3A · Chapter 3 · Lesson 1
Addition with Regrouping
When a column has ten or more units, exchange ten for one unit of the next place.
Today's challenge
Add 958 and 1,757. Explain one exchange of ten units. Try your own method, then compare it with a model.
What you'll learn
- When a column has ten or more units, exchange ten for one unit of the next place.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Place value and mental addition.
Prerequisite competency: 3A-C02-L01
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Add 253 + 185. Show a place-value breakdown.
Show answer and reasoning
Answer: 438
253 is 200 + 53; add the two parts to 185. The sum is 438.
- E2
Add 290 + 30. Show a place-value breakdown.
Show answer and reasoning
Answer: 320
290 is 200 + 90; add the two parts to 30. The sum is 320.
Learn the concept
Words to know
- regroup
- exchange ten of one unit for one larger unit
- place value
- a digit’s value according to its position
When a column has ten or more units, exchange ten for one unit of the next place.
Combine ones in the ones column. If you have at least ten ones, exchange ten ones for one ten; repeat with tens and hundreds. Use blocks or a place-value chart first.
Why this works
Regrouping is an exchange, not a change in value. When adding 478 + 356, the ones make 14: exchange 10 ones for one ten, leaving 4 ones. The tens now make 13: exchange 10 tens for one hundred, leaving 3 tens. The result is 834; each exchange preserves the total.
Check the meaning
Estimate the size beforehand, and subtract one addend afterward to verify the exact result.
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
Add 958 and 1,757. Explain one exchange of ten units.
- Combine ones in the ones column. If you have at least ten ones, exchange ten ones for one ten; repeat with tens and hundreds. Use blocks or a place-value chart first.
- Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 958 + 1,757 = 2,715.
- Estimate the size beforehand, and subtract one addend afterward to verify the exact result.
Result: 2715
Understanding check 1 — your turn
Add 1,848 and 1,237. Explain one exchange of ten units.
Reveal reasoning
Answer: 3085 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,848 + 1,237 = 3,085.
Worked example 2
Reason and verify
Add 1,128 and 1,897. Explain one exchange of ten units.
- Combine ones in the ones column. If you have at least ten ones, exchange ten ones for one ten; repeat with tens and hundreds. Use blocks or a place-value chart first.
- Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,128 + 1,897 = 3,025.
- Estimate the size beforehand, and subtract one addend afterward to verify the exact result.
Result: 3025
Understanding check 2 — your turn
Add 2,018 and 1,377. Explain one exchange of ten units.
Reveal reasoning
Answer: 3395 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,018 + 1,377 = 3,395.
Worked example 3
Reason and verify
Add 1,298 and 2,037. Explain one exchange of ten units.
- Combine ones in the ones column. If you have at least ten ones, exchange ten ones for one ten; repeat with tens and hundreds. Use blocks or a place-value chart first.
- Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,298 + 2,037 = 3,335.
- Estimate the size beforehand, and subtract one addend afterward to verify the exact result.
Result: 3335
Understanding check 3 — your turn
Add 2,198 and 1,517. Explain one exchange of ten units.
Reveal reasoning
Answer: 3715 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,198 + 1,517 = 3,715.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Add 1,718 and 997. Explain one exchange of ten units.
Show answer and reasoning
Answer: 2715
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,718 + 997 = 2,715.
- G2
Add 1,888 and 1,127. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3015
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,888 + 1,127 = 3,015.
- G3
Add 2,058 and 1,267. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3325
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,058 + 1,267 = 3,325.
- G4
Add 2,228 and 1,407. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3635
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,228 + 1,407 = 3,635.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Add 918 and 1,297. Explain one exchange of ten units.
Show answer and reasoning
Answer: 2215
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 918 + 1,297 = 2,215.
- I2
Add 1,088 and 1,427. Explain one exchange of ten units.
Show answer and reasoning
Answer: 2515
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,088 + 1,427 = 2,515.
- I3
Add 1,258 and 1,567. Explain one exchange of ten units.
Show answer and reasoning
Answer: 2825
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,258 + 1,567 = 2,825.
- I4
Add 1,428 and 1,707. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3135
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,428 + 1,707 = 3,135.
- I5
Add 1,608 and 1,837. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3445
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,608 + 1,837 = 3,445.
- I6
Add 1,778 and 1,977. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3755
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,778 + 1,977 = 3,755.
- I7
Add 1,948 and 2,117. Explain one exchange of ten units.
Show answer and reasoning
Answer: 4065
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,948 + 2,117 = 4,065.
- I8
Add 2,128 and 2,247. Explain one exchange of ten units.
Show answer and reasoning
Answer: 4375
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,128 + 2,247 = 4,375.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
A sum has 14 ones in its ones column. Explain the exchange needed.
Show answer and reasoning
Answer: 1 ten and 4 ones
14 ones = 10 ones + 4 ones. Exchange ten ones for one ten; the quantity does not change.
- C2
Can 478 + 356 be represented as 7 hundreds, 12 tens, and 14 ones? Find the normalized number.
Show answer and reasoning
Answer: 834
4+3=7 hundreds; 7+5=12 tens; 8+6=14 ones. Trade 14 ones for 1 ten and 4 ones; then 13 tens for 1 hundred and 3 tens; total 834.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Add 2,718 and 1,897. Explain one exchange of ten units.
Show answer and reasoning
Answer: 4615
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,718 + 1,897 = 4,615.
- E2
Add 2,888 and 2,027. Explain one exchange of ten units.
Show answer and reasoning
Answer: 4915
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,888 + 2,027 = 4,915.
- E3
Add 3,058 and 2,167. Explain one exchange of ten units.
Show answer and reasoning
Answer: 5225
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 3,058 + 2,167 = 5,225.