Grade 1 · Place Value · MAT-01-PV-007
Add a One-Digit Number to a Two-Digit Number
Add a one-digit number to a two-digit number using place-value reasoning.
Learning objectives
What you should be able to do
- Add a one-digit number to a two-digit number using place-value reasoning.
- Determine when adding ones creates a new ten and when it does not.
- Use counting on, base-ten blocks, and make-ten strategies to explain sums.
Prerequisite check
Make sure the foundation is ready.
Checks one-digit addition strategies.
Checks place-value model.
Learn
Build the idea from meaning, not memorization.
A one-digit addend changes the ones first
In 32+5, think 3 tens and 2 ones plus 5 ones. The tens stay three because 2+5=7, giving 37.
Sometimes the ones make a new ten
In 38+5, eight ones plus five ones equals thirteen ones. Regroup ten of those ones as one new ten: 3 tens becomes 4 tens, with 3 ones left, so 43.
Make-ten can make crossing a decade easier
For 38+5, split 5 into 2 and 3. 38+2=40, then 40+3=43.
Estimate the decade before computing
If 38 gains 5, the answer should be a little more than 40. This helps catch errors such as 83 or 48.
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.
- add ones
- make new ten
- bridge decade
- write equation
Worked examples
Twenty different ways to see the concept work.
31+4
351+4=5 ones; tens stay 3.
42+5
472+5=7.
53+6
593+6=9.
60+7
67Add seven ones.
24+3
27No regrouping.
35+4
395+4=9.
38+2
40Eight ones plus two make a new ten.
38+5
4338+2=40, then +3.
47+6
5347+3=50, then +3.
56+7
6356+4=60, then +3.
69+4
7369+1=70, then +3.
75+8
8375+5=80, then +3.
89+6
9589+1=90, then +5.
91+7
981+7=8 ones.
99+1
100One more completes a hundred.
43+0
43Adding zero changes nothing.
Which place changes first?
OnesA one-digit addend represents ones.
When does tens increase?
When ones total reaches 10 or moreA new ten is regrouped.
Explain 58+7 with make-ten.
58+2+5=60+5=65Split seven.
Explain 72+6.
2+6=8, so 7 tens 8 ones =78No new ten.
Practice
Guided practice with hints
01Solve 34+5.
Hint: Add the ones.
Answer: 39
02Solve 48+3.
Hint: Reach 50 first.
Answer: 51
03Solve 57+6.
Hint: 57+3=60, then +3.
Answer: 63
04Solve 69+5.
Hint: 69+1=70, then +4.
Answer: 74
05Does 52+4 regroup?
Hint: 2+4=6.
Answer: No
06Does 58+4 regroup?
Hint: 8+4=12.
Answer: Yes
Practice
Independent practice
0123+6
Answer: 29
0236+3
Answer: 39
0347+5
Answer: 52
0458+6
Answer: 64
0569+7
Answer: 76
0684+5
Answer: 89
0797+3
Answer: 100
08When does regrouping occur?
Answer: When ones total is 10 or more.
Common mistakes
Learn to catch the error, not just the answer.
A one-digit whole number represents ones; combine it with the ones place first.
Regroup ten ones as one ten.
Write the split explicitly and add the remainder after reaching the decade.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Update a two-digit count after adding a few items.
- Add a small number of points to a larger score.
Challenge problems
Solve 96+7.
103
Why is 58+7 equal 65?
8+7=15 ones; regroup 10 ones to create an extra ten.
Which is easier for 49+6: counting on all six or make-ten?
Make-ten: +1 to 50, then +5.
Create a problem where adding 4 does not regroup and one where it does.
Examples: 32+4=36; 38+4=42.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Cross the Decade
Add a one-digit number and decide whether the ones stay within the decade or create a new ten.
Practice
Mastery check
0132+6
Answer: 38
0248+5
Answer: 53
0357+7
Answer: 64
0469+4
Answer: 73
0599+1
Answer: 100
06Which place receives the one-digit addend first?
Answer: Ones
07When does tens increase?
Answer: When ten ones regroup.
08Explain 58+5.
Answer: 58+2=60, then +3=63.
Terminology
Words to know
- regroup
- Exchange ten ones for one ten.
- decade boundary
- A transition such as 39→40 or 69→70.
- make-ten
- Complete a group of ten as an intermediate step.
- 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.