3A · Chapter 5 · Lesson 3
Multiplication with Regrouping Tens
Regroup when the tens-place partial product exceeds nine tens.
Today's challenge
Calculate 63 × 2 and show the exchanges. Try your own method, then compare it with a model.
What you'll learn
- Regroup when the tens-place partial product exceeds nine tens.
- 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.
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 323 × 2 using partial products.
Show answer and reasoning
Answer: 646
Split 323 by place value; multiply each part by 2 and add. Total is 646.
- E2
Calculate 321 × 3 using partial products.
Show answer and reasoning
Answer: 963
Split 321 by place value; multiply each part by 3 and add. Total is 963.
Learn the concept
Words to know
- exchange
- trade ten tens for one hundred
- partial product
- one product of decomposed place values
Regroup when the tens-place partial product exceeds nine tens.
If multiplying the tens creates ten or more tens, move complete hundreds into the next place. Keep a written record of the exchange.
Why this works
When the tens product reaches at least ten tens, exchange ten tens for a hundred. For 70 × 3, the product is 21 tens, or two hundreds and one ten: 210. A carried 2 in the hundreds place represents two hundreds, not two ones.
Check the meaning
Each carried digit has units: a carried 1 in the hundreds column is 100.
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 63 × 2 and show the exchanges.
- 3 1-unit groups × 2, plus 0 carried 1-unit groups, gives 6 groups. Write 6 in the 1s place.
- 6 10-unit groups × 2, plus 0 carried 10-unit groups, gives 12 groups. Write 2 in the 10s place and exchange 1 groups into the next place.
- Record the final 1 group(s) in the next place.
- Check by partial products: 120 + 6 = 126.
Result: 126
Understanding check 1 — your turn
Calculate 71 × 3 and show the exchanges.
Reveal reasoning
Answer: 213 — 71×3 = 0 + 210 + 3 = 213; combine partial products and exchange groups of ten.
Worked example 2
Reason and verify
Calculate 73 × 2 and show the exchanges.
- 3 1-unit groups × 2, plus 0 carried 1-unit groups, gives 6 groups. Write 6 in the 1s place.
- 7 10-unit groups × 2, plus 0 carried 10-unit groups, gives 14 groups. Write 4 in the 10s place and exchange 1 groups into the next place.
- Record the final 1 group(s) in the next place.
- Check by partial products: 140 + 6 = 146.
Result: 146
Understanding check 2 — your turn
Calculate 81 × 3 and show the exchanges.
Reveal reasoning
Answer: 243 — 81×3 = 0 + 240 + 3 = 243; combine partial products and exchange groups of ten.
Worked example 3
Reason and verify
Calculate 83 × 2 and show the exchanges.
- 3 1-unit groups × 2, plus 0 carried 1-unit groups, gives 6 groups. Write 6 in the 1s place.
- 8 10-unit groups × 2, plus 0 carried 10-unit groups, gives 16 groups. Write 6 in the 10s place and exchange 1 groups into the next place.
- Record the final 1 group(s) in the next place.
- Check by partial products: 160 + 6 = 166.
Result: 166
Understanding check 3 — your turn
Calculate 91 × 3 and show the exchanges.
Reveal reasoning
Answer: 273 — 91×3 = 0 + 270 + 3 = 273; 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 51 × 3 and show the exchanges.
Show answer and reasoning
Answer: 153
51×3 = 0 + 150 + 3 = 153; combine partial products and exchange groups of ten.
- G2
Calculate 61 × 3 and show the exchanges.
Show answer and reasoning
Answer: 183
61×3 = 0 + 180 + 3 = 183; combine partial products and exchange groups of ten.
- G3
Calculate 71 × 2 and show the exchanges.
Show answer and reasoning
Answer: 142
71×2 = 0 + 140 + 2 = 142; combine partial products and exchange groups of ten.
- G4
Calculate 81 × 2 and show the exchanges.
Show answer and reasoning
Answer: 162
81×2 = 0 + 160 + 2 = 162; 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 52 × 3 and show the exchanges.
Show answer and reasoning
Answer: 156
52×3 = 0 + 150 + 6 = 156; combine partial products and exchange groups of ten.
- I2
Calculate 62 × 3 and show the exchanges.
Show answer and reasoning
Answer: 186
62×3 = 0 + 180 + 6 = 186; combine partial products and exchange groups of ten.
- I3
Calculate 72 × 3 and show the exchanges.
Show answer and reasoning
Answer: 216
72×3 = 0 + 210 + 6 = 216; combine partial products and exchange groups of ten.
- I4
Calculate 82 × 3 and show the exchanges.
Show answer and reasoning
Answer: 246
82×3 = 0 + 240 + 6 = 246; combine partial products and exchange groups of ten.
- I5
Calculate 92 × 3 and show the exchanges.
Show answer and reasoning
Answer: 276
92×3 = 0 + 270 + 6 = 276; combine partial products and exchange groups of ten.
- I6
Calculate 53 × 3 and show the exchanges.
Show answer and reasoning
Answer: 159
53×3 = 0 + 150 + 9 = 159; combine partial products and exchange groups of ten.
- I7
Calculate 63 × 3 and show the exchanges.
Show answer and reasoning
Answer: 189
63×3 = 0 + 180 + 9 = 189; combine partial products and exchange groups of ten.
- I8
Calculate 73 × 3 and show the exchanges.
Show answer and reasoning
Answer: 219
73×3 = 0 + 210 + 9 = 219; 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 7 tens are multiplied by 3, how many hundreds and tens is the result?
Show answer and reasoning
Answer: 2 hundreds and 1 ten
7×3=21 tens = 2 hundreds + 1 ten.
- C2
In 64×3, explain why writing 12 as the tens digit would be a place-value error.
Show answer and reasoning
Answer: 192
6 tens×3=18 tens, plus ones product 4×3=12 ones=1 ten+2 ones. Total 19 tens and 2 ones: 192; each position holds a single digit.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Calculate 51 × 2 and show the exchanges.
Show answer and reasoning
Answer: 102
51×2 = 0 + 100 + 2 = 102; combine partial products and exchange groups of ten.
- E2
Calculate 61 × 2 and show the exchanges.
Show answer and reasoning
Answer: 122
61×2 = 0 + 120 + 2 = 122; combine partial products and exchange groups of ten.
- E3
Calculate 81 × 3 and show the exchanges.
Show answer and reasoning
Answer: 243
81×3 = 0 + 240 + 3 = 243; combine partial products and exchange groups of ten.