Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Rewrite a sum by taking out the GCF
Number sense
CCSS 6.NS.B.4England: KS3 NumberEngland: KS3 Algebra
Objective and success criteria
Students will: Rewrite a sum by taking out the GCF.
- 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: Greatest common factor of two or three numbers
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 · 5 min
- Quick retrieval from earlier learning (Greatest common factor of two or three numbers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the GCF (highest common factor) of 18 and 48. → 6Prompt: List the factors of the smaller number.
- 90 = 2 × 3² × 5 and 150 = 2 × 3 × 5². Use these to find the GCF of 90 and 150. → 30Prompt: Take each prime that appears in BOTH factorisations.
- Find the GCF of 25, 10, 35. → 5Prompt: Find a number that divides all three.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Rewrite a sum by taking out the GCF. 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: 36 + 42 = □ × (6 + 7). What number goes in the box?
- Step 1: 6 × 6 = 36, 6 × 7 = 42
- Step 2: The box is 6.
- Answer: 6
- 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.
- 40 + 72 = □ × (5 + 9). What number goes in the box? → 8Prompt: The box multiplies each number in the brackets.
- Complete using the GCF: 18 + 10 = 2(9 + □) → 5Prompt: 2(9 + □) means 2 × 9 + 2 × □.
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.
- Write 12 + 60 as the GCF times a sum of two whole numbers with no common factor, like 4(2 + 3). → 12(1 + 5)Prompt: Find the GCF of 12 and 60.
- Complete using the GCF: 66 + 55 = 11(6 + □) → 5Prompt: 11(6 + □) means 11 × 6 + 11 × □.
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: Greatest common factor of two or three numbers.
- 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