---
title: "Using structure to calculate efficiently"
description: "Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently"
canonical: https://lightmysky.com/learn/mathematics/using-structure-to-calculate-efficiently-mt_DW2D1c0fKx
source: https://lightmysky.com/learn/mathematics/using-structure-to-calculate-efficiently-mt_DW2D1c0fKx.md
retrieved: 2026-09-02
---

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# 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

Subject: Mathematics · Area: Mathematical Thinking · Ages 6 to 7
Page: https://lightmysky.com/learn/mathematics/using-structure-to-calculate-efficiently-mt_DW2D1c0fKx

## 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)

## Lesson: Using structure to calculate efficiently

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.

**Example.** 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.

*(drawing: Jumping from 47 to 57 only changes the tens digit. The 7 stays the same.)*

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.

**Example.** 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.

**Recap.** Spotting a pattern, in numbers or in shapes, helps you solve problems the fast, smart way.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Addition in any order](https://lightmysky.com/learn/mathematics/addition-in-any-order-mt_QCgbiVrwnp)
- [The two digits of a two-digit number](https://lightmysky.com/learn/mathematics/the-two-digits-of-a-two-digit-number-mt_THl9GLxwoL)
- [Spotting mathematical patterns](https://lightmysky.com/learn/mathematics/spotting-mathematical-patterns-mt_uG2mjHFOlO)

## Opens up

- [Using place-value structure to calculate](https://lightmysky.com/learn/mathematics/using-place-value-structure-to-calculate-mt_FAXjFkgG6X)