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.

• Year 6
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Classify numbers up to 100 as either prime or composite, providing justification for each classification.
2. Explain why the number 1 is neither prime nor composite, referencing the definition of prime numbers.
3. Analyze sequences of numbers to predict the next prime number, articulating the reasoning based on divisibility rules.
4. Compare and contrast the properties of prime numbers with composite numbers, identifying key differences in their factors.

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.

Prepare & details

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.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

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

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.

Prepare & details

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.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

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

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.

Prepare & details

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.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

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

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.

Prepare & details

Justify why 1 is not considered a prime number.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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?'

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After the Sieve of Eratosthenes Grid activity, 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.

Discussion Prompt

During the Factor Pairs Card Sort, 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 sorted factor pairs and the properties of primes and composites to justify their ideas.

Exit Ticket

After the Prime Prediction Chain, 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.

Extensions & Scaffolding

• Challenge: Ask early finishers to find all prime numbers between 100 and 200 using the Sieve of Eratosthenes method, then present their findings to the class.
• Scaffolding: Provide a partially completed sieve grid for students who struggle, focusing on numbers up to 50, and pair them with a peer to complete the task together.
• Deeper exploration: Introduce the concept of prime factorisation by having students break down composite numbers into their prime factors, using factor trees or repeated division.

Key Vocabulary

Prime Number	A whole number greater than 1 that has only two factors: 1 and itself. For example, 7 is prime because its only factors are 1 and 7.
Composite Number	A whole number greater than 1 that has more than two factors. For example, 10 is composite because its factors are 1, 2, 5, and 10.
Factor	A number that divides exactly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Divisibility Rule	A shortcut or guideline used to determine if a number can be divided by another number without a remainder. For example, a number is divisible by 2 if its last digit is even.