Mental Addition & Subtraction Strategies | Grade 2 Math

Grade 2 Math ›  Addition & Subtraction Within 100  ›  Lesson 13

Grade 2 Math — Addition & Subtraction Strategies

Mental Addition & Subtraction Strategies

Build confidence with mental math in second grade. Learn to make a ten, count on and back, use doubles and near doubles, break numbers into tens and ones, and use compensation to make addition and subtraction easier.

Practice choosing smart strategies for facts within 20 and two-digit calculations within 100. Step-by-step worked examples, colorful visual models, 30 practice problems, and a 15-question lesson test help you explain why each method works.

Make a tenCount on and backDoubles & near doublesBreak apartCompensationAddition–subtraction facts

🎯 What You Will Learn

Choose a smart strategy
Look at the numbers before deciding whether to count, make ten, use doubles, or break apart.

Work confidently within 20
Use known facts to add and subtract without counting every object from one.

Think with tens and ones
Add and subtract two-digit numbers mentally using place value and helpful jumps.

Explain and check
Tell why your strategy keeps the correct total or difference and verify with the opposite operation.

For parents & teachers — standards alignment: Common Core alignment: CCSS 2.OA.B.2 (fluent mental addition and subtraction within 20), CCSS 2.NBT.B.5 (place-value and related strategies for fluency within 100), and CCSS 2.NBT.B.9 (explain why strategies work). Texas alignment: TEKS 2.4(A) (basic facts within 20) and 2.4(B) (mental strategies for addition and subtraction with two-digit numbers). Common Core is a reference framework, not a claim that every state uses identical standards.

🧠 Key Vocabulary

mental math
Solving with number relationships instead of writing every step of an algorithm.

make a ten
Break a number into parts so another number reaches 10 or the next multiple of ten.

count on / count back
Start from a helpful number and move forward or backward by a small amount.

double / near double
A double adds a number to itself. Near doubles have two addends that differ by one; use a known double and then adjust the sum by one.

break apart
Split a number into tens and ones, or into other helpful parts.

compensation
Change a number to make a calculation easier, then adjust to keep the correct result.

related facts
Addition and subtraction equations made from the same numbers.

difference
The result of subtraction; it tells how many remain or how far apart two numbers are.

✨ Mental Math Is Smart Thinking — Not Just Speed

Big idea: There may be several correct mental strategies for one problem. A good choice uses number patterns you already know. It is okay to draw a number line or write a short equation while you learn. The goal is accurate, flexible thinking, not rushing.

🧩 Make a tenBest near 10 or a new ten

8 + 6 = 10 + 4

👣 Count on / backBest for small changes

27 + 5 = 32

💜 Doubles & near doublesUse known pairs

6 + 7 = 6 + 6 + 1

🏠 Break apartTens first, then ones

47 + 26 = 47 + 20 + 6

⚖️ CompensationUse 9, 19, 29 as almost 10, 20, 30

38 + 9 = 38 + 10 − 1

🔗 Related factsTurn subtraction into a known addition

17 − 8 = 9, since 8 + 9 = 17

🟦 Strategy 1: Make a Ten

To find 8 + 6, look for the amount that 8 needs to reach 10. It needs 2. Split the 6 into 2 + 4. Use 2 to complete the ten, then add the remaining 4.

Fill the ten-frame: 8 blue + 2 yellow = 10.

These 4 yellow ones are left from the original 6.

8 + 6 = 8 + 2 + 4 = 10 + 4 = 14

Subtraction can make a ten, too: To solve 14 − 6, take away 4 to reach 10, then take away the remaining 2. So 14 − 4 − 2 = 8.

💜 Strategy 2: Doubles and Near Doubles

A double is a fact you know, such as 6 + 6 = 12. A near double is only one away: 6 + 7 is one more than 6 + 6.

Known double: 6 + 6

6 + 6 = 12

Near double: 6 + 7

6 + 7 = 12 + 1 = 13

Near doubles are especially useful when two addends differ by just one. You can also use 7 + 8 = 7 + 7 + 1.

👣 Strategy 3: Count On or Back in Helpful Jumps

To find 27 + 5, start at 27. Jump 3 to the friendly number 30, then jump the remaining 2 to 32. You have jumped forward 5 altogether, using the next ten to make your mental math easier.

27 → 30 → 32: first reach the next ten (+3), then add the remaining 2.

For subtraction, count backward. To find 34 − 6, go back 4 to 30, then back 2 more to 28.

34 → 30 → 28: jumps of −4 and −2 make −6.

🏠 Strategy 4: Break Apart Tens and Ones

Add 47 + 26

Split 26 into 20 and 6. First 47 + 20 = 67. Then 67 + 6 = 73.

47 + 26 = 47 + 20 + 6 = 73

Subtract 68 − 24

Split 24 into 20 and 4. First 68 − 20 = 48. Then 48 − 4 = 44.

68 − 24 = 68 − 20 − 4 = 44

Be careful: In subtraction, when you split the number being subtracted, take away each part. For example, 68 − 24 = 68 − 20 − 4, not 68 − 20 + 4.

⚖️ Strategy 5: Compensation for Almost-Tens

A number such as 9 is almost 10. You can use the easier 10, then fix the result. Adding 9 means adding 10 and taking back 1. Subtracting 9 means subtracting 10 and giving back 1.

38 + 9

38 + 10 − 1 = 47

We added 1 extra when we used 10 instead of 9, so we subtract 1.

63 − 9

63 − 10 + 1 = 54

We took away 1 extra when we used 10 instead of 9, so we add 1 back.

The same idea works for 19 (almost 20) or 29 (almost 30). There is also a useful constant-difference trick: 52 − 29 = 53 − 30 = 23. Adding 1 to both numbers in a subtraction keeps their distance apart the same. That is a different adjustment from subtracting 30 and then adding 1 back.

🔗 Strategy 6: Use Related Addition and Subtraction Facts

When you know an addition fact, use it to solve a related subtraction. For 17 − 8, ask, “What plus 8 makes 17?” Since 8 + 9 = 17, the missing amount is 9.

8 + 9 = 17   ⇄   17 − 8 = 9

Self-check: After subtracting, add the answer to the number taken away. You should get the starting number. For example, 17 − 8 = 9 because 9 + 8 = 17.

🧭 How Do You Choose a Strategy?

When you notice ...	Try this strategy	Example
A number is close to the next ten	Make a ten	28 + 7 = 30 + 5 = 35
The change is small	Count on or back	34 − 6 = 30 − 2 = 28
Two addends are the same or almost the same	Doubles / near doubles	6 + 7 = 6 + 6 + 1 = 13
Both numbers have tens and ones	Break apart	46 + 13 = 46 + 10 + 3 = 59
You see 9, 19, or 29	Compensation	74 − 19 = 74 − 20 + 1 = 55
Subtraction looks like a missing-addend fact	Related facts	17 − 8 = 9 because 8 + 9 = 17

Think → Choose → Solve → Check. You do not need to use the same strategy for every problem. Try a second method when you are unsure, and explain what each step means.

🌟 25 Worked Examples

Think first, then open Show solution. The examples move from mental facts within 20 to two-digit strategies, helpful regrouping, word problems, and error analysis.

1Make a ten

Find 8 + 6 mentally.

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Eight needs 2 to make 10. Split 6 into 2 and 4. Then 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14.

2Make a ten with nine

Find 9 + 7.

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Nine needs 1 more to make 10. Split 7 into 1 and 6. Add 9 + 1 = 10; then 10 + 6 = 16.

3Subtract to ten first

Find 14 − 6.

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Split the 6 into 4 and 2. From 14, subtract 4 to reach 10. Then subtract the remaining 2: 10 − 2 = 8. We subtracted 4 + 2 = 6 in all.

4Use a near double

Find 6 + 7.

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Use the known double 6 + 6 = 12. Seven is one more than six, so the sum is 12 + 1 = 13.

5Recall a double

Find 8 + 8.

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Two equal groups of eight make a double. The known fact 8 + 8 = 16 gives the answer without counting from one.

