Add Up to Four Two-Digit Numbers | Grade 2 Math

Add Up to Four Two-Digit Numbers — Grade 2 place-value addition and grouping
Grade 2 Math ›  Addition & Subtraction Within 100  ›  Lesson 12
Grade 2 Math — Addition and Place Value

Add Up to Four Two-Digit Numbers

Learn to add three or four two-digit numbers by combining tens and ones, making friendly pairs, and choosing helpful groupings. See how the order and grouping of addends can change without changing the sum.

Use base-ten models, place-value charts, equations, and an open number line to explain your thinking. When four two-digit addends make a total greater than 100, learn how ten tens become one hundred.

Add four numbersTwo-digit addendsFriendly number pairsPlace-value strategiesSums over 100

๐ŸŽฏ What You Will Learn

Add three or four two-digit numbers
Add several amounts without leaving out an addend.
Use tens, ones, and hundreds
Combine place-value units and regroup when needed.
Make friendly pairs
Choose groups that make easy tens, such as 36 + 24 = 60.
Explain and check your sum
Use different groupings or a place-value chart to confirm the total.
For parents & teachers — standards alignment: This lesson directly addresses CCSS 2.NBT.B.6, which expects students to add up to four two-digit numbers using place value and properties of operations. Explaining why a strategy works supports CCSS 2.NBT.B.9, while totals above 100 connect naturally to the base-ten understanding in 2.NBT.A.1. Texas Grade 2 TEKS 2.4(B) also explicitly includes adding up to four two-digit numbers with mental strategies and algorithms based on place value and properties of operations. "Two-digit" describes each addend, not necessarily the final sum; four such addends may have a three-digit total, including totals above 200.

๐Ÿง  Key Vocabulary

addend
One of the numbers being added.
sum
The total after adding all the addends.
place value
The value of a digit based on whether it represents hundreds, tens, or ones.
friendly pair
Two numbers that are convenient to add, often making a multiple of ten.
change the order
Move addends around when adding; the sum stays the same (commutative property).
change the grouping
Put addition parentheses in different places; the sum stays the same (associative property).
regroup
Rename equal amounts using place-value units, such as 10 ones as 1 ten.
hundred
A group of 10 tens, equal to 100 ones.

➕ Start with Four Two-Digit Addends

We will solve 36 + 28 + 17 + 24. There are four addends. You must include each one exactly once. First, split every number into tens and ones.

36 + 28 + 17 + 24 = 105

๐Ÿ  Add by Place Value in Four Steps

Start with the tens and ones separately. Because there are 25 ones, we can make two new tens. Then ten tens make one hundred.

1. Add tens30 + 20 + 10 + 20 = 80
2. Add ones6 + 8 + 7 + 4 = 25
3. Make new tens25 ones = 2 tens + 5 ones
4. Make a hundred8 tens + 2 tens = 10 tens = 100; total 105
Big idea: eight tens and twenty-five ones are the same value as ten tens and five ones, or one hundred and five ones. Regrouping changes the representation, not the total.

๐Ÿ“Š Use a Place-Value Chart

It is fine to record more than nine ones while working, but we regroup to write a number in standard hundreds–tens–ones form.

StepHundredsTensOnes
36036
+ 28028
+ 17017
+ 24024
Before regrouping0825
Make 2 new tens0105
Regroup 10 tens105

๐Ÿ’ฏ Ten Tens Become One Hundred

After regrouping the ones, we have 10 tens and 5 ones. Ten tens are worth 100, so we can trade them for one hundred flat. The 5 ones stay as they are.

1 hundred = 100
5 ones = 5
100 + 5 = 105
Do not stop at 85: 8 tens + 25 ones is 80 + 25 = 105. Twenty-five ones make two tens and five ones, not just five ones.

๐Ÿค Make Friendly Pairs Instead

When adding, you may change the order of the addends and regroup them with parentheses. Every addend still appears exactly once.

Pair numbers that make easy tens
(36 + 24) + (28 + 17)

60 + 45 = 105

Keep the original order but group in pairs
(36 + 28) + (17 + 24)

64 + 41 = 105

Why this works: changing the order (commutative property) and the grouping (associative property) of addends does not change their sum. These two methods show the same total, 105.

➡️ See the Addends as Jumps on an Open Number Line

Try a helpful order: start at 36, add 24 to reach 60, add 28 to reach 88, and add 17 to reach 105.

Open number line showing 36 plus 24 is 60, plus 28 is 88, plus 17 is 105. +24+28+17 366088105

36 → 60 → 88 → 105; the jumps are +24, +28, and +17.

