Year 6 Mathematics · AC9M6N02

Prime, Composite and Square Numbers

Use factor structure to classify numbers and simplify calculations

Ready to project and teach

Learning goalsSay it simply

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

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. 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 conceptTeach from the board

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.

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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N02 - Prime, Composite and Square Numbers
Example 1

number factor pairs classification 17 1 × 17 prime 18 1×18, 2×9, 3×6 composite 25 1×25, 5×5 square and composite 1 1 only neither prime nor composite

Example 2

factorise 84 2 × 2 × 3 × 7

Example 3

: using the definition of a prime number to explain why one is not a prime number

Example 4

: testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns

Curriculum examplesCopied content

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.

Questions and answersWith answers

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.

Practice and reviewReady for practice
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.
Curriculum alignmentStart here

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

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
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