Mathematical Thinking

Reasoning, estimating and problem-solving habits — 48 skills across 6 years. Every skill below shows what it builds on and how to tell your child has it.

Mathematics48 skillsages 5–11

Grouped by the age children typically start each skill. Ages are typical, not deadlines — follow your child’s pace.

Around age 5

Early Maths Vocabularyages 5–6AC ✓ Finding efficient methodsages 5–6AC ✓ Hands-On Problem Solvingages 5–6AC ✓ Making Sense of Problemsages 5–6AC ✓ Real-World to Maths Connectionsages 5–6AC ✓ Showing Your Workingages 5–6AC ✓ Spotting mathematical patternsages 5–6AC ✓ Using objects to model real problemsages 5–6AC ✓

Around age 6

Connecting maths to real lifeages 6–7AC ✓ Connecting Representationsages 6–7AC ✓ Explaining Mathematical Reasoningages 6–7AC ✓ Generalising Patternsages 6–7AC ✓ Guided Multi-Step Problem Solvingages 6–7AC ✓ Numbers on a number lineages 6–7AC ✓ Precise Maths Communicationages 6–7AC ✓ Shape patternsages 6–7AC ✓

Around age 7

Choosing the right strategyages 7–8AC ✓ Extending Table Patternsages 7–8AC ✓ Justifying mathematical reasoningages 7–8AC ✓ Multi-Step Problem Solvingages 7–8AC ✓ Shape patterns (age 7+)ages 7–8AC ✓ Understanding fractionsages 7–8AC ✓ Understanding fractions (age 7+)ages 7–8AC ✓ Working with moneyages 7–8AC ✓

Around age 8

Choosing mathematical toolsages 8–9AC ✓ Fractions on a number lineages 8–9AC ✓ Justifying mathematical reasoning (age 8+)ages 8–9AC ✓ Mathematical Precisionages 8–9AC ✓ Modelling with multiplication and fractionsages 8–9AC ✓ Multi-Step Problem Solvingages 8–9AC ✓ Times tables (age 8+)ages 8–9AC ✓ Using Mathematical Structureages 8–9AC ✓

Around age 9

Choosing representations strategicallyages 9–10AC ✓ Complex Multi-Step Problemsages 9–10AC ✓ Fractions on a number line (age 9+)ages 9–10AC ✓ Fractions, Decimals & Percentagesages 9–10AC ✓ Precise Maths Vocabularyages 9–10AC ✓ Real-World Maths Modellingages 9–10AC ✓ Reasoning with Equivalencesages 9–10AC ✓ Understanding fractions (age 9+)ages 9–10AC ✓

Around age 10

Advanced Maths Vocabularyages 10–11AC ✓ Advanced Multi-Step Problemsages 10–11AC ✓ Choosing Maths Toolsages 10–11AC ✓ Constructing mathematical argumentsages 10–11AC ✓ Generalising with repeated reasoningages 10–11AC ✓ Order of operations (age 10+)ages 10–11AC ✓ Real-World Mathematical Modellingages 10–11AC ✓ Understanding fractions (age 10+)ages 10–11AC ✓

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