๐Ÿง  Choose a Strategy That Fits

Add tens and ones
Use place value when the numbers have clear tens and ones patterns. Regroup 10 ones as a ten and 10 tens as a hundred when needed.
Make friendly pairs
Look for pairs such as 27 + 13 = 40, or 35 + 25 = 60.
Add in small steps
Break an addend into tens and ones; 23 + 35 + 12 can be solved as +30, +5, +10, +2.
Check with another grouping
Rearrange the addends and confirm you get the same result; do not omit or count an addend twice.
Remember: the addends must each be two-digit numbers in this lesson, but their total may have three digits. For example, 36 + 28 + 17 + 24 = 105.

๐ŸŒŸ 25 Worked Examples

Try each problem before opening “Show solution.” The examples build from two and three addends to four addends, friendly groupings, hundreds, missing numbers, and error analysis.
1Warm up with two addends
Find 34 + 23.
Show solutionHide solution

Break 34 into 30 + 4 and 23 into 20 + 3. Add tens: 30 + 20 = 50. Add ones: 4 + 3 = 7. Combine 50 + 7 = 57.

2Add three two-digit numbers
Find 12 + 25 + 31.
Show solutionHide solution

Add the tens: 10 + 20 + 30 = 60. Add the ones: 2 + 5 + 1 = 8. Together, 60 + 8 = 68.

3Add four numbers with a total over 100
Find 36 + 28 + 17 + 24.
Show solutionHide solution

Pair 36 and 24 to make 60. Pair 28 and 17 to make 45. Add the pair totals: 60 + 45 = 105. Four two-digit addends can have a three-digit sum.

4Make friendly pairs
Find 26 + 14 + 35 + 25.
Show solutionHide solution

Group the numbers to make convenient tens: (26 + 14) + (35 + 25) = 40 + 60 = 100. We may change the order and grouping of addends without changing the total.

5Regroup ones from three addends
Find 18 + 27 + 35.
Show solutionHide solution

The tens total 10 + 20 + 30 = 60. The ones total 8 + 7 + 5 = 20 ones, or 2 tens. Add 60 + 20 = 80.

6Collect ten ones from four addends
Find 41 + 12 + 23 + 14.
Show solutionHide solution

There are 4 + 1 + 2 + 1 = 8 tens, or 80. The ones total 1 + 2 + 3 + 4 = 10, which makes one more ten. Then 80 + 10 = 90.

7Double a helpful pair
Find 24 + 24 + 16 + 16.
Show solutionHide solution

Put a 24 with a 16: 24 + 16 = 40. The other 24 + 16 also makes 40. Thus 40 + 40 = 80.

8Add friendly multiples of ten
Find 30 + 20 + 15 + 25.
Show solutionHide solution

Add 30 + 20 = 50. Then 15 + 25 = 40. The total is 50 + 40 = 90.

9Make two groups that total 100
Find 47 + 13 + 18 + 22.
Show solutionHide solution

Make the convenient pairs 47 + 13 = 60 and 18 + 22 = 40. Then 60 + 40 = 100.

10Regroup more than one ten from ones
Find 28 + 17 + 26.
Show solutionHide solution

The tens are 20 + 10 + 20 = 50. The ones total 8 + 7 + 6 = 21 ones: 2 tens and 1 one. Then 50 + 20 + 1 = 71.

11Add four numbers to make 110
Find 55 + 25 + 12 + 18.
Show solutionHide solution

Group the addends as (55 + 25) + (12 + 18) = 80 + 30 = 110.

12Combine a multiple of ten with two addends
Find 60 + 14 + 26.
Show solutionHide solution

Add 14 + 26 = 40, then add 60 + 40 = 100.

13Make a friendly ten by moving one
Find 39 + 21 + 18.
Show solutionHide solution

Move 1 from 21 to 39. This does not change the total: 39 + 21 = 40 + 20 = 60. Then 60 + 18 = 78.

14Choose a new grouping
Find 46 + 19 + 24.
Show solutionHide solution

Group 46 with 24 to make 70. Add the remaining 19: 70 + 19 = 89.

15Recognize different correct groupings
Find 27 + 33 + 16 + 24 in two ways.
Show solutionHide solution

First way: (27 + 33) + (16 + 24) = 60 + 40 = 100. Another way: (27 + 16) + (33 + 24) = 43 + 57 = 100. Both give 100.

16Add four numbers with place-value regrouping
Find 64 + 28 + 17 + 31.
Show solutionHide solution

The tens are 60 + 20 + 10 + 30 = 120. The ones are 4 + 8 + 7 + 1 = 20, or 2 extra tens. Together, 120 + 20 = 140.

17Use an open number line with several jumps
Find 23 + 35 + 12.
Show solutionHide solution

Start at 23. Add 30 to reach 53, then 5 to reach 58. Add 10 to reach 68 and 2 to reach 70. So 23 + 35 + 12 = 70.

