3A · Chapter 6 · Lesson 1
Dividing Tens and Hundreds
Divide groups of tens or hundreds, not just strings of digits.
Today's challenge
Calculate 250 ÷ 5. Explain how you check your quotient. Try your own method, then compare it with a model.
What you'll learn
- Divide groups of tens or hundreds, not just strings of digits.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Division facts and place value.
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
64 counters are shared equally among 8 children. How many does each receive?
Show answer and reasoning
Answer: 8
8 equal groups contain 64 counters: 64÷8=8; verify 8×8=64.
- E2
99 counters are shared equally among 9 children. How many does each receive?
Show answer and reasoning
Answer: 11
9 equal groups contain 99 counters: 99÷9=11; verify 11×9=99.
Learn the concept
Words to know
- quotient
- the result of division
- place-value unit
- a one, ten, hundred, or larger group
Divide groups of tens or hundreds, not just strings of digits.
If 240 is 24 tens, divide 24 tens into groups first. Rename the quotient as tens. The same logic works with hundreds.
Why this works
Dividing a place-value unit keeps that unit attached to the answer. Three hundred sixty is 36 tens. Divide 36 tens into three equal groups and each gets 12 tens, which is 120 ones. That is why 360 ÷ 3 = 120, not 12.
Check the meaning
Check by multiplying quotient × divisor in the original units.
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 250 ÷ 5. Explain how you check your quotient.
- At the 100s place, make groups of 5: record 0 quotient digit and exchange remainder 2 to smaller units.
- At the 10s place, make groups of 5: record 5 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 5: record 0 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 50. Check: 50 × 5 = 250.
Result: 50
Understanding check 1 — your turn
Calculate 1,800 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 900 — Group 1,800 into 2 equal parts using place-value exchanges. Each group has 900. Verify 900×2=1,800.
Worked example 2
Reason and verify
Calculate 1,800 ÷ 2. Explain how you check your quotient.
- At the 1,000s place, make groups of 2: record 0 quotient digit and exchange remainder 1 to smaller units.
- At the 100s place, make groups of 2: record 9 quotient digit; no units remain to exchange.
- At the 10s place, make groups of 2: record 0 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 2: record 0 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 900. Check: 900 × 2 = 1,800.
Result: 900
Understanding check 2 — your turn
Calculate 120 ÷ 3. Explain how you check your quotient.
Reveal reasoning
Answer: 40 — Group 120 into 3 equal parts using place-value exchanges. Each group has 40. Verify 40×3=120.
Worked example 3
Reason and verify
Calculate 120 ÷ 3. Explain how you check your quotient.
- At the 100s place, make groups of 3: record 0 quotient digit and exchange remainder 1 to smaller units.
- At the 10s place, make groups of 3: record 4 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 3: record 0 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 40. Check: 40 × 3 = 120.
Result: 40
Understanding check 3 — your turn
Calculate 2,800 ÷ 4. Explain how you check your quotient.
Reveal reasoning
Answer: 700 — Group 2,800 into 4 equal parts using place-value exchanges. Each group has 700. Verify 700×4=2,800.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 800 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 400
Group 800 into 2 equal parts using place-value exchanges. Each group has 400. Verify 400×2=800.
- G2
Calculate 210 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 70
Group 210 into 3 equal parts using place-value exchanges. Each group has 70. Verify 70×3=210.
- G3
Calculate 800 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 200
Group 800 into 4 equal parts using place-value exchanges. Each group has 200. Verify 200×4=800.
- G4
Calculate 250 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 50
Group 250 into 5 equal parts using place-value exchanges. Each group has 50. Verify 50×5=250.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 1,200 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 600
Group 1,200 into 2 equal parts using place-value exchanges. Each group has 600. Verify 600×2=1,200.
- I2
Calculate 270 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 90
Group 270 into 3 equal parts using place-value exchanges. Each group has 90. Verify 90×3=270.
- I3
Calculate 1,600 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 400
Group 1,600 into 4 equal parts using place-value exchanges. Each group has 400. Verify 400×4=1,600.
- I4
Calculate 350 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 70
Group 350 into 5 equal parts using place-value exchanges. Each group has 70. Verify 70×5=350.
- I5
Calculate 400 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 200
Group 400 into 2 equal parts using place-value exchanges. Each group has 200. Verify 200×2=400.
- I6
Calculate 150 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 50
Group 150 into 3 equal parts using place-value exchanges. Each group has 50. Verify 50×3=150.
- I7
Calculate 3,200 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 800
Group 3,200 into 4 equal parts using place-value exchanges. Each group has 800. Verify 800×4=3,200.
- I8
Calculate 150 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 30
Group 150 into 5 equal parts using place-value exchanges. Each group has 30. Verify 30×5=150.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Explain why 360 ÷ 3 is 120 rather than 12.
Show answer and reasoning
Answer: 120
360 is 36 tens. 36 tens ÷3=12 tens = 120 ones.
- C2
A class has 480 stickers and gives the same number to each of 4 groups. Explain why the answer is 120, not 12.
Show answer and reasoning
Answer: 120 per group
480=48 tens, and 48 tens÷4=12 tens = 120 ones.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 600 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 300
Group 600 into 2 equal parts using place-value exchanges. Each group has 300. Verify 300×2=600.
- E2
Calculate 180 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 60
Group 180 into 3 equal parts using place-value exchanges. Each group has 60. Verify 60×3=180.
- E3
Calculate 3,600 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 900
Group 3,600 into 4 equal parts using place-value exchanges. Each group has 900. Verify 900×4=3,600.