6Subtract almost ten

Find 15 − 9.

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Nine is one less than ten. First subtract ten: 15 − 10 = 5. You subtracted one too many, so add one back: 5 + 1 = 6.

7Count on in two jumps

Find 27 + 5.

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Start at 27. Count on 3 to reach the next ten, 30. There are 2 more to add because 3 + 2 = 5. Then 30 + 2 = 32. Check: 27 + 5 = 32.

8Count back across a ten

Find 34 − 6.

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Break 6 into 4 and 2. From 34, jump back 4 to 30. Jump back 2 more to 28. You moved back 6 altogether.

9Add two tens

Find 47 + 20.

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The number 47 is 4 tens and 7 ones. Adding 20 adds 2 tens, making 6 tens and 7 ones. The answer is 67.

10Subtract three tens

Find 68 − 30.

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The number 68 is 6 tens and 8 ones. Take away 3 tens; 3 tens and 8 ones remain. So 68 − 30 = 38.

11Break apart an addend

Find 46 + 13.

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Break 13 into 10 and 3. Add ten: 46 + 10 = 56. Then add three: 56 + 3 = 59.

12Subtract tens, then ones

Find 72 − 24.

Show solutionHide solution

Break 24 into 20 and 4. First 72 − 20 = 52. Then 52 − 4 = 48. Check: 48 + 24 = 72.

13Make the next multiple of ten

Find 28 + 7.

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Twenty-eight needs 2 to reach 30. Split 7 into 2 and 5. Then 28 + 2 = 30 and 30 + 5 = 35.

14Count back to the previous ten

Find 52 − 7.

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Break 7 into 2 and 5. Subtract 2 from 52 to reach 50; subtract the remaining 5: 50 − 5 = 45.

15Compensate when adding nine

Find 38 + 9.

Show solutionHide solution

Adding 10 is easy: 38 + 10 = 48. But 10 is one more than 9, so subtract 1: 48 − 1 = 47.

16Compensate when subtracting nine

Find 63 − 9.

Show solutionHide solution

Subtract 10 first: 63 − 10 = 53. You took away 1 too many, so add 1 back. The answer is 53 + 1 = 54.

17Compensate when adding nineteen

Find 26 + 19.

Show solutionHide solution

Nineteen is one less than twenty. Add 20 first: 26 + 20 = 46. Then take away the extra 1: 46 − 1 = 45.

18Compensate when subtracting nineteen

Find 74 − 19.

Show solutionHide solution

Subtract 20 first: 74 − 20 = 54. You subtracted one extra, so put one back: 54 + 1 = 55.

19Break apart, then make a ten

Find 36 + 27.

Show solutionHide solution

Split 27 into 20 and 7. First 36 + 20 = 56. Split 7 into 4 and 3: 56 + 4 = 60, then 60 + 3 = 63.

20Subtract using a helpful ten

Find 81 − 36.

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Take away 30 first: 81 − 30 = 51. Six still needs to come away. Split 6 into 1 and 5: 51 − 1 = 50, then 50 − 5 = 45.

21Make thirty first

Find 29 + 14.

Show solutionHide solution

Move 1 from 14 to 29. Now the numbers are 30 and 13, with the same total: 30 + 13 = 43.

22Keep the difference the same

Find 52 − 29.

Show solutionHide solution

Add 1 to both numbers: 52 − 29 has the same difference as 53 − 30. Since 53 − 30 = 23, the original difference is also 23.

23Use a related addition fact

Find 17 − 8 using a fact you know.

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Ask what number added to 8 makes 17. Since 8 + 9 = 17, the missing part is 9. So 17 − 8 = 9.

24Use mental math in a story

Liam has 27 stickers and receives 18 more. How many stickers does Liam have now?

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Start with 27. Use 3 from the 18 to make 30. There are 15 left to add, so 30 + 15 = 45 stickers. Check: 27 + 18 = 45.

25Find and fix an error

A student says 64 − 9 = 53 because 64 − 10 = 54 and then takes away 1 more. Explain and correct the mistake.

