Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Find and fix mistakes in equation solutions
Algebra
CCSS 7.EE.B.4.AEngland: KS3 Algebra
Objective and success criteria
Students will: Find and fix mistakes in equation solutions.
- 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 two-step equations with negative numbers
Leads to: the next skill in this area.
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 two-step equations with negative numbers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: −6x + 20 = −4 → x = 4Prompt: First undo the addition: subtract 20 on both sides.
- Solve: 11 − 8x = −61 → x = 9Prompt: Subtract 11 from both sides.
- Solve and check by substituting: 4x + 11 = 11 → x = 0Prompt: To undo + 11, do the opposite.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find and fix mistakes in equation solutions. 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: Solving 3x + 6 = 3: Step 1: 3x = -3. Step 2: x = −1. Where is the first mistake?
- Step 1: 3x = 3 − 6 = -3
- Step 2: x = -3 ÷ 3 = −1
- Step 3: No mistake
- Answer: No mistake
- 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.
- Solving 4x + 14 = -10: Step 1: 4x = -24. Step 2: x = −6. Where is the first mistake? (Step 1 / Step 2 / No mistake) → No mistakePrompt: Step 1 should undo + 14.
- Elena expanded 3(x + 1) = -6 as 3x + 1 = -6, which gives a wrong answer. What is the correct value of x? → x = -3Prompt: Elena forgot to multiply 1 by 3.
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.
- Sofia expanded 5(x + 3) = 65 as 5x + 3 = 65, which gives a wrong answer. What is the correct value of x? → x = 10Prompt: Sofia forgot to multiply 3 by 5.
- Solving 5x + 11 = 66: Step 1: 5x = 55. Step 2: x = 11. Where is the first mistake? (Step 1 / Step 2 / No mistake) → No mistakePrompt: Step 1 should undo + 11.
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 two-step equations with negative numbers.
- 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
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder