Math lesson plan · 7th grade (Year 8 in England) · 30 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 · 4 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 8x + 8? → 8Prompt: Find the largest number that divides both coefficients.
- Which is 28x + 36 fully factorised? (4x(7x + 9) / 2(14x + 18) / 4(7x + 36) / 4(7x + 9)) → 4(7x + 9)Prompt: Take out the highest common factor of both terms.
- Factorise fully: 3x² + 3x (3x(x² + 1) / 3x(x + 1) / x(3x + 3) / 3(x² + x)) → 3x(x + 1)Prompt: Both terms share a number AND an x.
Hook · 3 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 · 7 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 · 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.
- Factorise −6x − 30 by taking out a negative common factor. (−6(x + 5) / 6(x + 5) / −6(x − 5) / −(6x − 30)) → −6(x + 5)Prompt: Take out −6 from both terms.
- Factorise fully: 4xy + 28x (4x(y + 28) / 4x(y + 7) / x(4y + 28) / 4y(x + 7)) → 4x(y + 7)Prompt: Find the HCF of the numbers AND of the letters.
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.
- Kai factorises 16x + 4 as 4(4x + 1). Is it fully factorised? (Yes / No, it should be 4(4x + 1)) → YesPrompt: Is there still a common factor inside the brackets?
- Factorise fully: 5xy + 15x (5x(y + 3) / x(5y + 15) / 5(xy + 3x) / 5y(x + 3)) → 5x(y + 3)Prompt: Find the HCF of the numbers AND of the letters.
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