Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Greatest common factor and least common multiple
Number sense
CCSS 6.NS.B.4England: Y6 NumberEngland: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Greatest common factor and least common multiple.
- 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: Factors, multiples, primes
Leads to: Prime factorisation; Factorise linear expressions; Greatest common factor of two or three numbers
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 (Factors, multiples, primes). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which number is a factor of 48? (11 / 10 / 4 / 7) → 4Prompt: A factor divides the number exactly, with no remainder.
- Is 56 prime or composite? (Prime / Composite) → CompositePrompt: A prime number has exactly two factors: 1 and itself.
- What is the 9th multiple of 8? (The 1st multiple is 8.) → 72Prompt: Multiples of 8: 8, 16, 24, …
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Greatest common factor and least common multiple. 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: Find the greatest common factor (highest common factor) of 88 and 55.
- Step 1: 88 = 11 × 8
- Step 2: 55 = 11 × 5
- Step 3: 8 and 5 share no common factor, so the GCF is 11.
- Answer: 11
- 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.
- Find the greatest common factor (highest common factor) of 12 and 15. → 3Prompt: List the factors of each number.
- Find the least common multiple (lowest common multiple) of 8 and 7. → 56Prompt: Count in 8s.
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.
- Mei buys bread rolls in packs of 8 and veggie sausages in packs of 10. What is the smallest number of rolls Mei can buy so that there are exactly as many rolls as sausages? → 40Prompt: The number must be a multiple of both pack sizes.
- Find the least common multiple (lowest common multiple) of 9 and 15. → 45Prompt: Count in 15s.
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: Factors, multiples, primes.
- 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: Prime factorisation; Factorise linear expressions; Greatest common factor of two or three numbers.
- 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