3A · Chapter 6 · Lesson 5
Dividing a 3-digit Number by 2
Divide hundreds, tens, and ones by 2, regrouping when required.
Today's challenge
Calculate 364 ÷ 2. Explain how you check your quotient. Try your own method, then compare it with a model.
What you'll learn
- Divide hundreds, tens, and ones by 2, regrouping when required.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Two-digit division.
Prerequisite competency: 3A-C06-L03
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
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.
- E2
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.
Learn the concept
Words to know
- quotient
- the result of division
- place holder zero
- a zero that records an empty quotient column
Divide hundreds, tens, and ones by 2, regrouping when required.
Share hundreds first; exchange an unshareable hundred into tens, then continue. Record quotient place values carefully.
Why this works
When sharing a three-digit amount, begin with the hundreds. For 408 ÷ 2, share four hundreds into two groups, then share zero tens and eight ones. Each group has 204. The zero in the tens place records that no tens are in each share.
Check the meaning
If a place has no units after grouping, the corresponding quotient digit can be zero.
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 364 ÷ 2. Explain how you check your quotient.
- At the 100s place, make groups of 2: record 1 quotient digit and exchange remainder 1 to smaller units.
- At the 10s place, make groups of 2: record 8 quotient digit; no units remain to exchange.
- At the 1s place, make groups of 2: record 2 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 182. Check: 182 × 2 = 364.
Result: 182
Understanding check 1 — your turn
Calculate 334 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 167 — Group 334 into 2 equal parts using place-value exchanges. Each group has 167. Verify 167×2=334.
Worked example 2
Reason and verify
Calculate 438 ÷ 2. Explain how you check your quotient.
- At the 100s place, make groups of 2: record 2 quotient digit; no units remain to exchange.
- 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 9 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 219. Check: 219 × 2 = 438.
Result: 219
Understanding check 2 — your turn
Calculate 408 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 204 — Group 408 into 2 equal parts using place-value exchanges. Each group has 204. Verify 204×2=408.
Worked example 3
Reason and verify
Calculate 512 ÷ 2. Explain how you check your quotient.
- At the 100s place, make groups of 2: record 2 quotient digit and exchange remainder 1 to smaller units.
- At the 10s place, make groups of 2: record 5 quotient digit and exchange remainder 1 to smaller units.
- At the 1s place, make groups of 2: record 6 quotient digit; no units remain to exchange.
- Read all quotient digits in their correct columns, including zero placeholders: 256. Check: 256 × 2 = 512.
Result: 256
Understanding check 3 — your turn
Calculate 482 ÷ 2. Explain how you check your quotient.
Reveal reasoning
Answer: 241 — Group 482 into 2 equal parts using place-value exchanges. Each group has 241. Verify 241×2=482.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 190 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 95
Group 190 into 2 equal parts using place-value exchanges. Each group has 95. Verify 95×2=190.
- G2
Calculate 264 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 132
Group 264 into 2 equal parts using place-value exchanges. Each group has 132. Verify 132×2=264.
- G3
Calculate 338 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 169
Group 338 into 2 equal parts using place-value exchanges. Each group has 169. Verify 169×2=338.
- G4
Calculate 412 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 206
Group 412 into 2 equal parts using place-value exchanges. Each group has 206. Verify 206×2=412.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 350 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 175
Group 350 into 2 equal parts using place-value exchanges. Each group has 175. Verify 175×2=350.
- I2
Calculate 424 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 212
Group 424 into 2 equal parts using place-value exchanges. Each group has 212. Verify 212×2=424.
- I3
Calculate 498 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 249
Group 498 into 2 equal parts using place-value exchanges. Each group has 249. Verify 249×2=498.
- I4
Calculate 572 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 286
Group 572 into 2 equal parts using place-value exchanges. Each group has 286. Verify 286×2=572.
- I5
Calculate 646 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 323
Group 646 into 2 equal parts using place-value exchanges. Each group has 323. Verify 323×2=646.
- I6
Calculate 720 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 360
Group 720 into 2 equal parts using place-value exchanges. Each group has 360. Verify 360×2=720.
- I7
Calculate 134 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 67
Group 134 into 2 equal parts using place-value exchanges. Each group has 67. Verify 67×2=134.
- I8
Calculate 208 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 104
Group 208 into 2 equal parts using place-value exchanges. Each group has 104. Verify 104×2=208.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Calculate 408 ÷ 2 and explain why there is a zero in the tens place of the quotient.
Show answer and reasoning
Answer: 204
Four hundreds shared in two groups give 2 hundreds each. Zero tens remain zero, and 8 ones give 4 each; the quotient is 204.
- C2
A student writes 606÷2=33 because the tens digit is zero. Explain the missing place and correct answer.
Show answer and reasoning
Answer: 303
Six hundreds make 3 hundreds per group; zero tens makes 0 tens; six ones make 3 ones. The zero placeholder is necessary: 303.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 670 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 335
Group 670 into 2 equal parts using place-value exchanges. Each group has 335. Verify 335×2=670.
- E2
Calculate 744 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 372
Group 744 into 2 equal parts using place-value exchanges. Each group has 372. Verify 372×2=744.
- E3
Calculate 158 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 79
Group 158 into 2 equal parts using place-value exchanges. Each group has 79. Verify 79×2=158.