Add Within 100 Using Tens and Ones | 1st Grade Math

Grade 1 Math  ›  Operations with Place Value  ›  Lesson 18

Grade 1 Math - Operations with Place Value

Add Within 100 Using Tens and Ones

Learn how to add within 100 by breaking two-digit numbers into tens and ones. Students use base-ten thinking, expanded form, drawings, and written equations to combine place values correctly.

Start by adding tens with tens and ones with ones. When the ones total 10 or more, compose 10 ones into a new ten and then combine the remaining tens and ones.

Add within 100 Tens and ones Place value addition Compose a ten 1st Grade Math

🎯 What You Will Learn

Break numbers into tens and ones
See a number such as 37 as 3 tens and 7 ones, or 30 + 7.

Add like place values
Combine tens with tens and ones with ones instead of mixing the places.

Compose a new ten when needed
When the ones make 10 or more, trade 10 ones for 1 new ten.

Explain your strategy
Connect a drawing or base-ten model to expanded form and a written equation.

For parents & teachers — standards alignment: This lesson develops the central place-value reasoning of CCSS 1.NBT.C.4: add within 100 using concrete models, drawings, place-value strategies, properties of operations, and written methods. Students add tens with tens and ones with ones and learn that sometimes 10 ones must be composed into a new ten. Lessons 19 and 20 continue the same standard with its explicitly named cases: adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10. The lesson also draws on CCSS 1.NBT.B.2. For Texas alignment, TEKS 1.2(B) and 1.2(C) support composing, decomposing, and representing numbers through 120; general two-digit + two-digit addition is treated here as a Common Core-aligned extension.

🧠 Key Vocabulary

tens — groups of 10 ones.

ones — single units.

place value — the value a digit has because of its position in a number.

expanded form — writing a number as the value of its tens and ones, such as 37 = 30 + 7.

sum — the result of addition.

compose a ten — make 1 new ten from 10 ones.

🔢 Break Numbers Into Tens and Ones

Before adding two-digit numbers, identify the tens and ones in each addend. For example, 24 has 2 tens and 4 ones, while 13 has 1 ten and 3 ones.

24

2 tens = 20

4 ones = 4

13

1 ten = 10

3 ones = 3

➕ Add Tens, Add Ones, Then Combine

24 = 20 + 4 and 13 = 10 + 3

20 + 10 = 30 and 4 + 3 = 7

30 + 7 = 37

Place-value rule: add tens with tens and ones with ones. Keep the places organized so the value of each digit stays clear.

🔟 What If the Ones Make 10 or More?

Sometimes the ones add to 10 or more. Then 10 of those ones can be composed into 1 new ten.

8 ones + 5 ones = 13 ones

→

13 ones = 1 ten + 3 ones

For 28 + 15, the tens make 30 and the ones make 13. The 13 ones become 1 new ten and 3 ones, so the total is 43.

🛠️ Four Useful Strategies

Base-ten model Show tens rods and ones cubes, then combine like units.

Expanded form Break numbers apart, such as 46 = 40 + 6.

Add by place Add tens with tens and ones with ones.

Count on by tens and ones Add the tens first, then count on the ones.

Common mistake: do not treat all digits as if they have the same value. In 24 + 13, the 2 means 2 tens, not 2 ones. Place value tells you what each digit is worth.

🌟 25 Worked Examples

Try each problem first. Then open “Show solution” to compare your place-value strategy.

1 Add tens and ones separately

Find the sum: 21 + 13 = □.

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Break the numbers apart: 21 = 20 + 1 and 13 = 10 + 3. Add the tens: 20 + 10 = 30. Add the ones: 1 + 3 = 4. Combine: 30 + 4 = 34.

2 Use expanded form

Find the sum: 32 + 14 = □.

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Write 32 as 30 + 2 and 14 as 10 + 4. Tens: 30 + 10 = 40. Ones: 2 + 4 = 6. Combine: 40 + 6 = 46.

3 Add by place value

Find the sum: 43 + 25 = □.

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Add tens with tens: 40 + 20 = 60. Add ones with ones: 3 + 5 = 8. Then 60 + 8 = 68.

4 Build the sum with tens and ones

Find the sum: 51 + 27 = □.

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51 has 5 tens and 1 one. 27 has 2 tens and 7 ones. Together there are 7 tens and 8 ones, so the sum is 78.

5 Match the cover example

Find the sum: 24 + 13 = □.

