Mathematics Number Representation & Place Valueusually ages 13–14

Number Sets & Infinity

Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers

How to tell they’ve got it

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

Explain that rational numbers can be written as a fraction of two integers and have terminating or repeating decimals
Give examples of irrational numbers and explain why their decimal expansions neither terminate nor repeat
Appreciate that between any two numbers there are infinitely many other numbers

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Try this together

Can your child explain that numbers like √2 and π can't be written as exact fractions — and that their decimal expansions go on forever without repeating?

Where this sits on the map

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

Builds on

Decimals and fractions (age 11+)ages 11–13Understanding rational vs irrational requires fluency with fraction-decimal conversion

Square and cube numbersages 11–14Understanding irrational numbers like √2 requires knowledge of square roots

Number Sets & Infinitythis skill · ages 13–14

Unlocks

Nothing on the map depends on this yet.

solid = must come firstdashed = helps

Curriculum alignment

Candidate matches to official curriculum codes — machine-suggested, unreviewed (v0.1).

This skill sits beyond Year 6 in the Australian Curriculum, so no F–6 code is matched. It also sits beyond the NSW K–6 syllabuses. It also sits beyond Level 6 in the Victorian Curriculum.

Nearby on the map

Estimating by roundingages 12–14 Powers of Ten Notationages 12–14 Decimal place value (age 11+)ages 11–13 Fractions on a number lineages 11–12

All Number Representation & Place Value skills →