How can you tell they’ve got it: Explaining Mathematical Reasoning?

If they’ve got it, you’ll see things like: Explain a solution strategy using a drawing or number sentence (e.g. 'I made ten first, then added the rest'); Justify why an answer is correct by showing an alternative method that gives the same result; Identify and explain an error in a worked example or a peer's solution. Or just try it together: If you ask your child "how did you work that out?", can they show you with a drawing or explain their steps in simple words?

Mathematics Mathematical Thinking Ages 6–7

Explaining Mathematical Reasoning

Your child can explain how they solved a problem, using a drawing or simple words. Asked 'how do you know?', they can show you.

In curriculum terms

With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words

Ages are typical, not deadlines — follow your child’s pace. How to help at home →

How to tell they’ve got it

Tick these off as you see them — no test required.

Explain a solution strategy using a drawing or number sentence (e.g. 'I made ten first, then added the rest')
Justify why an answer is correct by showing an alternative method that gives the same result
Identify and explain an error in a worked example or a peer's solution

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Try this together

If you ask your child "how did you work that out?", can they show you with a drawing or explain their steps in simple words?

Where this sits on the map

Stuck here? Check the skills it builds on first. Confident? Here’s what it unlocks.

Builds on

Showing Your Workingages 5–6Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects

Addition in any orderages 6–7Justifying why a+b=b+a exercises logical mathematical argument

What the equals sign meansages 6–7Determining whether equations are true/false exercises evaluating and justifying

Explaining Mathematical Reasoningthis skill · ages 6–7

Unlocks

Justifying mathematical reasoningages 7–8Age 7-8 arguing/justifying builds on age 6-7

Teaching It Backages 7–8The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)

solid = must come firstdashed = helps

Curriculum alignment

Where this fits in the official school curriculum — our best automated guess, not yet checked by a person.

Show candidate curriculum codes · 3 ACARA · 2 NSW · 3 VIC

Australian Curriculum v9 candidate

AC9M2N04medium confidenceYear 2 · Number

add and subtract one- and two-digit numbers, representing problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies

AC9M2A02low confidenceYear 2 · Algebra

recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts

AC9M3N04low confidenceYear 3 · Number

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

NSW syllabus codes & stages only

MAO-WM-01medium confidenceMathematics K-10 · Early Stage 1, Stage 1, Stage 2, Stage 3

MAE-RWN-01low confidenceMathematics K-10 · Early Stage 1

Victorian Curriculum 2.0 codes & levels only

VC2M2N04medium confidenceMathematics · Level 2 · Number strand

VC2M1A02low confidenceMathematics · Level 1 · Algebra strand

VC2M2A02low confidenceMathematics · Level 2 · Algebra strand

These are candidate alignments generated by semantic matching — machine-suggested and unreviewed (v0.1), not official or verified mappings. For official curriculum content see australiancurriculum.edu.au, curriculum.nsw.edu.au and f10.vcaa.vic.edu.au. Don’t rely on them for registration or compliance purposes.

Nearby on the map

Connecting maths to real lifeages 6–7 Connecting Representationsages 6–7 Generalising Patternsages 6–7 Guided Multi-Step Problem Solvingages 6–7

All Mathematical Thinking skills →