Find the error: the distributive property

A find-the-error worksheet for expanding a(x + b): every term inside gets multiplied, signs included. 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

Multiplied only the first term. 4 multiplies everything in the parentheses, so the 2 also gets multiplied: 4 × 2 = 8.Example: Expand: 4(y + 2) worked to 4y + 2 instead of 4y + 8.
Lost the sign when multiplying by a negative. −8 × (−9) = 72: a negative times a negative is positive.Example: Expand: −8(a − 9) worked to −8a − 72 instead of −8a + 72.

Grade 6 · 6.EE.A.3, 7.EE.A.1

Find the error: the distributive property

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 Expand: 4(y + 2)

Omar's work
1. 4 × y = 4y.
2. The 2 stays as it is: 2.
3. So the answer is 4y + 2.
Omar's answer: 4y + 2

Wrong step: What went wrong: Correct answer:
2 Expand: −8(a − 9)

Mia's work
1. −8 × a = −8a.
2. −8 × (−9) = −72.
3. So the answer is −8a − 72.
Mia's answer: −8a − 72

Wrong step: What went wrong: Correct answer:
3 Expand: 6(n + 1)

Ravi's work
1. 6 × n = 6n.
2. The 1 stays as it is: 1.
3. So the answer is 6n + 1.
Ravi's answer: 6n + 1

Wrong step: What went wrong: Correct answer:
4 Expand: −3(y − 5)

Ivy's work
1. −3 × y = −3y.
2. −3 × (−5) = −15.
3. So the answer is −3y − 15.
Ivy's answer: −3y − 15

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 6 · 6.EE.A.3, 7.EE.A.1

Find the error: the distributive property

#	Wrong step	The mistake	Correct answer
1	Step 2	Multiplied only the first term. 4 multiplies everything in the parentheses, so the 2 also gets multiplied: 4 × 2 = 8.Correct step 2: 4 × 2 = 8.	4y + 8not 4y + 2
2	Step 2	Lost the sign when multiplying by a negative. −8 × (−9) = 72: a negative times a negative is positive.Correct step 2: −8 × (−9) = 72.	−8a + 72not −8a − 72
3	Step 2	Multiplied only the first term. 6 multiplies everything in the parentheses, so the 1 also gets multiplied: 6 × 1 = 6.Correct step 2: 6 × 1 = 6.	6n + 6not 6n + 1
4	Step 2	Lost the sign when multiplying by a negative. −3 × (−5) = 15: a negative times a negative is positive.Correct step 2: −3 × (−5) = 15.	−3y + 15not −3y − 15

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