--- title: "What a 12-year-old learns" description: "361 topics are written for age 12, across 13 subjects." canonical: https://lightmysky.com/learn/age/12 source: https://lightmysky.com/learn/age/12.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # What a 12-year-old learns 361 topics are written for age 12, across 13 subjects. Topics are placed by what they need, not by school year, so this is a starting point rather than a syllabus. Page: https://lightmysky.com/learn/age/12 ## English - [Advanced Punctuation for Clarity](https://lightmysky.com/learn/english/advanced-punctuation-for-clarity-mt_lsO9O-_eZH): 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 - [Grammar for Effect](https://lightmysky.com/learn/english/grammar-for-effect-mt_N5tiL3uIeq): 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 - [Literary and Language Terminology](https://lightmysky.com/learn/english/literary-and-language-terminology-mt_HCweOHWSiu): 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 - [Phrases & Clauses](https://lightmysky.com/learn/english/phrases-and-clauses-mt_IdFxLz-UW9): 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 - [Standard English](https://lightmysky.com/learn/english/standard-english-mt_S2fP8rUwrl): Distinguish speech from writing, formal from informal register, and Standard English grammar from other English varieties. Use Standard English in speech and writing, choosing a register that suits the audience and purpose. - [Types of Sentences](https://lightmysky.com/learn/english/types-of-sentences-mt_T9IXrlxfx2): 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 - [Verb Voice and Mood](https://lightmysky.com/learn/english/verb-voice-and-mood-mt_N5tciHU8cE): 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 - [Analysing Text Structure](https://lightmysky.com/learn/english/analysing-text-structure-mt_II6iw4BmJI): 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 - [Critical comparison across texts](https://lightmysky.com/learn/english/critical-comparison-across-texts-mt_1GF5MeNZPA): Make critical comparisons of themes, characters, settings, styles, or arguments across two or more works, including texts from different periods, genres, or cultures - [Evaluating arguments in non-fiction](https://lightmysky.com/learn/english/evaluating-arguments-in-non-fiction-mt_gMSFymQlrW): Evaluate arguments and claims in non-fiction texts. Assess whether reasoning is sound and evidence is relevant and sufficient. Distinguish between fact and opinion, and recognise bias, propaganda, and rhetorical techniques. - [Figurative Language and Literary Devices](https://lightmysky.com/learn/english/figurative-language-and-literary-devices-mt_DVSHx3YMkN): 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 - [Narrative Perspective and Unreliable Narrators](https://lightmysky.com/learn/english/narrative-perspective-and-unreliable-narrators-mt_x2sWtfTeYT): 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 - [Plot Structure and Character Development](https://lightmysky.com/learn/english/plot-structure-and-character-development-mt_Hqz5y_tWz2): 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 - [Poetic forms and conventions](https://lightmysky.com/learn/english/poetic-forms-and-conventions-mt_aClzPBiS9k): 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 - [Purpose, audience, and context](https://lightmysky.com/learn/english/purpose-audience-and-context-mt_jIcgbCmziD): 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 - [Tracing Theme Across a Text](https://lightmysky.com/learn/english/tracing-theme-across-a-text-mt_wGxq92Na5g): 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 - [Understanding drama and performance](https://lightmysky.com/learn/english/understanding-drama-and-performance-mt_tIi6L1n7kF): 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 - [Using and Evaluating Textual Evidence](https://lightmysky.com/learn/english/using-and-evaluating-textual-evidence-mt_dmFnJzxKwz): 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 - [Wide Independent Reading Across Genres](https://lightmysky.com/learn/english/wide-independent-reading-across-genres-mt_9k1qcpvVi_): 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 - [Performing Scripts & Poetry](https://lightmysky.com/learn/english/performing-scripts-and-poetry-mt_ylFTYS80d1): 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 - [Speaking Formally and Giving Presentations](https://lightmysky.com/learn/english/speaking-formally-and-giving-presentations-mt_z07UNAIsNc): Use Standard English confidently in formal and informal spoken contexts. Give short speeches and presentations expressing your own ideas clearly, keeping to the point, and adapting register and vocabulary to the audience. - [Formal Debates](https://lightmysky.com/learn/english/formal-debates-mt_Yrjn8jAt1c): 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 - [Applying Spelling Rules to Complex Words](https://lightmysky.com/learn/english/applying-spelling-rules-to-complex-words-mt_4PA9IrxtCQ): 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 - [Academic Vocabulary](https://lightmysky.com/learn/english/academic-vocabulary-mt_OLwNsTI6C7): 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 - [Advanced Figurative Language](https://lightmysky.com/learn/english/advanced-figurative-language-mt_MlmIrLb_7x): 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 - [Vocabulary Strategies](https://lightmysky.com/learn/english/vocabulary-strategies-mt_WZnwITSWr8): 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 - [Cohesion and Transitions Across Writing](https://lightmysky.com/learn/english/cohesion-and-transitions-across-writing-mt_tn1rY9GbEZ): 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 - [Developed Informational and Explanatory Writing](https://lightmysky.com/learn/english/developed-informational-and-explanatory-writing-mt_zCUIJLdK_s): 