk_jzQWLNuOphc

First French words and the classroom phrases immersion teachers use every day, for kids starting French immersion school.

#### Greetings (ages 4-7)

First French hellos and goodbyes: bonjour, salut, au revoir.

https://lightmysky.com/learn/french/greetings-ct_f8suouOlTuY

#### Being polite (ages 4-7)

Polite French words: s'il vous plaît, merci, de rien, pardon.

https://lightmysky.com/learn/french/being-polite-ct_6-rtrCl-i_0

#### Classroom phrases (ages 4-8)

The French your teacher says all day: asseyez-vous, écoutez, levez la main.

https://lightmysky.com/learn/french/classroom-phrases-ct_M8Rn43GV6-0

#### Counting one to ten (ages 4-8)

The French numbers from un to dix.

https://lightmysky.com/learn/french/counting-one-to-ten-ct_4tbNL6R5BZE

#### Counting eleven to twenty (ages 5-9)

The French numbers from onze to vingt.

https://lightmysky.com/learn/french/counting-eleven-to-twenty-ct_8HklNYP1ciM

#### Colors (ages 4-8)

French color words: rouge, bleu, vert, jaune, and more.

https://lightmysky.com/learn/french/colors-ct_Jo54cFtvunQ

#### Family words (ages 4-7)

French names for the family: maman, papa, frère, sœur.

https://lightmysky.com/learn/french/family-words-ct_JFs4XP40nCA

#### Animals (ages 5-8)

French animal words: chat, chien, oiseau, poisson, and more.

https://lightmysky.com/learn/french/animals-ct_rZ_Qea18A1s

#### Food and snack time (ages 4-8)

French words for snack time: pomme, pain, lait, eau, collation.

https://lightmysky.com/learn/french/food-and-snack-time-ct_mrE-oK64nZU

#### Days of the week (ages 5-9)

The French days: lundi to dimanche, plus aujourd'hui and demain.

https://lightmysky.com/learn/french/days-of-the-week-ct_mPv10Z4XvjI

#### My body (ages 4-8)

French body words: tête, épaules, genoux, pieds, and the song.

https://lightmysky.com/learn/french/my-body-ct_FMpBAD2dNBU

#### Saying who I am (ages 5-10)

First French sentences about yourself: je m'appelle, j'ai six ans.

https://lightmysky.com/learn/french/saying-who-i-am-ct_gvykZ_dESs0

## Licence and attribution

The taxonomy (topics, prerequisite edges, curriculum alignment) comes from the open
Marble Skill Taxonomy: structure under ODbL, text under CC BY-SA 4.0. Lessons and
practice questions are written by LightMySky. Quoting either is welcome; please
attribute to LightMySky and link to the topic page you took it from.