---
title: "Using Mathematical Structure"
description: "Look for and use mathematical structure: exploit place-value patterns for ×10/×100, use the distributive property to break apart multiplications, apply fraction equivalence to compare and compute, use"
canonical: https://lightmysky.com/learn/mathematics/using-mathematical-structure-mt__Itf4aQZUj
source: https://lightmysky.com/learn/mathematics/using-mathematical-structure-mt__Itf4aQZUj.md
retrieved: 2026-10-19
---

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# Using Mathematical Structure

Look for and use mathematical structure: exploit place-value patterns for ×10/×100, use the distributive property to break apart multiplications, apply fraction equivalence to compare and compute, use shape properties to classify quadrilaterals

Subject: Mathematics · Area: Mathematical Thinking · Ages 8 to 9
Page: https://lightmysky.com/learn/mathematics/using-mathematical-structure-mt__Itf4aQZUj

## Ready when they can

- Decompose 7×13 into 7×10 + 7×3 using the distributive property
- Explain why multiplying by 10 shifts digits one place left using place-value structure
- Use the fact that a square is a special rectangle to reason about quadrilateral properties

## Lesson: Using Mathematical Structure

You already know how to spot patterns and split numbers apart. Mathematical structure means noticing a pattern in numbers or shapes and using it to make a problem easier. Instead of solving from scratch, look for a shortcut hiding inside the problem.

*(drawing: This array has 7 rows and 9 columns. Split 9 into 5 and 4: 7×9 = 7×5 + 7×4 = 35 + 28 = 63.)*

**Example.** Leo needs 7 × 13. He splits 13 into 10 and 3: 7×13 = 7×10 + 7×3 = 70 + 21 = 91. Breaking the bigger number apart makes the multiplication easier to do in his head.

*(drawing: A square has 4 right angles and equal sides, so it follows every rule of a rectangle too. That makes it a special rectangle.)*

Multiplying by 10 makes each digit ten times bigger. 17 x 10 = 170. The digits 1 and 7 shift one place left and a zero fills the ones place.

**Tip.** Before you multiply, divide, or compare, pause and look for structure: can you split a number apart, shift its place value, or match a shape to one you already know?

**Recap.** Look for the pattern hiding inside a problem, in numbers or in shapes, and use it to make the work easier.

## Practice

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

## Needs first

- [Using structure in numbers and shapes](https://lightmysky.com/learn/mathematics/using-structure-in-numbers-and-shapes-mt_FAXjFkgG6X)
- [Dividing by 10 and 100](https://lightmysky.com/learn/mathematics/dividing-by-10-and-100-mt_kDMKJ5Ztt6)
- [Spotting Patterns](https://lightmysky.com/learn/learning-to-learn/spotting-patterns-mt_wvcFlwOrDl)
- [Classifying quadrilaterals](https://lightmysky.com/learn/mathematics/classifying-quadrilaterals-mt_Xt1cRqaBOW)

## Opens up

- [Fractions, Decimals & Percentages](https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ)
- [Thousandths (age 9+)](https://lightmysky.com/learn/mathematics/thousandths-age-9-mt_kdWoAel3Zl)