3A · Chapter 6 · Lesson 4
Dividing a 2-digit Number by 3, 4, and 5
Use multiplication facts and place-value partitions for exact quotients.
Today's challenge
Calculate 65 ÷ 5. Explain how you check your quotient. Try your own method, then compare it with a model.
What you'll learn
- Use multiplication facts and place-value partitions for exact quotients.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Equal-group division by 2.
Prerequisite competency: 3A-C04-L03
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
42 counters are shared equally among 6 children. How many does each receive?
Show answer and reasoning
Answer: 7
6 equal groups contain 42 counters: 42÷6=7; verify 7×6=42.
- E2
70 counters are shared equally among 7 children. How many does each receive?
Show answer and reasoning
Answer: 10
7 equal groups contain 70 counters: 70÷7=10; verify 10×7=70.
Learn the concept
Words to know
- dividend
- the quantity being divided
- divisor
- the number used to divide
Use multiplication facts and place-value partitions for exact quotients.
Identify a convenient product of the divisor and a multiple of ten, then handle what remains. Multiply the proposed quotient by the divisor.
Why this works
Use multiplication facts to check division. For 87 ÷ 3, the answer is 29 because 29 × 3 = 87. When a place cannot be shared exactly, exchange its remaining units into the next smaller place. The quotient must account for every item.
Check the meaning
Check the multiplication rather than relying on the shape of the digits.
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 65 ÷ 5. Explain how you check your quotient.
- At the 10s place, make groups of 5: record 1 quotient digit and exchange remainder 1 to smaller units.
- At the 1s place, make groups of 5: record 3 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 13. Check: 13 × 5 = 65.
Result: 13
Understanding check 1 — your turn
Calculate 87 ÷ 3. Explain how you check your quotient.
Reveal reasoning
Answer: 29 — Group 87 into 3 equal parts using place-value exchanges. Each group has 29. Verify 29×3=87.
Worked example 2
Reason and verify
Calculate 57 ÷ 3. Explain how you check your quotient.
- At the 10s place, make groups of 3: record 1 quotient digit and exchange remainder 2 to smaller units.
- At the 1s place, make groups of 3: record 9 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 19. Check: 19 × 3 = 57.
Result: 19
Understanding check 2 — your turn
Calculate 64 ÷ 4. Explain how you check your quotient.
Reveal reasoning
Answer: 16 — Group 64 into 4 equal parts using place-value exchanges. Each group has 16. Verify 16×4=64.
Worked example 3
Reason and verify
Calculate 60 ÷ 4. Explain how you check your quotient.
- At the 10s place, make groups of 4: record 1 quotient digit and exchange remainder 2 to smaller units.
- At the 1s place, make groups of 4: record 5 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 15. Check: 15 × 4 = 60.
Result: 15
Understanding check 3 — your turn
Calculate 80 ÷ 5. Explain how you check your quotient.
Reveal reasoning
Answer: 16 — Group 80 into 5 equal parts using place-value exchanges. Each group has 16. Verify 16×5=80.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 36 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 9
Group 36 into 4 equal parts using place-value exchanges. Each group has 9. Verify 9×4=36.
- G2
Calculate 50 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 10
Group 50 into 5 equal parts using place-value exchanges. Each group has 10. Verify 10×5=50.
- G3
Calculate 87 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 29
Group 87 into 3 equal parts using place-value exchanges. Each group has 29. Verify 29×3=87.
- G4
Calculate 28 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 7
Group 28 into 4 equal parts using place-value exchanges. Each group has 7. Verify 7×4=28.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 33 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 11
Group 33 into 3 equal parts using place-value exchanges. Each group has 11. Verify 11×3=33.
- I2
Calculate 64 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 16
Group 64 into 4 equal parts using place-value exchanges. Each group has 16. Verify 16×4=64.
- I3
Calculate 70 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 14
Group 70 into 5 equal parts using place-value exchanges. Each group has 14. Verify 14×5=70.
- I4
Calculate 78 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 26
Group 78 into 3 equal parts using place-value exchanges. Each group has 26. Verify 26×3=78.
- I5
Calculate 52 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 13
Group 52 into 4 equal parts using place-value exchanges. Each group has 13. Verify 13×4=52.
- I6
Calculate 80 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 16
Group 80 into 5 equal parts using place-value exchanges. Each group has 16. Verify 16×5=80.
- I7
Calculate 45 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 15
Group 45 into 3 equal parts using place-value exchanges. Each group has 15. Verify 15×3=45.
- I8
Calculate 44 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 11
Group 44 into 4 equal parts using place-value exchanges. Each group has 11. Verify 11×4=44.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Use a multiplication check to show 96 ÷ 4 = 24.
Show answer and reasoning
Answer: 24
24 groups of 4 total 96; equivalently 20×4=80 and 4×4=16.
- C2
A baker has 87 cookies and fills trays of 3. Find the number of full trays and verify by multiplication.
Show answer and reasoning
Answer: 29 trays
87÷3=29, and 29×3=87. No cookies remain.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 90 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 18
Group 90 into 5 equal parts using place-value exchanges. Each group has 18. Verify 18×5=90.
- E2
Calculate 99 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 33
Group 99 into 3 equal parts using place-value exchanges. Each group has 33. Verify 33×3=99.
- E3
Calculate 40 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 8
Group 40 into 5 equal parts using place-value exchanges. Each group has 8. Verify 8×5=40.