Subtract Within 100 Using Place Value | Grade 2 Math

Grade 2 Math  ›  Addition & Subtraction Within 100  ›  Lesson 9

Grade 2 Math — Subtraction and Place Value

Subtract Within 100 Using Place Value

Learn to subtract within 100 by taking away tens from tens and ones from ones. Use base-ten blocks, place-value charts, expanded form, and backward jumps on an open number line to understand each difference.

We begin with subtraction problems that do not require exchanging a ten for ten ones. This helps you see how place value works. A later lesson teaches how to decompose a ten when the ones in a number are not enough to subtract.

Subtract within 100 Tens & ones Base-ten models Open number lines Check with addition

🎯 What You Will Learn

Subtract tens and ones
Take away groups of ten and single ones without mixing their values.

Show subtraction with models
Use tens rods and ones cubes to represent the starting number, the amount taken away, and what remains.

Explain your reasoning
Write expanded-form equations and use a place-value chart to show each subtraction step.

Subtract mentally and check
Use backward jumps, related addition facts, and place-value thinking to verify the difference.

For parents & teachers — standards alignment: This introductory lesson develops the subtraction portion of CCSS 2.NBT.B.5: fluently adding and subtracting within 100 using place-value strategies, properties of operations, and relationships between addition and subtraction. Explaining why a method works also supports CCSS 2.NBT.B.9. Texas TEKS 2.4(B) includes subtracting two-digit numbers using mental strategies and algorithms grounded in place value and operation properties. This lesson intentionally uses examples without decomposing a ten, preparing students for the dedicated lesson on exchanging one ten for ten ones. These examples develop part of the standards rather than claiming to complete the entire required range of strategies.

🧠 Key Vocabulary

subtract — take one amount away from another, or compare two amounts to find the difference.

difference — the result of subtraction.

tens — groups of 10 ones, such as the 6 tens in 67.

ones — individual units, such as the 7 ones in 67.

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

expanded form — a number written as the sum of its place values, such as 67 = 60 + 7.

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

decompose a ten — exchange one ten for ten ones, a strategy you will learn later.

🏠 Start with Tens and Ones

Think about 67 − 24. The starting number 67 has 6 tens and 7 ones. The amount to take away, 24, has 2 tens and 4 ones. Take away the same kinds of units: tens from tens and ones from ones.

1. Break apart67 = 60 + 7
24 = 20 + 4

2. Subtract tens60 − 20 = 40

3. Subtract ones7 − 4 = 3

4. Combine40 + 3 = 43

Big idea: 6 tens minus 2 tens leaves 4 tens, worth 40 — not 4 ones. Keep track of the unit in each place.

🧱 Build 67 − 24 with Base-Ten Blocks

Each rod represents 10 and each small cube represents 1. The three models below show 67 at the start, 24 taken away, and 43 left. The models show the separate quantities, not an animated removal.

67

6 tens + 7 ones

24

2 tens + 4 ones

43

4 tens + 3 ones

67 − 24 = 43

Begin with 6 tens and 7 ones. Remove 2 tens and 4 ones. You have 4 tens and 3 ones remaining — that is 43.

📊 Organize the Subtraction in a Place-Value Chart

Number	Tens	Ones
67	6	7
− 24	− 2	− 4
= 43	4	3

Important: this chart works directly because 67 has enough ones to take away 4, and enough tens to take away 2. When there are not enough ones, you need to exchange a ten for ones; that comes in Lesson 11.

🧮 Two Ways to Subtract with Place Value

Expanded-form method

1. 67 = 60 + 7.
2. 24 = 20 + 4.
3. Subtract the tens: 60 − 20 = 40.
4. Subtract the ones: 7 − 4 = 3.
5. Combine: 40 + 3 = 43.

Take away tens, then ones

1. Start at 67.
2. Take away 20: 67 − 20 = 47.
3. Take away 4 more: 47 − 4 = 43.
4. 67 − 24 = 43.

Both methods give 43. We can break 24 into 20 + 4 and remove those two parts in order. Since the ones digit of 67 is at least 4, no ten needs to be decomposed.

⬅️ Show Backward Jumps on an Open Number Line

Start at 67. Jump −20 to 47, then jump −4 to 43. An open number line shows the main jumps without labeling every whole number.

67 → 47 → 43: first subtract 20, then subtract 4.

🔟 Subtract Multiples of Ten

80 − 30 = 50
8 tens − 3 tens = 5 tens, and 0 ones − 0 ones = 0 ones.

93 − 40 = 53
Take away 4 tens from 9 tens. The 3 ones stay unchanged.

Check with addition: If 67 − 24 = 43, then 43 + 24 must equal 67. Adding the difference back to the amount taken away gives the starting number.

🌟 25 Worked Examples

Try each problem first. Open “Show solution” to see the tens-and-ones steps. All worked examples use subtraction that does not require exchanging a ten for ones.

1Subtract groups of tens

Find 60 − 20.

Show solutionHide solution

Six tens minus two tens leaves four tens. Four tens equal 40. So 60 − 20 = 40.

2Subtract ones

Find 8 − 3.

Show solutionHide solution

Take away 3 ones from 8 ones. There are 5 ones left, so 8 − 3 = 5.

3Use tens and ones

Find 67 − 24.

Show solutionHide solution

Write 67 as 6 tens and 7 ones. Take away 2 tens and 4 ones. Six tens minus two tens leaves 4 tens; seven ones minus four ones leaves 3 ones. Therefore 67 − 24 = 43.

4Use a place-value chart

Find 58 − 16.

Show solutionHide solution

Subtract tens from tens: 5 tens − 1 ten = 4 tens. Subtract ones from ones: 8 − 6 = 2 ones. Four tens and two ones make 42.

5Subtract in expanded form

Find 94 − 32.

Show solutionHide solution

Break apart each number: 94 = 90 + 4 and 32 = 30 + 2. Subtract tens: 90 − 30 = 60. Subtract ones: 4 − 2 = 2. Combine: 60 + 2 = 62.

6Subtract tens and ones separately

Find 76 − 25.

Show solutionHide solution

Subtract 70 − 20 = 50. Subtract 6 − 5 = 1. Combine 50 + 1 to get 51.

7Check the tens difference

Find 89 − 46.

Show solutionHide solution

Eight tens minus four tens leaves four tens. Nine ones minus six ones leaves three ones. The difference is 43.

8Subtract a smaller two-digit number

Find 53 − 21.

Show solutionHide solution

Five tens minus two tens leaves three tens. Three ones minus one one leaves two ones, so 53 − 21 = 32.

9Use each place value

Find 87 − 43.

Show solutionHide solution

Tens: 80 − 40 = 40. Ones: 7 − 3 = 4. Put the parts together: 40 + 4 = 44.

10Keep tens and ones separate

Find 65 − 14.

Show solutionHide solution

Tens: 60 − 10 = 50. Ones: 5 − 4 = 1. The result is 50 + 1 = 51.

11Write the full expanded-form subtraction

Find 78 − 35.

Show solutionHide solution

78 = 70 + 8 and 35 = 30 + 5. Subtract like units: (70 − 30) + (8 − 5) = 40 + 3 = 43.

12Subtract with larger tens

Find 96 − 24.

Show solutionHide solution

Break 96 into 90 + 6 and 24 into 20 + 4. Tens: 90 − 20 = 70. Ones: 6 − 4 = 2. Combine to get 72.

13Take away tens, then ones

Find 68 − 23.

Show solutionHide solution

Start with 68 and remove 20: 68 − 20 = 48. Now remove the other 3: 48 − 3 = 45. This matches subtracting tens and ones separately.

14Use an open number line

Find 67 − 24 using backward jumps.

Show solutionHide solution

Break 24 into 20 + 4. Start at 67, jump backward 20 to reach 47, and jump backward 4 more to reach 43.

15Subtract three tens

Find 84 − 30.

Show solutionHide solution

Take away 3 tens from 8 tens. Five tens remain, and the 4 ones do not change. The answer is 54.

16Start with zero ones

Find 80 − 30.

Show solutionHide solution

80 has 8 tens and 0 ones. Subtract 3 tens to leave 5 tens; the ones remain 0. Therefore 80 − 30 = 50.

