3A · Chapter 6 · Lesson 7
Dividing a 3-digit Number, Quotient is 2 Digits
Understand why a three-digit dividend can produce a two-digit quotient.
Today's challenge
Calculate 385 ÷ 5. Explain how you check your quotient. Try your own method, then compare it with a model.
What you'll learn
- Understand why a three-digit dividend can produce a two-digit quotient.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Three-digit division by one digit.
Prerequisite competency: 3A-C06-L06
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Calculate 575 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 115
Group 575 into 5 equal parts using place-value exchanges. Each group has 115. Verify 115×5=575.
- E2
Calculate 378 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 126
Group 378 into 3 equal parts using place-value exchanges. Each group has 126. Verify 126×3=378.
Learn the concept
Words to know
- quotient
- the result of division
- place value
- the size of each digit’s unit
Understand why a three-digit dividend can produce a two-digit quotient.
If the hundreds are fewer than the groups, rename hundreds as tens before dividing. The quotient may start in the tens place.
Why this works
Three digits in the number being divided do not guarantee three digits in the answer. When 168 is shared among four groups, each group cannot receive 100 because that would require 400. Exchange the hundreds into smaller units and divide: 168 ÷ 4 = 42.
Check the meaning
Estimate divisor × 100 to see why a quotient of 100 or more would be impossible.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
Calculate 385 ÷ 5. Explain how you check your quotient.
- At the 100s place, make groups of 5: record 0 quotient digit and exchange remainder 3 to smaller units.
- At the 10s place, make groups of 5: record 7 quotient digit and exchange remainder 3 to smaller units.
- At the 1s place, make groups of 5: record 7 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 77. Check: 77 × 5 = 385.
Result: 77
Understanding check 1 — your turn
Calculate 282 ÷ 3. Explain how you check your quotient.
Reveal reasoning
Answer: 94 — Group 282 into 3 equal parts using place-value exchanges. Each group has 94. Verify 94×3=282.
Worked example 2
Reason and verify
Calculate 258 ÷ 3. Explain how you check your quotient.
- At the 100s place, make groups of 3: record 0 quotient digit and exchange remainder 2 to smaller units.
- At the 10s place, make groups of 3: record 8 quotient digit and exchange remainder 1 to smaller units.
- At the 1s place, make groups of 3: record 6 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 86. Check: 86 × 3 = 258.
Result: 86
Understanding check 2 — your turn
Calculate 192 ÷ 4. Explain how you check your quotient.
Reveal reasoning
Answer: 48 — Group 192 into 4 equal parts using place-value exchanges. Each group has 48. Verify 48×4=192.
Worked example 3
Reason and verify
Calculate 160 ÷ 4. Explain how you check your quotient.
- At the 100s place, make groups of 4: record 0 quotient digit and exchange remainder 1 to smaller units.
- At the 10s place, make groups of 4: record 4 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 4: record 0 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 40. Check: 40 × 4 = 160.
Result: 40
Understanding check 3 — your turn
Calculate 285 ÷ 5. Explain how you check your quotient.
Reveal reasoning
Answer: 57 — Group 285 into 5 equal parts using place-value exchanges. Each group has 57. Verify 57×5=285.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 292 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 73
Group 292 into 4 equal parts using place-value exchanges. Each group has 73. Verify 73×4=292.
- G2
Calculate 410 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 82
Group 410 into 5 equal parts using place-value exchanges. Each group has 82. Verify 82×5=410.
- G3
Calculate 273 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 91
Group 273 into 3 equal parts using place-value exchanges. Each group has 91. Verify 91×3=273.
- G4
Calculate 184 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 46
Group 184 into 4 equal parts using place-value exchanges. Each group has 46. Verify 46×4=184.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 132 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 44
Group 132 into 3 equal parts using place-value exchanges. Each group has 44. Verify 44×3=132.
- I2
Calculate 212 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 53
Group 212 into 4 equal parts using place-value exchanges. Each group has 53. Verify 53×4=212.
- I3
Calculate 310 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 62
Group 310 into 5 equal parts using place-value exchanges. Each group has 62. Verify 62×5=310.
- I4
Calculate 213 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 71
Group 213 into 3 equal parts using place-value exchanges. Each group has 71. Verify 71×3=213.
- I5
Calculate 320 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 80
Group 320 into 4 equal parts using place-value exchanges. Each group has 80. Verify 80×4=320.
- I6
Calculate 450 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 90
Group 450 into 5 equal parts using place-value exchanges. Each group has 90. Verify 90×5=450.
- I7
Calculate 445 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 89
Group 445 into 5 equal parts using place-value exchanges. Each group has 89. Verify 89×5=445.
- I8
Calculate 129 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 43
Group 129 into 3 equal parts using place-value exchanges. Each group has 43. Verify 43×3=129.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Why can 168 ÷ 4 have a two-digit answer although 168 has three digits?
Show answer and reasoning
Answer: 42
Four groups of 100 would require 400, more than 168. Instead 168÷4=42, which is two-digit.
- C2
A class has 168 pencils for 4 tables. Prove each table gets fewer than 100 pencils, then find the share.
Show answer and reasoning
Answer: 42 pencils
100 per table would require 400 pencils, which is too many. 168÷4=42, checked 42×4=168.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 160 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 40
Group 160 into 4 equal parts using place-value exchanges. Each group has 40. Verify 40×4=160.
- E2
Calculate 245 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 49
Group 245 into 5 equal parts using place-value exchanges. Each group has 49. Verify 49×5=245.
- E3
Calculate 177 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 59
Group 177 into 3 equal parts using place-value exchanges. Each group has 59. Verify 59×3=177.