Mathematics Mathematical Thinkingusually ages 9–10

Reasoning with Equivalences

Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms

How to tell they’ve got it

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

Notice that multiplying any number by 25 can be done by multiplying by 100 then dividing by 4, and explain why
Describe the general rule for a sequence and predict the 20th term
Generalise: to find 10% divide by 10, to find 5% halve 10%, and use this to find 35% of any number

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Try this together

When your child sees a sequence of equivalent fractions — like 1/2, 2/4, 3/6… — can they describe the rule and use it to find the next few terms, or to quickly convert between fractions and percentages?

Where this sits on the map

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

Builds on

Times tables (age 8+)ages 8–9Age 8-9 repeated reasoning is prerequisite to age 9-10 level

Describing Rules & Patternsages 8–9Describing general rules for sequences and predicting terms applies the universal generalisation habit in a mathematical context

Equivalent fractions (age 9+)ages 9–10Equivalent fraction patterns exercise generalisation

Shape patternsages 9–10Generating patterns from rules exercises repeated reasoning and generalisation

Reasoning with Equivalencesthis skill · ages 9–10

Unlocks

Generalising with repeated reasoningages 10–11Y6 generalisation extends Y5 repeated reasoning

solid = must come firstdashed = helps

Curriculum alignment

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

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

Australian Curriculum v9 candidate

AC9M3A03medium confidenceYear 3 · Algebra

recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts

AC9M3A02medium confidenceYear 3 · Algebra

extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator

AC9M4A02medium confidenceYear 4 · Algebra

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

NSW syllabus codes & stages only

MA3-RN-03low confidenceMathematics K-10 · Stage 3

MA2-AR-01low confidenceMathematics K-10 · Stage 2

Victorian Curriculum 2.0 codes & levels only

VC2M3A03medium confidenceMathematics · Level 3 · Algebra strand

VC2M4A02medium confidenceMathematics · Level 4 · Algebra strand

VC2M5N07medium confidenceMathematics · Level 5 · Number 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

Choosing representations strategicallyages 9–10 Complex Multi-Step Problemsages 9–10 Fractions on a number line (age 9+)ages 9–10 Fractions, Decimals & Percentagesages 9–10

All Mathematical Thinking skills →