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 - [Persuasive Writing](https://lightmysky.com/learn/english/persuasive-writing-mt_Qxyikkkzam): 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 - [Planning, Revising and Editing Writing](https://lightmysky.com/learn/english/planning-revising-and-editing-writing-mt_av-uRBrhwT): 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 - [Research & Source Evaluation](https://lightmysky.com/learn/english/research-and-source-evaluation-mt_Qcsl1Z1x0l): 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 - [Writing Across Genres](https://lightmysky.com/learn/english/writing-across-genres-mt_9lN0SpKlEH): 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 - [Writing Character & Dialogue](https://lightmysky.com/learn/english/writing-character-and-dialogue-mt_BLzNxSSdWu): 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 - [Writing Techniques for Effect](https://lightmysky.com/learn/english/writing-techniques-for-effect-mt_s6-6FYb5UQ): 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 - [Analysing Connections in Informational Texts](https://lightmysky.com/learn/english/analysing-connections-in-informational-texts-mt_1F3cnUHjMb): 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 - [Comparing Texts Across Media](https://lightmysky.com/learn/english/comparing-texts-across-media-mt_wpLz5Y17cJ): 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 - [Following Multi-Step Procedures](https://lightmysky.com/learn/english/following-multi-step-procedures-mt_b_3jwAsZ7a): 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 - [Advanced Collaborative Discussions](https://lightmysky.com/learn/english/advanced-collaborative-discussions-mt_4oegcJcRlQ): 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 - [Multimedia in Presentations](https://lightmysky.com/learn/english/multimedia-in-presentations-mt_7LrPGIbf8Z): 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 - [Digital Writing and Publishing](https://lightmysky.com/learn/english/digital-writing-and-publishing-mt_dN7QLqqJ4j): 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 - ...and 4 more at https://lightmysky.com/learn/english ## History - [Modern Archaeology and Egyptian Ethics](https://lightmysky.com/learn/history/modern-archaeology-and-egyptian-ethics-mt_B1LdSGMP66): 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 - [Egyptian Maths, Engineering and Medicine](https://lightmysky.com/learn/history/egyptian-maths-engineering-and-medicine-mt_PPNDO7BUrY): 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 - [Historical Sources on Ancient Egypt](https://lightmysky.com/learn/history/historical-sources-on-ancient-egypt-mt_bhEuF-CCuY): 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 - [Egypt and Its Neighbours](https://lightmysky.com/learn/history/egypt-and-its-neighbours-mt_NnlnxCx1DO): 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 - [Who Really Built the Pyramids](https://lightmysky.com/learn/history/who-really-built-the-pyramids-mt_xAG0aMeAIN): 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 - [Hidden Voices of Greece and Rome](https://lightmysky.com/learn/history/hidden-voices-of-greece-and-rome-mt_c-F__Qe23X): 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 - [Inclusion and Exclusion in Athens](https://lightmysky.com/learn/history/inclusion-and-exclusion-in-athens-mt_EHiM4_qg1R): 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 - [Troy: Myth or History?](https://lightmysky.com/learn/history/troy-myth-or-history-mt_aXNlkbAeIk): 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 - [Fall of the Roman Republic](https://lightmysky.com/learn/history/fall-of-the-roman-republic-mt__o3TCmfomv): 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 - [Weighing Historical Causes](https://lightmysky.com/learn/history/weighing-historical-causes-mt_BjY92Ahl-S): 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 - [Change and Continuity](https://lightmysky.com/learn/history/change-and-continuity-mt_OusQE68QDs): 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 - [Historical Significance](https://lightmysky.com/learn/history/historical-significance-mt_dy3l8XHcb1): 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 - [China's First Empires](https://lightmysky.com/learn/history/chinas-first-empires-mt_l1uAV1oGid): 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. - [The Silk Roads](https://lightmysky.com/learn/history/the-silk-roads-mt_Ud5GTBfVTz): 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. - [India From the Vedas to the Gupta](https://lightmysky.com/learn/history/india-from-the-vedas-to-the-gupta-mt_WylqxfbwwJ): 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. - [Belief Systems That Travelled](https://lightmysky.com/learn/history/belief-systems-that-travelled-mt_1RVIe0k2AU): 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. - [The Rise of Islam and Its First Empires](https://lightmysky.com/learn/history/the-rise-of-islam-and-its-first-empires-mt_kgkvNTMNCD): 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. - [Baghdad, Cordoba and the Work of Translation](https://lightmysky.com/learn/history/baghdad-cordoba-and-the-work-of-translation-mt_ZkjqYHk0cN): 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. - [Gold, Salt and the Kingdoms of the Sahel](https://lightmysky.com/learn/history/gold-salt-and-the-kingdoms-of-the-sahel-mt_EUkNLax9Yz): 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. - [The Indian Ocean and the Swahili Coast](https://lightmysky.com/learn/history/the-indian-ocean-and-the-swahili-coast-mt_0hVCaCE7QL): 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. - [The Mongol Century](https://lightmysky.com/learn/history/the-mongol-century-mt_9dNatkNqRt): 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. - [When Plague Crossed a Continent](https://lightmysky.com/learn/history/when-plague-crossed-a-continent-mt_852vI5oN6Y): 