Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Solve equations with 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 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: Equations with the unknown on both sides; Solve two-step equations with negative numbers
Leads to: Solve equations with brackets and x on both sides; Solve equations with fractions or decimals on both sides; When are two plans equal? Equations from real comparisons
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 (Equations with the unknown on both sides; Solve two-step equations with negative numbers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 4x + 5 = 7x + 23 → x = -6Prompt: Collect the x terms on one side.
- Solve: −9x + 16 = −92 → x = 12Prompt: First undo the addition: subtract 16 on both sides.
- Solve: 6(x + 4) = 5(x − 2) + 44 → x = 10Prompt: Expand the brackets on both sides first.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve equations with x on both sides. 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: Solve: −6x − 1 = 2x − 17
- Step 1: −1 = 8x − 17
- Step 2: 16 = 8x
- Step 3: x = 2
- Answer: x = 2
- 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.
- Solve: −4x + 5 = 5x − 58 → x = 7Prompt: Add 4x to both sides so the x-term stays positive.
- Omar solved 5x − 6 = 3x − 10 by adding 3x to both sides. Explain the mistake by finding the correct value of x. → x = -2Prompt: To remove 3x from the right, you must SUBTRACT 3x.
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.
- Ravi solved 7x + 9 = 5x + 27 by adding 5x to both sides. Explain the mistake by finding the correct value of x. → x = 9Prompt: To remove 5x from the right, you must SUBTRACT 5x.
- Solve: −3x − 2 = 2x − 7 → x = 1Prompt: Add 3x to both sides so the x-term stays positive.
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: Equations with the unknown 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: Solve equations with brackets and x on both sides; Solve equations with fractions or decimals on both sides; When are two plans equal? Equations from real comparisons.
- 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