Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Greatest common factor of two or three numbers
Number sense
CCSS 6.NS.B.4England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Greatest common factor of two or three numbers.
- 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: Find every factor using factor pairs; Greatest common factor and least common multiple
Leads to: Choose GCF or LCM to solve a problem; Rewrite a sum by taking out the GCF
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 (Find every factor using factor pairs; Greatest common factor and least common multiple). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- How many factors does 36 have? → 9Prompt: Work in pairs: 1 × ?, 2 × ?, 3 × ? … until the pairs meet.
- Find the greatest common factor (highest common factor) of 24 and 40. → 8Prompt: List the factors of each number.
- Complete the factor pair: 90 = 15 × ? → 6Prompt: Divide 90 by 15.
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Greatest common factor of two or three numbers. 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: Find the GCF (highest common factor) of 24 and 15.
- Step 1: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Step 2: Factors of 15: 1, 3, 5, 15
- Step 3: GCF = 3
- Answer: 3
- 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.
- Find the GCF (highest common factor) of 6 and 16. → 2Prompt: List the factors of the smaller number.
- 60 = 2² × 3 × 5 and 150 = 2 × 3 × 5². Use these to find the GCF of 60 and 150. → 30Prompt: Take each prime that appears in BOTH factorisations.
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.
- Find the GCF (highest common factor) of 14 and 16. → 2Prompt: List the factors of the smaller number.
- 108 = 2² × 3³ and 180 = 2² × 3² × 5. Use these to find the GCF of 108 and 180. → 36Prompt: Take each prime that appears in BOTH factorisations.
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: Find every factor using factor pairs.
- 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: Choose GCF or LCM to solve a problem; Rewrite a sum by taking out the GCF.
- 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