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24 = 2 tens 4 ones and 13 = 1 ten 3 ones. Add: 2 tens + 1 ten = 3 tens, and 4 ones + 3 ones = 7 ones. The sum is 37.

6 Add two two-digit numbers

Find the sum: 35 + 22 = □.

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Tens: 30 + 20 = 50. Ones: 5 + 2 = 7. Combine 50 + 7 to get 57.

7 Keep each place together

Find the sum: 46 + 12 = □.

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Add 40 + 10 = 50 and 6 + 2 = 8. Then 50 + 8 = 58.

8 Use a tens-and-ones model

Find the sum: 52 + 36 = □.

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52 has 5 tens and 2 ones. 36 has 3 tens and 6 ones. Altogether: 8 tens and 8 ones = 88.

9 Add without composing a new ten

Find the sum: 61 + 18 = □.

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Tens: 60 + 10 = 70. Ones: 1 + 8 = 9. Since 9 ones is less than 10, no new ten is needed. The sum is 79.

10 Add equal-sized tens groups

Find the sum: 33 + 44 = □.

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30 + 40 = 70 and 3 + 4 = 7. Combine: 70 + 7 = 77.

11 Explain the parts

Find the sum: 22 + 25 = □.

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22 = 20 + 2 and 25 = 20 + 5. Add the tens to get 40 and the ones to get 7. So 40 + 7 = 47.

12 Choose tens first

Find the sum: 41 + 38 = □.

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Add the tens first: 40 + 30 = 70. Add the ones: 1 + 8 = 9. Then 70 + 9 = 79.

13 Order does not change the sum

Find the sum: 14 + 52 = □.

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You may think 52 + 14. Add 50 + 10 = 60 and 2 + 4 = 6. The sum is 66.

14 Add larger tens

Find the sum: 63 + 16 = □.

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60 + 10 = 70 and 3 + 6 = 9. Combine to get 79.

15 Preview: add a one-digit number

Find the sum: 35 + 4 = □.

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35 has 3 tens and 5 ones. Adding 4 changes only the ones: 5 + 4 = 9. The tens stay 3 tens, so the sum is 39. Lesson 19 will focus on this type of addition in depth.

16 Compose a new ten

Find the sum: 28 + 15 = □.

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Add the tens: 20 + 10 = 30. Add the ones: 8 + 5 = 13. Thirteen ones is 1 ten and 3 ones. Add that new ten to 30: 30 + 10 + 3 = 43.

17 Rename 13 ones

Find the sum: 37 + 26 = □.

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30 + 20 = 50. Then 7 + 6 = 13 ones, which is 1 ten and 3 ones. Now 50 + 10 + 3 = 63.

18 Make a new ten from ones

Find the sum: 46 + 27 = □.

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40 + 20 = 60. The ones make 6 + 7 = 13, so compose 10 ones into 1 new ten. Then 60 + 10 + 3 = 73.

19 Use expanded form and compose a ten

Find the sum: 58 + 14 = □.

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50 + 10 = 60. Ones: 8 + 4 = 12 = 10 + 2. Combine 60 + 10 + 2 = 72.

20 Compose one ten

Find the sum: 29 + 34 = □.

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20 + 30 = 50. Ones: 9 + 4 = 13, which is 1 ten and 3 ones. So 50 + 10 + 3 = 63.

21 Start with the ones

Find the sum: 17 + 25 = □.

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Ones: 7 + 5 = 12, so that makes 1 ten and 2 ones. Tens: 10 + 20 + the new 10 = 40. Add the 2 ones: 42.

22 Add across a new ten

Find the sum: 39 + 42 = □.

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30 + 40 = 70. Ones: 9 + 2 = 11 = 1 ten and 1 one. So 70 + 10 + 1 = 81.

23 Combine models and equations

Find the sum: 26 + 47 = □.

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20 + 40 = 60. Ones: 6 + 7 = 13, so compose a new ten. Then 60 + 10 + 3 = 73.

24 Make an exact ten from the ones

Find the sum: 48 + 32 = □.

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40 + 30 = 70. Ones: 8 + 2 = 10, which becomes 1 new ten and 0 ones. Then 70 + 10 = 80.

25 Explain two ways

Find the sum: 35 + 47 = □. Explain one place-value method and one counting-on method.

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Place-value method: 30 + 40 = 70 and 5 + 7 = 12, so 70 + 10 + 2 = 82. Counting-on method: start at 47, add 30 to get 77, then add 5 to get 82. The sum is 82.

