Mathematics · Year 6

Active learning ideas

Prime Numbers and Composite Numbers

Active learning helps Year 6 students grasp the abstract concepts of prime and composite numbers by providing concrete, hands-on experiences. When students physically manipulate numbers, sort factor pairs, and apply sieving techniques, they build lasting understanding through visual and kinesthetic engagement. This approach transforms a challenging topic into an accessible and memorable set of discoveries.

• National Curriculum Attainment Targets
• KS2: Mathematics - Number and Place Value

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Chalk Talk
• 35 min · Small Groups

Small Groups: Sieve of Eratosthenes Grid

Provide each group with a 1-100 number grid. Starting from 2, students use coloured pens to cross out multiples collaboratively. Remaining numbers are primes; groups justify exclusions and note 1 separately. Share findings class-wide.

Justify why 1 is not considered a prime number.

Facilitation Tip

During the Sieve of Eratosthenes Grid, circulate with a timer to ensure students systematically cross out multiples without skipping, reinforcing the concept of prime numbers remaining unmarked.

What to look for

Present students with a list of numbers from 1 to 30. Ask them to circle all the prime numbers and underline all the composite numbers. Then, ask them to write one sentence explaining their choice for the number 29.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Activity 02

• Chalk Talk
• 25 min · Pairs

Pairs: Factor Pairs Card Sort

Prepare cards with numbers 1-100 and possible factor pairs. Pairs sort into prime, composite, or neither piles, testing factors systematically. Discuss borderline cases like 1 and 2, then verify with multiplication checks.

Predict the next prime number in a sequence and explain your reasoning.

Facilitation Tip

For the Factor Pairs Card Sort, provide blank cards for students to create their own examples once the initial set is sorted correctly, deepening their understanding through creation.

What to look for

Pose the question: 'If you were to create a new number system, would you include prime numbers? Why or why not?' Facilitate a class discussion where students use their understanding of prime and composite properties to justify their ideas.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Activity 03

• Chalk Talk
• 30 min · Whole Class

Whole Class: Prime Prediction Chain

Display a prime sequence on the board. Students suggest and justify the next prime in turn, using divisibility tests. Class votes and tests predictions together, extending to spotting patterns beyond 100.

Compare the properties of prime numbers with composite numbers.

Facilitation Tip

In the Prime Prediction Chain, model the first two predictions aloud, then step back to let students lead the reasoning while you observe and note common misconceptions.

What to look for

Give each student a card with a number (e.g., 49, 53, 77). Ask them to write down whether the number is prime or composite, list all its factors, and explain their reasoning in one to two sentences.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Activity 04

• Chalk Talk
• 20 min · Individual

Individual: Prime Hunt Scavenger

Give students a 1-100 chart with hidden primes marked. They hunt, list, and explain three properties of their finds. Pairs then swap lists to verify and discuss predictions for larger numbers.

Justify why 1 is not considered a prime number.

What to look for

Present students with a list of numbers from 1 to 30. Ask them to circle all the prime numbers and underline all the composite numbers. Then, ask them to write one sentence explaining their choice for the number 29.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

A few notes on teaching this unit

Teaching prime and composite numbers effectively requires a balance of direct instruction and active investigation. Start with a clear definition and examples, then move quickly into hands-on activities where students apply the concepts themselves. Avoid over-explaining or giving away answers; instead, guide students to discover properties through guided questioning and peer collaboration. Research shows that students retain concepts better when they construct their own understanding through exploration and correction.

Successful learning looks like students confidently identifying prime and composite numbers up to 100, explaining why 1 fits neither category, and using factor knowledge to justify their reasoning. They should also predict the next prime in a sequence and compare properties with composite numbers independently or in small groups. Misconceptions are addressed through guided peer discussion and active correction.

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Watch Out for These Misconceptions

• During the Factor Pairs Card Sort, watch for students who categorise 1 as a prime number.

  Have these students list the factors of 1 on the back of their card, then compare it to the factor lists of known primes like 2, 3, and 5. Use the card sort structure to prompt them to ask, 'Does 1 have exactly two distinct factors?'

• During the Sieve of Eratosthenes Grid, watch for students who assume all odd numbers greater than 2 are prime.

  Direct these students to examine the grid for odd composites like 9, 15, and 21, asking them to identify the crossed-out multiples and explain why those numbers are composite. Encourage peer teaching by having them explain their findings to a partner.

• During the Prime Prediction Chain, watch for students who exclude 2 as a prime number.

  Pause the chain and ask students to list the factors of 2, then compare it to the definition of a prime number. Use the chain’s sequential nature to highlight that 2 is the only even prime and must be included to maintain the pattern.

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Methods used in this brief

• Chalk Talk