18Find a missing two-digit addend
Complete 25 + 17 + □ = 80.
Show solutionHide solution

First add 25 + 17 = 42. Ask what must be added to 42 to make 80: 80 − 42 = 38. So □ = 38. Check: 25 + 17 + 38 = 80.

19Solve a four-group story problem
A class collected 18 cans on Monday, 24 on Tuesday, 16 on Wednesday, and 22 on Thursday. How many cans were collected?
Show solutionHide solution

Pair the days to make friendly totals: 18 + 22 = 40 and 24 + 16 = 40. Thus the class collected 80 cans.

20Add three numbers without making a new ten
Find 32 + 21 + 15.
Show solutionHide solution

The tens make 30 + 20 + 10 = 60. The ones make 2 + 1 + 5 = 8. The total is 68.

21Recognize a three-digit total
Find 11 + 22 + 33 + 44.
Show solutionHide solution

Group 11 + 44 = 55 and 22 + 33 = 55. The sum is 55 + 55 = 110.

22Regroup two tens from four sets of ones
Find 72 + 19 + 14 + 25.
Show solutionHide solution

The tens total 70 + 10 + 10 + 20 = 110. The ones total 2 + 9 + 4 + 5 = 20, or two tens. Then 110 + 20 = 130.

23Correct a missing-ten mistake
A student writes 26 + 18 + 15 = 49 after finding that the ones total 19. Explain the error.
Show solutionHide solution

Nineteen ones are 1 ten and 9 ones. The original tens total 20 + 10 + 10 = 40, and the new ten adds 10 more. So 40 + 10 + 9 = 59, not 49.

24Check whether regrouping changes the sum
True or false? (32 + 18) + (27 + 23) = 32 + 18 + 27 + 23.
Show solutionHide solution

True. We have only changed how the addition is grouped. Each pair makes 50, so both sides equal 100.

25Extension challenge: add four larger two-digit numbers
Find 78 + 22 + 65 + 85 and explain your grouping.
Show solutionHide solution

Group 78 + 22 = 100 and 65 + 85 = 150. Then 100 + 150 = 250. Check by place value: the tens total 70 + 20 + 60 + 80 = 230, and the ones total 8 + 2 + 5 + 5 = 20. Therefore 230 + 20 = 250.

๐ŸŽฎ Independent Practice — 30 Problems

Directions: add the numbers. Look for convenient pairs and use place value to check. When asked, show your grouping or explain the regrouping. Keep the answer key closed until you finish.

  1. 12 + 23 + 34 = ___.
  2. 26 + 14 + 31 = ___.
  3. 18 + 25 + 37 = ___.
  4. 42 + 17 + 21 = ___.
  5. 35 + 28 + 16 = ___.
  6. 47 + 13 + 26 = ___.
  7. 29 + 18 + 34 = ___.
  8. 53 + 27 + 12 = ___.
  9. 16 + 24 + 35 = ___.
  10. 38 + 22 + 19 = ___.
  11. 61 + 15 + 24 = ___.
  12. 45 + 19 + 26 = ___.
  13. 12 + 18 + 27 + 23 = ___.
  14. 34 + 26 + 15 + 25 = ___.
  15. 41 + 18 + 17 + 23 = ___.
  16. 28 + 33 + 14 + 26 = ___.
  17. 36 + 24 + 19 + 21 = ___.
  18. 17 + 23 + 29 + 32 = ___.
  19. 25 + 35 + 18 + 12 = ___.
  20. 44 + 16 + 27 + 12 = ___.
  21. 56 + 14 + 22 + 18 = ___.
  22. 38 + 27 + 16 + 29 = ___.
  23. 47 + 33 + 28 + 12 = ___.
  24. Extension challenge: 62 + 78 + 45 + 35 = ___.
  25. Use tens and ones to add 23 + 34 + 12 + 21.
  26. Group 28 + 17 + 22 + 33 into two friendly pairs. Write your pairs and the sum.
  27. Find the missing number: 18 + 24 + □ = 75.
  28. Find the missing number: 31 + 19 + 25 + □ = 100.
  29. Four classes collect 18, 23, 27, and 32 bottles. How many bottles are collected altogether?
  30. A student writes 34 + 19 + 28 = 71. The student found 6 tens and 21 ones but added only 1 new ten. Explain the mistake and correct the answer.

๐Ÿ† Lesson Test — 15 Questions

Directions: work independently. Include an equation or a few clear words for the grouping, model, and error-analysis questions. Check your answers after finishing the whole test.