🎮 Independent Practice — 30 Problems

1. Find the sum: 23 + 14 = □.
2. Find the sum: 31 + 26 = □.
3. Find the sum: 42 + 15 = □.
4. Find the sum: 54 + 23 = □.
5. Find the sum: 62 + 17 = □.
6. Find the sum: 34 + 25 = □.
7. Find the sum: 71 + 18 = □.
8. Find the sum: 45 + 12 = □.
9. Find the sum: 53 + 24 = □.
10. Find the sum: 16 + 42 = □.
11. Find the sum: 27 + 31 = □.
12. Find the sum: 64 + 15 = □.
13. Find the sum: 21 + 56 = □.
14. Find the sum: 43 + 34 = □.
15. Find the sum: 32 + 47 = □.
16. Find the sum: 27 + 16 = □.
17. Find the sum: 38 + 25 = □.
18. Find the sum: 49 + 14 = □.
19. Find the sum: 56 + 27 = □.
20. Find the sum: 68 + 15 = □.
21. Find the sum: 19 + 24 = □.
22. Find the sum: 36 + 48 = □.
23. Find the sum: 57 + 26 = □.
24. Find the sum: 28 + 43 = □.
25. Find the sum: 47 + 36 = □.
26. Find the sum: 59 + 21 = □.
27. Find the sum: 18 + 63 = □.
28. Find the sum: 29 + 52 = □.
29. Solve 46 + 28. Show how the ones make a new ten.
30. Solve 34 + 45 in two ways: add tens and ones separately, and count on by tens and ones.

🏆 Lesson Test — 15 Questions

1. Find the sum: 22 + 16 = □.
2. Find the sum: 41 + 27 = □.
3. Find the sum: 53 + 14 = □.
4. Find the sum: 65 + 22 = □.
5. Find the sum: 33 + 46 = □.
6. Find the sum: 27 + 18 = □.
7. Find the sum: 38 + 14 = □.
8. Find the sum: 49 + 23 = □.
9. Find the sum: 57 + 18 = □.
10. Find the sum: 68 + 24 = □.
11. Find the sum: 29 + 41 = □.
12. Find the sum: 17 + 54 = □.
13. Find the sum: 36 + 27 = □.
14. Solve 48 + 25. Explain what happens to the 13 ones.
15. Solve 32 + 49. Name one place-value strategy you could use.

🔐 Complete Answer Key

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Practice Answers

1. 37

2. 57

3. 57

4. 77

5. 79

6. 59

7. 89

8. 57

9. 77

10. 58

11. 58

12. 79

13. 77

14. 77

15. 79

16. 43

17. 63

18. 63

19. 83

20. 83

21. 43

22. 84

23. 83

24. 71

25. 83

26. 80

27. 81

28. 81

29. 74. Ones: 6 + 8 = 14 = 1 ten and 4 ones; tens: 40 + 20 + 10 = 70; 70 + 4 = 74.

30. 79. Place value: 30 + 40 = 70 and 4 + 5 = 9, so 79. Counting on: 45 + 30 = 75, then +4 = 79.

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Test Answers

1. 38

2. 68

3. 67

4. 87

5. 79

6. 45

7. 52

8. 72

9. 75

10. 92

11. 70

12. 71

13. 63

14. 73. The ones make 8 + 5 = 13, so 10 of the ones are composed into 1 new ten and 3 ones remain.

15. 81. Possible strategy: add tens with tens and ones with ones, then compose a new ten because 2 + 9 = 11.

💡 Common Mistakes to Watch For

Mixing tens and ones
Add like place values: tens with tens and ones with ones.

Forgetting to compose a ten
If the ones make 10 or more, trade 10 ones for 1 new ten.

Changing the value of a digit
In 47, the 4 means 40, not 4.

Using a rule without a model
Be able to explain your addition with tens, ones, a drawing, or expanded form.

What comes next: Lesson 19 focuses specifically on adding a two-digit number and a one-digit number, including cases where the ones make a new ten.

🔗 Related Lessons

Lesson 2 — Tens and Ones: Understanding Place Value Review how two-digit numbers are built from tens and ones. Lesson 17 — Addition & Subtraction Fluency Within 10 Review the basic facts that help when adding the ones in larger numbers.

🖨️ Printable Companion

A future Add Within 100 Using Tens and Ones Practice Pack can include base-ten drawings, expanded-form addition, place-value practice, compose-a-ten challenges, mixed problems, and a complete answer key.

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