Grade 1 · Place Value · MAT-01-PV-005
Add Tens and Ones Without Regrouping
Add two-digit quantities without regrouping by combining tens with tens and ones with ones.
Learning objectives
What you should be able to do
- Add two-digit quantities without regrouping by combining tens with tens and ones with ones.
- Represent the addition with base-ten blocks, expanded form, and equations.
- Explain why place values must be combined with matching place values.
Prerequisite check
Make sure the foundation is ready.
Checks place-value decomposition.
Checks basic addition facts.
Learn
Build the idea from meaning, not memorization.
Add matching place values
To add 23+14, combine the tens: 20+10=30. Then combine the ones: 3+4=7. Put the place values together: 30+7=37.
Base-ten blocks show why the method works
Two tens rods plus one ten rod make three tens. Three ones plus four ones make seven ones. No group reaches ten ones, so no regrouping is needed.
Expanded form keeps place values visible
23+14 can be written (20+3)+(10+4). Rearranging by place gives (20+10)+(3+4)=30+7=37.
Estimate before solving
Twenty-something plus ten-something should be thirty-something when the ones do not create a new ten. This helps detect unreasonable answers.
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.
- build addends
- combine tens
- combine ones
- write expanded form
Worked examples
Twenty different ways to see the concept work.
21+13
3420+10=30 and 1+3=4.
22+15
3720+10=30; 2+5=7.
31+16
4730+10=40; 1+6=7.
42+17
5940+10=50; 2+7=9.
53+24
7750+20=70; 3+4=7.
64+25
8960+20=80; 4+5=9.
70+18
8870+10=80; 0+8=8.
41+20
61Add two tens; ones stay one.
35+12
4730+10=40; 5+2=7.
26+13
3920+10=30; 6+3=9.
10+25
35One ten joins two tens.
32+7
39Ones 2+7=9; tens stay 3.
50+34
84Five tens plus three tens = eight tens.
11+11
22One ten+one ten; one+one.
43+6
49Only ones change.
52+7
592+7=9; tens unchanged.
Which is wrong: add tens to ones?
Place values must match20+4 and 3+10 mix units unnecessarily.
Expanded form of 24+15.
(20+10)+(4+5)=39Group like places.
Why is 38+11=49 without regrouping?
8+1=9Ones total stays below 10.
Explain 46+13.
40+10=50; 6+3=9; total 59Place-value combination.
Practice
Guided practice with hints
01Solve 23+14.
Hint: Add tens, then ones.
Answer: 37
02Solve 42+15.
Hint: 40+10 and 2+5.
Answer: 57
03Solve 51+28.
Hint: 50+20, 1+8.
Answer: 79
04Solve 32+6.
Hint: Tens stay 3; add ones.
Answer: 38
05Why no regrouping in 26+13?
Hint: 6+3 stays below ten.
Answer: Ones total 9.
06Check 35+12 with expanded form.
Hint: 30+10 and 5+2.
Answer: 47
Practice
Independent practice
0121+16
Answer: 37
0234+25
Answer: 59
0342+7
Answer: 49
0460+18
Answer: 78
0551+27
Answer: 78
0633+14
Answer: 47
07What place values combine?
Answer: Tens with tens; ones with ones.
08When is regrouping not needed?
Answer: When ones total is less than 10.
Common mistakes
Learn to catch the error, not just the answer.
Use place-value units: tens combine with tens, ones with ones.
Represent 40 as 4 tens 0 ones.
Rebuild the final number from total tens and total ones.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine two classroom counts that do not require regrouping.
- Add small prices or quantities represented in tens and ones.
Challenge problems
Why does 54+23=77?
5 tens+2 tens=7 tens; 4 ones+3 ones=7 ones.
Find a pair of two-digit numbers that add to 88 without regrouping.
Example: 53+35=88.
What tells you regrouping would be required?
The ones add to 10 or more.
Explain why expanded form is useful.
It makes the value of each place visible and prevents mixing tens with ones.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Place Value Merge
Merge two base-ten models and build the resulting number without regrouping.
Practice
Mastery check
0122+15
Answer: 37
0231+18
Answer: 49
0353+24
Answer: 77
0442+6
Answer: 48
0570+19
Answer: 89
06Which places combine?
Answer: Like places.
07Why no regrouping in 42+17?
Answer: 2+7=9, below ten.
08Explain 35+12.
Answer: 30+10=40 and 5+2=7, total 47.
Terminology
Words to know
- like place values
- Units of the same place, such as tens with tens.
- expanded form
- A number written as the sum of its place values.
- regrouping
- Exchanging equivalent units, such as ten ones for one ten.
- sum
- The result of addition.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 1 Number & Operations in Base Ten
Grade 1 place-value arithmetic and mental-ten relationships.