Find the error: one-step equations

A find-the-error worksheet for solving x + a = b, x − a = b and ax = b with inverse operations. 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

Used the same operation instead of the inverse. To undo − 4, add 4 to both sides.Example: y − 4 = 9 worked to 5 instead of 13.
Divided the wrong way round. To undo × 6, divide both sides by 6: 90 ÷ 6, not 6 ÷ 90.Example: 6m = 90 worked to 1/15 instead of 15.
Subtracted the coefficient instead of dividing. 6x means 6 × x, so divide both sides by 6.Example: 6x = 60 worked to 54 instead of 10.

Grade 6 · 6.EE.B.7

Find the error: one-step equations

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 y − 4 = 9

Finn's work
1. Subtract 4 from both sides: y = 9 − 4.
2. y = 5.
Finn's answer: 5

Wrong step: What went wrong: Correct answer:
2 6x = 60

Noah's work
1. Subtract 6 from both sides: x = 60 − 6.
2. x = 54.
Noah's answer: 54

Wrong step: What went wrong: Correct answer:
3 6m = 90

Omar's work
1. Divide: m = 6 ÷ 90.
2. m = 115.
Omar's answer: 115

Wrong step: What went wrong: Correct answer:
4 4y = 32

Mia's work
1. Subtract 4 from both sides: y = 32 − 4.
2. y = 28.
Mia's answer: 28

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 6 · 6.EE.B.7

Find the error: one-step equations

#	Wrong step	The mistake	Correct answer
1	Step 1	Used the same operation instead of the inverse. To undo − 4, add 4 to both sides.Correct step 1: Add 4 to both sides: y = 9 + 4.	13not 5
2	Step 1	Subtracted the coefficient instead of dividing. 6x means 6 × x, so divide both sides by 6.Correct step 1: Divide both sides by 6: x = 60 ÷ 6.	10not 54
3	Step 1	Divided the wrong way round. To undo × 6, divide both sides by 6: 90 ÷ 6, not 6 ÷ 90.Correct step 1: Divide both sides by 6: m = 90 ÷ 6.	15not 115
4	Step 1	Subtracted the coefficient instead of dividing. 4y means 4 × y, so divide both sides by 4.Correct step 1: Divide both sides by 4: y = 32 ÷ 4.	8not 28

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