Math lesson plan · 8th grade (Year 9 in England) · 60 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 · 6 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: 5(x + 3) → 5x+15Prompt: Multiply every term inside the bracket by the number outside.
- Solve: −6x − 18 = −18 → x = 0Prompt: Add 18 to both sides.
- Expand: 2(x − 8) → 2x-16Prompt: Multiply every term inside the bracket by the number outside.
Hook · 6 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 · 12 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 · 12 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 − 13 = 5x − 9 → x = -2Prompt: Collect the x terms on one side.
- Solve: 4(x + 6) = 1(x − 3) + 9 → x = -6Prompt: Expand the brackets on both sides first.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: 7x − 6 = 8x − 17 → x = 11Prompt: Collect the x terms on one side.
- Solve: 3(x + 2) = 2(x + 5) → x = 4Prompt: Expand both brackets.
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