Add Within 100 Using Place Value | Grade 2 Math

Grade 2 Math  ›  Addition & Subtraction Within 100  ›  Lesson 8

Grade 2 Math — Addition and Place Value

Add Within 100 Using Place Value

Learn how to add two-digit numbers by combining tens with tens and ones with ones. Use base-ten blocks, place-value charts, expanded form, and mental jumps to explain how addition works.

We begin with sums that do not require making a new ten, so you can see the place-value idea clearly. A later lesson will teach how to compose a ten when the ones total is 10 or more.

Add within 100 Tens & ones Base-ten blocks Expanded form Mental addition

🎯 What You Will Learn

Combine tens and ones
Add tens to tens and ones to ones to find the total.

Represent addition with models
Build two-digit numbers from tens rods and ones cubes.

Explain a written strategy
Use expanded form or a place-value chart to show each step.

Add mentally and check
Use jumps of tens and ones, then explain why the sum makes sense.

For parents & teachers — standards alignment: This introductory, no-regrouping lesson develops the addition portion of CCSS 2.NBT.B.5: fluently adding and subtracting within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. Students also explain their reasoning, supporting CCSS 2.NBT.B.9. Texas TEKS 2.4(B) expects students to add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms grounded in place value and properties of operations. Here we focus on addition of two numbers without composing a new ten; later MathLattice lessons extend the work to composing a ten, subtraction, and more addends.

🧠 Key Vocabulary

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

tens — groups of ten ones, such as the 3 tens in 34.

ones — single units, such as the 4 ones in 34.

addend — a number being added to another number.

sum — the result of adding the addends.

expanded form — a way to show a number by the values of its digits, such as 34 = 30 + 4.

base-ten blocks — models with tens rods and single ones cubes.

compose a ten — make a new group of ten from 10 ones; we will learn this later.

🏠 Start with Place Value

Every two-digit number has tens and ones. For example, 34 = 30 + 4 and 23 = 20 + 3. In addition, you can combine equal place-value units: tens with tens, and ones with ones.

1. Break apart34 = 30 + 4
23 = 20 + 3

2. Add tens30 + 20 = 50

3. Add ones4 + 3 = 7

4. Combine50 + 7 = 57

Big idea: 3 tens + 2 tens makes 5 tens, not 5 ones. The place-value units must stay attached to the numbers you are adding.

🧱 Build 34 + 23 with Base-Ten Blocks

Each long rod represents 10. Each small cube represents 1. The models below have exactly the tens and ones shown in their labels.

34

3 tens + 4 ones

23

2 tens + 3 ones

57

5 tens + 7 ones

34 + 23 = 57

We start with 3 tens + 4 ones and 2 tens + 3 ones. Together we have 5 tens + 7 ones, which is 57.

📊 Organize the Numbers in a Place-Value Chart

Number	Tens	Ones
34	3	4
+ 23	+ 2	+ 3
= 57	5	7

Important: the tens column represents groups of 10, not single ones. In this lesson, the ones we add total less than 10, so we do not need to make a new ten.

🧮 Use Expanded Form

Break apart both addends

1. 34 = 30 + 4
2. 23 = 20 + 3
3. (30 + 20) + (4 + 3) = 50 + 7
4. 34 + 23 = 57

Add tens first, then ones

1. Start at 34.
2. Add 2 tens: 34 + 20 = 54.
3. Add 3 ones: 54 + 3 = 57.
4. 34 + 23 = 57

Both strategies work because we can break 23 into 20 + 3 and group tens with tens and ones with ones. We are rearranging and grouping addends, not composing a new ten; the ones total is only 7.

➡️ Show the Jumps on an Open Number Line

Start at 34. Make one jump of +20 to reach 54, then another jump of +3 to reach 57. An open number line shows the jumps without drawing every number.

Start at 34. Jump 20 to reach 54, then jump 3 to reach 57.

0️⃣ Add When a Place Has Zero

40 + 27 = 67
4 tens + 2 tens = 6 tens. 0 ones + 7 ones = 7 ones.

63 + 20 = 83
Adding 2 tens changes 6 tens to 8 tens. The 3 ones remain.

Check by changing the order: 34 + 23 and 23 + 34 have the same sum, 57. For addition, changing the order of the two addends does not change the total.

🌟 25 Worked Examples

Try each problem first. Open “Show solution” to see the tens-and-ones reasoning. These examples do not require composing a new ten.

1Add tens to tens

Find 30 + 20.

Show solutionHide solution

Three tens plus two tens make five tens. Five tens equal 50, so 30 + 20 = 50.

2Add ones to ones

Find 4 + 3.

Show solutionHide solution

Four ones plus three ones make seven ones. Therefore 4 + 3 = 7.

3Combine tens and ones

Use place value to find 34 + 23.

