Compose a Ten When Adding | Grade 2 Math

Compose a Ten When Adding — Grade 2 place-value addition lesson
Grade 2 Math  ›  Addition & Subtraction Within 100  ›  Lesson 10
Grade 2 Math — Place Value and Addition

Compose a Ten When Adding

Learn how to add two-digit numbers when their ones make 10 or more. Use base-ten blocks, ten-frames, place-value charts, expanded form, and mental strategies to understand how 10 ones become 1 new ten.

In this lesson, students move from addition without regrouping to composing a ten. Practice the exchange carefully, explain why it works, and check answers without relying on a memorized carrying rule.

Addition within 100Compose a tenRegroupingBase-ten blocksMake-ten strategies

๐ŸŽฏ What You Will Learn

Notice when a new ten is needed
When the ones add to 10 or more, rename them as a ten and the ones left over.
Build and trade with models
Use tens rods, ones cubes, and ten-frames to see that exchanging 10 ones for 1 ten does not change the number.
Add by place value
Combine tens with tens, ones with ones, then include the new ten in the sum.
Explain and check the result
Solve using expanded form, jumps, or another sensible method and explain why each step is valid.
For parents & teachers — standards alignment: This lesson develops CCSS 2.NBT.B.5 through addition within 100 using place-value strategies and properties of operations. Students justify why composing 10 ones as 1 ten preserves the value, supporting CCSS 2.NBT.B.9. Texas TEKS 2.4(B) includes adding up to four two-digit numbers with mental strategies and algorithms based on place value and properties of operations. This lesson addresses the two-addend regrouping step; later lessons extend the work to more addends and subtraction with decomposition.

๐Ÿง  Key Vocabulary

compose a ten — put 10 ones together to make 1 new group of ten.
regroup — rename an amount using equal place-value units without changing its total.
trade / exchange — replace 10 ones with 1 ten because they have the same value.
tens and ones — groups of 10 and single units in a number.
addend — a number being added.
sum — the result of addition.
expanded form — writing a number as its place-value parts, such as 28 = 20 + 8.
ten-frame — a grid of 10 spaces used to show combinations that fill one ten.

๐Ÿ”Ÿ Big Idea: Ten Ones Make One Ten

Ten ones and one ten are equal amounts. If you collect 10 single cubes, you can trade them for one tens rod. The value stays the same, even though one tens rod now replaces ten separate cubes.

Keep the value, change the name: 13 ones = 1 ten + 3 ones. This is why you must count the new ten when you add.

๐Ÿงฑ Build 28 + 15 with Base-Ten Blocks

Begin with 2 tens and 8 ones, then add 1 ten and 5 ones. The ones total 13, so make one new ten and keep 3 ones. That leaves 4 tens and 3 ones in all.

28 + 15 = 43

๐ŸŸ  See 8 + 5 Become 10 + 3

The 8 blue counters and 5 orange counters represent the ones in 28 and 15. Use 2 of the orange counters to fill the first ten-frame. The other 3 orange counters stay in the second frame.

8 ones + 5 ones = 13 ones = 1 ten + 3 ones

Nothing disappears: there are still 8 blue and 5 orange counters, or 13 altogether.

๐Ÿ  Compose a Ten in Four Steps

1. Break apart28 = 20 + 8
15 = 10 + 5
2. Add the ones8 + 5 = 13
3. Compose a ten13 ones = 1 ten + 3 ones
4. Count all tens2 + 1 + 1 = 4 tens
Answer: 43
Common mistake: stopping at 3 tens and 3 ones gives 33, not 43. You must add the extra ten made by the 13 ones.

๐Ÿ“Š Use a Place-Value Chart

The ones column may temporarily contain more than nine ones. Trade 10 of them for a ten, then show the result with fewer than 10 ones.

StepTensOnes
2828
+ 15+ 1+ 5
Before trading313
Trade 10 ones for 1 ten3 + 113 − 10
Sum43

๐Ÿงฎ Two Ways to Show the Same Addition

Expanded-form strategy
  1. 28 = 20 + 8 and 15 = 10 + 5.
  2. Add tens: 20 + 10 = 30.
  3. Add ones: 8 + 5 = 13.
  4. Regroup 13 as 10 + 3.
  5. 30 + 10 + 3 = 43.
Make a friendly ten mentally
  1. Start with 28.
  2. Break 15 into 2 + 10 + 3.
  3. 28 + 2 = 30.
  4. 30 + 10 = 40.
  5. 40 + 3 = 43. Check: 2 + 10 + 3 = 15.

These methods use different steps but describe the same amount. You do not have to use a single method for every addition problem.

➡️ Show the Jumps on an Open Number Line

Another way to see 28 + 15 is to add 10, then add 2 to reach 40, then add 3 more. Each jump is a part of the original 15.

