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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.
  1. Solve: 8x − 8 = −32 → x = -3Prompt: First undo the subtraction: add 8 on both sides.
  2. Solve: 18 − 9x = 90 → x = -8Prompt: Subtract 18 from both sides.
  3. Mei solved 2x + 10 = −2 and got x = 4. Check by substituting, then give the correct solution. → x = -6Prompt: To undo + 10, 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.
  1. Solving 6x + 10 = -2: Step 1: 6x = 8. Step 2: x = 1.33. Where is the first mistake? (Step 1 / Step 2 / No mistake) → Step 1Prompt: Step 1 should undo + 10.
  2. Sofia expanded 3(x + 4) = 0 as 3x + 4 = 0, which gives a wrong answer. What is the correct value of x? → x = -4Prompt: Sofia forgot to multiply 4 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.
  1. Diego expanded 5(x + 7) = 80 as 5x + 7 = 80, which gives a wrong answer. What is the correct value of x? → x = 9Prompt: Diego forgot to multiply 7 by 5.
  2. Solving 3x + 10 = 28: Step 1: 3x = 18. Step 2: x = 15. Where is the first mistake? (Step 1 / Step 2 / No mistake) → Step 2Prompt: Step 1 should undo + 10.

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

eurekami

Find and fix mistakes in equation solutions

Name

Date

Score/ 8

  1. Question 1

    Solving 5x + 5 = -20: Step 1: 5x = -25. Step 2: x = −5. Where is the first mistake?

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

  2. Question 2

    Nia expanded 4(x + 5) = 4 as 4x + 5 = 4, which gives a wrong answer. What is the correct value of x?

    x =

  3. Question 3

    Solving 4x + 13 = 29: Step 1: 4x = 42. Step 2: x = 10.5. Where is the first mistake?

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

  4. Question 4

    Kofi expanded 5(x + 4) = 0 as 5x + 4 = 0, which gives a wrong answer. What is the correct value of x?

    x =

  5. Question 5

    Solving 9x + 13 = 40: Step 1: 9x = 53. Step 2: x = 5.89. Where is the first mistake?

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

  6. Question 6

    Aisha expanded 4(x + 7) = 56 as 4x + 7 = 56, which gives a wrong answer. What is the correct value of x?

    x =

  7. Question 7

    Solving 3x + 4 = 37: Step 1: 3x = 33. Step 2: x = 30. Where is the first mistake?

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

  8. Question 8

    Leo expanded 2(x + 6) = 22 as 2x + 6 = 22, 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 = -4

  3. 3. A. Step 1

  4. 4. x = -4

  5. 5. A. Step 1

  6. 6. x = 7

  7. 7. B. Step 2

  8. 8. x = 5