Show solutionHide solution

34 is 3 tens and 4 ones; 23 is 2 tens and 3 ones. Add 3 tens + 2 tens = 5 tens, and 4 ones + 3 ones = 7 ones. The total is 57.

4Use a place-value chart

Find 24 + 13.

Show solutionHide solution

In the tens column: 2 + 1 = 3 tens. In the ones column: 4 + 3 = 7 ones. So 24 + 13 = 37.

5Use expanded form

Find 41 + 27.

Show solutionHide solution

Write 41 as 40 + 1 and 27 as 20 + 7. Add the tens: 40 + 20 = 60. Add the ones: 1 + 7 = 8. Combine: 60 + 8 = 68.

6Add the tens and ones separately

Find 52 + 16.

Show solutionHide solution

Add 50 + 10 = 60 and 2 + 6 = 8. Combine 60 + 8 = 68.

7Check both place values

Find 23 + 35.

Show solutionHide solution

23 has 2 tens and 3 ones. 35 has 3 tens and 5 ones. Five tens and eight ones make 58.

8Add two two-digit numbers

Find 62 + 25.

Show solutionHide solution

Add 60 + 20 = 80, then 2 + 5 = 7. Therefore 62 + 25 = 87.

9Add the ones in the ones place

Find 74 + 12.

Show solutionHide solution

Add 70 + 10 = 80 and 4 + 2 = 6. The sum is 86.

10Add a larger number of tens

Find 31 + 48.

Show solutionHide solution

Add 30 + 40 = 70 and 1 + 8 = 9. Therefore 31 + 48 = 79.

11Add tens before ones

Find 46 + 22.

Show solutionHide solution

46 + 20 = 66. Now add 2 more ones: 66 + 2 = 68.

12Add by breaking apart an addend

Find 53 + 26.

Show solutionHide solution

Break 26 into 20 + 6. Then 53 + 20 = 73 and 73 + 6 = 79.

13Add multiples of ten

Find 20 + 40.

Show solutionHide solution

Two tens plus four tens make six tens, so 20 + 40 = 60.

14Add two tens to a two-digit number

Find 34 + 20.

Show solutionHide solution

Adding 20 adds 2 tens to 34: 3 tens become 5 tens. The 4 ones stay the same. The result is 54.

15Add ones to a multiple of ten

Find 60 + 7.

Show solutionHide solution

Six tens and seven ones make 67.

16Add a one-digit number

Find 42 + 5.

Show solutionHide solution

42 is 4 tens and 2 ones. Add 5 ones to make 7 ones. Four tens and seven ones make 47.

17Switch the addends

Find 3 + 64.

Show solutionHide solution

You may change the order in addition: 3 + 64 = 64 + 3. Four ones plus three ones make seven ones. The sum is 67.

18Add a number with zero ones

Find 70 + 19.

Show solutionHide solution

Seven tens plus one ten make eight tens. Zero ones plus nine ones make nine ones. So 70 + 19 = 89.

19Use a chart mentally

Find 25 + 14.

Show solutionHide solution

Add 2 tens + 1 ten = 3 tens and 5 ones + 4 ones = 9 ones. The sum is 39.

20Explain the value of each digit

Find 43 + 36.

Show solutionHide solution

In 43, the 4 means 4 tens (40) and the 3 means 3 ones. In 36, the 3 means 3 tens (30) and the 6 means 6 ones. Add the tens: 40 + 30 = 70. Add the ones: 3 + 6 = 9. Combine: 70 + 9 = 79.

21Add numbers near 100

Find 81 + 16.

Show solutionHide solution

80 + 10 = 90 and 1 + 6 = 7, so 81 + 16 = 97. The total is still within 100.

22Show the same answer two ways

Find 27 + 32.

Show solutionHide solution

Expanded form: (20 + 30) + (7 + 2) = 50 + 9 = 59. Or add in jumps: 27 + 30 = 57, then 57 + 2 = 59.

23A zero in the ones place

Find 40 + 37.

Show solutionHide solution

40 is 4 tens and 0 ones. Combine with 3 tens and 7 ones. That makes 7 tens and 7 ones: 77.

24Solve an addition story

A library has 32 picture books on one shelf and 26 picture books on another shelf. How many picture books are there altogether?

Show solutionHide solution

Combine both groups because the question asks for the total. Add 30 + 20 = 50 and 2 + 6 = 8. Therefore 32 + 26 = 58 picture books.

25Find a place-value mistake

A student says 34 + 23 = 12 because 3 + 2 = 5, 4 + 3 = 7, and 5 + 7 = 12. Explain the mistake.

Show solutionHide solution

The 3 and 2 are tens digits, not ones. They represent 30 + 20 = 50. The ones are 4 + 3 = 7. So 50 + 7 = 57, not 12.

🎮 Independent Practice — 30 Problems

Directions: add using tens and ones, expanded form, or jumps. Explain your thinking when asked. Keep the answer key hidden until you finish.

