stepcheck / Skills / 2-digit by 2-digit multiplication
Grade 4 · 4.NBT.B.5, 5.NBT.B.5
Find the error: 2-digit by 2-digit multiplication
A find-the-error worksheet for partial products with the standard algorithm, like 34 × 27. 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.
Mistakes this sheet plants
- Forgot the placeholder zero. The second row multiplies by 7 tens, so it needs a 0 in the ones place: 34 × 70 = 2,380.Example: 34 × 78 worked to 510 instead of 2,652.
- Added the carried digit before multiplying. The carried digit is added after multiplying the next digit, not before.Example: 82 × 35 worked to 2,910 instead of 2,870.
- Multiplied only tens by tens and ones by ones. Each part of 42 must be multiplied by each part of 94: four partial products, not two.Example: 42 × 94 worked to 3,608 instead of 3,948.
Related: 3-digit addition with regrouping · Rounding to the nearest 10, 100 or 1,000 · Subtraction across zeros · Comparing decimals · Multiplying a fraction by a whole number · Adding decimals
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.
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1 34 × 78
Maya's work
34×78272+238510
- Multiply 34 by the ones digit 8: 8 × 4 = 32: write 2, carry 3. 8 × 3 = 24, plus 3 = 27. First partial product: 272.
- Multiply 34 by the tens digit 7: 7 × 4 = 28: write 8, carry 2. 7 × 3 = 21, plus 2 = 23. Second partial product: 238.
- Add the partial products: 272 + 238 = 510.
Maya's answer: 510
Wrong step: What went wrong: Correct answer:
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2 42 × 94
Eli's work
- Tens times tens: 40 × 90 = 3,600.
- Ones times ones: 2 × 4 = 8.
- Add: 3,600 + 8 = 3,608.
Eli's answer: 3,608
Wrong step: What went wrong: Correct answer:
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3 82 × 35
Omar's work
82×35450+24602910
- Multiply 82 by the ones digit 5: 5 × 2 = 10: write 0, carry 1. 8 + 1 = 9, then 9 × 5 = 45. First partial product: 450.
- Multiply 82 by the tens digit 3: write 0 in the ones place, then 3 × 2 = 6: write 6. 3 × 8 = 24. Second partial product: 2,460.
- Add the partial products: 450 + 2,460 = 2,910.
Omar's answer: 2,910
Wrong step: What went wrong: Correct answer:
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4 17 × 13
Mia's work
17×1391+170261
- Multiply 17 by the ones digit 3: 3 × 7 = 21: write 1, carry 2. 1 + 2 = 3, then 3 × 3 = 9. First partial product: 91.
- Multiply 17 by the tens digit 1: write 0 in the ones place, then 1 × 7 = 7: write 7. 1 × 1 = 1. Second partial product: 170.
- Add the partial products: 91 + 170 = 261.
Mia's answer: 261
Wrong step: What went wrong: Correct answer:
| # | Wrong step | The mistake | Correct answer |
|---|
| 1 | Step 2 | Forgot the placeholder zero. The second row multiplies by 7 tens, so it needs a 0 in the ones place: 34 × 70 = 2,380.Correct step 2: Multiply 34 by the tens digit 7: write 0 in the ones place, then 7 × 4 = 28: write 8, carry 2. 7 × 3 = 21, plus 2 = 23. Second partial product: 2,380. | 2,652not 510 |
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| 2 | Step 1 | Multiplied only tens by tens and ones by ones. Each part of 42 must be multiplied by each part of 94: four partial products, not two.Correct step 1: Multiply 42 by the ones digit 4: 4 × 2 = 8: write 8. 4 × 4 = 16. First partial product: 168. | 3,948not 3,608 |
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| 3 | Step 1 | Added the carried digit before multiplying. The carried digit is added after multiplying the next digit, not before.Correct step 1: Multiply 82 by the ones digit 5: 5 × 2 = 10: write 0, carry 1. 5 × 8 = 40, plus 1 = 41. First partial product: 410. | 2,870not 2,910 |
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| 4 | Step 1 | Added the carried digit before multiplying. The carried digit is added after multiplying the next digit, not before.Correct step 1: Multiply 17 by the ones digit 3: 3 × 7 = 21: write 1, carry 2. 3 × 1 = 3, plus 2 = 5. First partial product: 51. | 221not 261 |
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A sample: open this exact sheet or make one with new numbers.