Prime Numbers and Composite Numbers

Active learning turns abstract number theory into concrete patterns students can touch and see. When Year 5 learners sieve multiples with pencils or hunt for prime factors with counters, they build lasting mental models instead of memorising rules. Every mark on a grid or pair of cubes reinforces what makes primes unique and composites rich with factors.

• Year 5
• Mathematics
• 4 activities
• 15 min–35 min

Learning Objectives

1. Identify all prime numbers up to 100, demonstrating understanding of the definition.
2. Explain why 2 is the only even prime number, using divisibility rules.
3. Compare and contrast prime and composite numbers, providing at least three examples of each with their factors.
4. Apply the Sieve of Eratosthenes method to systematically identify prime numbers within a given range.

Escape Room

⏱ 35 min·Whole Class

Whole Class: Sieve of Eratosthenes Grid

Project a 1-100 number grid on the board. Call students to the front in sequence to cross out multiples of each prime starting from 2. Remaining numbers become primes. Conclude with a class discussion on the process and why 2 is unique.

Prepare & details

Justify why 2 is the only even prime number.

Facilitation Tip: During the Whole Class Sieve of Eratosthenes Grid, circulate and ask each group to explain why they stopped crossing at 10 rather than 11.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

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

Escape Room

⏱ 25 min·Small Groups

Small Groups: Prime Factor Hunt

Provide groups with number cards from 1 to 100. Each group lists factors for 10 numbers, sorts them as prime or composite, and justifies choices on mini-whiteboards. Groups share one example with the class.

Prepare & details

Analyze the Sieve of Eratosthenes method for finding prime numbers.

Facilitation Tip: In Small Groups Prime Factor Hunt, provide square tiles so students can physically build arrays that reveal prime or composite structure.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

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

Escape Room

⏱ 20 min·Pairs

Pairs: Even Prime Debate

Pairs receive statements about even numbers and primes. They debate and draw factor trees or arrays to prove why only 2 qualifies as an even prime. Switch pairs to defend opposing views.

Prepare & details

Compare prime numbers with composite numbers, providing examples of each.

Facilitation Tip: For the Pairs Even Prime Debate, give each pair a mini-whiteboard to sketch factor pairs for 2 and 4 side-by-side before sharing aloud.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

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

Escape Room

⏱ 15 min·Individual

Individual: Prime Sieve Journal

Students create personal 1-100 grids, apply the sieve independently, and note observations like patterns in primes. They write one justification for 2 being prime.

Prepare & details

Justify why 2 is the only even prime number.

Facilitation Tip: During the Individual Prime Sieve Journal, instruct students to write a reflection question for a peer to answer by checking their sieve accuracy.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

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

Teaching This Topic

Start with hands-on sieves so students experience the algorithm firsthand; avoid rushing to abstract definitions. Emphasise factor pairs over divisibility tests—seeing 7 as 1×7 helps more than checking 2, 3, 4, 5, 6. Research shows that pupils who manipulate materials classify numbers more reliably and retain concepts longer than those who only list factors on paper.

What to Expect

By the end of the sequence, students confidently identify primes up to 100, explain why 1 and 2 are special cases, and justify classifications using factor lists. You will hear clear language like ‘two factors only’ and see accurate sieves with all multiples crossed out correctly.

Watch Out for These Misconceptions

Common Misconception

During Whole Class Sieve of Eratosthenes Grid, watch for students who circle 1 as prime.

What to Teach Instead

Have those students list the factors of 1 on their grid margin and compare it to the factor list for 2; guide them to see that 1 lacks a second factor.

Common Misconception

During Pairs Even Prime Debate, watch for students who claim all primes are odd.

What to Teach Instead

Ask the pair to write factor pairs for 2 and 4 on their mini-whiteboards, then prompt them to explain why 2 is the exception.

Common Misconception

During Small Groups Prime Factor Hunt, watch for students who list 4 as prime because it feels ‘small’.

What to Teach Instead

Have them build a 2×2 array with tiles and count the total factors; guide them to recognise 1, 2, and 4 as three factors, so 4 is composite.

Assessment Ideas

Exit Ticket

After Whole Class Sieve of Eratosthenes Grid, give students a list of numbers from 1 to 50. Ask them to circle primes and underline composites, then write one sentence explaining why 1 is neither.

Quick Check

During Small Groups Prime Factor Hunt, display the number 30 on the board. Ask each group to write all factor pairs on their whiteboard and classify 30 as prime or composite, justifying with their pairs.

Discussion Prompt

After Individual Prime Sieve Journal, pose the question: ‘If you are given a very large number, how can you be sure it is prime?’ Facilitate a class discussion comparing trial division strategies with sieve methods.

Extensions & Scaffolding

• Challenge: Ask early finishers to extend their sieve to 200 and predict how many primes exist between 100 and 200.
• Scaffolding: Provide a partially completed sieve grid with only multiples of 2 and 3 already marked to reduce cognitive load.
• Deeper Exploration: Invite students to research how the Sieve of Eratosthenes relates to modern cryptography and share findings in a brief class presentation.

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.
Sieve of Eratosthenes	An ancient algorithm for finding all prime numbers up to a specified integer. It works by iteratively marking as composite the multiples of each prime, starting with the multiples of 2.