17Subtract a number with zero ones

Find 93 − 40.

Show solutionHide solution

Remove 4 tens from 9 tens and keep the 3 ones. Five tens and three ones make 53.

18Subtract a one-digit number

Find 57 − 5.

Show solutionHide solution

57 contains 5 tens and 7 ones. Remove 5 ones: 7 − 5 = 2 ones. The 5 tens stay the same, so 57 − 5 = 52.

19Subtract zero

Find 64 − 0.

Show solutionHide solution

Taking away zero does not change the number. So 64 − 0 = 64.

20Subtract all the units

Find 48 − 48.

Show solutionHide solution

Subtract 4 tens from 4 tens and 8 ones from 8 ones. No tens or ones remain, so 48 − 48 = 0.

21Subtract six tens

Find 90 − 60.

Show solutionHide solution

Nine tens minus six tens leaves three tens and no ones. Thus 90 − 60 = 30.

22Check a difference using addition

Find 76 − 24 and check the answer.

Show solutionHide solution

Tens: 70 − 20 = 50. Ones: 6 − 4 = 2. The difference is 52. Check: 52 + 24 = 76, so the subtraction is correct.

23Find the missing number in subtraction

Complete 87 − □ = 52.

Show solutionHide solution

Find the missing part: 87 − 52 = 35. Check using addition: 52 + 35 = 87. Therefore the missing number is 35.

24Solve a subtraction story

A supply box holds 68 crayons. Students take 23 crayons out of the box for an art project. How many crayons remain in the box?

Show solutionHide solution

The students removed 23 crayons from the box. Subtract the tens: 60 − 20 = 40. Subtract the ones: 8 − 3 = 5. Therefore 68 − 23 = 45 crayons remaining in the box.

25Correct a place-value error

A student says 74 − 32 = 6 because 7 − 3 = 4, 4 − 2 = 2, and 4 + 2 = 6. Explain the mistake.

Show solutionHide solution

The 7 and 3 stand for tens, not single ones. Seven tens minus three tens leave four tens, or 40. Four ones minus two ones leave 2 ones. The correct difference is 40 + 2 = 42, not 6.

🎮 Independent Practice — 30 Problems

Directions: subtract using tens and ones, expanded form, or backward jumps. Explain your reasoning when asked, and check with addition when it helps. Keep the answer key hidden until you finish.

1. 76 − 24 = ___.
2. 59 − 17 = ___.
3. 88 − 45 = ___.
4. 97 − 36 = ___.
5. 64 − 21 = ___.
6. 75 − 13 = ___.
7. 83 − 42 = ___.
8. 69 − 27 = ___.
9. 58 − 14 = ___.
10. 95 − 51 = ___.
11. 84 − 30 = ___.
12. 67 − 20 = ___.
13. 90 − 40 = ___.
14. 70 − 20 = ___.
15. 60 − 0 = ___.
16. 63 − 3 = ___.
17. 49 − 7 = ___.
18. 87 − 87 = ___.
19. 92 − 60 = ___.
20. 55 − 22 = ___.
21. Use expanded form: (80 + 6) − (30 + 4) = ___.
22. A model has 7 tens and 5 ones. Take away 3 tens and 2 ones. How many remain?
23. Start at 76 on an open number line. Jump back 20, then back 3. Where do you land?
24. Which difference is 45? A) 68 − 23   B) 79 − 35   C) 96 − 50.
25. Find the missing addend: 56 + □ = 89. Use a related subtraction fact.
26. Find the missing number: 78 − □ = 45.
27. Find the starting number: □ − 24 = 53.
28. Explain why 92 − 40 = 52 using tens and ones.
29. A library has 74 books on a shelf. Students borrow 31. How many books remain?
30. A student writes 76 − 23 = 8 after computing 7 − 2 = 5 and 6 − 3 = 3, then adding 5 + 3. Explain the mistake and correct the answer.

🏆 Lesson Test — 15 Questions

Directions: work independently. For the model and explanation problems, show how tens and ones help you solve the subtraction. Check the answer key after you finish the whole test.