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. - [Cities of the Americas Before 1500](https://lightmysky.com/learn/history/cities-of-the-americas-before-1500-mt_KMAiatbUp8): 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. - [Tudor England and the Break With Rome](https://lightmysky.com/learn/history/tudor-england-and-the-break-with-rome-mt_RUPYnRkH7i): Henry VIII rejected the Pope's authority in England. Closing monasteries gave the crown land, valuables and income. Later Tudor rulers changed religious laws, and people could be punished for refusing them. - [The King, Parliament and the Civil War](https://lightmysky.com/learn/history/the-king-parliament-and-the-civil-war-mt_OGW1jWquJn): Disputes over taxation, religion and control of the army led to war between Charles I and Parliament. A disputed court tried and executed Charles in 1649. The monarchy returned in 1660, and later laws limited royal power. - [Britain, the Slave Trade and Abolition](https://lightmysky.com/learn/history/britain-the-slave-trade-and-abolition-mt_va8IlbmszO): British traders forced enslaved Africans across the Atlantic. Merchants, investors and port businesses profited from this trade and plantation goods. Campaigners and enslaved people challenged slavery. Banning British participation in the trade and ending slavery required different laws. - [The Victorian City](https://lightmysky.com/learn/history/the-victorian-city-mt__vBvBBi8cO): 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. - [Votes for Women and the Long Fight for the Ballot](https://lightmysky.com/learn/history/votes-for-women-and-the-long-fight-for-the-ballot-mt_7Cr6IwxFFv): 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. - [Britain After the War](https://lightmysky.com/learn/history/britain-after-the-war-mt_mLUFonfZlC): After the Second World War, Britain faced heavy debts and bomb damage. The NHS began in 1948, councils expanded housing, and employers recruited workers from abroad. New homes, services and migration changed many communities between 1945 and 1975. ## Mathematics - [Positive and Negative Numbers](https://lightmysky.com/learn/mathematics/positive-and-negative-numbers-mt_9QzSnn8m80): 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 - [Algebraic Notation](https://lightmysky.com/learn/mathematics/algebraic-notation-mt_KwdjWEmMNo): 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 - [Modelling Situations with Formulae and Graphs](https://lightmysky.com/learn/mathematics/modelling-situations-with-formulae-and-graphs-mt_z5iwdZyeDr): 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 - [Collecting Like Terms](https://lightmysky.com/learn/mathematics/collecting-like-terms-mt_nNNVrLqPW3): 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 - [Coordinates (age 11+)](https://lightmysky.com/learn/mathematics/coordinates-age-11-mt_hVpGOEz2kG): Plot and read coordinates in all four quadrants of the Cartesian plane, using positive and negative x- and y-values to describe positions precisely - [Expanding Single Brackets](https://lightmysky.com/learn/mathematics/expanding-single-brackets-mt_FX4a2Q8XXN): 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 - [Expressions & Equations Vocabulary](https://lightmysky.com/learn/mathematics/expressions-and-equations-vocabulary-mt_g_fkAqmz72): 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) - [Generating Sequences](https://lightmysky.com/learn/mathematics/generating-sequences-mt_yXO7lQ9Yn7): 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 - [Inequalities and their solution sets](https://lightmysky.com/learn/mathematics/inequalities-and-their-solution-sets-mt_i2F1nWxJjv): 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 - [Solving linear equations](https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO): Use algebraic methods to solve linear equations in one variable, including rearranging, expanding brackets, collecting terms on both sides, and working with rational coefficients. - [Substituting into Formulae](https://lightmysky.com/learn/mathematics/substituting-into-formulae-mt_vHzVa3SURC): 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 - [Factorising Expressions](https://lightmysky.com/learn/mathematics/factorising-expressions-mt_uESbzWCZIq): 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) - [Linear Function Graphs](https://lightmysky.com/learn/mathematics/linear-function-graphs-mt_WBdHkc2HTf): 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 - [Nth-Term Rules](https://lightmysky.com/learn/mathematics/nth-term-rules-mt_HRKzwEQJgO): 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 - [Plotting Linear Graphs](https://lightmysky.com/learn/mathematics/plotting-linear-graphs-mt_-3udyo6VyB): 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 - [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU): Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable - [Comparing data sets with averages and range](https://lightmysky.com/learn/mathematics/comparing-data-sets-with-averages-and-range-mt_XSXnTQoQ4l): 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 - [Frequency tables, bar charts and pie charts](https://lightmysky.com/learn/mathematics/frequency-tables-bar-charts-and-pie-charts-mt_eKJG-0eC6D): 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 - [Decimals and fractions (age 11+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ): 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 - [Dividing fractions](https://lightmysky.com/learn/mathematics/dividing-fractions-mt_9Y96vxG_LH): 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 - [Calculations with fractions, decimals and negatives](https://lightmysky.com/learn/mathematics/calculations-with-fractions-decimals-and-negatives-mt_gNUE4B3vuk): Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative - [Fractions and percentages of