Open number line: start at twenty-eight, jump ten to thirty-eight, two to forty, and three to forty-three. +10+2+3 28384043

28 → 38 → 40 → 43: add 10, then 2, then 3.

๐Ÿ’ก When Do You Need to Compose a Ten?

28 + 15 = 43
8 ones + 5 ones = 13 ones, so make a new ten.
34 + 23 = 57
4 ones + 3 ones = 7 ones. No new ten is needed in this example.
48 + 22 = 70
8 ones + 2 ones = exactly 10 ones. Make one ten and leave zero ones.
29 + 16 = 45
Make a friendly ten by moving one from 16 to 29: 30 + 15 = 45.
Quick check: the sum should be greater than each positive addend. For 28 + 15, the result 43 is greater than both 28 and 15. Use this to catch some mistakes, then verify with place-value reasoning.

๐ŸŒŸ 25 Worked Examples

Try each problem first. Then open “Show solution” to see exactly how the new ten is made and used. The final example includes an error-analysis challenge.
1Make a ten using ones
Find 8 + 5 by making ten.
Show solutionHide solution

Eight needs 2 more to make 10. Break 5 into 2 + 3. Then 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13. This same idea helps when adding two-digit numbers.

2Compose a new ten with base-ten blocks
Find 28 + 15.
Show solutionHide solution

There are 2 tens and 8 ones in 28, plus 1 ten and 5 ones in 15. The ones give 8 + 5 = 13 ones. Trade 10 ones for 1 new ten, leaving 3 ones. Now 2 + 1 + 1 = 4 tens, so the sum is 43.

3Add tens, then regroup the ones
Find 27 + 16.
Show solutionHide solution

The tens are 20 + 10 = 30. The ones are 7 + 6 = 13. Write 13 as 10 + 3 and add the extra ten: 30 + 10 + 3 = 43.

4Show the new ten in a place-value chart
Find 36 + 27.
Show solutionHide solution

Six ones plus seven ones make 13 ones, or 1 new ten and 3 ones. Three tens plus two tens plus the new ten make 6 tens. The answer is 63.

5Regroup when the ones total 13
Find 47 + 26.
Show solutionHide solution

Add the ones: 7 + 6 = 13. Trade 10 of those ones for 1 ten and keep 3 ones. The tens become 4 + 2 + 1 = 7 tens, so 47 + 26 = 73.

6Regroup when the ones total 15
Find 58 + 17.
Show solutionHide solution

Eight ones plus seven ones make 15 ones. Rename this as 1 ten and 5 ones. Five tens plus one ten plus the new ten make 7 tens. Therefore the sum is 75.

7Add in expanded form
Find 45 + 28.
Show solutionHide solution

Write 45 as 40 + 5 and 28 as 20 + 8. Combine tens: 40 + 20 = 60. Combine ones: 5 + 8 = 13 = 10 + 3. Then 60 + 10 + 3 = 73.

8Cross the next group of ten
Find 39 + 14.
Show solutionHide solution

Add 9 + 4 = 13 ones, or 1 ten and 3 ones. The original tens are 3 + 1 = 4 tens; add the new ten to make 5 tens. The result is 53.

9Compose a ten from 14 ones
Find 26 + 18.
Show solutionHide solution

Six ones plus eight ones make 14 ones. Trade 10 ones for 1 ten, leaving 4 ones. Two tens plus one ten plus the new ten make 4 tens. Therefore 26 + 18 = 44.

10Regroup when the second addend has nine ones
Find 54 + 19.
Show solutionHide solution

The ones are 4 + 9 = 13, so trade 10 ones for a ten and leave 3 ones. The tens are 5 + 1 + 1 = 7 tens. The total is 73.

11Use the same idea with larger addends
Find 68 + 17.
Show solutionHide solution

The ones make 8 + 7 = 15, or 1 ten and 5 ones. The tens make 6 + 1 + 1 = 8 tens. Combine to obtain 85.

12Regroup when the ones total 12
Find 25 + 37.
Show solutionHide solution

Five ones plus seven ones make 12 ones. Trade 10 ones for 1 ten and keep 2 ones. Two tens plus three tens plus one new ten make 6 tens. So the sum is 62.

13Change the order of the addends
Find 19 + 43.
Show solutionHide solution

For addition, the addends may switch order. Think 43 + 19. The ones give 3 + 9 = 12, or 1 ten and 2 ones. The tens give 4 + 1 + 1 = 6 tens. The sum is 62.

14Regroup with eleven ones
Find 52 + 29.
Show solutionHide solution

Two ones plus nine ones make 11 ones, or 1 ten and 1 one. Five tens plus two tens plus one new ten make 8 tens. Thus 52 + 29 = 81.

15Use mental place-value thinking
Find 37 + 25.
Show solutionHide solution

Start with the tens: 30 + 20 = 50. Add the ones: 7 + 5 = 12 = 10 + 2. Now 50 + 10 + 2 = 62.

16Add with a nine in the ones place
Find 69 + 12.
Show solutionHide solution

The ones are 9 + 2 = 11, which makes 1 new ten and 1 one. The tens become 6 + 1 + 1 = 8 tens. The result is 81.

17Make exactly ten ones
Find 48 + 22.
Show solutionHide solution

Eight ones plus two ones make exactly 10 ones. Trade them for 1 new ten and leave 0 ones. Four tens plus two tens plus one new ten make 7 tens. Therefore 48 + 22 = 70.

18Regroup to make a multiple of ten
Find 31 + 49.
Show solutionHide solution

One one plus nine ones make 10 ones, or 1 new ten and 0 ones. Three tens plus four tens plus one more ten make 8 tens. The sum is 80.

19Show every regrouping step
Find 56 + 18.
Show solutionHide solution

Six ones plus eight ones make 14 ones. Rename 14 as 1 ten and 4 ones. Five tens and one ten are 6 tens; adding the new ten gives 7 tens. The answer is 74.

20Regroup near one hundred
Find 74 + 17.
Show solutionHide solution

The ones are 4 + 7 = 11, or 1 new ten and 1 one. The tens are 7 + 1 + 1 = 9 tens. Therefore 74 + 17 = 91.

21Use an open number line
Find 28 + 15 using jumps.
Show solutionHide solution

Break 15 into 10 + 2 + 3. Start at 28, jump +10 to 38, jump +2 to 40, and jump +3 to 43. The combined jump is 15, so 28 + 15 = 43.

22Make a friendly ten by compensating
Find 29 + 16.
Show solutionHide solution

Move 1 from 16 to 29. The total does not change: 29 + 16 = 30 + 15. Now add 30 + 15 = 45. You made a ten without changing the sum.

23Extension: reach exactly one hundred
Find 58 + 42.
Show solutionHide solution

Eight ones plus two ones make 10 ones, or 1 new ten and 0 ones. Five tens plus four tens plus that new ten give 10 tens. Ten tens are 1 hundred, so the sum is 100.

24Solve a story with a new ten
A class collected 38 bottles in the morning and 26 bottles in the afternoon. How many bottles did it collect altogether?
Show solutionHide solution

Add the two groups. The ones are 8 + 6 = 14, which is 1 ten and 4 ones. The tens are 3 + 2 + 1 = 6 tens. The class collected 64 bottles.

25Find and fix a missing ten
A student writes 47 + 28 = 65 after finding 7 + 8 = 15. What went wrong?
Show solutionHide solution

The student kept the 5 ones but did not add the new ten from 15 ones. Regroup 15 ones as 1 ten and 5 ones. Then 4 + 2 + 1 = 7 tens. The correct sum is 75.

๐ŸŽฎ Independent Practice — 30 Problems

Directions: add using tens and ones, drawings, an open number line, or another strategy that explains the new ten. Keep the answer key hidden until you have tried the problems.

  1. 26 + 17 = ___.
  2. 38 + 15 = ___.
  3. 47 + 18 = ___.
  4. 29 + 14 = ___.
  5. 56 + 27 = ___.
  6. 45 + 16 = ___.
  7. 68 + 13 = ___.
  8. 37 + 28 = ___.
  9. 24 + 19 = ___.
  10. 59 + 12 = ___.
  11. 18 + 27 = ___.
  12. 35 + 26 = ___.
  13. 49 + 25 = ___.
  14. 63 + 18 = ___.
  15. 27 + 35 = ___.
  16. 42 + 29 = ___.
  17. 58 + 16 = ___.
  18. 36 + 45 = ___.
  19. 71 + 19 = ___.
  20. 46 + 34 = ___.
  21. 39 + 31 = ___.
  22. 75 + 16 = ___.
  23. 48 + 27 = ___.
  24. 57 + 25 = ___.
  25. Extension challenge: 58 + 42 = ___.
  26. Use tens and ones to solve 34 + 28. Show the ones before and after trading 10 ones for 1 ten.
  27. Start at 47. Jump forward 20, then 9 more. Where do you land?
  28. Which sum equals 63? A) 38 + 25   B) 47 + 15   C) 54 + 18.
  29. A student says 28 + 15 = 33 because 8 + 5 = 13. Explain the mistake and correct the sum.
  30. A student group picked 37 apples in one orchard and 26 apples in another. How many apples did it pick altogether?

๐Ÿ† Lesson Test — 15 Questions

Directions: work independently. Show your place-value thinking on the model and explanation problems. Use the answer key to check after finishing the test.

  1. 28 + 15 = ___.
  2. 46 + 27 = ___.
  3. 37 + 18 = ___.
  4. 59 + 24 = ___.
  5. 68 + 13 = ___.
  6. 45 + 38 = ___.
  7. 27 + 16 = ___.
  8. 52 + 29 = ___.
  9. Extension challenge: 58 + 42 = ___.
  10. A box holds 28 blue crayons and 35 red crayons. How many crayons are in the box?
  11. Use a base-ten model: combine 3 tens and 8 ones with 2 tens and 5 ones. What is the total?
  12. For 26 + 17, how many tens and ones are there after trading 10 ones for 1 new ten?
  13. Start at 37. Jump forward 20, then 8 more. What number do you reach?
  14. Find the missing addend: 29 + □ = 64. Explain a way to count on to the answer.
  15. A student says 27 + 38 = 55. Explain the place-value mistake and give the correct sum.

๐Ÿ” Complete Answer Key

Show practice answer keyHide practice answer key

Practice Answers

Answer-key note: Accept equivalent drawings, numbers, and explanations when they show the correct trade and final answer. Different valid addition strategies are welcome.

1. 43
2. 53
3. 65
4. 43
5. 83
6. 61
7. 81
8. 65
9. 43
10. 71
11. 45
12. 61
13. 74
14. 81
15. 62
16. 71
17. 74
18. 81
19. 90
20. 80
21. 70
22. 91
23. 75
24. 82
25. 100. 8 + 2 = 10 ones; trade for 1 ten. 5 + 4 + 1 = 10 tens, or 100.
26. 62. 3 tens + 2 tens = 5 tens; 4 ones + 8 ones = 12 ones. Trade 10 ones for 1 ten: 6 tens and 2 ones remain.
27. 76. 47 + 20 = 67; then 67 + 9 = 76.
28. A. 38 + 25 = 63. B = 62 and C = 72.
29. 43. The student left out the new ten: 8 + 5 = 13 ones = 1 ten and 3 ones. The tens are 2 + 1 + 1 = 4 tens.
30. 63 apples. 37 + 26 = 63; 7 + 6 = 13 ones, which make 1 ten and 3 ones.
Show test answer keyHide test answer key

Test Answers

Answer-key note: For models and explanations, other mathematically correct place-value strategies are acceptable.

1. 43
2. 73
3. 55
4. 83
5. 81
6. 83
7. 43
8. 81
9. 100. Eight ones plus two ones make a new ten; ten tens make one hundred.
10. 63 crayons. 28 + 35 = 63.
11. 63. Five tens and thirteen ones become six tens and three ones.
12. 4 tens and 3 ones (43). Six plus seven ones make 13 ones; the new ten joins 2 + 1 tens.
13. 65. 37 + 20 = 57; 57 + 8 = 65.
14. 35. Count from 29: +1 to 30, +30 to 60, +4 to 64. Altogether 1 + 30 + 4 = 35.
15. 65. Seven ones plus eight ones are 15 ones, or 1 ten and 5 ones. Two tens plus three tens plus the new ten make 6 tens.

๐Ÿ’ก Common Mistakes to Watch For

Forgetting the newly made ten
Eight ones plus five ones make 13 ones: 1 ten and 3 ones, not only 3 ones.
Keeping 13 as a single ones digit
A standard two-digit place-value chart needs 0–9 ones. Trade ten of the thirteen ones for one ten.
Adding the new ten twice
When you trade 10 ones for 1 ten, the 10 ones are no longer counted separately. It is one equal exchange, not a bonus ten.
Thinking every problem needs regrouping
Check the ones first. For 34 + 23, 4 + 3 = 7, so no new ten is needed.
What comes next: Lesson 11 — Decompose a Ten When Subtracting — reverses the exchange. You will learn how to trade 1 ten for 10 ones when a number does not have enough ones to subtract directly.

๐Ÿ”— Related Lessons

Grade 2 Lesson 8 — Add Within 100 Using Place ValueReview adding tens and ones before working with totals that make a new ten. Grade 2 Lesson 9 — Subtract Within 100 Using Place ValueReview how place-value units are organized in the previous subtraction lesson. Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20Practice the make-ten facts that help add ones quickly. Grade 1 — Number Bonds & Ways to Make 10Review number pairs that build a full ten.

๐Ÿ–จ️ Printable Companion

A future Compose a Ten When Adding Practice Pack can include base-ten trading mats, ten-frame puzzles, place-value charts, expanded-form practice, number-line jumps, word problems, error analysis, and a complete answer key.

← Lesson 9: Subtract Within 100 Using Place Value Grade 2 Math Hub Next: Decompose a Ten When Subtracting →

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