Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Factorise fully, including variable and negative common factors
Algebra
CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Factorise fully, including variable and negative common factors.
- 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: Factorise linear expressions
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Factorise linear expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the highest common factor of the terms in 28x − 36? → 4Prompt: Find the largest number that divides both coefficients.
- Which is 12x + 10 fully factorised? (2x(6x + 5) / 2(6x + 10) / 2(6x + 5) / 12(x + 5)) → 2(6x + 5)Prompt: Take out the highest common factor of both terms.
- Factorise fully: 12x² + 6x (6x(2x² + 1) / 6(2x² + x) / x(12x + 6) / 6x(2x + 1)) → 6x(2x + 1)Prompt: Both terms share a number AND an x.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise fully, including variable and negative common factors. 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: Factorise −2x − 18 by taking out a negative common factor.
- Step 1: −2 × x = −2x, −2 × 9 = −18
- Step 2: −2(x + 9)
- Answer: −2(x + 9)
- 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.
- Factorise −3x − 6 by taking out a negative common factor. (−3(x + 2) / −(3x − 6) / 3(x + 2) / −3(x − 2)) → −3(x + 2)Prompt: Take out −3 from both terms.
- Factorise fully: 7xy + 63x (7x(y + 9) / 7(xy + 9x) / 7x(y + 63) / 7y(x + 9)) → 7x(y + 9)Prompt: Find the HCF of the numbers AND of the letters.
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.
- Factorise −3x − 21 by taking out a negative common factor. (−(3x − 21) / −3(x + 7) / 3(x + 7) / −3(x − 7)) → −3(x + 7)Prompt: Take out −3 from both terms.
- Ben factorises 30x + 36 as 2(15x + 18). Is it fully factorised? (Yes / No, it should be 6(5x + 6)) → No, it should be 6(5x + 6)Prompt: Is there still a common factor inside the brackets?
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Factorise linear expressions.
- Use concrete materials: balance scales or a balance drawing.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder