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📄 Sheet #1•10 Problems

PanMaths.comMental Subtraction Compensation Strategy Worksheets • Worksheet #1

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 10

1.Compensation (+1)

73 − 29 = ?

Add +1 to both numbers to make a decade:

(73 + 1) − (29 + 1) = 74 − 30

Answer:

2.Compensation (+2)

85 − 38 = ?

Add +2 to both numbers to make a decade:

(85 + 2) − (38 + 2) = 87 − 40

Answer:

3.Compensation (+1)

62 − 19 = ?

Add +1 to both numbers to make a decade:

(62 + 1) − (19 + 1) = 63 − 20

Answer:

4.Compensation (+2)

94 − 48 = ?

Add +2 to both numbers to make a decade:

(94 + 2) − (48 + 2) = 96 − 50

Answer:

5.Compensation (+1)

51 − 29 = ?

Add +1 to both numbers to make a decade:

(51 + 1) − (29 + 1) = 52 − 30

Answer:

6.Compensation (+1)

83 − 39 = ?

Add +1 to both numbers to make a decade:

(83 + 1) − (39 + 1) = 84 − 40

Answer:

7.Compensation (+2)

76 − 28 = ?

Add +2 to both numbers to make a decade:

(76 + 2) − (28 + 2) = 78 − 30

Answer:

8.Compensation (+2)

65 − 38 = ?

Add +2 to both numbers to make a decade:

(65 + 2) − (38 + 2) = 67 − 40

Answer:

9.Compensation (+1)

91 − 49 = ?

Add +1 to both numbers to make a decade:

(91 + 1) − (49 + 1) = 92 − 50

Answer:

10.Compensation (+2)

84 − 58 = ?

Add +2 to both numbers to make a decade:

(84 + 2) − (58 + 2) = 86 − 60

Answer:

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PanMaths.comAnswer Key & Worked Solutions • Worksheet #1

Answer Key

Total Problems: 10

1.Compensation (+1)

73 − 29 = ?

Add +1 to both numbers to make a decade:

(73 + 1) − (29 + 1) = 74 − 30

Answer:44

4. Therefore, 73 − 29 = 44 ✅

2.Compensation (+2)

85 − 38 = ?

Add +2 to both numbers to make a decade:

(85 + 2) − (38 + 2) = 87 − 40

Answer:47

4. Therefore, 85 − 38 = 47 ✅

3.Compensation (+1)

62 − 19 = ?

Add +1 to both numbers to make a decade:

(62 + 1) − (19 + 1) = 63 − 20

Answer:43

4. Therefore, 62 − 19 = 43 ✅

4.Compensation (+2)

94 − 48 = ?

Add +2 to both numbers to make a decade:

(94 + 2) − (48 + 2) = 96 − 50

Answer:46

4. Therefore, 94 − 48 = 46 ✅

5.Compensation (+1)

51 − 29 = ?

Add +1 to both numbers to make a decade:

(51 + 1) − (29 + 1) = 52 − 30

Answer:22

4. Therefore, 51 − 29 = 22 ✅

6.Compensation (+1)

83 − 39 = ?

Add +1 to both numbers to make a decade:

(83 + 1) − (39 + 1) = 84 − 40

Answer:44

4. Therefore, 83 − 39 = 44 ✅

7.Compensation (+2)

76 − 28 = ?

Add +2 to both numbers to make a decade:

(76 + 2) − (28 + 2) = 78 − 30

Answer:48

4. Therefore, 76 − 28 = 48 ✅

8.Compensation (+2)

65 − 38 = ?

Add +2 to both numbers to make a decade:

(65 + 2) − (38 + 2) = 67 − 40

Answer:27

4. Therefore, 65 − 38 = 27 ✅

9.Compensation (+1)

91 − 49 = ?

Add +1 to both numbers to make a decade:

(91 + 1) − (49 + 1) = 92 − 50

Answer:42

4. Therefore, 91 − 49 = 42 ✅

10.Compensation (+2)

84 − 58 = ?

Add +2 to both numbers to make a decade:

(84 + 2) − (58 + 2) = 86 − 60

Answer:26

4. Therefore, 84 − 58 = 26 ✅

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Worksheet Info

Categorygrade-3

Grade LevelGrade 3

DifficultyEasy, Medium, Hard, Sprint

Time5-10 min

CCSS CodeCCSS.MATH.CONTENT.3.NBT.A.2

Skills Practiced

✓ Mental Subtraction Compensation Strategy

Key Strategies

🎯 Step 1: Look at the Subtrahend (Second Number): Check if the subtrahend ends in 8 or 9 (e.g., 29, 38, 49). Identify how many units are needed to round it up to the next friendly multiple of 10.
➕ Step 2: Add the Adjustment to BOTH Numbers: Because subtraction measures the distance between two points on a number line, shifting both points by +k maintains the exact same difference: (a + k) − (b + k) = a − b.
🧠 Step 3: Perform Instant Mental Subtraction: Subtract the clean multiple of 10 from the adjusted minuend. Since the subtrahend ends in 0, no regrouping or borrowing is ever required.
✅ Step 4: Confirm Invariant Difference: Verify that your mental solution matches the original problem. For 85 − 38, add 2 to both: 87 − 40 = 47. Check: 47 + 38 = 85.

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Related Worksheets

📄 Place Value to 10,000View →📄 Rounding to Nearest 10 and 100View →📄 Multiplying Multiples of 10View →📄 Comparing Numbers (<, >, = within 20)View →📄 Tens and Ones Base-10 BlocksView →📄 Skip Counting by 2sView →

📜 Standard: CCSS.MATH.CONTENT.3.NBT.A.2🔗 CCSS.MATH.CONTENT.2.NBT.B.5🔗 CCSS.MATH.CONTENT.3.OA.D.8

Mastering Mental Subtraction Compensation Strategy: Core Concepts & Mental Models

The compensation strategy for subtraction is built on the mathematical law of Constant Difference: if you add (or subtract) the exact same amount to both numbers in a subtraction problem, the distance (difference) between them remains completely unchanged. When subtracting a number close to a decade (like 29 or 38), students add a small adjusting amount (+1 or +2) to BOTH numbers. This turns an intimidating problem with regrouping (such as 73 − 29) into an effortless mental subtraction (74 − 30 = 44) without any borrowing.

Worked Example & SolutionTeacher Step-by-Step Method

📝 Problem: Use the compensation strategy to mentally calculate: 73 − 29.

Worked Solution: Step 1: 29 is 1 away from 30. Step 2: Add +1 to BOTH numbers: (73 + 1) − (29 + 1) = 74 − 30. Step 3: Subtract mentally: 74 − 30 = 44. Final answer: 44.

💡 Essential Strategies for Mental Subtraction Compensation Strategy

🎯 Step 1: Look at the Subtrahend (Second Number)

Check if the subtrahend ends in 8 or 9 (e.g., 29, 38, 49). Identify how many units are needed to round it up to the next friendly multiple of 10.

➕ Step 2: Add the Adjustment to BOTH Numbers

Because subtraction measures the distance between two points on a number line, shifting both points by +k maintains the exact same difference: (a + k) − (b + k) = a − b.

🧠 Step 3: Perform Instant Mental Subtraction

Subtract the clean multiple of 10 from the adjusted minuend. Since the subtrahend ends in 0, no regrouping or borrowing is ever required.

✅ Step 4: Confirm Invariant Difference

Verify that your mental solution matches the original problem. For 85 − 38, add 2 to both: 87 − 40 = 47. Check: 47 + 38 = 85.

📖 Key Mathematical Vocabulary

Constant Difference

The mathematical principle stating that the difference between two numbers remains identical when the same value is added to or subtracted from both.

Compensation Strategy

A mental computation method of adjusting numbers to make them easier to calculate mentally, then accounting for the adjustment.

Friendly Number (Decade)

A multiple of 10 or 100 (such as 30, 50, or 200) that is exceptionally easy to subtract mentally.

Subtrahend

The quantity being subtracted from another number (in a − b, b is the subtrahend).

❓ Frequently Asked Questions

How do you solve a mental subtraction compensation strategy problem step by step?

Here is a worked example: "Use the compensation strategy to mentally calculate: 73 − 29.". Solution: Step 1: 29 is 1 away from 30. Step 2: Add +1 to BOTH numbers: (73 + 1) − (29 + 1) = 74 − 30. Step 3: Subtract mentally: 74 − 30 = 44. Final answer: 44.

What is the core learning objective for mental subtraction compensation strategy?

Fluently subtract multi-digit whole numbers within 1,000 using mental math strategies based on place value, specifically the constant difference compensation strategy (adding the same number to both minuend and subtrahend to create friendly decade numbers without regrouping). This directly aligns with Common Core Standard CCSS.MATH.CONTENT.3.NBT.A.2.

How does the unlimited mental subtraction compensation strategy worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of mental subtraction compensation strategy problems with unique numbers. No two worksheets are ever the same — perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

Are these mental subtraction compensation strategy worksheets free to print with answer keys?

Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.