3A · Chapter 6 · Lesson 2
Dividing a 2-digit Number by 2 — Part 1
Partition a two-digit number into tens and ones that divide evenly by 2.
Today's challenge
Calculate 42 ÷ 2. Explain how you check your quotient. Try your own method, then compare it with a model.
What you'll learn
- Partition a two-digit number into tens and ones that divide evenly by 2.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Equal halves and place value.
Prerequisite competency: 3A-C06-L01
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Calculate 1,400 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 700
Group 1,400 into 2 equal parts using place-value exchanges. Each group has 700. Verify 700×2=1,400.
- E2
Calculate 60 ÷ 3. Explain how you check your quotient.
Show answer and reasoning
Answer: 20
Group 60 into 3 equal parts using place-value exchanges. Each group has 20. Verify 20×3=60.
Learn the concept
Words to know
- halve
- divide into two equal parts
- quotient
- the result of division
Partition a two-digit number into tens and ones that divide evenly by 2.
Break an even-ten number into tens and ones that can be split evenly. Divide each part by two and recombine.
Why this works
Numbers can be divided in convenient parts when each part divides evenly. To find half of 86, split it into 80 and 6. Half of 80 is 40, and half of 6 is 3, so half of 86 is 43. Putting the two equal shares together returns 86.
Check the meaning
Verify by doubling the quotient.
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 42 ÷ 2. Explain how you check your quotient.
- At the 10s place, make groups of 2: record 2 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 2: record 1 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 21. Check: 21 × 2 = 42.
Result: 21
Understanding check 1 — your turn
Calculate 84 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 42 — Group 84 into 2 equal parts using place-value exchanges. Each group has 42. Verify 42×2=84.
Worked example 2
Reason and verify
Calculate 62 ÷ 2. Explain how you check your quotient.
- At the 10s place, make groups of 2: record 3 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 2: record 1 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 31. Check: 31 × 2 = 62.
Result: 31
Understanding check 2 — your turn
Calculate 26 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 13 — Group 26 into 2 equal parts using place-value exchanges. Each group has 13. Verify 13×2=26.
Worked example 3
Reason and verify
Calculate 82 ÷ 2. Explain how you check your quotient.
- At the 10s place, make groups of 2: record 4 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 2: record 1 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 41. Check: 41 × 2 = 82.
Result: 41
Understanding check 3 — your turn
Calculate 46 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 23 — Group 46 into 2 equal parts using place-value exchanges. Each group has 23. Verify 23×2=46.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 24 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 12
Group 24 into 2 equal parts using place-value exchanges. Each group has 12. Verify 12×2=24.
- G2
Calculate 44 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 22
Group 44 into 2 equal parts using place-value exchanges. Each group has 22. Verify 22×2=44.
- G3
Calculate 64 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 32
Group 64 into 2 equal parts using place-value exchanges. Each group has 32. Verify 32×2=64.
- G4
Calculate 84 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 42
Group 84 into 2 equal parts using place-value exchanges. Each group has 42. Verify 42×2=84.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 26 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 13
Group 26 into 2 equal parts using place-value exchanges. Each group has 13. Verify 13×2=26.
- I2
Calculate 46 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 23
Group 46 into 2 equal parts using place-value exchanges. Each group has 23. Verify 23×2=46.
- I3
Calculate 66 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 33
Group 66 into 2 equal parts using place-value exchanges. Each group has 33. Verify 33×2=66.
- I4
Calculate 86 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 43
Group 86 into 2 equal parts using place-value exchanges. Each group has 43. Verify 43×2=86.
- I5
Calculate 28 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 14
Group 28 into 2 equal parts using place-value exchanges. Each group has 14. Verify 14×2=28.
- I6
Calculate 48 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 24
Group 48 into 2 equal parts using place-value exchanges. Each group has 24. Verify 24×2=48.
- I7
Calculate 68 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 34
Group 68 into 2 equal parts using place-value exchanges. Each group has 34. Verify 34×2=68.
- I8
Calculate 88 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 44
Group 88 into 2 equal parts using place-value exchanges. Each group has 44. Verify 44×2=88.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Why can you halve 84 as 80÷2 + 4÷2?
Show answer and reasoning
Answer: 42
Because 84=80+4 and equal halving distributes over the sum: 40+2=42.
- C2
Split 86 into 80+6 and halve each part. Why does this give the same answer as one division?
Show answer and reasoning
Answer: 43
(80+6)÷2 = 40+3=43; both parts are split into the same two groups.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 22 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 11
Group 22 into 2 equal parts using place-value exchanges. Each group has 11. Verify 11×2=22.
- E2
Calculate 42 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 21
Group 42 into 2 equal parts using place-value exchanges. Each group has 21. Verify 21×2=42.
- E3
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.