Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Write a prime factorisation using powers
Number sense
CCSS 6.NS.B.4CCSS 6.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Write a prime factorisation using powers.
- 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: Prime factorisation
Leads to: the next skill in this area.
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Prime factorisation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which is 108 written as a product of prime factors? (2³ × 3³ / 2² × 3³ / 2² × 3² × 5 / 2 × 3³) → 2² × 3³Prompt: Keep dividing by the smallest prime that works (2, 3, 5, 7…).
- 52 is written as a product of primes. What is the largest prime factor? → 13Prompt: Start dividing by 2, then 3, then 5…
- Which is 60 written as a product of prime factors? (2² × 3² / 2³ × 3 × 5 / 2 × 3 × 5 / 2² × 3 × 5) → 2² × 3 × 5Prompt: Keep dividing by the smallest prime that works (2, 3, 5, 7…).
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Write a prime factorisation using powers. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Write 45 as a product of prime factors in index form (for example 2^3 × 5).
- Step 1: 3 × 3 × 5
- Step 2: = 3² × 5
- Answer: 3² × 5
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Write 54 as a product of prime factors in index form (for example 2^3 × 5). → 2 × 3³Prompt: Divide by 2 as many times as you can, then 3, then 5, then 7.
- What number has the prime factorisation 2³ × 3 × 5²? → 600Prompt: Work out each power first.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Write 45 as a product of prime factors in index form (for example 2^3 × 5). → 3² × 5Prompt: Divide by 2 as many times as you can, then 3, then 5, then 7.
- 330 = □ × 3 × 5 × 11. Every factor is prime. What prime goes in the box? → 2Prompt: Multiply the primes you know.
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: Prime factorisation.
- 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
- 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