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Subtracting 10 instead of 9 takes away one too many. After 64 − 10 = 54, you must add 1 back, not subtract it. Thus 64 − 9 = 54 + 1 = 55. Check: 55 + 9 = 64.

🎮 Independent Practice — 30 Problems

Directions: choose a mental math strategy that fits each problem. If a problem asks for a reason, write a short equation or sentence. Do not open the answer key until you finish.

1. 7 + 8 = ___.
2. 9 + 5 = ___.
3. 16 − 7 = ___.
4. 13 − 5 = ___.
5. 8 + 9 = ___.
6. 18 − 9 = ___.
7. 25 + 4 = ___.
8. 42 − 5 = ___.
9. 34 + 10 = ___.
10. 79 − 20 = ___.
11. 35 + 12 = ___.
12. 86 − 23 = ___.
13. 57 + 6 = ___.
14. 61 − 8 = ___.
15. 47 + 9 = ___.
16. 72 − 9 = ___.
17. 39 + 19 = ___.
18. 83 − 19 = ___.
19. 45 + 28 = ___.
20. 92 − 37 = ___.
21. 59 + 16 = ___.
22. 71 − 39 = ___.
23. 15 − 7 = ___. Use a related fact.
24. 25 + 25 = ___. Use a double.
25. 48 + 17 = ___.
26. 80 − 26 = ___.
27. Avery has 36 crayons and gets 19 more. How many crayons does Avery have?
28. A book has 54 pages. Noah reads 28 pages. How many pages are left?
29. Find 68 + 9 and explain how compensating by 1 helps.
30. A student says 53 − 9 = 43 because 53 − 10 = 43. What was forgotten? Give the correct answer.

🏆 Lesson Test — 15 Questions

Directions: complete the test independently. For questions that ask for an explanation, show the mental step you chose. Check your work only when you have finished the full test.

1. 6 + 9 = ___.
2. 14 − 8 = ___.
3. 5 + 6 = ___. Use a double or near double.
4. 24 + 6 = ___.
5. 43 − 7 = ___.
6. 56 + 10 = ___.
7. 88 − 30 = ___.
8. 44 + 15 = ___.
9. 95 − 42 = ___.
10. 67 + 8 = ___.
11. 84 − 9 = ___. Show a compensation step.
12. 37 + 18 = ___. Show a helpful grouping.
13. 91 − 48 = ___. Show an efficient mental strategy.
14. A team has 46 points and scores 27 more. What is the new total?
15. A student says 43 + 29 = 73 because 43 + 30 = 73. Explain the mistake and give the correct answer.

🔐 Complete Answer Key

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Practice Answers

Teacher note: Alternative correct mental strategies are welcome. Questions with an explanation should show why the steps keep the result correct.

1. 15. Use a near double: 7 + 7 = 14, plus 1 = 15.

2. 14. 9 + 1 + 4 = 10 + 4 = 14.

3. 9. 16 − 6 = 10; 10 − 1 = 9.

4. 8. 13 − 3 = 10; 10 − 2 = 8.

5. 17. 8 + 8 + 1 = 17.

6. 9. 18 − 10 + 1 = 9.

7. 29. Count on 4 from 25 to 29.

8. 37. 42 − 2 = 40; 40 − 3 = 37.

9. 44. Add one ten; the ones stay 4.

10. 59. Remove two tens; the ones stay 9.

11. 47. 35 + 10 + 2 = 47.

12. 63. 86 − 20 − 3 = 63.

13. 63. 57 + 3 = 60; 60 + 3 = 63.

14. 53. 61 − 1 = 60; 60 − 7 = 53.

15. 56. 47 + 10 − 1 = 56.

16. 63. 72 − 10 + 1 = 63.

17. 58. 39 + 20 − 1 = 58.

18. 64. 83 − 20 + 1 = 64.

19. 73. 45 + 20 = 65; 65 + 5 = 70; 70 + 3 = 73.

20. 55. 92 − 30 = 62; 62 − 2 = 60; 60 − 5 = 55.

21. 75. 59 + 1 = 60; 60 + 15 = 75.

