3A · Chapter 5 · Lesson 6
Multiply a 3-digit Number with Regrouping Once
Multiply hundreds, tens, and ones by one digit with one exchange.
Today's challenge
Calculate 329 × 2 and show the exchanges. Try your own method, then compare it with a model.
What you'll learn
- Multiply hundreds, tens, and ones by one digit with one exchange.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Two-digit multiplication and place value.
Prerequisite competency: 3A-C05-L04
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Calculate 37 × 2 and show the exchanges.
Show answer and reasoning
Answer: 74
37×2 = 0 + 60 + 14 = 74; combine partial products and exchange groups of ten.
- E2
Calculate 47 × 2 and show the exchanges.
Show answer and reasoning
Answer: 94
47×2 = 0 + 80 + 14 = 94; combine partial products and exchange groups of ten.
Learn the concept
Words to know
- three-digit number
- a number from 100 through 999
- regrouping
- an exchange of place-value units
Multiply hundreds, tens, and ones by one digit with one exchange.
Write the hundreds, tens, and ones. Multiply each place by the one-digit factor; perform the needed exchange and combine.
Why this works
A three-digit product can need just one exchange. In 126 × 2, the 6 ones make 12, so record two ones and exchange one ten. The 2 tens × 2 plus the carried ten becomes five tens, while one hundred × 2 becomes two hundreds. The product is 252.
Check the meaning
Watch where the carry goes: ten tens equals one hundred, not ten hundreds.
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 329 × 2 and show the exchanges.
- 9 1-unit groups × 2, plus 0 carried 1-unit groups, gives 18 groups. Write 8 in the 1s place and exchange 1 groups into the next place.
- 2 10-unit groups × 2, plus 1 carried 10-unit groups, gives 5 groups. Write 5 in the 10s place.
- 3 100-unit groups × 2, plus 0 carried 100-unit groups, gives 6 groups. Write 6 in the 100s place.
- Check by partial products: 600 + 40 + 18 = 658.
Result: 658
Understanding check 1 — your turn
Calculate 327 × 2 and show the exchanges.
Reveal reasoning
Answer: 654 — 327×2 = 600 + 40 + 14 = 654; combine partial products and exchange groups of ten.
Worked example 2
Reason and verify
Calculate 139 × 2 and show the exchanges.
- 9 1-unit groups × 2, plus 0 carried 1-unit groups, gives 18 groups. Write 8 in the 1s place and exchange 1 groups into the next place.
- 3 10-unit groups × 2, plus 1 carried 10-unit groups, gives 7 groups. Write 7 in the 10s place.
- 1 100-unit groups × 2, plus 0 carried 100-unit groups, gives 2 groups. Write 2 in the 100s place.
- Check by partial products: 200 + 60 + 18 = 278.
Result: 278
Understanding check 2 — your turn
Calculate 137 × 2 and show the exchanges.
Reveal reasoning
Answer: 274 — 137×2 = 200 + 60 + 14 = 274; combine partial products and exchange groups of ten.
Worked example 3
Reason and verify
Calculate 239 × 2 and show the exchanges.
- 9 1-unit groups × 2, plus 0 carried 1-unit groups, gives 18 groups. Write 8 in the 1s place and exchange 1 groups into the next place.
- 3 10-unit groups × 2, plus 1 carried 10-unit groups, gives 7 groups. Write 7 in the 10s place.
- 2 100-unit groups × 2, plus 0 carried 100-unit groups, gives 4 groups. Write 4 in the 100s place.
- Check by partial products: 400 + 60 + 18 = 478.
Result: 478
Understanding check 3 — your turn
Calculate 237 × 2 and show the exchanges.
Reveal reasoning
Answer: 474 — 237×2 = 400 + 60 + 14 = 474; combine partial products and exchange groups of ten.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Calculate 128 × 2 and show the exchanges.
Show answer and reasoning
Answer: 256
128×2 = 200 + 40 + 16 = 256; combine partial products and exchange groups of ten.
- G2
Calculate 228 × 2 and show the exchanges.
Show answer and reasoning
Answer: 456
228×2 = 400 + 40 + 16 = 456; combine partial products and exchange groups of ten.
- G3
Calculate 328 × 2 and show the exchanges.
Show answer and reasoning
Answer: 656
328×2 = 600 + 40 + 16 = 656; combine partial products and exchange groups of ten.
- G4
Calculate 138 × 2 and show the exchanges.
Show answer and reasoning
Answer: 276
138×2 = 200 + 60 + 16 = 276; combine partial products and exchange groups of ten.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Calculate 325 × 2 and show the exchanges.
Show answer and reasoning
Answer: 650
325×2 = 600 + 40 + 10 = 650; combine partial products and exchange groups of ten.
- I2
Calculate 135 × 2 and show the exchanges.
Show answer and reasoning
Answer: 270
135×2 = 200 + 60 + 10 = 270; combine partial products and exchange groups of ten.
- I3
Calculate 235 × 2 and show the exchanges.
Show answer and reasoning
Answer: 470
235×2 = 400 + 60 + 10 = 470; combine partial products and exchange groups of ten.
- I4
Calculate 335 × 2 and show the exchanges.
Show answer and reasoning
Answer: 670
335×2 = 600 + 60 + 10 = 670; combine partial products and exchange groups of ten.
- I5
Calculate 116 × 2 and show the exchanges.
Show answer and reasoning
Answer: 232
116×2 = 200 + 20 + 12 = 232; combine partial products and exchange groups of ten.
- I6
Calculate 216 × 2 and show the exchanges.
Show answer and reasoning
Answer: 432
216×2 = 400 + 20 + 12 = 432; combine partial products and exchange groups of ten.
- I7
Calculate 316 × 2 and show the exchanges.
Show answer and reasoning
Answer: 632
316×2 = 600 + 20 + 12 = 632; combine partial products and exchange groups of ten.
- I8
Calculate 126 × 2 and show the exchanges.
Show answer and reasoning
Answer: 252
126×2 = 200 + 40 + 12 = 252; combine partial products and exchange groups of ten.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Calculate 126 × 2 and identify the one place-value exchange.
Show answer and reasoning
Answer: 252
2×6=12 ones, exchange into 1 ten and 2 ones; 2×2 tens plus carried 1 gives 5 tens; 2×1 hundred gives 2 hundreds.
- C2
Calculate 136×2; identify the place that needs an exchange.
Show answer and reasoning
Answer: 272; ones
6×2=12 ones=1 ten+2 ones. Three tens×2 plus the carried ten gives 7 tens; 1 hundred×2 gives 2 hundreds. Product 272.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 115 × 2 and show the exchanges.
Show answer and reasoning
Answer: 230
115×2 = 200 + 20 + 10 = 230; combine partial products and exchange groups of ten.
- E2
Calculate 215 × 2 and show the exchanges.
Show answer and reasoning
Answer: 430
215×2 = 400 + 20 + 10 = 430; combine partial products and exchange groups of ten.
- E3
Calculate 315 × 2 and show the exchanges.
Show answer and reasoning
Answer: 630
315×2 = 600 + 20 + 10 = 630; combine partial products and exchange groups of ten.