1. 23 + 14 = ___.
2. 42 + 16 = ___.
3. 35 + 22 = ___.
4. 61 + 18 = ___.
5. 54 + 25 = ___.
6. 72 + 17 = ___.
7. 46 + 12 = ___.
8. 30 + 45 = ___.
9. 20 + 50 = ___.
10. 63 + 20 = ___.
11. 80 + 9 = ___.
12. 34 + 5 = ___.
13. 7 + 42 = ___.
14. 50 + 36 = ___.
15. 24 + 31 = ___.
16. 43 + 26 = ___.
17. 52 + 37 = ___.
18. 81 + 14 = ___.
19. 33 + 44 = ___.
20. 58 + 21 = ___.
21. 40 + 40 = ___.
22. 26 + 13 = ___.
23. Complete: 20 + 30 = ___.
24. Add the parts: 30 + 4 + 20 + 3 = ___.
25. A model has 3 tens and 7 ones. Add 2 tens and 2 ones. What number do you get?
26. Start at 34. Jump forward 20, then jump forward 3. Where do you land?
27. Find the missing addend: 24 + ___ = 57.
28. Which equals 68? A) 42 + 26   B) 45 + 21   C) 53 + 14.
29. Explain why 43 + 25 = 68 using tens and ones.
30. A class collected 32 cans on Monday and 26 cans on Tuesday. How many cans did it collect altogether?

🏆 Lesson Test — 15 Questions

Directions: work independently. Show tens-and-ones reasoning for the model and explanation problems. Check your answers after finishing the whole test.

1. 24 + 15 = ___.
2. 43 + 26 = ___.
3. 62 + 17 = ___.
4. 51 + 28 = ___.
5. 35 + 42 = ___.
6. 70 + 19 = ___.
7. 40 + 30 = ___.
8. 53 + 20 = ___.
9. 60 + 8 = ___.
10. 7 + 81 = ___.
11. A model shows 2 tens and 4 ones. Add 3 tens and 2 ones. What is the total?
12. Add: 30 + 5 + 20 + 3 = ___.
13. Use two jumps: start at 35, add 20, then add 4. Where do you land?
14. Find the missing addend: 43 + ___ = 68.
15. A student says 32 + 25 = 12 by adding 3 + 2 = 5 and 2 + 5 = 7, then combining 5 + 7. Explain and correct the mistake.

🔐 Complete Answer Key

Show practice answer keyHide practice answer key

Practice Answers

Answer-key note: Accept equivalent drawings, words, and equations when the final sum and place-value reasoning are correct.

1. 37

2. 58

3. 57

4. 79

5. 79

6. 89

7. 58

8. 75

9. 70

10. 83

11. 89

12. 39

13. 49

14. 86

15. 55

16. 69

17. 89

18. 95

19. 77

20. 79

21. 80

22. 39

23. 50

24. 57

25. 59

26. 57

27. 33

28. A) 42 + 26 = 68.

29. Four tens plus two tens make six tens; three ones plus five ones make eight ones, so 43 + 25 = 68.

30. 58 cans; 32 + 26 = 58.

Show test answer keyHide test answer key

Test Answers

Answer-key note: For explanations, accept other correct place-value strategies, not only the example wording.

1. 39

2. 69

3. 79

4. 79

5. 77

6. 89

7. 70

8. 73

9. 68

10. 88

11. 56

12. 58

13. 59

14. 25

15. The tens are 30 + 20 = 50, not 3 + 2 = 5 ones. The ones are 2 + 5 = 7. The correct sum is 50 + 7 = 57.

💡 Common Mistakes to Watch For

Forgetting that tens are worth 10
In 34 + 23, the tens give 30 + 20 = 50, not 3 + 2 = 5 ones.

Adding the wrong places together
Combine tens with tens and ones with ones instead of mixing them.

Leaving out one part
After finding 30 + 20 = 50, remember to add the 4 + 3 = 7 ones.

Thinking every problem needs a new ten
Check the ones total. If it is less than 10, no new ten is needed.

What comes next: Lesson 9 uses the same place-value idea to subtract within 100. Lesson 10 will show how to compose a ten when an addition problem has 10 or more ones.

🔗 Related Lessons

Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20 Review basic facts that make it easier to add the ones in two-digit numbers. Grade 1 — Add Within 100 Using Tens & Ones Review the earlier base-ten approach before moving to larger two-digit addends. Grade 2 Lesson 2 — Compose & Decompose Three-Digit Numbers Revisit how place-value units can be combined to represent the same total.

🖨️ Printable Companion

A future Add Within 100 Using Place Value Practice Pack can include base-ten drawings, place-value charts, expanded-form tasks, number-line jumps, error-analysis problems, mixed addition practice, and a complete answer key.

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