Math lesson plan · 8th grade (Year 9 in England) · 45 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 · 5 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: 2(x − 7) → 2x-14Prompt: Multiply every term inside the bracket by the number outside.
- Solve: 4x − 13 = −1 → x = 3Prompt: Add 13 to both sides.
- Expand: 7(x + 3) → 7x+21Prompt: Multiply every term inside the bracket by the number outside.
Hook · 5 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 · 10 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 · 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: 4x − 11 = 7x − 35 → x = 8Prompt: Collect the x terms on one side.
- Solve: 4(x + 7) = 1(x − 5) + 33 → x = 0Prompt: Expand the brackets on both sides first.
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: 4(x − 4) = 1(x + 7) − 8 → x = 5Prompt: Expand the brackets on both sides first.
- How many solutions does 2x + 4 = 2x + 4 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