amounts](https://lightmysky.com/learn/mathematics/fractions-and-percentages-of-amounts-mt_J339bO7qLe): 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) - [Transformations on a grid](https://lightmysky.com/learn/mathematics/transformations-on-a-grid-mt_SH7QgFl8-v): 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 - [Geometric diagram conventions](https://lightmysky.com/learn/mathematics/geometric-diagram-conventions-mt_e4V6hvcuEJ): 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 - [3-D shapes (age 11+)](https://lightmysky.com/learn/mathematics/3-d-shapes-age-11-mt_nRksLqt-iR): 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 - [Area and volume formulae](https://lightmysky.com/learn/mathematics/area-and-volume-formulae-mt_tAJH5BrpOx): 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 - [Angle sums in triangles and polygons](https://lightmysky.com/learn/mathematics/angle-sums-in-triangles-and-polygons-mt_J03RFlVdas): 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 - [Coordinate Transformations](https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY): 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 - [Accurate drawing and scale diagrams](https://lightmysky.com/learn/mathematics/accurate-drawing-and-scale-diagrams-mt_Jf8xcX4UTq): Draw and measure line segments and angles accurately using ruler and protractor, and interpret scale drawings to extract real measurements - [Properties of triangles, quadrilaterals and circles](https://lightmysky.com/learn/mathematics/properties-of-triangles-quadrilaterals-and-circles-mt_DNYQLahbfa): Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths - [Geometric terms and notation](https://lightmysky.com/learn/mathematics/geometric-terms-and-notation-mt_WtIFJSCQIT): 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 - [Understanding angles (age 11+)](https://lightmysky.com/learn/mathematics/understanding-angles-age-11-mt_tedML_iu4Y): 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 - [Triangle congruence criteria](https://lightmysky.com/learn/mathematics/triangle-congruence-criteria-mt_167X6Ax8P7): 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 - [Angles with parallel lines](https://lightmysky.com/learn/mathematics/angles-with-parallel-lines-mt_H_pNJ3ZI_S): 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 - [Circles: Circumference & Area](https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_): 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 - [Similarity and enlargement](https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B): 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 - [Ruler and compass constructions](https://lightmysky.com/learn/mathematics/ruler-and-compass-constructions-mt_ZrsqGVG-Wt): 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 - [Factors, multiples, and primes (age 11+)](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-age-11-mt_xhoOWnhtHq): 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 - [Order of operations with powers and roots](https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU): Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions - [Sign Rules for Multiplication and Division](https://lightmysky.com/learn/mathematics/sign-rules-for-multiplication-and-division-mt_rxInpOQ74w): Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient - ...and 35 more at https://lightmysky.com/learn/mathematics ## Personal & Social Development - [Brain science of emotions](https://lightmysky.com/learn/personal-and-social-development/brain-science-of-emotions-mt_gf4RUcACLg): Explore how connected brain systems, including the amygdala and prefrontal cortex, contribute to emotional responses and choices. Recognise that brain development continues during adolescence and varies between people. Describe stress-related body changes, distinguish holding back emotional expression from changing a feeling, and practise realistic cognitive reappraisal. - [Identity and belonging in adolescence](https://lightmysky.com/learn/personal-and-social-development/identity-and-belonging-in-adolescence-mt_p-8Hlf6_9k): Explore how interests, values and group memberships can shape identity during adolescence. Recognise that people may feel settled, uncertain or mixed feelings about belonging. Consider conflicting group expectations and selective presentation on social media. Practise discussing uncertainty and seeking support when it causes distress. - [Systemic Inequality and Allyship](https://lightmysky.com/learn/personal-and-social-development/systemic-inequality-and-allyship-mt_oqvJJKCJXw): 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 - [Sympathy Versus Empathy](https://lightmysky.com/learn/personal-and-social-development/sympathy-versus-empathy-mt_VA126P6Wp5): 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 - [Social Cues and Group Dynamics](https://lightmysky.com/learn/personal-and-social-development/social-cues-and-group-dynamics-mt_nqM2OW0Qlm): 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 - [Honest Conversations and Conflict Repair](https://lightmysky.com/learn/personal-and-social-development/honest-conversations-and-conflict-repair-mt_NCrbQe0LdB): 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 - [Risk, Uncertainty, and Cognitive Bias](https://lightmysky.com/learn/personal-and-social-development/risk-uncertainty-and-cognitive-bias-mt_JiZ3H90Xg8): 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 - [Online Identity and Misinformation](https://lightmysky.com/learn/personal-and-social-development/online-identity-and-misinformation-mt_WtO50EZQkf): 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 - [Good Stress and Bad Stress](https://lightmysky.com/learn/personal-and-social-development/good-stress-and-bad-stress-mt_0VOZSVjo6c): 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 - [Habits and Motivation](https://lightmysky.com/learn/personal-and-social-development/habits-and-motivation-mt_0ewYhTSHtP): 