Discovering Prime Numbers

Overview

This 60-minute lesson introduces Year 5 pupils to prime numbers, aligned with the National Curriculum for England’s mathematics programme of study for Year 5 (Number - Multiplication and Division). The aim is to develop conceptual understanding and practical skills through exploration, discussion, and assessment.

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National Curriculum Links

Year 5 Number - Multiplication and Division:

• Pupils should be taught to identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
• Prime numbers to be recognised and understood as numbers greater than 1 with exactly two factors — 1 and itself.

Relevant Objectives:

• Recognise and use prime numbers, prime factors and composite numbers.
• Establish whether a number up to 100 is prime and recall prime numbers up to 19.
• Use their knowledge of multiplication and division to identify factors.

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Learning Objectives

By the end of this lesson, pupils will be able to:

• Define what a prime number is and describe its properties.
• Identify prime numbers up to 100 confidently.
• Distinguish between prime and composite numbers using multiplication and division strategies.
• Work collaboratively to explore the ‘sieve of Eratosthenes’ as a method to find prime numbers.
• Complete an independent activity to demonstrate understanding of prime numbers.

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Resources Needed

• Whiteboard and markers
• Individual mini-whiteboards and pens
• Number cards (1 – 100)
• A large printed 1–100 number grid for classroom display
• Worksheets with prime number activities
• Timer or stopwatch
• Sticky notes or small stickers

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Lesson Structure (60 minutes)

1. Introduction & Starter (10 minutes)

• Engage: Ask pupils what they know about multiplication and factors to activate prior knowledge.
• Explain: Define prime numbers: "A prime number is a number greater than 1 that has only two factors: 1 and itself."
• Demonstrate: Use low numbers (2, 3, 4, 5, 6, 7) on the whiteboard; show how to test if each is prime by listing their factors.
• Recall: Ask pupils to shout out any prime numbers they already know (expect mention of numbers like 2, 3, 5, 7, 11, 13, 17, 19).

Check for understanding: Use mini whiteboards to quickly write “prime” or “not prime” for numbers you call out.

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2. Main Activity: Sieve of Eratosthenes (20 minutes)

• Explain the method: Introduce the ancient ‘sieve of Eratosthenes’ method as a fun, hands-on way to find primes up to 100:

  • Start from 2, cross out all multiples.
  • Move to the next non-crossed number, repeat crossing multiples.

• Group work: Divide kids into 5 groups of 5. Each group receives a printed 1-100 grid and sets of sticky notes or stickers.

• Pupils take turn “crossing out” multiples by sticking notes on numbers.

• Encourage pupils to explain why multiples are crossed out (because they're composite).

• After full sieve, groups identify and mark all primes remaining.

• Discussion: Groups share discoveries and clarify any misunderstandings.

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3. Guided Practice (15 minutes)

• Worksheet Task: Pupils individually complete a worksheet featuring:

  • Colouring prime numbers in a 1-100 grid.
  • Circling all factors of given numbers and deciding prime/composite status.
  • Short reasoning questions, e.g., “Is 29 prime? Why? List its factors.”

• Teacher support: Circulate to scaffold reasoning; use questioning techniques such as:

  • “How do you know that number is prime?”
  • “What happens if you try to divide by numbers other than 1 and itself?”

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4. Plenary & Assessment (10 minutes)

• Quick Quiz: Oral quiz where the teacher calls out numbers 1-50. Pupils hold up green (prime) or red (not prime) cards.
• Self-assessment: Pupils tick which learning objective they achieved on a mini checklist.
• Reflect: Pupils explain to a partner what a prime number is and give two examples.
• Exit Ticket: On a sticky note, write down one prime number and why it is prime.

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5. Differentiation

• Support: Provide factor lists or multiplication tables for pupils who need it.
• Challenge: Ask more able pupils to find prime factor decompositions of two-digit numbers or consider why 1 is not prime.

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Assessment Criteria

• Can the pupil explain the definition of a prime number verbally or in writing?
• Can they identify prime numbers within 100 with minimal error?
• Can they apply the sieve method collaboratively?
• Can they distinguish between prime and composite through factorisation?

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Extension Ideas

• Investigate larger prime numbers beyond 100.
• Explore real-world applications, such as cryptography or prime numbers in computer science.
• Create prime number artistic patterns or ‘prime spirals’ inspired by the Ulam spiral.

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This lesson plan is designed to actively involve pupils and engage their critical thinking, helping embed deep understanding of prime numbers with references directly taken from the statutory requirements of the National Curriculum for England in Year 5 Mathematics.