Using structure to calculate efficiently
Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently
What a learner can do afterwards
- 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)
1 · Read
Math is full of patterns. Once you spot one, you can use it again and again instead of solving everything from scratch. Here is one: addition gives the same total in any order, so 2 + 7 and 7 + 2 both come to 9.
Mia has 3 red counters and 9 blue counters. She could count 3, then add 9 more one at a time. But she notices she can flip it around: 9 + 3 gives the same answer, and now she only counts on 3 more from 9. Same total, less counting.
Adding ten works the same way every time. Ten is one whole ten, so only the tens digit goes up by one. The ones digit does not move. That is why 47 + 10 = 57: the 4 tens become 5 tens and the 7 ones stay 7.
A square has 4 sides and 4 right angles. Look at a rectangle: it also has 4 sides and 4 right angles. They share the same pattern, even though a square's sides are all equal and a rectangle's are not.
Spotting a pattern, in numbers or in shapes, helps you solve problems the fast, smart way.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.