Grade 2 · Operations · MAT-02-OPS-004
Add Two-Digit Numbers with Regrouping
Add two-digit numbers when ones total 10 or more.
Learning objectives
What you should be able to do
- Add two-digit numbers when ones total 10 or more.
- Regroup 10 ones as 1 ten using models and symbols.
- Explain each step using place-value language.
Prerequisite check
Make sure the foundation is ready.
Checks both algorithm and regrouping foundations.
Learn
Build the idea from meaning, not memorization.
Ten ones can be traded for one ten
When the ones total 10 or more, bundle 10 ones into 1 ten. This does not change the value; it changes the representation.
Regroup before combining final tens
In 38+27, the ones are 8+7=15. Write 5 ones and regroup 10 of the 15 ones as 1 additional ten. Then 3 tens+2 tens+1 regrouped ten=6 tens, so the sum is 65.
The written algorithm records a base-ten trade
The small carried 1 in a standard vertical method means 1 ten, not 1 one. Understanding that value prevents mechanical mistakes.
Estimate before and after
38+27 is near 40+30=70, so 65 is plausible. A result such as 515 would violate the expected magnitude.
Interactive math lab
Change it. See what stays true.
Base-Ten Lab
Change hundreds, tens, and ones and watch the total rebuild from place value.
- combine ones
- bundle ten ones
- carry ten
- check estimate
Worked examples
Twenty different ways to see the concept work.
38+27
658+7=15; regroup10 ones as1 ten.
46+19
656+9=15; 4T+1T+1T=6T.
57+28
857+8=15; regroup.
64+29
934+9=13; regroup1 ten.
35+47
825+7=12; write2 ones, add1 ten.
48+36
848+6=14; regroup.
29+54
839+4=13.
67+18
857+8=15.
58+24
828+4=12.
73+19
923+9=12.
45+38
835+8=13.
26+57
836+7=13.
39+42
819+2=11.
68+25
938+5=13.
47+46
937+6=13.
56+37
936+7=13.
28+65
938+5=13.
49+44
939+4=13.
Explain regrouping in 27+35.
7+5=12; 10 ones become1 ten, leaving2 ones;2T+3T+1T=6T.Sum62.
Check 38+27 with expanded form.
30+8+20+7=50+15=65Expanded form confirms regrouping.
Practice
Guided practice with hints
0127+36
Hint: Add ones first; regroup if ≥10.
Answer: 63
0248+25
Hint: 8+5=13.
Answer: 73
0356+29
Hint: 6+9=15.
Answer: 85
0439+47
Hint: 9+7=16.
Answer: 86
0568+16
Hint: 8+6=14.
Answer: 84
06Why is the carried 1 worth ten?
Hint: It came from bundling 10 ones.
Answer: It represents one ten.
Practice
Independent practice
0138+45
Answer: 83
0247+26
Answer: 73
0359+24
Answer: 83
0467+18
Answer: 85
0528+37
Answer: 65
0646+39
Answer: 85
0775+18
Answer: 93
0856+28
Answer: 84
Common mistakes
Learn to catch the error, not just the answer.
Regroup 10 ones as 1 ten, leaving only 5 ones.
It represents one ten because it came from 10 ones.
Include it when combining the tens column.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine two counts when the ones create a new group of ten.
- Use base-ten blocks to model inventory bundles and loose items.
Challenge problems
Why can 10 ones be replaced by 1 ten?
Both represent the same value, 10.
Find two addends with sum 100 requiring regrouping.
Example 58+42.
Explain 49+36 without vertical algorithm.
40+30=70;9+6=15;70+15=85.
Why does estimation help catch regrouping errors?
The exact sum should be near the estimated magnitude.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Regrouping Workshop
Bundle ten ones into a ten and finish two-digit sums correctly.
Practice
Mastery check
0128+37
Answer: 65
0246+29
Answer: 75
0357+36
Answer: 93
0439+44
Answer: 83
05What happens to 10 ones?
Answer: They regroup as 1 ten.
06What does the regrouped 1 represent?
Answer: One ten.
07Estimate 48+36.
Answer: About 80; exact84.
08Explain 27+38.
Answer: 7+8=15; regroup10 ones, then2T+3T+1T=6T, yielding65.
Terminology
Words to know
- regroup
- Exchange 10 units of one place for 1 unit of the next place.
- carry
- Informal term for recording a regrouped unit in the next place.
- sum
- The result of addition.
- estimate
- A close approximation used to judge reasonableness.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.NBT.B.5–6
Place-value strategies and addition within 100.