Build and annotate the model
Represent prime, composite and square numbers and label the important parts, quantities or choices.
Learning goals
Learning goal
Students classify numbers from complete factor sets, recognise square numbers as equal-factor products and use factorisation to solve divisibility and arrangement problems.
Success criteria
- I can represent or identify the concept.
- I can explain the underlying relationship.
- I can select an appropriate strategy or feature.
- I can apply it in a new context.
- I can justify and verify the response.
Teaching routine
- Represent
- Reason
- Calculate
- Interpret
- Verify
Curriculum focus: identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
Key concept
Classify numbers through factor pairs
Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.
numberfactor pairsclassification171 × 17prime181×18, 2×9, 3×6composite251×25, 5×5square and composite11 onlyneither prime nor composite
A prime has exactly two positive factors. A square number has an odd number of positive factors because one pair repeats at the square root.
Worked examples
Use number properties strategically
Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.
factorise 842 × 2 × 3 × 7
recognise 14412² and composite
simplify 25 × 16(5²)(4²) = 20² = 400
arrange 29 objectsonly 1 × 29 rectangle
Properties can reduce calculation and explain constraints. Classification may overlap: every square greater than 1 is composite.
Curriculum elaborations explicitly taught
AC9M6N02: identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
- E1: using the definition of a prime number to explain why one is not a prime number
- E2: testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns
- E3: representing composite numbers as a product of their factors, including prime factors when necessary and using this form to simplify calculations involving multiplication such as 15 \times 16 as 5 \times 3 \times 4 \times 4 which can be rearranged to simplify calculation to 5 \times 4 \times 3 \times 4 = 20 \times 12
- E4: identifying and describing the product of a number with itself as square; for example, 3 \times 3 is the same as 3^2
- E5: using spreadsheets to list all the numbers that have up to 3 factors, using combinations of only the first 3 prime numbers, recognise any emerging patterns, making conjectures and experimenting with other combinations
Use the central and application models above to connect each elaboration to the same underlying concept.
Common misconceptions
1 is primeOne has only one positive factor, so it is neither prime nor composite.
Odd means prime9, 15 and 21 are odd composite numbers.
Square and composite treated as exclusiveMost square numbers are composite.
Factor list stopped too earlySearch systematically through factor pairs to the square root.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
Check understanding
- Classify 1, 17, 25 and 27.
- List factors of 36.
- Explain why 49 is square.
- Find a prime factor of 84.
- Use a square-number shortcut.
Evidence of mastery
- Represent or identify the concept
- Explain the underlying relationship
- Select an appropriate strategy or feature
- Apply it in a new context
- Justify and verify the response
Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.
Curriculum wording and references
Australian Curriculum v9.0
AC9M6N02: identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Factoring
Math Antics — Use factors to distinguish prime and composite numbers; square numbers remain in the written lesson.
As you watch: How does the complete list of factors show whether a number is prime?
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Try it: List the factors of 13, 16 and 18. Classify each as prime or composite and identify the square number.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for And describe the properties of prime, composite and square numbers...
Mapped skill: identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6N02 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6N02 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-MR-01 + MA3-MR-02 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M6N02 — Prime, Composite and Square Numbers
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