Students fix three parentheses errors — each producing a wrong result when the inner group is not evaluated first. Part B has four problems evaluating expressions with parentheses. Part C has two questions comparing expressions with and without parentheses and placing parentheses to reach a target value.
Correcting parentheses evaluation errors and comparing expressions with versus without grouping symbols directly shows fifth graders how parentheses control which operation happens first.
Style:
Order of Operations (PEMDAS)
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
(3 + 5) × 2 = 13
Rewrite: (3 + 5) × 2 = 16
2. Fix the sentence:
4 × (6 - 2) = 22
Rewrite: 4 × (6 - 2) = 16
3. Fix the sentence:
(10 + 2) ÷ 4 = 10.5
Rewrite: (10 + 2) ÷ 4 = 3
Part B: Fill in the Blank
Write the missing word or number on each line.
1. (4 + 6) × 3 = 30.
2. 5 × (8 - 3) = 25.
3. (9 + 1) ÷ 2 = 5.
4. (7 - 4) × (2 + 3) = 15.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Compare 3 × 4 + 2 and 3 × (4 + 2). Are they equal? Explain.
3 × 4 + 2 = 14 because you multiply first: 12 + 2 = 14. But 3 × (4 + 2) = 18 because parentheses come first: 3 × 6 = 18. They are not equal.
2. Where would you place parentheses in 2 + 3 × 4 to make it equal 20?
Place parentheses around 2 + 3 to get (2 + 3) × 4 = 5 × 4 = 20.
Order of Operations (PEMDAS)
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
(3 + 5) × 2 = 13
Rewrite: (3 + 5) × 2 = 16
2) Fix the sentence:
4 × (6 - 2) = 22
Rewrite: 4 × (6 - 2) = 16
3) Fix the sentence:
(10 + 2) ÷ 4 = 10.5
Rewrite: (10 + 2) ÷ 4 = 3
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) (4 + 6) × 3 = 30.
2) 5 × (8 - 3) = 25.
3) (9 + 1) ÷ 2 = 5.
4) (7 - 4) × (2 + 3) = 15.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Compare 3 × 4 + 2 and 3 × (4 + 2). Are they equal? Explain.
3 × 4 + 2 = 14 because you multiply first: 12 + 2 = 14. But 3 × (4 + 2) = 18 because parentheses come first: 3 × 6 = 18. They are not equal.
2) Where would you place parentheses in 2 + 3 × 4 to make it equal 20?
Place parentheses around 2 + 3 to get (2 + 3) × 4 = 5 × 4 = 20.
Ready to Practice?
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9 Questions
15-20 minutes
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