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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: 5x + 20 = −40 → x = -12Prompt: First undo the addition: subtract 20 on both sides.
  2. Solve: 9 − 2x = 13 → x = -2Prompt: Subtract 9 from both sides.
  3. Hiro solved 2x + 5 = 23 and got x = 14. Check by substituting, then give the correct solution. → x = 9Prompt: To undo + 5, 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 9x + 20 = 20: Step 1: 9x = 0. Step 2: x = -9. Where is the first mistake? (Step 1 / Step 2 / No mistake) → Step 2Prompt: Step 1 should undo + 20.
  2. Zara expanded 4(x + 8) = 16 as 4x + 8 = 16, which gives a wrong answer. What is the correct value of x? → x = -4Prompt: Zara forgot to multiply 8 by 4.

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. Arjun expanded 4(x + 6) = 40 as 4x + 6 = 40, which gives a wrong answer. What is the correct value of x? → x = 4Prompt: Arjun forgot to multiply 6 by 4.
  2. Solving 8x + 7 = -1: Step 1: 8x = -8. Step 2: x = -16. Where is the first mistake? (Step 1 / Step 2 / No mistake) → Step 2Prompt: Step 1 should undo + 7.

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 5x + 19 = -11: Step 1: 5x = -30. Step 2: x = −6. Where is the first mistake?

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

  2. Question 2

    Luis expanded 4(x + 9) = 36 as 4x + 9 = 36, which gives a wrong answer. What is the correct value of x?

    x =

  3. Question 3

    Solving 9x + 2 = -7: Step 1: 9x = -9. Step 2: x = -18. Where is the first mistake?

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

  4. Question 4

    Elena expanded 3(x + 8) = 21 as 3x + 8 = 21, which gives a wrong answer. What is the correct value of x?

    x =

  5. Question 5

    Solving 7x + 11 = -17: Step 1: 7x = -28. Step 2: x = -35. Where is the first mistake?

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

  6. Question 6

    Kwame expanded 3(x + 3) = 33 as 3x + 3 = 33, which gives a wrong answer. What is the correct value of x?

    x =

  7. Question 7

    Solving 3x + 2 = 26: Step 1: 3x = 28. Step 2: x = 9.33. Where is the first mistake?

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

  8. Question 8

    Ava expanded 5(x + 5) = 35 as 5x + 5 = 35, 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 = 0

  3. 3. B. Step 2

  4. 4. x = -1

  5. 5. B. Step 2

  6. 6. x = 8

  7. 7. A. Step 1

  8. 8. x = 2