Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Factorise linear expressions
Algebra
CCSS 6.EE.A.3CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Factorise linear expressions.
- 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: Expand brackets (distributive property); Greatest common factor and least common multiple
Leads to: Factorise quadratics x² + bx + c; Factorise fully, including variable and negative common factors; Take out the greatest common factor of a polynomial
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Expand brackets (distributive property); Greatest common factor and least common multiple). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand: 3(x − 5) → 3x-15Prompt: Multiply every term inside the bracket by the number outside.
- Find the greatest common factor (highest common factor) of 72 and 40. → 8Prompt: List the factors of each number.
- Expand: −4(6x + 6) → -24x-24Prompt: The negative outside multiplies every term inside.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Factorise linear expressions. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is the highest common factor of the terms in 8x + 12?
- Step 1: 8x + 12 = 4(2x + 3)
- Answer: 4
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- What is the highest common factor of the terms in 15x − 10? → 5Prompt: Find the largest number that divides both coefficients.
- Which is 25x + 5 fully factorised? (5x(5x + 1) / 5(5x + 1) / 25(x + 1) / 5(6x + 1)) → 5(5x + 1)Prompt: Take out the highest common factor of both terms.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Which is 48x + 8 fully factorised? (8(6x + 8) / 2(24x + 4) / 8x(6x + 1) / 8(6x + 1)) → 8(6x + 1)Prompt: Take out the highest common factor of both terms.
- Factorise fully: 3x² + 3x (3(x² + x) / 3x(x² + 1) / x(3x + 3) / 3x(x + 1)) → 3x(x + 1)Prompt: Both terms share a number AND an x.
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: Expand brackets (distributive property).
- 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
- Move on to: Factorise quadratics x² + bx + c; Factorise fully, including variable and negative common factors; Take out the greatest common factor of a polynomial.
- 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