Math lesson plan · 7th grade (Year 8 in England) · 30 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 · 4 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 − 1) → 3x-3Prompt: Multiply every term inside the bracket by the number outside.
Find the greatest common factor (highest common factor) of 8 and 6. → 2Prompt: List the factors of each number.
Expand: −4(5x − 2) → -20x+8Prompt: The negative outside multiplies every term inside.

Hook · 3 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 · 7 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 · 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.

What is the highest common factor of the terms in 35x − 63? → 7Prompt: Find the largest number that divides both coefficients.
Which is 8x + 12 fully factorised? (4x(2x + 3) / 4(2x + 3) / 8(x + 3) / 4(2x + 12)) → 4(2x + 3)Prompt: Take out the highest common factor of both terms.

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.

Which is 21x + 56 fully factorised? (7(3x + 8) / 21(x + 8) / 7x(3x + 8) / 7(3x + 56)) → 7(3x + 8)Prompt: Take out the highest common factor of both terms.
Factorise fully: 3x² + 3x (3x(x + 1) / 3x(x² + 1) / 3(x² + x) / x(3x + 3)) → 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