---
title: "Justifying mathematical reasoning"
description: "Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work"
canonical: https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-mt_pyMD_SIiYO
source: https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-mt_pyMD_SIiYO.md
retrieved: 2026-10-19
---

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# Justifying mathematical reasoning

Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work

Subject: Mathematics · Area: Mathematical Thinking · Ages 7 to 8
Page: https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-mt_pyMD_SIiYO

## Ready when they can

- Explain step by step why a columnar addition method gives the correct answer
- Find and explain an error in a worked example (e.g. incorrect regrouping)
- Construct a simple argument for why a general statement is true (e.g. 'adding two even numbers always gives an even number')

## Lesson: Checking if a maths argument makes sense

When someone shows you how they solved a maths problem, you can check if their thinking makes sense. Look at each step, not just the final answer. If every step follows the rules, the whole answer is right too.

**Example.** Look at 27 + 15 added in columns. First add the ones: 7 + 5 = 12. Since 12 is more than 9, write the 2 and carry a ten to the tens column. Then add the tens: 1 carried, plus 2, plus 1, makes 4. The answer is 42. Each step follows from the one before, so the method works.

**Example.** Now look at 46 + 38 done wrong. The ones were added as 6 + 8 = 14, but 14 was written straight into the ones column with no carry. Then the tens were added as 4 + 3 = 7, giving 714. The mistake is the step where the ten hiding inside 14 never moved to the tens column. Fixing that one step gives 84.

*(drawing: 4 dots and 2 dots can both be split into pairs with none left over, so both are even. Put them together and they still split into pairs with none left over: 6 is even too. This works for any two even numbers, not just these.)*

**Tip.** When you check someone's maths, follow the reasoning one step at a time. The exact step that breaks the rule is where the mistake is, even if the rest of the working looks neat.

**Recap.** Check every step, not just the final answer, and you can find exactly where reasoning breaks down.

## Practice

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

## Needs first

- [Describing Aloud](https://lightmysky.com/learn/english/describing-aloud-mt_4A7FYmvVhA)
- [Teaching It Back](https://lightmysky.com/learn/learning-to-learn/teaching-it-back-mt_6eTZUwKQZr)
- [Explaining Mathematical Reasoning](https://lightmysky.com/learn/mathematics/explaining-mathematical-reasoning-mt_kJ5wYzO8qC)
- [Adding and subtracting (age 7+)](https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-7-mt_SrrsLiJkr3)
- [Addition and subtraction strategies (age 7+)](https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-age-7-mt_zxST3MarI9)

## Opens up

- [Justifying mathematical reasoning (age 8+)](https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-age-8-mt_a3dov8CZkq)