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Math lesson plan · 5th grade (Year 6 in England) · 60 minutes

Evaluate expressions with brackets, including nested brackets

Algebra

CCSS 5.OA.A.1England: Y6 Number – multiplication and division

Objective and success criteria

Students will: Evaluate expressions with brackets, including nested brackets.

  • 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: Order of operations

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 (Order of operations). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. 20 + 7 × 2 = ? → 34Prompt: Multiplication comes before addition and subtraction.
  2. (7 + 9) × 5 − 4 = ? → 76Prompt: Brackets first.
  3. (36 − 1) ÷ 5 × 2 + 2² = ? → 18Prompt: Brackets, then powers, then × and ÷ from left to right, then + and −.

Hook · 6 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Evaluate expressions with brackets, including nested brackets. 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: 6 × [14 − (1 + 2)] = ?
  • Step 1: 1 + 2 = 3
  • Step 2: 14 − 3 = 11
  • Step 3: 6 × 11 = 66
  • Answer: 66
  • 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. 3 × [14 − (3 + 4)] = ? → 21Prompt: Work from the innermost brackets outwards.
  2. Liam worked out (5 + 7) × 4 as 33. Spot the mistake. What is the right answer? → 48Prompt: What do the brackets tell you to do 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.
  1. Fatima worked out (7 + 8) × 2 as 23. Spot the mistake. What is the right answer? → 30Prompt: What do the brackets tell you to do first?
  2. 6 × [15 − (1 + 2)] = ? → 72Prompt: Work from the innermost brackets outwards.

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: Order of operations.
  • 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-5.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Evaluate expressions with brackets, including nested brackets

Name

Date

Score/ 8

  1. Question 1

    Where do brackets go to make this true? 45 − 3 × 3 + 5 = 131

    • A. 45 − 3 × 3 + 5
    • B. (45 − 3) × 3 + 5
    • C. 45 − 3 × (3 + 5)
    • D. 45 − (3 × 3 + 5)

  2. Question 2

    3 × [17 − (4 + 3)] = ?

    Answer

  3. Question 3

    Omar worked out (2 + 7) × 4 as 30. Spot the mistake. What is the right answer?

    Answer

  4. Question 4

    Where do brackets go to make this true? 57 − 3 × 4 + 2 = 218

    • A. (57 − 3) × 4 + 2
    • B. 57 − 3 × (4 + 2)
    • C. 57 − 3 × 4 + 2
    • D. 57 − (3 × 4 + 2)

  5. Question 5

    2 × [11 − (2 + 2)] = ?

    Answer

  6. Question 6

    Jamal worked out (8 + 2) × 5 as 18. Spot the mistake. What is the right answer?

    Answer

  7. Question 7

    Where do brackets go to make this true? 52 − 2 × 4 + 5 = 205

    • A. 52 − 2 × (4 + 5)
    • B. 52 − 2 × 4 + 5
    • C. (52 − 2) × 4 + 5
    • D. 52 − (2 × 4 + 5)

  8. Question 8

    5 × [20 − (3 + 4)] = ?

    Answer

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Answer key: Evaluate expressions with brackets, including nested brackets

  1. 1. B. (45 − 3) × 3 + 5

  2. 2. 30

  3. 3. 36

  4. 4. A. (57 − 3) × 4 + 2

  5. 5. 14

  6. 6. 50

  7. 7. C. (52 − 2) × 4 + 5

  8. 8. 65