Mathematics · Year 5

Active learning ideas

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.

• National Curriculum Attainment Targets
• KS2: Mathematics - Multiplication and Division

• 15–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Provide students with a list of numbers from 1 to 50. Ask them to circle all prime numbers and underline all composite numbers. Then, ask them to write one sentence explaining why 1 is neither prime nor composite.

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

Activity 02

• 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.

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.

What to look for

Display the number 30 on the board. Ask students to write down all of its factors. Then, have them classify 30 as either prime or composite, justifying their answer with reference to its factors.

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

Activity 03

• 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.

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.

What to look for

Pose the question: 'If you are given a very large number, how can you be sure it is prime?' Facilitate a class discussion where students explain their strategies, comparing the efficiency of trial division versus methods like the Sieve of Eratosthenes.

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

Activity 04

• 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.

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.

What to look for

Provide students with a list of numbers from 1 to 50. Ask them to circle all prime numbers and underline all composite numbers. Then, ask them to write one sentence explaining why 1 is neither prime nor composite.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Escape Room