22. 32. Add 1 to both numbers: 72 − 40 = 32.

23. 8. 7 + 8 = 15, so 15 − 7 = 8.

24. 50. Double 25: 25 + 25 = 50.

25. 65. 48 + 2 = 50; 50 + 15 = 65.

26. 54. 80 − 20 = 60, then 60 − 6 = 54.

27. 55 crayons. 36 + 20 − 1 = 55 crayons.

28. 26 pages. 54 − 30 + 2 = 26 pages.

29. 77. 68 + 10 − 1 = 77. Adding 10 is one too many, so take 1 back.

30. 44. Subtracting 10 removes 1 more than subtracting 9. Add that 1 back: 43 + 1 = 44.

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Test Answers

Teacher note: Accept equivalent equations and correct explanations, including different but mathematically valid strategies.

1. 15. Make a ten: 9 + 1 + 5 = 15.

2. 6. 14 − 4 − 4 = 6.

3. 11. 5 + 5 + 1 = 11.

4. 30. 24 + 6 reaches the next ten, 30.

5. 36. 43 − 3 = 40; 40 − 4 = 36.

6. 66. Add one ten to 5 tens and 6 ones: 66.

7. 58. Remove three tens from 8 tens and 8 ones: 58.

8. 59. 44 + 10 + 5 = 59.

9. 53. 95 − 40 = 55; 55 − 2 = 53.

10. 75. 67 + 3 = 70, then add 5 more: 75.

11. 75. 84 − 10 + 1 = 75.

12. 55. 37 + 3 + 15 = 40 + 15 = 55.

13. 43. 91 − 50 + 2 = 43, because 50 is 2 more than 48.

14. 73 points. 46 + 20 = 66; 66 + 4 = 70; 70 + 3 = 73 points.

15. 72. 29 is one less than 30. Subtract the extra 1: 43 + 29 = 43 + 30 − 1 = 72.

💡 Common Mistakes to Watch For

Counting every number from one
Try starting at the larger number or using a known fact. Mental strategies grow from counting, but help make it more efficient.

Mixing up +9 and −9 compensation
Adding 9: add 10, then subtract 1. Subtracting 9: subtract 10, then add 1 back.

Forgetting a part when making ten
If 28 + 7 becomes 30 + 5, remember that 7 was split into 2 and 5. Both parts must be used.

Breaking apart subtraction with a plus sign
For 68 − 24, subtract both 20 and 4. Do not accidentally add the ones back.

Mixing up the two compensation tricks
In 52 − 29, either compute 52 − 30 + 1 or change both numbers to 53 − 30. Explain which adjustment you used.

Thinking mental math means racing
Accuracy comes first. A good explanation or quick number-line sketch is more useful than a guessed answer.

Family practice idea: Ask, “What did you notice about the numbers?” and “Can you solve it another way?” A short explanation often reveals more understanding than a fast answer.

🔗 Related Lessons

Grade 2 Lesson 12 — Add Up to Four Two-Digit NumbersReview helpful grouping and friendly pairs when adding several numbers. Grade 2 Lesson 11 — Decompose a Ten When SubtractingUse tens and ones to understand why making a ten can help subtraction. Grade 2 Lesson 10 — Compose a Ten When AddingReview how ten ones become one ten when adding. Grade 2 Lesson 9 — Subtract Within 100 Using Place ValueConnect mental subtraction jumps to tens and ones. Grade 2 Lesson 8 — Add Within 100 Using Place ValueBreak apart tens and ones to add two-digit numbers. Grade 2 Lesson 7 — Addition & Subtraction Fluency Within 20Practice known facts that make mental strategies faster and clearer. Grade 1 — Number Bonds & Ways to Make 10Revisit the number bonds that make ten. Grade 1 — Doubles, Near Doubles & Easier FactsReview familiar doubles that help with new addition facts.

🖨️ Printable Companion

A future Mental Addition & Subtraction Strategies Practice Pack can include ten-frames, mental number lines, make-ten puzzles, near-double cards, compensation challenges, strategy-choice questions, and full answer keys.

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