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 - [Body Image and the Pictures You Scroll Past](https://lightmysky.com/learn/personal-and-social-development/body-image-and-the-pictures-you-scroll-past-mt_OyBLI3T0jX): 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. ## Science - [The Red Queen Hypothesis](https://lightmysky.com/learn/science/the-red-queen-hypothesis-mt_mKNmXqz_Oo): 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 - [Deep-Sea Survival](https://lightmysky.com/learn/science/deep-sea-survival-mt_ot9rcUwBtK): 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 - [Mates, Kin and Animal Strategies](https://lightmysky.com/learn/science/mates-kin-and-animal-strategies-mt_YNrrNE23dZ): 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 - [The Biodiversity Crisis](https://lightmysky.com/learn/science/the-biodiversity-crisis-mt_44HkROUnzE): 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 - [Dinosaur-to-Bird Transition](https://lightmysky.com/learn/science/dinosaur-to-bird-transition-mt_mqQ-DtH5m-): 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 - [Radiometric Dating](https://lightmysky.com/learn/science/radiometric-dating-mt_bHbpLW1HUg): 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) - [Mass Extinctions in Earth History](https://lightmysky.com/learn/science/mass-extinctions-in-earth-history-mt_IP0PTVfTXp): 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 - [Reconstructing Ancient Ecosystems](https://lightmysky.com/learn/science/reconstructing-ancient-ecosystems-mt_8_BxtNDrLZ): 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 - [Energy Loss Between Levels](https://lightmysky.com/learn/science/energy-loss-between-levels-mt_BOG5zRYtQz): 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 - [Food Webs & Interdependence](https://lightmysky.com/learn/science/food-webs-and-interdependence-mt_URTJbS3hhs): Construct and interpret food webs showing the interdependence of organisms in an ecosystem, explaining how a change in one population affects others - [Pollination & Pollinator Decline](https://lightmysky.com/learn/science/pollination-and-pollinator-decline-mt_wWpa5fFDZP): Explain the importance of insect pollination for plant reproduction and human food security, and discuss the consequences of pollinator decline - [The Water Cycle in Detail](https://lightmysky.com/learn/science/the-water-cycle-in-detail-mt_V2lNzEex_a): Describe the water cycle, tracing water through evaporation, condensation, precipitation, surface runoff, and transpiration in plants, explaining how the sun drives the cycle - [Biodiversity & Resilience](https://lightmysky.com/learn/science/biodiversity-and-resilience-mt_xSs0xAd6i1): 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) - [Chromosomes, Genes & DNA](https://lightmysky.com/learn/science/chromosomes-genes-and-dna-mt_6aJUzBYGNs): 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 - [Evidence for Evolution](https://lightmysky.com/learn/science/evidence-for-evolution-mt_ohUnzoI_nx): 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 - [Extinction & Rapid Change](https://lightmysky.com/learn/science/extinction-and-rapid-change-mt_-r3B4FQyX3): Explain how environmental change can outpace a species' ability to adapt through natural selection, leading to extinction, using historical and contemporary examples - [Genetic Mutation](https://lightmysky.com/learn/science/genetic-mutation-mt_rOqo-8GeKt): 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 - [How Natural Selection Works](https://lightmysky.com/learn/science/how-natural-selection-works-mt_FuVEZ1Ac9s): Explain how heritable variation and unequal reproductive success can change trait frequencies across generations through natural selection, one mechanism of evolution; competition is one possible source of selection pressure. - [Species Distribution & Change](https://lightmysky.com/learn/science/species-distribution-and-change-mt_JSUGQ5Repv): Explain how environmental change (climate change, habitat loss, pollution) affects the distribution of species, including range shifts, local extinction, and invasive species - [The Carbon Cycle](https://lightmysky.com/learn/science/the-carbon-cycle-mt_Be1A88GUpu): Describe the carbon cycle, tracing carbon through photosynthesis, respiration, feeding, decomposition, and combustion, and explain the role of each process - [Toxins in Food Chains and Organisms Changing Habitats](https://lightmysky.com/learn/science/toxins-in-food-chains-and-organisms-changing-habitats-mt_YvCgDM0Scg): Explain how organisms affect and are affected by their environment, including the bioaccumulation of toxic materials (e.g. pesticides, heavy metals) through food chains - [Variation in Species](https://lightmysky.com/learn/science/variation-in-species-mt_k1HXbEwG8f): 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 - [Current, voltage, and what they measure](https://lightmysky.com/learn/science/current-voltage-and-what-they-measure-mt_2bnXrfS4Iq): Understand current as charge flow rate and voltage as energy transferred per unit charge, then connect each quantity to its meter and circuit connection. - [Energy can't be created or destroyed](https://lightmysky.com/learn/science/energy-cant-be-created-or-destroyed-mt_68pIoiiG4g): 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 - [Energy stores and transfers](https://lightmysky.com/learn/science/energy-stores-and-transfers-mt_Jvg_r4yWaY): Identify kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, magnetic and electrostatic energy stores. Describe transfers mechanically, electrically, by heating and by radiation, distinguishing stores from transfer pathways. - [Static electricity and sparks](https://lightmysky.com/learn/science/static-electricity-and-sparks-mt_2_YoprauaJ): 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 - [Conduction, convection, and