Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Solve equations with brackets and x on both sides
Algebra
CCSS 8.EE.C.7.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve equations with brackets and x on both sides.
- 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: Solve equations with x on both sides; Expand brackets with a negative multiplier
Leads to: Equations with one solution, no solution or infinitely many
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 (Solve equations with x on both sides; Expand brackets with a negative multiplier). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand −3(x − 2). → -3x+6Prompt: Multiply BOTH terms by −3.
- Solve: −5x − 5 = 2x − 54 → x = 7Prompt: Add 5x to both sides so the x-term stays positive.
- Expand −6(x + 6). → -6x-36Prompt: Multiply BOTH terms by −6.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve equations with brackets and x on both sides. 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: Solve: 4(x + 4) = 2x + 8
- Step 1: 4x + 16 = 2x + 8
- Step 2: 2x = −8
- Step 3: x = −4
- Answer: x = -4
- 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.
- Solve: 3(x + 4) = 5x + 10 → x = 1Prompt: Expand the brackets first.
- Solve: 5(x + 1) = 6(x − 3) + 15 → x = 8Prompt: Expand both brackets.
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.
- Solve: 5(x + 1) = 6(x + 1) − 8 → x = 7Prompt: Expand both brackets.
- A rectangle is (x + 6) cm long and 3 cm wide. A square has sides of (x − 3) cm. Their perimeters are equal, so 2(x + 6 + 3) = 4(x − 3). Find x. → x = 15Prompt: Expand both sides.
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: Solve equations with x on both sides.
- 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: Equations with one solution, no solution or infinitely many.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder