Decompose a Ten When Subtracting | Grade 2 Math

Grade 2 Math ›  Addition & Subtraction Within 100  ›  Lesson 11

Grade 2 Math — Subtraction and Place Value

Decompose a Ten When Subtracting

Learn to subtract two-digit numbers when there are not enough ones to subtract directly. Trade one ten for ten ones, use base-ten blocks and ten-frames, and explain how regrouping works without changing a number's value.

Students will use place-value charts, expanded form, open number lines, related addition facts, and clear step-by-step strategies to subtract within 100 with understanding.

Subtract within 100Decompose a tenRegroupingTens & onesGrade 2 Math

🎯 What You Will Learn

Know when a trade is needed
If the ones you must take away are greater than the ones you have, exchange a ten for ten ones.

Rename the starting number
Understand why 42 is both 4 tens + 2 ones and 3 tens + 12 ones.

Subtract the correct units
After trading, subtract ones from ones and tens from tens.

Explain and check
Use models, drawings, related addition facts, or mental jumps to show why the difference is correct.

For parents & teachers — standards alignment: This lesson develops the subtraction component of CCSS 2.NBT.B.5, which includes fluent subtraction within 100 through place-value strategies and related operations. Students explain why their representations work, supporting CCSS 2.NBT.B.9. Texas TEKS 2.4(B) expects students to subtract two-digit numbers using mental strategies and algorithms grounded in place value and properties of operations. MathLattice focuses here on exchanging one ten for ten ones and connecting that trade to other valid methods; this is one part of the broader grade-level expectations.

🧠 Key Vocabulary

decompose a ten — rename 1 ten as 10 ones, keeping the same value.

regroup / trade — use equal place-value units to rename a number without changing its value.

tens and ones — groups of ten and single units.

starting number — the amount you begin with in a subtraction equation.

amount taken away — the number you subtract from the starting number.

difference — the result after subtracting.

expanded form — a number written as its place-value parts, such as 42 = 40 + 2.

related addition fact — an equation used to check subtraction, such as 25 + 17 = 42.

🔟 Big Idea: One Ten Equals Ten Ones

In 42 − 17, you have only 2 ones, but you need to take away 7 ones. Trade 1 of the 4 tens for 10 ones. Now 42 is represented as 3 tens and 12 ones, still worth the same 42.

42 = 4 tens + 2 ones = 3 tens + 12 ones

Important: a trade does not add anything or take anything away. The value stays 42. Only the number of tens rods and ones cubes changes.

🧱 Build 42 − 17 with Base-Ten Blocks

The first model shows 42 with 4 tens rods and 2 ones. The second model shows the same value after trading one ten for ten ones. The last model shows what remains after removing 1 ten and 7 ones.

42

4 tens + 2 ones

42

3 tens + 12 ones

25

2 tens + 5 ones

In the middle model, the orange cubes represent the ten ones obtained by trading one ten; the two original green ones are still there.

42 − 17 = 25

🧮 Take Away Seven Ones from Twelve Ones

After trading, there are 12 ones. To subtract the 7 ones in 17, cross out 7 of them. Five ones remain. Together, the two ten-frames show all 12 ones: seven counters are crossed out, and five remain.

12 ones − 7 ones = 5 ones

Seven pink counters are crossed out. Three green counters in the first frame and two green counters in the second frame remain: 3 + 2 = 5 ones.

🏠 Decompose a Ten in Four Steps

1. Break apart42 = 4 tens + 2 ones17 = 1 ten + 7 ones

2. Trade a ten42 = 3 tens + 12 ones

3. Subtract12 − 7 = 5 ones3 − 1 = 2 tens

4. Combine2 tens + 5 ones = 25

Common mistake: after trading one ten, you have 3 tens, not 4 tens. Subtracting 1 ten from the original 4 tens would count the traded ten twice.

📊 Use a Place-Value Chart

Step	Tens	Ones
42	4	2
Trade 1 ten for 10 ones	3	12
Subtract 17	3 − 1	12 − 7
Difference	2	5

The ones column can temporarily show 12 ones because we have renamed one ten. After subtraction, we have 2 tens and 5 ones, a standard representation of 25.

🧠 Two Ways to Subtract

Use expanded form with a trade

1. Start with 42 = 40 + 2.
2. Rename it as 30 + 12.
3. Write 17 = 10 + 7.
4. Subtract like units: (30 − 10) + (12 − 7).
5. Combine: 20 + 5 = 25.

Subtract in mental jumps

1. Start at 42.
2. Subtract 10 to reach 32.
3. Subtract 7 more to reach 25.
4. Check that 10 + 7 = 17, so 42 − 17 = 25.

Compare the methods: the first explains the place-value trade directly; the second breaks the number taken away into convenient parts. Both give the same difference.

⬅️ Backward Jumps on an Open Number Line

Start at 42. Move back 10 to 32, then back 7 to 25. An open number line shows these useful jumps without marking every single number.

42 → 32 → 25: subtract 10, then subtract 7.

🔎 When Is a Trade Needed?

42 − 17 needs a trade
The starting number has 2 ones, but you need to subtract 7 ones. Since 2 is less than 7, rename one ten as ten ones.

67 − 24 does not need a trade
The starting number already has 7 ones and you only subtract 4 ones, so 7 − 4 works directly.

Look at the ones digits to decide whether you need to decompose a ten. This lesson focuses on examples that do need the exchange.

0️⃣ Special Case: No Ones to Start With

Look at 50 − 17. Even though 50 has no ones, you can still subtract 7 ones. Trade one of its 5 tens for 10 ones. Then 50 becomes 4 tens and 10 ones.

50 − 17 = 33
Rename 50 as 4 tens and 10 ones. Remove 1 ten and 7 ones: 3 tens and 3 ones remain.

70 − 38 = 32
Rename 70 as 6 tens and 10 ones. Remove 3 tens and 8 ones: 3 tens and 2 ones remain.

Check with addition: 42 − 17 = 25 is correct because 25 + 17 = 42. Use the relationship between addition and subtraction to confirm your answer.

🌟 25 Worked Examples

Try each problem first. Then open “Show solution” to see the regrouping steps. The examples stay within 100 and include models, missing numbers, error analysis, and a story problem.

1Understand the ten exchange

Find 42 − 17.

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In 42, there are 4 tens and 2 ones. Because you need to remove 7 ones, trade 1 ten for 10 ones. Now 42 is 3 tens and 12 ones. Subtract 1 ten to leave 2 tens, and subtract 7 ones from 12 to leave 5 ones. Therefore 42 − 17 = 25. Check: 25 + 17 = 42.

2Trade one ten and subtract

Find 53 − 28.

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Start with 5 tens and 3 ones. Trade 1 ten for 10 ones, so 53 is renamed as 4 tens and 13 ones. Subtract 2 tens and 8 ones: 4 − 2 = 2 tens, and 13 − 8 = 5 ones. Therefore 53 − 28 = 25. Check: 25 + 28 = 53.

3Subtract with seven ones taken away

Find 64 − 37.

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Start with 6 tens and 4 ones. Trade 1 ten for 10 ones, so 64 is renamed as 5 tens and 14 ones. Subtract 3 tens and 7 ones: 5 − 3 = 2 tens, and 14 − 7 = 7 ones. Therefore 64 − 37 = 27. Check: 27 + 37 = 64.

4Regroup when the starting ones digit is one

Find 71 − 46.

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Start with 7 tens and 1 one. Trade 1 ten for 10 ones, so 71 is renamed as 6 tens and 11 ones. Subtract 4 tens and 6 ones: 6 − 4 = 2 tens, and 11 − 6 = 5 ones. Therefore 71 − 46 = 25. Check: 25 + 46 = 71.

5Subtract across a ten

Find 82 − 57.

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Start with 8 tens and 2 ones. Trade 1 ten for 10 ones, so 82 is renamed as 7 tens and 12 ones. Subtract 5 tens and 7 ones: 7 − 5 = 2 tens, and 12 − 7 = 5 ones. Therefore 82 − 57 = 25. Check: 25 + 57 = 82.

6Use the ones before the tens

Find 45 − 19.

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Start with 4 tens and 5 ones. Trade 1 ten for 10 ones, so 45 is renamed as 3 tens and 15 ones. Subtract 1 ten and 9 ones: 3 − 1 = 2 tens, and 15 − 9 = 6 ones. Therefore 45 − 19 = 26. Check: 26 + 19 = 45.

7Rename sixty-three to subtract

Find 63 − 28.

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Start with 6 tens and 3 ones. Trade 1 ten for 10 ones, so 63 is renamed as 5 tens and 13 ones. Subtract 2 tens and 8 ones: 5 − 2 = 3 tens, and 13 − 8 = 5 ones. Therefore 63 − 28 = 35. Check: 35 + 28 = 63.

8Decompose and subtract

Find 54 − 26.

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Start with 5 tens and 4 ones. Trade 1 ten for 10 ones, so 54 is renamed as 4 tens and 14 ones. Subtract 2 tens and 6 ones: 4 − 2 = 2 tens, and 14 − 6 = 8 ones. Therefore 54 − 26 = 28. Check: 28 + 26 = 54.

9Subtract a number with eight ones

Find 92 − 48.

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Start with 9 tens and 2 ones. Trade 1 ten for 10 ones, so 92 is renamed as 8 tens and 12 ones. Subtract 4 tens and 8 ones: 8 − 4 = 4 tens, and 12 − 8 = 4 ones. Therefore 92 − 48 = 44. Check: 44 + 48 = 92.

10Start with zero ones

Find 50 − 17.

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There are no single ones in 50, so we must trade. Rename 50 as 4 tens and 10 ones. Remove 1 ten and 7 ones to get 3 tens and 3 ones. The difference is 33. Check: 33 + 17 = 50.

11Trade from a multiple of ten

Find 70 − 38.

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Start with 7 tens and 0 ones. Trade 1 ten for 10 ones, so 70 is renamed as 6 tens and 10 ones. Subtract 3 tens and 8 ones: 6 − 3 = 3 tens, and 10 − 8 = 2 ones. Therefore 70 − 38 = 32. Check: 32 + 38 = 70.

12Subtract from eighty

Find 80 − 46.

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Start with 8 tens and 0 ones. Trade 1 ten for 10 ones, so 80 is renamed as 7 tens and 10 ones. Subtract 4 tens and 6 ones: 7 − 4 = 3 tens, and 10 − 6 = 4 ones. Therefore 80 − 46 = 34. Check: 34 + 46 = 80.

13Decompose when you have one one

Find 61 − 27.

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Start with 6 tens and 1 one. Trade 1 ten for 10 ones, so 61 is renamed as 5 tens and 11 ones. Subtract 2 tens and 7 ones: 5 − 2 = 3 tens, and 11 − 7 = 4 ones. Therefore 61 − 27 = 34. Check: 34 + 27 = 61.

14Find a difference of eighteen

Find 36 − 18.

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Start with 3 tens and 6 ones. Trade 1 ten for 10 ones, so 36 is renamed as 2 tens and 16 ones. Subtract 1 ten and 8 ones: 2 − 1 = 1 ten, and 16 − 8 = 8 ones. Therefore 36 − 18 = 18. Check: 18 + 18 = 36.

15Subtract a number with nine ones

Find 47 − 29.

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Start with 4 tens and 7 ones. Trade 1 ten for 10 ones, so 47 is renamed as 3 tens and 17 ones. Subtract 2 tens and 9 ones: 3 − 2 = 1 ten, and 17 − 9 = 8 ones. Therefore 47 − 29 = 18. Check: 18 + 29 = 47.

16Regroup in the nineties

Find 94 − 58.

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Rename 94 as 8 tens and 14 ones. Remove 5 tens and 8 ones, leaving 3 tens and 6 ones, or 36. Another way is to subtract in jumps: 94 − 50 = 44 and 44 − 8 = 36. Both methods agree.

17Keep track of remaining tens

Find 73 − 56.

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Start with 7 tens and 3 ones. Trade 1 ten for 10 ones, so 73 is renamed as 6 tens and 13 ones. Subtract 5 tens and 6 ones: 6 − 5 = 1 ten, and 13 − 6 = 7 ones. Therefore 73 − 56 = 17. Check: 17 + 56 = 73.

18Use tens and ones carefully

Find 62 − 39.

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Think of the related addition fact 39 + □ = 62. Count on: 39 + 1 = 40, 40 + 20 = 60, and 60 + 2 = 62. The missing amount is 1 + 20 + 2 = 23. With a trade, 62 becomes 5 tens and 12 ones; subtract 3 tens and 9 ones to get 23.

19Subtract a two-digit number

Find 43 − 25.

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Start with 4 tens and 3 ones. Trade 1 ten for 10 ones, so 43 is renamed as 3 tens and 13 ones. Subtract 2 tens and 5 ones: 3 − 2 = 1 ten, and 13 − 5 = 8 ones. Therefore 43 − 25 = 18. Check: 18 + 25 = 43.

20Subtract to reach a smaller number

Find 85 − 67.

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Rename 85 as 7 tens and 15 ones. Take away 6 tens and 7 ones: 1 ten and 8 ones remain, so the answer is 18. A mental check is 85 − 70 + 3 = 15 + 3 = 18.

21Subtract three tens and eight ones

Find 52 − 38.

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Start with 5 tens and 2 ones. Trade 1 ten for 10 ones, so 52 is renamed as 4 tens and 12 ones. Subtract 3 tens and 8 ones: 4 − 3 = 1 ten, and 12 − 8 = 4 ones. Therefore 52 − 38 = 14. Check: 14 + 38 = 52.

22Remove tens and ones from sixty

Find 60 − 27.

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Start with 6 tens and 0 ones. Trade 1 ten for 10 ones, giving 5 tens and 10 ones. Remove 2 tens and 7 ones. This leaves 3 tens and 3 ones, or 33. Check: 33 + 27 = 60.

23Find the missing number in subtraction

Complete 72 − □ = 38.

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The number taken away must be 72 − 38. Rename 72 as 6 tens and 12 ones; subtract 3 tens and 8 ones. That leaves 3 tens and 4 ones, or 34. Check: 72 − 34 = 38, so □ = 34.

24Solve a subtraction story

A supply box holds 64 crayons. Students take 28 crayons out for a project. How many crayons remain in the box?

Show solutionHide solution

Start with 64 crayons and take away 28. Rename 64 as 5 tens and 14 ones. Remove 2 tens and 8 ones. Three tens and six ones remain, so 36 crayons are left in the box. Check: 36 + 28 = 64.

25Find and correct a regrouping mistake

A student writes 52 − 28 = 34, reasoning that 12 − 8 = 4 and 5 − 2 = 3 tens. Explain and fix the mistake.

Show solutionHide solution

Trading a ten changes the number of tens. After renaming 52, there are 4 tens and 12 ones, not 5 tens and 12 ones. Subtract 2 tens and 8 ones to get 2 tens and 4 ones, or 24. Check: 24 + 28 = 52.

🎮 Independent Practice — 30 Problems

Directions: use a place-value trade, a drawing, or a mental strategy to subtract. Explain your thinking when asked. Do not open the answer key until you have tried the problems.

1. 41 − 16 = ___.
2. 52 − 27 = ___.
3. 73 − 48 = ___.
4. 64 − 29 = ___.
5. 85 − 67 = ___.
6. 56 − 38 = ___.
7. 62 − 46 = ___.
8. 94 − 59 = ___.
9. 83 − 37 = ___.
10. 70 − 24 = ___.
11. 60 − 18 = ___.
12. 50 − 36 = ___.
13. 91 − 47 = ___.
14. 72 − 58 = ___.
15. 43 − 16 = ___.
16. 35 − 17 = ___.
17. 81 − 64 = ___.
18. 92 − 75 = ___.
19. 44 − 27 = ___.
20. 66 − 49 = ___.
21. 53 − 35 = ___.
22. 75 − 28 = ___.
23. 82 − 64 = ___.
24. 61 − 45 = ___.
25. 90 − 53 = ___.
26. Which expression equals 25? A) 42 − 17   B) 63 − 37   C) 71 − 56.
27. A model shows 4 tens and 2 ones. Take away 1 ten and 7 ones. How many remain? Show the exchange.
28. Rename 63 by trading one ten. How many tens and ones are there before you subtract?
29. Find the missing number: 72 − □ = 38. Check with addition.
30. A classroom supply bin contains 65 markers. Students take 29 markers out of the bin. How many markers remain?

🏆 Lesson Test — 15 Questions

Directions: solve independently. Use tens-and-ones reasoning for the models and explanations. Check your answers at the end.

1. 42 − 18 = ___.
2. 53 − 27 = ___.
3. 64 − 38 = ___.
4. 71 − 55 = ___.
5. 85 − 49 = ___.
6. 90 − 46 = ___.
7. 60 − 25 = ___.
8. 74 − 57 = ___.
9. 82 − 36 = ___.
10. 93 − 67 = ___.
11. A model shows 5 tens and 2 ones. Take away 2 tens and 7 ones. What remains?
12. When preparing to subtract 71 − 46, how can you rename 71 after trading one ten?
13. Start at 82 on an open number line. Jump back 30 and then back 7. Where do you land?
14. Find the missing number: 63 − □ = 27. Show a way to check.
15. A student writes 52 − 28 = 34 using 12 − 8 = 4 and 5 − 2 = 3 tens. Explain the mistake and give the correct answer.

🔐 Complete Answer Key

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Practice Answers

Answer-key note: Accept other correct strategies when the difference, the exchange, and the place-value explanation are mathematically valid.

1. 25

2. 25

3. 25

4. 35

5. 18

6. 18

7. 16

8. 35

9. 46

10. 46

11. 42

12. 14

13. 44

14. 14

15. 27

16. 18

17. 17

18. 17

19. 17

20. 17

21. 18

22. 47

23. 18

24. 16

25. 37

26. A) 42 − 17 = 25. B is 26; C is 15.

27. 25. Trade 1 ten from 42: 3 tens and 12 ones. Subtract 1 ten and 7 ones to leave 2 tens and 5 ones.

28. 5 tens and 13 ones (same value: 63).

29. 34. Check: 38 + 34 = 72.

30. 36 markers remain; 65 − 29 = 36.

Show test answer keyHide test answer key

Test Answers

Answer-key note: Students may explain with models, words, or equivalent equations if their reasoning and answers are correct.

1. 24

2. 26

3. 26

4. 16

5. 36

6. 44

7. 35

8. 17

9. 46

10. 26

11. 25; rename 52 as 4 tens and 12 ones, then remove 2 tens and 7 ones.

12. 6 tens and 11 ones; the value remains 71.

13. 45; 82 − 30 = 52 and 52 − 7 = 45.

14. 36. Check: 27 + 36 = 63.

15. The student did not reduce the tens count after trading. 52 becomes 4 tens and 12 ones. Then 4 tens − 2 tens = 2 tens and 12 ones − 8 ones = 4 ones, so the correct difference is 24.

💡 Common Mistakes to Watch For

Forgetting to reduce the tens
When you exchange one ten for ten ones, the tens count goes down by one: 42 becomes 3 tens and 12 ones, not 4 tens and 12 ones.

Taking away the wrong number of ones
In 42 − 17, you must remove 7 ones from the 12 ones after trading, leaving 5 ones.

Thinking a trade changes the amount
4 tens + 2 ones and 3 tens + 12 ones both equal 42. Regrouping changes the representation, not the value.

Not checking the difference
Use addition to check: 25 + 17 = 42, so 42 − 17 = 25.

What comes next: Lesson 12 — Add Up to Four Two-Digit Numbers — uses efficient grouping and place-value thinking to add more than two numbers.

🔗 Related Lessons

Grade 2 Lesson 10 — Compose a Ten When AddingSee the opposite trade: 10 ones become 1 ten during addition. Grade 2 Lesson 9 — Subtract Within 100 Using Place ValueReview subtracting tens and ones before exchanging a ten. Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20Review subtraction facts that help when taking away the ones. Grade 1 — Subtraction Strategies Within 20Build fluency with subtracting across ten and checking with addition.

🖨️ Printable Companion

A future Decompose a Ten When Subtracting Practice Pack can include base-ten trading models, ones-and-tens charts, ten-frame tasks, number-line jumps, word problems, error analysis, and a complete answer key.

← Lesson 10: Compose a Ten When Adding Grade 2 Math Hub Next → Lesson 12: Add Up to Four Two-Digit Numbers