---
title: "Patterns in addition and multiplication tables"
description: "Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations"
canonical: https://lightmysky.com/learn/mathematics/patterns-in-addition-and-multiplication-tables-mt_w6MxaaoMXZ
source: https://lightmysky.com/learn/mathematics/patterns-in-addition-and-multiplication-tables-mt_w6MxaaoMXZ.md
retrieved: 2026-09-12
---

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# Patterns in addition and multiplication tables

Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations

Subject: Mathematics · Area: Multiplication & Division · Ages 8 to 9
Page: https://lightmysky.com/learn/mathematics/patterns-in-addition-and-multiplication-tables-mt_w6MxaaoMXZ

## Ready when they can

- Notice that all products of 5 end in 0 or 5 and explain why
- Observe that the sum of two even numbers is always even
- Identify a pattern in the multiplication table and explain it using commutativity or the distributive property

## Lesson: Patterns in Times Tables

Times tables are full of patterns. Once you notice one, you can explain why it happens using rules you already know, like commutativity and the distributive property.

*(drawing: Look at the last digit of each multiple of 5: 5, 0, 5, 0, 5. It keeps flipping between two digits.)*

**Example.** Look at the multiplication table: 4 x 7 gives 28, and 7 x 4 also gives 28. That's the commutative property. You can swap the order of the two numbers and the answer stays the same. It's why every row and its matching column hold the same numbers.

**Tip.** Even numbers always pair up evenly, with nothing left over. That's why two even numbers added together always make another even number, like 6 + 8 = 14.

**Recap.** Spot the pattern, then explain it with what you know: commutativity, the distributive property, or how evens combine.

## Practice

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

## Needs first

- [Odd and even numbers](https://lightmysky.com/learn/mathematics/odd-and-even-numbers-mt_0u4KLbvBa1)
- [Properties of Operations](https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR)
- [Fluent multiplication and division facts](https://lightmysky.com/learn/mathematics/fluent-multiplication-and-division-facts-mt_WX30dzi4dt)

## Opens up

- [Generating a pattern from a rule](https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy)