Find the error: order of operations

A find-the-error worksheet for multiply before adding, exponents before everything: 3 + 4 × 6, 20 − 6 + 3, 5 + 3². Each problem shows a student's worked solution with one planted mistake; students find the wrong step, name the misconception and solve it correctly. The answer key is computed, so it is always right.

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Mistakes this sheet plants

Worked left to right, ignoring multiplication first. Multiplication comes before addition: 9 × 5 first.Example: 13 + 9 × 5 − 5 worked to 105 instead of 53.
Added before subtracting. Addition and subtraction have the same rank: work them from left to right.Example: 33 − 13 + 11 worked to 9 instead of 31.
Read the exponent as multiplication. 3² means 3 × 3 = 9, not 3 × 2.Example: 11 + 6 × 3² worked to 47 instead of 65.

Grade 6 · 5.OA.A.1, 6.EE.A.2c

Find the error: order of operations

Name Date

Each problem was solved by a student, and each has exactly one mistake. Find the step with the mistake, say what went wrong, and solve the problem correctly.

1 11 + 6 × 3²

Finn's work
1. Exponent first: 3² = 3 × 2 = 6.
2. Multiply: 6 × 6 = 36.
3. Add: 11 + 36 = 47.
Finn's answer: 47

Wrong step: What went wrong: Correct answer:
2 13 + 9 × 5 − 5

Theo's work
1. Work left to right: 13 + 9 = 22.
2. 22 × 5 = 110.
3. 110 − 5 = 105.
Theo's answer: 105

Wrong step: What went wrong: Correct answer:
3 33 − 13 + 11

Sam's work
1. Add first: 13 + 11 = 24.
2. 33 − 24 = 9.
Sam's answer: 9

Wrong step: What went wrong: Correct answer:
4 17 − 5 + 6

Ana's work
1. Add first: 5 + 6 = 11.
2. 17 − 11 = 6.
Ana's answer: 6

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 6 · 5.OA.A.1, 6.EE.A.2c

Find the error: order of operations

#	Wrong step	The mistake	Correct answer
1	Step 1	Read the exponent as multiplication. 3² means 3 × 3 = 9, not 3 × 2.Correct step 1: Exponent first: 3² = 3 × 3 = 9.	65not 47
2	Step 1	Worked left to right, ignoring multiplication first. Multiplication comes before addition: 9 × 5 first.Correct step 1: Multiply first: 9 × 5 = 45.	53not 105
3	Step 1	Added before subtracting. Addition and subtraction have the same rank: work them from left to right.Correct step 1: Left to right, subtract first: 33 − 13 = 20.	31not 9
4	Step 1	Added before subtracting. Addition and subtraction have the same rank: work them from left to right.Correct step 1: Left to right, subtract first: 17 − 5 = 12.	18not 6

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