Prime Factorisation Mastery

Curriculum Reference

Key Stage 3 - Number (Year 8)
National Curriculum (England):

• Prime Factor Decomposition: Understand and use prime factorisation, including using it to find the highest common factor (HCF) and lowest common multiple (LCM).
• Express any positive integer as a product of prime factors using factor trees and index notation.

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Lesson Objectives

By the end of this 30-minute lesson, students will be able to:
✅ Identify prime numbers up to at least 50.
✅ Apply prime factorisation using factor trees.
✅ Express numbers as products of prime factors in index notation.
✅ Use prime factorisation to find the HCF and LCM of two numbers.

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Resources & Materials

• Mini whiteboards & markers
• Printed factor tree worksheet
• One set of number cards (1-100) for each pair
• Stopwatch for a timed challenge
• Coloured paper strips for a visual group exercise

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Lesson Breakdown (30 minutes)

1. Engaging Starter – "Prime Detective" (5 mins)

🕵️ Challenge students to quickly identify prime numbers from a list on the board.

• Teacher: "What makes a number prime?"
• Activity: Call out numbers rapidly (e.g., 17, 25, 31, 49). Students write 'P' (Prime) or 'C' (Composite) on mini whiteboards and hold them up.
• Class discussion: Why is 1 not a prime? What about 2?

✅ Reinforces prime vs. composite numbers before decomposition.

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2. Main Activity – Factor Trees Challenge (15 mins)

Step 1: Demonstration (5 mins)

• Teacher models prime factor decomposition using 48:
  • Draw a factor tree
  • Circle prime numbers
  • Write final answer in index notation (e.g., 48 = 2⁴ × 3).
  • Explain why prime numbers cannot be broken down further.

✅ Ensures clear understanding before practice.

Step 2: Paired Factorisation Race (5 mins)

• Pairs receive a random number card (20-100).
• Task: Break it down using a factor tree and write in index notation.
• The fastest accurate pair wins a reward (e.g., coloured stickers).

✅ Encourages active engagement and peer learning.

Step 3: HCF & LCM Connection (5 mins)

• Teacher writes two numbers (e.g., 36 & 48).
• Students use their factorisation to:
  1. Identify common factors.
  2. Find HCF (biggest common factor).
  3. Find LCM (multiply highest powers of each factor).
• Class discussion: "Why is prime factorisation useful in real life?"

✅ Embeds real-world relevance.

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3. Plenary – "Mystery Number" Challenge (5 mins)

• Teacher provides clues:
  • "It has three distinct prime factors…"
  • "Its HCF with 30 is 6…"
• Students deduce the number on mini whiteboards.
• Quick reflection: "What did we learn today?"

✅ Final reinforcement of skills in a fun, interactive way.

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Differentiation

✔ Support: Use colour-coded factor trees for guidance.
✔ Extension: Find HCF & LCM for three numbers instead of two.
✔ Challenge: Given an index notation, reconstruct the original number.

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Assessment for Learning

✅ Whiteboard responses: Quick check of prime number recognition.
✅ Factor trees race: Accuracy of students’ decomposition.
✅ Mystery number challenge: Checks deep understanding.

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Teacher Reflection

• Which students grasped HCF/LCM easily?
• Were students engaged and actively participating?
• What could be improved for next time?

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⚡ Outcome: Year 8 students leave with a strong grasp of prime factor decomposition, feeling confident to apply it further!