  1. 24 + 15 + 31 = ___.
  2. 28 + 17 + 23 = ___.
  3. 46 + 23 + 18 = ___.
  4. 35 + 26 + 17 = ___.
  5. 14 + 26 + 38 + 22 = ___.
  6. 19 + 23 + 34 + 27 = ___.
  7. 27 + 13 + 28 + 32 = ___.
  8. 44 + 18 + 26 + 11 = ___.
  9. 58 + 22 + 17 + 23 = ___.
  10. Extension challenge: 66 + 34 + 58 + 42 = ___.
  11. Find 54 + 16 + 37 + 23. Show a helpful grouping.
  12. Use place value to add 43 + 26 + 18 + 15. Explain the ones regrouping.
  13. Find the missing addend: 27 + 18 + □ = 92.
  14. A box contains 24 red beads, 16 blue beads, 37 green beads, and 29 yellow beads. How many beads are in the box?
  15. A student writes 49 + 18 + 27 + 36 = 120 after finding 10 tens and 30 ones. The student made only 2 new tens from the ones. Explain the mistake and correct the total.

๐Ÿ” Complete Answer Key

Show practice answer keyHide practice answer key

Practice Answers

Answer-key note: Accept other correct orders, pairings, place-value drawings, and explanations. Students must use every addend exactly once and give the correct sum.

1. 69
2. 71
3. 80
4. 80
5. 79
6. 86
7. 81
8. 92
9. 75
10. 79
11. 100
12. 90
13. 80
14. 100
15. 99
16. 101
17. 100
18. 101
19. 90
20. 99
21. 110
22. 110
23. 120
24. 220
25. 90. The tens total 80; the ones total 10, making one more ten.
26. (28 + 22) + (17 + 33) = 50 + 50 = 100.
27. 33. First 18 + 24 = 42; then 75 − 42 = 33.
28. 25. The known numbers total 75; 100 − 75 = 25.
29. 100 bottles. Pair 18 + 32 = 50 and 23 + 27 = 50.
30. 81. The tens total 30 + 10 + 20 = 60, and the ones total 4 + 9 + 8 = 21. Twenty-one ones make 2 tens and 1 one, so 60 + 20 + 1 = 81, not 71.
Show test answer keyHide test answer key

Test Answers

Answer-key note: For questions requiring reasoning, mathematically equivalent grouping strategies are correct if they preserve all the addends.

1. 70
2. 68
3. 87
4. 78
5. 100
6. 103
7. 100
8. 99
9. 120
10. 200. Group (66 + 34) + (58 + 42) = 100 + 100 = 200.
11. 130. One helpful grouping is (54 + 16) + (37 + 23) = 70 + 60 = 130.
12. 102. The tens make 40 + 20 + 10 + 10 = 80. The ones make 3 + 6 + 8 + 5 = 22, or 2 tens and 2 ones. Then 80 + 20 + 2 = 102.
13. 47. Since 27 + 18 = 45, the missing number is 92 − 45 = 47. Check: 27 + 18 + 47 = 92.
14. 106 beads. Pair 24 + 16 = 40 and 37 + 29 = 66; 40 + 66 = 106.
15. 130. The original tens are 40 + 10 + 20 + 30 = 100. The ones are 9 + 8 + 7 + 6 = 30, which make 3 new tens, not 2. So 100 + 30 = 130, not 120.

๐Ÿ’ก Common Mistakes to Watch For

Leaving out an addend
Count the numbers in the question and make sure each one appears exactly once in your work.
Forgetting new tens from ones
In 36 + 28 + 17 + 24, 25 ones make two tens and five ones. Add both new tens.
Thinking the sum must stay below 100
Two-digit addends can have a three-digit total. Ten tens make 100.
Changing the operation
You may rearrange or group addends in addition, but you may not accidentally subtract or change one of the addends.
What comes next: Continue your math journey with Lesson 13 — Mental Addition & Subtraction Strategies . Learn to make tens, use compensation, recognize related facts, and choose smart mental math strategies to solve addition and subtraction problems more easily.

๐Ÿ”— Related Lessons

Grade 2 Lesson 10 — Compose a Ten When AddingReview how ten ones are traded for one new ten. Grade 2 Lesson 8 — Add Within 100 Using Place ValueReview how to combine tens with tens and ones with ones. Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20Use known addition facts to make adding several numbers easier. Grade 1 — Number Bonds & Ways to Make 10Review pairs that make ten, a foundation for helpful regrouping.

๐Ÿ–จ️ Printable Companion

A future Add Up to Four Two-Digit Numbers Practice Pack can include four-addend place-value charts, friendly-pair puzzles, number-line jumps, word problems, regrouping activities, error analysis, and a complete answer key.

← Lesson 11: Decompose a Ten When Subtracting Grade 2 Math Hub Next → Lesson 13: Mental Addition & Subtraction Strategies

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