Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Equations with the unknown on both sides
Algebra
CCSS 8.EE.C.7England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Equations with the unknown 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: Two-step equations; Expand brackets (distributive property)
Leads to: Systems of linear equations (simultaneous equations); Rational equations; Solve equations with x on both sides
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 (Two-step equations; Expand brackets (distributive property)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand: 3(x − 6) → 3x-18Prompt: Multiply every term inside the bracket by the number outside.
- Solve: −2x − 9 = 9 → x = -9Prompt: Add 9 to both sides.
- Expand: 4(x + 8) → 4x+32Prompt: Multiply every term inside the bracket by the number outside.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Equations with the unknown 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: 5x + 10 = 6x + 17
- Step 1: 5x + 10 = 6x + 17
- Step 2: −x + 10 = 17
- Step 3: −x = 7
- Step 4: x = −7
- Answer: x = -7
- 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: 3x − 3 = 2x + 1 → x = 4Prompt: Collect the x terms on one side.
- Solve: 2(x + 8) = 3(x + 5) + 5 → x = -4Prompt: Expand the brackets on both sides first.
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.
- Solve: 5x − 15 = 4x − 12 → x = 3Prompt: Collect the x terms on one side.
- How many solutions does 2x + 8 = 2x + 8 have? (No solution / Infinitely many solutions / Exactly one solution) → Infinitely many solutionsPrompt: Subtract the x terms from both sides. What is left?
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: Two-step equations.
- 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: Systems of linear equations (simultaneous equations); Rational equations; Solve equations with x on both sides.
- 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