Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Prime factorisation
Number sense
CCSS 6.NS.B.4England: KS3 NumberEngland: GCSE Foundation NumberEngland: 11+ Number
Objective and success criteria
Students will: Prime factorisation.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Primes, squares and cubes; Greatest common factor and least common multiple
Leads to: Simplify surds (radicals); Write a prime factorisation using powers
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Primes, squares and cubes; Greatest common factor and least common multiple). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 6² = ? → 36Prompt: Squared means multiply the number by itself.
- Find the greatest common factor (highest common factor) of 35 and 14. → 7Prompt: List the factors of each number.
- Which of these is a prime number: 21, 33, 53, 55? (21 / 55 / 53 / 33) → 53Prompt: A prime has exactly two factors, 1 and itself.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Prime factorisation. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Which is 48 written as a product of prime factors?
- Step 1: Factor tree: 48 → 2 × 2 × 2 × 2 × 3
- Step 2: 2⁴ × 3
- Answer: 2⁴ × 3
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Which is 225 written as a product of prime factors? (3 × 5² / 3² × 5² / 3³ × 5 / 2 × 3² × 5²) → 3² × 5²Prompt: Keep dividing by the smallest prime that works (2, 3, 5, 7…).
- 66 is written as a product of primes. What is the largest prime factor? → 11Prompt: Start dividing by 2, then 3, then 5…
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Which is 360 written as a product of prime factors? (2² × 3² × 5 / 2³ × 3² × 5 / 2³ × 3³ / 2⁴ × 3² × 5) → 2³ × 3² × 5Prompt: Keep dividing by the smallest prime that works (2, 3, 5, 7…).
- 12 is written as a product of primes. What is the largest prime factor? → 3Prompt: Start dividing by 2, then 3, then 5…
Watch out for
- Reading 1,045 as one thousand four hundred five: point to each place and say its value.
- Thinking a longer number is always bigger, even with decimals (0.45 vs 0.5).
Support and stretch
Support
- Review first: Primes, squares and cubes.
- Use concrete materials: place value chart.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Simplify surds (radicals); Write a prime factorisation using powers.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-6.
Free lesson plan from eurekami.com/lesson-plan-builder