Mathematics · Year 6

Active learning ideas

Exploring Prime and Composite Numbers

Active learning helps students grasp prime and composite numbers because it turns abstract properties into concrete investigations. By physically manipulating numbers through sieves, factor pairs, and discussions, students move beyond memorisation to see patterns and relationships among them.

• ACARA Content Descriptions
• AC9M6N01

• 15–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 40 min · Small Groups

Inquiry Circle: The Sieve of Eratosthenes

In small groups, students use a large 1-100 grid to systematically cross out multiples of prime numbers. They discuss why certain numbers remain and identify the patterns that emerge, such as the 'diagonal' nature of multiples of three.

Why is the number 1 neither prime nor composite?

Facilitation Tip

During The Sieve of Eratosthenes, move between groups to prompt students to explain why they are crossing out certain numbers, reinforcing divisibility language.

What to look for

Present students with a list of numbers (e.g., 15, 23, 36, 41, 50). Ask them to write 'P' next to prime numbers and 'C' next to composite numbers. For two of their choices, ask them to write down the factor pairs that justify their classification.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Case of Number One

Students individually reflect on why the number 1 does not fit the definition of prime or composite. They then pair up to refine their argument before sharing their logical reasoning with the whole class.

How can prime factorization help us find the greatest common factor of two numbers?

Facilitation Tip

In The Case of Number One, listen carefully to students’ arguments before revealing the definition, allowing their misconceptions to surface naturally.

What to look for

Give each student a card with a composite number (e.g., 24). Ask them to create a factor tree to show its prime factorization. On the back, they should write one sentence explaining why the number 1 is not considered prime or composite.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Factor Pair Challenge

Students rotate through stations using different manipulatives like MAB blocks or tiles to create all possible rectangular arrays for a given number. They record which numbers only have one possible array (primes) and which have multiple (composites).

In what ways do prime numbers act as the building blocks for all other whole numbers?

Facilitation Tip

For the Factor Pair Challenge, provide mini whiteboards so students can quickly test and revise their pairs without erasing mistakes.

What to look for

Pose the question: 'If prime numbers are the building blocks of all whole numbers, what does that mean for composite numbers?' Facilitate a class discussion where students share their ideas, using examples of prime factorization to support their reasoning.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teachers approach this topic by balancing exploration with structure. Start with hands-on tools like sieves and arrays to build visual understanding, then formalise definitions with clear examples and counterexamples. Avoid rushing to the textbook—instead, let students articulate rules in their own words before introducing the precise terminology.

By the end of these activities, students confidently identify prime and composite numbers, justify their choices with factor pairs, and explain why 1 is neither. They use mathematical language precisely and support their reasoning in both written and spoken forms.

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Watch Out for These Misconceptions

• During Station Rotation: Factor Pair Challenge, watch for students labeling numbers like 9 and 15 as prime because they are odd.

  Have students list all factor pairs for these numbers on their whiteboards and circle the pairs. Ask them to compare with a partner whether these numbers fit the rule of having exactly two distinct factors.

• During Think-Pair-Share: The Case of Number One, listen for students arguing that 1 is prime because it has only one factor.

  Ask them to model factor pairs for 1 and compare it to the definition of a prime number. Use a T-chart to show that 1 has only one factor pair (1,1), which does not meet the requirement of two distinct factors.

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Methods used in this brief

• Inquiry Circle
• Think-Pair-Share
• Stations Rotation