Students fix three remainder errors — wrong quotients in 57 ÷ 4, 150 ÷ 7, and 239 ÷ 6. Part B has three fill-in-the-blank problems finding missing remainders in 85 ÷ 6, 193 ÷ 8, and 100 ÷ 7. Part C has two short-answer questions about why remainders must be smaller than the divisor and a sticker-sharing problem.
Verifying that remainders are less than the divisor forces students to engage with what division means, not just follow steps.
Style:
Long Division
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
57 ÷ 4 = 13 R5 because 4 × 13 = 52 and 57 − 52 = 5.
Rewrite: 57 ÷ 4 = 14 R1 because 4 × 14 = 56 and 57 − 56 = 1.
2. Fix the sentence:
150 ÷ 7 = 22 R1 because 7 × 22 = 154 and 154 − 150 = 1.
Rewrite: 150 ÷ 7 = 21 R3 because 7 × 21 = 147 and 150 − 147 = 3.
3. Fix the sentence:
239 ÷ 6 = 40 R1 because 6 × 40 = 240 and 240 − 239 = 1.
Rewrite: 239 ÷ 6 = 39 R5 because 6 × 39 = 234 and 239 − 234 = 5.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 85 ÷ 6 = 14 R 1
2. 193 ÷ 8 = 24 R1
3. 100 ÷ 7 = 14 R 2
4. 347 ÷ 9 = 38 R 5
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why must a remainder always be less than the divisor?
If the remainder equals or exceeds the divisor, you can divide one more time, so the quotient should be larger.
2. A teacher has 53 stickers to share equally among 8 students. How many does each student get, and how many are left over?
Each student gets 6 stickers with 5 left over because 8 × 6 = 48 and 53 − 48 = 5.
Long Division
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
57 ÷ 4 = 13 R5 because 4 × 13 = 52 and 57 − 52 = 5.
Rewrite: 57 ÷ 4 = 14 R1 because 4 × 14 = 56 and 57 − 56 = 1.
2) Fix the sentence:
150 ÷ 7 = 22 R1 because 7 × 22 = 154 and 154 − 150 = 1.
Rewrite: 150 ÷ 7 = 21 R3 because 7 × 21 = 147 and 150 − 147 = 3.
3) Fix the sentence:
239 ÷ 6 = 40 R1 because 6 × 40 = 240 and 240 − 239 = 1.
Rewrite: 239 ÷ 6 = 39 R5 because 6 × 39 = 234 and 239 − 234 = 5.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) 85 ÷ 6 = 14 R 1
2) 193 ÷ 8 = 24 R1
3) 100 ÷ 7 = 14 R 2
4) 347 ÷ 9 = 38 R 5
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Why must a remainder always be less than the divisor?
If the remainder equals or exceeds the divisor, you can divide one more time, so the quotient should be larger.
2) A teacher has 53 stickers to share equally among 8 students. How many does each student get, and how many are left over?
Each student gets 6 stickers with 5 left over because 8 × 6 = 48 and 53 − 48 = 5.
Ready to Practice?
Complete each section carefully.
9 Questions
15-20 minutes
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