radiation](https://lightmysky.com/learn/science/conduction-convection-and-radiation-mt_ySnOkVIu22): 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 - [Efficiency, Sankey diagrams, and work done](https://lightmysky.com/learn/science/efficiency-sankey-diagrams-and-work-done-mt_JyfLtl_nhw): 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 - [Heating experiments and Q = mcΔT](https://lightmysky.com/learn/science/heating-experiments-and-q-mc-t-mt_DI1cyAyGyN): 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 - [Ohm's Law: voltage, current, resistance](https://lightmysky.com/learn/science/ohms-law-voltage-current-resistance-mt_H3ZDK0EYNV): 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 - [Power: watts and energy per second](https://lightmysky.com/learn/science/power-watts-and-energy-per-second-mt_ckpA3oZQ44): Define power as the rate of energy transfer (power = energy ÷ time, measured in watts), and compare energy transfer rates in different everyday contexts - [Renewable vs non-renewable energy](https://lightmysky.com/learn/science/renewable-vs-non-renewable-energy-mt_w2A8D76ymp): Distinguish renewable resources, including solar, wind, hydroelectric, tidal, geothermal and replenished biomass, from non-renewable fuels such as coal, oil, gas and uranium. Compare cost, reliability and environmental impacts. - [Series vs parallel circuits](https://lightmysky.com/learn/science/series-vs-parallel-circuits-mt_loEMaQ8kFA): Describe and apply the rules for current, voltage, and resistance in series and parallel circuits, and explain the practical uses of each circuit type - [Drawing Force Diagrams](https://lightmysky.com/learn/science/drawing-force-diagrams-mt_k7GOtslF-x): Draw forces acting on one object as labelled arrows. Arrow length shows relative force size and arrow direction shows force direction. For two forces along one line, equal and opposite forces balance. Combine forces to find the resultant, which changes motion when it is not zero. Draw the resultant separately from the individual forces. - [Reading Distance-Time Graphs](https://lightmysky.com/learn/science/reading-distance-time-graphs-mt_OUv-QXmW7_): 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 - [Magnetic Fields](https://lightmysky.com/learn/science/magnetic-fields-mt_56aspHjU19): 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 - [Mass vs Weight](https://lightmysky.com/learn/science/mass-vs-weight-mt_sUVeVXzRuq): 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 - [Relative Motion](https://lightmysky.com/learn/science/relative-motion-mt_-OndzpVsrv): 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 - [Resultant Forces](https://lightmysky.com/learn/science/resultant-forces-mt_AiWlJfvC3O): 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) - [Speed & Distance-Time Graphs](https://lightmysky.com/learn/science/speed-and-distance-time-graphs-mt_q-1a86ydgU): 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 - ...and 87 more at https://lightmysky.com/learn/science ## Geography - [Latitude, Longitude and Time Zones](https://lightmysky.com/learn/geography/latitude-longitude-and-time-zones-mt_3LBzy7Jbxv): 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 - [Thematic Maps and GIS](https://lightmysky.com/learn/geography/thematic-maps-and-gis-mt_khsAUcwLke): 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 - [Comparing World Regions](https://lightmysky.com/learn/geography/comparing-world-regions-mt_cY5D2gWt0Y): 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 - [Migration and Movement](https://lightmysky.com/learn/geography/migration-and-movement-mt_kTmHn_iAZ_): 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 - [Settlements, Movement and Connections](https://lightmysky.com/learn/geography/settlements-movement-and-connections-mt_Kq3quvrn63): 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 - [Geography of World Trade](https://lightmysky.com/learn/geography/geography-of-world-trade-mt_Vpbi5Z4ypw): 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 - [Environmental Change and Conflict](https://lightmysky.com/learn/geography/environmental-change-and-conflict-mt_Vlp61dF3KL): 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 - [How a River Shapes Its Valley](https://lightmysky.com/learn/geography/how-a-river-shapes-its-valley-mt_v6D9mgcf0P): 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. - [From Source to Sea](https://lightmysky.com/learn/geography/from-source-to-sea-mt_VuUB9PiYan): 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. - [Coasts on the Move](https://lightmysky.com/learn/geography/coasts-on-the-move-mt_IVnXDRpfqE): 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. - [What the Ice Left Behind](https://lightmysky.com/learn/geography/what-the-ice-left-behind-mt_D-aB1k0K73): 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. - [Reading a Landscape Off a Map](https://lightmysky.com/learn/geography/reading-a-landscape-off-a-map-mt_MWlY_e59Rg): 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. ## Civics & Economics - [Constitutions and Separation of Powers](https://lightmysky.com/learn/civics-and-economics/constitutions-and-separation-of-powers-mt_kxIAbYuR5i): 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 - [Democratic Ideals and Founding Documents](https://lightmysky.com/learn/civics-and-economics/democratic-ideals-and-founding-documents-mt_dK8hcP-1tS): 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 - [Parties, Interest Groups and the Media](https://lightmysky.com/learn/civics-and-economics/parties-interest-groups-and-the-media-mt_Eb9SeGnavc): 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 - [Deliberation and Democratic Decision-Making](https://lightmysky.com/learn/civics-and-economics/deliberation-and-democratic-decision-making-mt_0U9eaCtm5u): 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 - [How People Change