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Math lesson plan · 7th grade (Year 8 in England) · 60 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 · 6 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.
  1. Solve: 7x + 17 = −53 → x = -10Prompt: First undo the addition: subtract 17 on both sides.
  2. Solve: 2 − 9x = 92 → x = -10Prompt: Subtract 2 from both sides.
  3. Solve and check by substituting: 5x + 7 = −38 → x = -9Prompt: To undo + 7, do the opposite.

Hook · 6 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 · 12 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 · 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.
  1. Solving 7x + 1 = 1: Step 1: 7x = 0. Step 2: x = 0. Where is the first mistake? (Step 1 / Step 2 / No mistake) → No mistakePrompt: Step 1 should undo + 1.
  2. Diego expanded 2(x + 2) = 2 as 2x + 2 = 2, which gives a wrong answer. What is the correct value of x? → x = -1Prompt: Diego forgot to multiply 2 by 2.

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.
  1. Solving 3x + 15 = 30: Step 1: 3x = 15. Step 2: x = 5. Where is the first mistake? (Step 1 / Step 2 / No mistake) → No mistakePrompt: Step 1 should undo + 15.
  2. Leo expanded 2(x + 7) = 8 as 2x + 7 = 8, which gives a wrong answer. What is the correct value of x? → x = -3Prompt: Leo forgot to multiply 7 by 2.

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

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Find and fix mistakes in equation solutions

Name

Date

Score/ 8

  1. Question 1

    Solving 3x + 15 = 24: Step 1: 3x = 9. Step 2: x = 3. Where is the first mistake?

    • A. Step 1
    • B. Step 2
    • C. No mistake

  2. Question 2

    Ava expanded 3(x + 9) = 42 as 3x + 9 = 42, which gives a wrong answer. What is the correct value of x?

    x =

  3. Question 3

    Solving 2x + 8 = 30: Step 1: 2x = 22. Step 2: x = 20. Where is the first mistake?

    • A. Step 1
    • B. Step 2
    • C. No mistake

  4. Question 4

    Mateo expanded 4(x + 9) = 72 as 4x + 9 = 72, which gives a wrong answer. What is the correct value of x?

    x =

  5. Question 5

    Solving 2x + 11 = 21: Step 1: 2x = 32. Step 2: x = 16. Where is the first mistake?

    • A. Step 1
    • B. Step 2
    • C. No mistake

  6. Question 6

    Liam expanded 3(x + 2) = 30 as 3x + 2 = 30, which gives a wrong answer. What is the correct value of x?

    x =

  7. Question 7

    Solving 6x + 8 = 26: Step 1: 6x = 34. Step 2: x = 5.67. Where is the first mistake?

    • A. Step 1
    • B. Step 2
    • C. No mistake

  8. Question 8

    Kofi expanded 3(x + 2) = 3 as 3x + 2 = 3, which gives a wrong answer. What is the correct value of x?

    x =

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Answer key: Find and fix mistakes in equation solutions

  1. 1. C. No mistake

  2. 2. x = 5

  3. 3. B. Step 2

  4. 4. x = 9

  5. 5. A. Step 1

  6. 6. x = 8

  7. 7. A. Step 1

  8. 8. x = -1