3A · Chapter 5 · Lesson 4
Multiplication with Regrouping Ones
Regroup ones into tens in a written multiplication algorithm.
Today's challenge
Calculate 47 × 2 and show the exchanges. Try your own method, then compare it with a model.
What you'll learn
- Regroup ones into tens in a written multiplication algorithm.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
No-regrouping multiplication.
Prerequisite competency: 3A-C05-L02
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Calculate 312 × 2 using partial products.
Show answer and reasoning
Answer: 624
Split 312 by place value; multiply each part by 2 and add. Total is 624.
- E2
Calculate 312 × 3 using partial products.
Show answer and reasoning
Answer: 936
Split 312 by place value; multiply each part by 3 and add. Total is 936.
Learn the concept
Words to know
- exchange
- trade ten ones for one ten
- carry
- a written record of a place-value exchange
Regroup ones into tens in a written multiplication algorithm.
Multiply the ones, turn groups of ten ones into tens, then incorporate those extra tens into the next column.
Why this works
When ones reach ten or more, exchange some for tens. For 27 × 3, multiply 7 × 3 = 21 ones, so record one one and carry two tens. Then 2 tens × 3 plus two carried tens gives eight tens. The product is 81.
Check the meaning
An accurate partial-products breakdown is a reliable independent check.
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 47 × 2 and show the exchanges.
- 7 1-unit groups × 2, plus 0 carried 1-unit groups, gives 14 groups. Write 4 in the 1s place and exchange 1 groups into the next place.
- 4 10-unit groups × 2, plus 1 carried 10-unit groups, gives 9 groups. Write 9 in the 10s place.
- Check by partial products: 80 + 14 = 94.
Result: 94
Understanding check 1 — your turn
Calculate 27 × 2 and show the exchanges.
Reveal reasoning
Answer: 54 — 27×2 = 0 + 40 + 14 = 54; combine partial products and exchange groups of ten.
Worked example 2
Reason and verify
Calculate 18 × 2 and show the exchanges.
- 8 1-unit groups × 2, plus 0 carried 1-unit groups, gives 16 groups. Write 6 in the 1s place and exchange 1 groups into the next place.
- 1 10-unit groups × 2, plus 1 carried 10-unit groups, gives 3 groups. Write 3 in the 10s place.
- Check by partial products: 20 + 16 = 36.
Result: 36
Understanding check 2 — your turn
Calculate 37 × 2 and show the exchanges.
Reveal reasoning
Answer: 74 — 37×2 = 0 + 60 + 14 = 74; combine partial products and exchange groups of ten.
Worked example 3
Reason and verify
Calculate 28 × 2 and show the exchanges.
- 8 1-unit groups × 2, plus 0 carried 1-unit groups, gives 16 groups. Write 6 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.
- Check by partial products: 40 + 16 = 56.
Result: 56
Understanding check 3 — your turn
Calculate 47 × 2 and show the exchanges.
Reveal reasoning
Answer: 94 — 47×2 = 0 + 80 + 14 = 94; 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 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.
- G2
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.
- G3
Calculate 18 × 2 and show the exchanges.
Show answer and reasoning
Answer: 36
18×2 = 0 + 20 + 16 = 36; combine partial products and exchange groups of ten.
- G4
Calculate 28 × 2 and show the exchanges.
Show answer and reasoning
Answer: 56
28×2 = 0 + 40 + 16 = 56; 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 38 × 2 and show the exchanges.
Show answer and reasoning
Answer: 76
38×2 = 0 + 60 + 16 = 76; combine partial products and exchange groups of ten.
- I2
Calculate 48 × 2 and show the exchanges.
Show answer and reasoning
Answer: 96
48×2 = 0 + 80 + 16 = 96; combine partial products and exchange groups of ten.
- I3
Calculate 19 × 2 and show the exchanges.
Show answer and reasoning
Answer: 38
19×2 = 0 + 20 + 18 = 38; combine partial products and exchange groups of ten.
- I4
Calculate 29 × 2 and show the exchanges.
Show answer and reasoning
Answer: 58
29×2 = 0 + 40 + 18 = 58; combine partial products and exchange groups of ten.
- I5
Calculate 39 × 2 and show the exchanges.
Show answer and reasoning
Answer: 78
39×2 = 0 + 60 + 18 = 78; combine partial products and exchange groups of ten.
- I6
Calculate 49 × 2 and show the exchanges.
Show answer and reasoning
Answer: 98
49×2 = 0 + 80 + 18 = 98; combine partial products and exchange groups of ten.
- I7
Calculate 15 × 2 and show the exchanges.
Show answer and reasoning
Answer: 30
15×2 = 0 + 20 + 10 = 30; combine partial products and exchange groups of ten.
- I8
Calculate 25 × 2 and show the exchanges.
Show answer and reasoning
Answer: 50
25×2 = 0 + 40 + 10 = 50; 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
When 8 ones are multiplied by 3, what should be recorded in the tens column?
Show answer and reasoning
Answer: 2 tens
8×3=24 ones = 2 tens and 4 ones.
- C2
A child computes 27×3 as 61 because they write 21 ones in the ones place. Diagnose and correct.
Show answer and reasoning
Answer: 81
7×3=21 ones=2 tens+1 one. The tens are 2×3 tens plus 2 carried tens =8 tens. Answer 81.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 35 × 2 and show the exchanges.
Show answer and reasoning
Answer: 70
35×2 = 0 + 60 + 10 = 70; combine partial products and exchange groups of ten.
- E2
Calculate 45 × 2 and show the exchanges.
Show answer and reasoning
Answer: 90
45×2 = 0 + 80 + 10 = 90; combine partial products and exchange groups of ten.
- E3
Calculate 16 × 2 and show the exchanges.
Show answer and reasoning
Answer: 32
16×2 = 0 + 20 + 12 = 32; combine partial products and exchange groups of ten.