Society](https://lightmysky.com/learn/civics-and-economics/how-people-change-society-mt_Wx2pvpg4QP): 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 - [Citizens in Public Life](https://lightmysky.com/learn/civics-and-economics/citizens-in-public-life-mt_G6PCjvFUCO): 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 - [Public Policy and Public Problems](https://lightmysky.com/learn/civics-and-economics/public-policy-and-public-problems-mt_5vYuvjkprY): 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 - [How Markets Work](https://lightmysky.com/learn/civics-and-economics/how-markets-work-mt_IWiQW8Sq2R): 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 - [Money, Banking and Interest Rates](https://lightmysky.com/learn/civics-and-economics/money-banking-and-interest-rates-mt__aqBHw2wZM): 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 - [Inflation, Unemployment and Growth](https://lightmysky.com/learn/civics-and-economics/inflation-unemployment-and-growth-mt_Zr0YyQwtKy): 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 - [Trade Policy and Barriers](https://lightmysky.com/learn/civics-and-economics/trade-policy-and-barriers-mt_l_l6qXfRle): Governments shape trade with tariffs, quotas and rules; 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 - [Externalities and Spillovers](https://lightmysky.com/learn/civics-and-economics/externalities-and-spillovers-mt_F4SQsGpZk9): 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 - [Productivity, Skills and Tools](https://lightmysky.com/learn/civics-and-economics/productivity-skills-and-tools-mt_q9wqRR_1Vk): 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 ## Design & Technology - [Iterative Design and Prototyping](https://lightmysky.com/learn/design-and-technology/iterative-design-and-prototyping-mt_fYD3KaViOZ): 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 - [Electronics in a Product: Switch, Sensor, Output](https://lightmysky.com/learn/design-and-technology/electronics-in-a-product-switch-sensor-output-mt_KNLW4qke5J): 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. - [Systems: Input, Process, Output](https://lightmysky.com/learn/design-and-technology/systems-input-process-output-mt_bMNTQ-3a_u): 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. - [Drawing a Design So Someone Else Can Build It](https://lightmysky.com/learn/design-and-technology/drawing-a-design-so-someone-else-can-build-it-mt_8ezErqUhZw): 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. - [Reading a Food Label](https://lightmysky.com/learn/design-and-technology/reading-a-food-label-mt_1oQ_cPb_-T): 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. - [Why Food Goes Bad and How to Stop It](https://lightmysky.com/learn/design-and-technology/why-food-goes-bad-and-how-to-stop-it-mt_Nw5F4g18lY): 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. - [Planning Meals for a Whole Week](https://lightmysky.com/learn/design-and-technology/planning-meals-for-a-whole-week-mt_T_GY879Oa7): 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. ## Learning to Learn - [Framing Research Questions](https://lightmysky.com/learn/learning-to-learn/framing-research-questions-mt_ngkBCLLMYu): 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 ## Arts & Music - [Scales, Keys and Musical Mood](https://lightmysky.com/learn/arts-and-music/scales-keys-and-musical-mood-mt_9XMu4MF7_t): Explore scales as ordered pitches with patterns of larger and smaller steps. Learn how a key combines a home note with a scale, compare major and minor, and explain why moving a song to another key can help a singer. Mood gives clues but does not prove the key. - [Chords and Harmony](https://lightmysky.com/learn/arts-and-music/chords-and-harmony-mt_SWhLE91u-E): 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. - [The Shape of a Piece](https://lightmysky.com/learn/arts-and-music/the-shape-of-a-piece-mt_sSoi-W_vs-): 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. - [The Families of the Orchestra](https://lightmysky.com/learn/arts-and-music/the-families-of-the-orchestra-mt_5asOXH89es): 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. - [Music Traditions Around the World](https://lightmysky.com/learn/arts-and-music/music-traditions-around-the-world-mt_FObFf1o8rL): 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. - [Looking at a Picture: What to Notice First](https://lightmysky.com/learn/arts-and-music/looking-at-a-picture-what-to-notice-first-mt_jJxX9-kw1V): 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. - [Perspective and the Illusion of Depth](https://lightmysky.com/learn/arts-and-music/perspective-and-the-illusion-of-depth-mt_viqsbnnXt5): 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. - [The Camera as an Art Tool](https://lightmysky.com/learn/arts-and-music/the-camera-as-an-art-tool-mt_TIdod5lPOl): 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. - [How a Play Gets Made](https://lightmysky.com/learn/arts-and-music/how-a-play-gets-made-mt_vuaFvRSoi2): 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. - [Dances People Do: Folk, Social and Stage](https://lightmysky.com/learn/arts-and-music/dances-people-do-folk-social-and-stage-mt_8i89DDjT_v): 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. ## Computing - [Events: Programs That React to What the User Does](https://lightmysky.com/learn/computing/events-programs-that-react-to-what-the-user-does-mt_HFtGUhZHz4): 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. - [Conditions That Combine: And, Or and Not](https://lightmysky.com/learn/computing/conditions-that-combine-and-or-and-not-mt_ZYdtXQZy5r): 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. - [Random Numbers and Programs That Differ Each Run](https://lightmysky.com/learn/computing/random-numbers-and-programs-that-differ-each-run-mt_t8GTOW3hyN): 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. - [Finding a Bug by Changing One Thing at a