3A · Chapter 6 · Lesson 3
Dividing a 2-digit Number by 2 — Part 2
Exchange a ten for ten ones when halving an odd number of tens.
Today's challenge
Calculate 94 ÷ 2. Explain how you check your quotient. Try your own method, then compare it with a model.
What you'll learn
- Exchange a ten for ten ones when halving an odd number of tens.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Dividing even tens and ones.
Prerequisite competency: 3A-C06-L02
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Calculate 62 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 31
Group 62 into 2 equal parts using place-value exchanges. Each group has 31. Verify 31×2=62.
- E2
Calculate 82 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 41
Group 82 into 2 equal parts using place-value exchanges. Each group has 41. Verify 41×2=82.
Learn the concept
Words to know
- exchange
- rename one ten as ten ones
- quotient
- the result of division
Exchange a ten for ten ones when halving an odd number of tens.
If a number has an odd number of tens, share the complete tens, then exchange the last ten into ten ones. Combine it with the existing ones.
Why this works
If a tens digit cannot be shared evenly, exchange one ten into ten ones. In 74 ÷ 2, share six tens so each group has three tens; rename the remaining ten along with four ones as 14 ones. Share those to get seven ones each. The answer is 37.
Check the meaning
Equal sharing does not discard the exchanged ten: its ten ones are still present.
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 94 ÷ 2. Explain how you check your quotient.
- At the 10s place, make groups of 2: record 4 quotient digit and exchange remainder 1 to smaller units.
- At the 1s place, make groups of 2: record 7 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 47. Check: 47 × 2 = 94.
Result: 47
Understanding check 1 — your turn
Calculate 70 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 35 — Group 70 into 2 equal parts using place-value exchanges. Each group has 35. Verify 35×2=70.
Worked example 2
Reason and verify
Calculate 36 ÷ 2. Explain how you check your quotient.
- At the 10s place, make groups of 2: record 1 quotient digit and exchange remainder 1 to smaller units.
- At the 1s place, make groups of 2: record 8 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 18. Check: 18 × 2 = 36.
Result: 18
Understanding check 2 — your turn
Calculate 90 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 45 — Group 90 into 2 equal parts using place-value exchanges. Each group has 45. Verify 45×2=90.
Worked example 3
Reason and verify
Calculate 56 ÷ 2. Explain how you check your quotient.
- At the 10s place, make groups of 2: record 2 quotient digit and exchange remainder 1 to smaller units.
- At the 1s place, make groups of 2: record 8 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 28. Check: 28 × 2 = 56.
Result: 28
Understanding check 3 — your turn
Calculate 32 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 16 — Group 32 into 2 equal parts using place-value exchanges. Each group has 16. Verify 16×2=32.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 30 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 15
Group 30 into 2 equal parts using place-value exchanges. Each group has 15. Verify 15×2=30.
- G2
Calculate 50 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 25
Group 50 into 2 equal parts using place-value exchanges. Each group has 25. Verify 25×2=50.
- G3
Calculate 70 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 35
Group 70 into 2 equal parts using place-value exchanges. Each group has 35. Verify 35×2=70.
- G4
Calculate 90 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 45
Group 90 into 2 equal parts using place-value exchanges. Each group has 45. Verify 45×2=90.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 32 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 16
Group 32 into 2 equal parts using place-value exchanges. Each group has 16. Verify 16×2=32.
- I2
Calculate 52 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 26
Group 52 into 2 equal parts using place-value exchanges. Each group has 26. Verify 26×2=52.
- I3
Calculate 72 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 36
Group 72 into 2 equal parts using place-value exchanges. Each group has 36. Verify 36×2=72.
- I4
Calculate 92 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 46
Group 92 into 2 equal parts using place-value exchanges. Each group has 46. Verify 46×2=92.
- I5
Calculate 34 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 17
Group 34 into 2 equal parts using place-value exchanges. Each group has 17. Verify 17×2=34.
- I6
Calculate 54 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 27
Group 54 into 2 equal parts using place-value exchanges. Each group has 27. Verify 27×2=54.
- I7
Calculate 74 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 37
Group 74 into 2 equal parts using place-value exchanges. Each group has 37. Verify 37×2=74.
- I8
Calculate 94 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 47
Group 94 into 2 equal parts using place-value exchanges. Each group has 47. Verify 47×2=94.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Explain how to divide 54 by 2 when five tens cannot be halved evenly.
Show answer and reasoning
Answer: 27
Share four tens as two tens each, exchange the remaining ten to get 14 ones, and share seven ones each: 27.
- C2
A child tries 74÷2 and says the seven tens cannot be shared. Show the exchange and quotient.
Show answer and reasoning
Answer: 37
Share 6 tens as 3 tens each; exchange the remaining ten into 10 ones, combining with 4 ones to make 14 ones. Share 7 ones each: 37.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 36 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 18
Group 36 into 2 equal parts using place-value exchanges. Each group has 18. Verify 18×2=36.
- E2
Calculate 56 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 28
Group 56 into 2 equal parts using place-value exchanges. Each group has 28. Verify 28×2=56.
- E3
Calculate 76 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 38
Group 76 into 2 equal parts using place-value exchanges. Each group has 38. Verify 38×2=76.