1. 78 − 35 = ___.
2. 96 − 42 = ___.
3. 85 − 23 = ___.
4. 69 − 27 = ___.
5. 57 − 14 = ___.
6. 90 − 30 = ___.
7. 68 − 20 = ___.
8. 74 − 4 = ___.
9. 50 − 0 = ___.
10. 44 − 44 = ___.
11. A model shows 8 tens and 6 ones. Take away 3 tens and 4 ones. What number remains?
12. Start at 85 on an open number line. Jump back 30, then back 2. Where do you land?
13. Find the missing number: 97 − □ = 52.
14. A teacher has 76 paper stars ready to give out. She hands 32 stars to students. How many paper stars does she still have?
15. A student says 82 − 41 = 5 because 8 − 4 = 4, 2 − 1 = 1, and 4 + 1 = 5. Explain the mistake and give the correct answer.

🔐 Complete Answer Key

Show practice answer keyHide practice answer key

Practice Answers

Answer-key note: Accept equivalent models, equations, and explanations when the subtraction reasoning and result are correct. For missing-number problems, students may also check their answers with addition.

1. 52

2. 42

3. 43

4. 61

5. 43

6. 62

7. 41

8. 42

9. 44

10. 44

11. 54

12. 47

13. 50

14. 50

15. 60

16. 60

17. 42

18. 0

19. 32

20. 33

21. 52; 80 − 30 = 50 and 6 − 4 = 2, so 50 + 2 = 52.

22. 43; 7 tens − 3 tens = 4 tens, and 5 ones − 2 ones = 3 ones.

23. 53; 76 − 20 = 56, then 56 − 3 = 53.

24. A) 68 − 23 = 45. B equals 44, and C equals 46.

25. 33; 89 − 56 = 33, and 56 + 33 = 89.

26. 33; 78 − 45 = 33, and 45 + 33 = 78.

27. 77; 53 + 24 = 77, and 77 − 24 = 53.

28. 92 is 9 tens and 2 ones. Remove 4 tens to leave 5 tens; the 2 ones stay. The difference is 52.

29. 43 books; 74 − 31 = 43.

30. The student combined the tens count and ones count as single ones. Five tens are 50, so 50 + 3 = 53. The correct difference is 76 − 23 = 53.

Show test answer keyHide test answer key

Test Answers

Answer-key note: Explanations may be worded differently as long as they correctly identify the tens and ones and produce the right difference.

1. 43

2. 54

3. 62

4. 42

5. 43

6. 60

7. 48

8. 70

9. 50

10. 0

11. 52; 8 tens − 3 tens = 5 tens, and 6 ones − 4 ones = 2 ones.

12. 53; 85 − 30 = 55 and 55 − 2 = 53.

13. 45; 97 − 52 = 45. Check: 52 + 45 = 97.

14. 44 paper stars; 76 − 32 = 44.

15. Four tens and one one remain, not five ones. 80 − 40 = 40 and 2 − 1 = 1, so 82 − 41 = 41.

💡 Common Mistakes to Watch For

Thinking tens are single ones
In 67 − 24, the tens digits represent 6 tens and 2 tens. Subtracting them leaves 4 tens, or 40 — not just 4 ones.

Mixing up the places
Subtract tens from tens and ones from ones. Label each part before combining the results.

Changing the subtraction order
Start with the number given first and remove the amount named second. Swapping the numbers changes the subtraction problem.

Taking away only the tens
After 67 − 20 = 47, remember to subtract the remaining 4 ones to reach 43.

What comes next: Lesson 10 introduces composing a ten when adding. Lesson 11 then explains how to decompose a ten when subtracting, including cases where there are not enough ones to take away directly.

🔗 Related Lessons

Grade 2 Lesson 8 — Add Within 100 Using Place ValueReview how place value works with tens and ones before using the same units in subtraction. Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20Strengthen the basic subtraction facts that help you find ones differences. Grade 1 — Add & Subtract Multiples of 10Review working with whole groups of tens before subtracting larger two-digit numbers. Grade 1 — Subtraction Strategies Within 20Review taking away, mental strategies, and checking with related addition facts.

🖨️ Printable Companion

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

← Lesson 8: Add Within 100 Using Place Value Grade 2 Math Hub Next: Compose a Ten When Adding →