---
title: "Using structure in shapes and expressions"
description: "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–per"
canonical: https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh
source: https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh.md
retrieved: 2026-09-02
---

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# Using structure in shapes and expressions

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

Subject: Mathematics · Area: Mathematical Thinking · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh

## 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

## Lesson: Structure in shapes and expressions

Look at 2 + 3 × 4. If you work left to right, you get 2 + 3 = 5, then 5 × 4 = 20. But if you multiply first, you get 3 × 4 = 12, then 2 + 12 = 14. Two different answers is a problem, so mathematicians agreed on one order to always use.

The order is: brackets first, then multiply and divide (left to right), then add and subtract (left to right). Follow this order every time and everyone gets the same answer.

*(drawing: Multiply first: 3 × 4 = 12. Then add: 2 + 12 = 14.)*

Brackets have structure you can use. In 3 × (n + 5) the 3 multiplies everything inside, not just the n. So 3 × n = 3n and 3 × 5 = 15, and the whole thing becomes 3n + 15. That works for any number outside the brackets.

Shapes fit inside each other. A parallelogram is any four-sided shape with two pairs of parallel sides, so every rectangle is also a parallelogram. That means every parallelogram fact works on a rectangle too, including the one that opposite angles are always equal.

**Example.** Priya compares 1/8 of a pizza with 12% of a cake. She remembers that 1/8 = 0.125 = 12.5%. Since 12.5% is more than 12%, the pizza slice is the bigger piece.

**Recap.** Follow the agreed order in a calculation, expand brackets by multiplying every part, and use the links between shapes and between fractions, decimals and percentages.

## Practice

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

## Needs first

- [Decimals and fractions (age 10+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi)
- [Fractions, Decimals & Percentages](https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ)
- [Classifying shapes by properties](https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh)
- [Spotting Patterns](https://lightmysky.com/learn/learning-to-learn/spotting-patterns-mt_wvcFlwOrDl)

## Opens up

- [Using a Calculator Well](https://lightmysky.com/learn/mathematics/using-a-calculator-well-mt_FZE80D2jS_)