Time](https://lightmysky.com/learn/computing/finding-a-bug-by-changing-one-thing-at-a-time-mt_DMgajrUSy_): 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. - [Inside the Box: Input, Processing, Storage and Output](https://lightmysky.com/learn/computing/inside-the-box-input-processing-storage-and-output-mt_Oms8067Pnm): 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. - [Why a Computer Works with Only Two Symbols](https://lightmysky.com/learn/computing/why-a-computer-works-with-only-two-symbols-mt_r0wLIjpi5R): 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. - [An Agreed Code: How the Same Bits Mean Letters or Colours](https://lightmysky.com/learn/computing/an-agreed-code-how-the-same-bits-mean-letters-or-colours-mt_IQY-PHtZVZ): 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. - [Reusing Someone Else's Work: Licences and Giving Credit](https://lightmysky.com/learn/computing/reusing-someone-elses-work-licences-and-giving-credit-mt_SeLxugBmM7): 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. - [Spreadsheets: Rows, Columns and a Formula That Updates Itself](https://lightmysky.com/learn/computing/spreadsheets-rows-columns-and-a-formula-that-updates-itself-mt_iWyPF0-Abz): 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. - [Sorting and Filtering a Table to Answer a Question](https://lightmysky.com/learn/computing/sorting-and-filtering-a-table-to-answer-a-question-mt_6-UzZXVWwV): 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. - [How a Chatbot Picks Its Next Token](https://lightmysky.com/learn/computing/how-a-chatbot-picks-its-next-token-mt_1Zbhamhzai): A language-model chatbot generates text in small pieces called tokens. It uses learned patterns and the available context to select a next token, adds it, and repeats. Some chatbots also retrieve information with tools. - [Why a Chatbot Can Be Confidently Wrong](https://lightmysky.com/learn/computing/why-a-chatbot-can-be-confidently-wrong-mt_TMHNkprrks): A language-model chatbot can generate fluent but false claims or references. Confident wording is not proof of accuracy. Retrieval can supply evidence, but claims and cited sources still need checking. ## Languages - [Talking about time: first tenses](https://lightmysky.com/learn/languages/talking-about-time-first-tenses-mt_6526HcZG0R): 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. - [Reading a whole story in a new language](https://lightmysky.com/learn/languages/reading-a-whole-story-in-a-new-language-mt__TM_JDJS1F): 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. - [Writing More Than One Sentence](https://lightmysky.com/learn/languages/writing-more-than-one-sentence-mt_o-mglXOz-_): 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. - [Practising a Language Week by Week](https://lightmysky.com/learn/languages/practising-a-language-week-by-week-mt_VIIT69dTyI): 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. - [Listening to Real Speech](https://lightmysky.com/learn/languages/listening-to-real-speech-mt_QC3x14zrgx): 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. - [Keeping a Conversation Going](https://lightmysky.com/learn/languages/keeping-a-conversation-going-mt_SZsWbcNJIv): 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. - [Telling a Story About Yourself](https://lightmysky.com/learn/languages/telling-a-story-about-yourself-mt_Y03mNSjNK9): 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. - [Gender, Case and Noun Classes](https://lightmysky.com/learn/languages/gender-case-and-noun-classes-mt_NavTs37V06): 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. - [Reading Material Written for Native Speakers](https://lightmysky.com/learn/languages/reading-material-written-for-native-speakers-mt_R2M7Qh2Rai): 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. - [Politeness and Everyday Culture](https://lightmysky.com/learn/languages/politeness-and-everyday-culture-mt_p44544zHZH): 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. - [Writing to Someone Who Will Reply](https://lightmysky.com/learn/languages/writing-to-someone-who-will-reply-mt_9l0fpUo3x0): 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. - [Knowing Where You Are and What to Fix](https://lightmysky.com/learn/languages/knowing-where-you-are-and-what-to-fix-mt_4qpc9U7hWx): 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. ## Life Skills - [Your First Bank Account and Card](https://lightmysky.com/learn/life-skills/your-first-bank-account-and-card-mt_YoV2gRHaLS): 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. - [Comparing Prices Properly](https://lightmysky.com/learn/life-skills/comparing-prices-properly-mt_v3i0WMP-Sl): 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. - [Saving for Something Months Away](https://lightmysky.com/learn/life-skills/saving-for-something-months-away-mt_NFZG8bDa5o): 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. - [The True Cost of a Phone](https://lightmysky.com/learn/life-skills/the-true-cost-of-a-phone-mt_L_o7NzVuh5): Phone deals can cover service alone or include a handset. Some handset deals use a loan. Compare each payment once over the same period, including price changes and extras, and check the exit terms. - [Spending Inside Games and Apps](https://lightmysky.com/learn/life-skills/spending-inside-games-and-apps-mt_DCmLETXmjd): 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. - [Finding Out If Anyone Wants It](https://lightmysky.com/learn/life-skills/finding-out-if-anyone-wants-it-mt_99X6saJ6Kt): 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. - [Pricing So the Numbers Work](https://lightmysky.com/learn/life-skills/pricing-so-the-numbers-work-mt_m4DGdFIm5h): 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. - [Doing It Right When Nobody Is Watching](https://lightmysky.com/learn/life-skills/doing-it-right-when-nobody-is-watching-mt_MViH0gLbvQ): 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.