Mental Math Addition and Subtraction Worksheets for 2nd Grade

Master mental math strategies: breaking apart numbers, counting on, compensation, place value, and more through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Breaking Apart Strategy
Exercise 1
Solve mentally: 47 + 26 = ?
Definition:

Breaking Apart Strategy: Separate tens and ones to add mentally: 47 + 26 = (40 + 7) + (20 + 6) = (40 + 20) + (7 + 6) = 60 + 13 = 73

Mental addition method:
  1. Separate tens and ones in each number
  2. Add tens together and ones together
  3. Combine the results
  4. Carry over if needed
Original
47 + 26
Break Apart
(40+7)+(20+6)
Group Tens
(40+20)+(7+6)
Result
60+13=73
Step 1: Break apart each number

47 = 40 + 7 and 26 = 20 + 6

Step 2: Add tens together

40 + 20 = 60

Step 3: Add ones together

7 + 6 = 13

Step 4: Combine the sums

60 + 13 = 73

47 + 26 = 73
Final answer:

47 + 26 = 73

Applied rules:

• Place Value: Understanding tens and ones

• Associative Property: Grouping numbers differently

• Mental Math: Adding smaller numbers first

2 Compensation Strategy
Exercise 2
Solve mentally: 53 - 28 = ?
Definition:

Compensation Strategy: Adjust one number to make subtraction easier, then adjust the result. 53 - 28 = (53 - 30) + 2 = 23 + 2 = 25

Original
53 - 28
Compensate
53 - 30 + 2
Simplify
23 + 2 = 25
Step 1: Round the number being subtracted

28 is close to 30, so we'll subtract 30 instead

Step 2: Subtract the rounded number

53 - 30 = 23

Step 3: Add back the difference

We subtracted 2 too many (30 - 28 = 2), so add 2: 23 + 2 = 25

Step 4: Verify the result

25 + 28 = 53 ✓

53 - 28 = 25
Final answer:

53 - 28 = 25

Applied rules:

• Compensation: Adjust numbers to make calculations easier

• Adjustment: Remember to compensate for the change

• Verification: Check by adding the result to the subtracted number

3 Counting On Strategy
Exercise 3
Solve mentally: 65 + 17 = ?
Definition:

Counting On Strategy: Start with the larger number and count up by the smaller number. 65 + 17: Start at 65, add 10 to get 75, then add 7 more to get 82.

Original
65 + 17
Break Down
65 + 10 + 7
Result
75 + 7 = 82
Step 1: Start with the larger number

Start with 65

Step 2: Break the second number into tens and ones

17 = 10 + 7

Step 3: Add the tens first

65 + 10 = 75

Step 4: Add the remaining ones

75 + 7 = 82

65 + 17 = 82
Final answer:

65 + 17 = 82

Applied rules:

• Sequential Addition: Add in parts for easier mental math

• Ten-Friendly Numbers: Adding multiples of 10 is easier

• Number Sense: Understanding relationships between numbers

Mental Math Strategies, Rules and Methods
Breaking: 47 + 26 = (40 + 7) + (20 + 6) = 60 + 13 = 73
Breaking Apart Strategy
Strategy 1
47 + 26 → (40+20) + (7+6)
Breaking Apart
Strategy 2
53 - 28 → 53 - 30 + 2
Compensation
Strategy 3
65 + 17 → 65 + 10 + 7
Counting On
Key definitions:

Mental Math: Calculating math problems in your head without paper or calculator

Place Value: Understanding that digits have different values based on their position (tens, ones)

Commutative Property: Order doesn't matter in addition (a + b = b + a)

Associative Property: Grouping doesn't matter in addition ((a + b) + c = a + (b + c))

Mental Math Methodology:
  1. Look for ten-friendly numbers: Numbers that end in 0 or 5
  2. Choose the best strategy: Breaking apart, compensation, or counting on
  3. Execute mentally: Follow the chosen technique
  4. Verify: Check your answer by estimating or reversing the operation
Tip 1: Practice with number bonds (pairs that make 10, 20, etc.)
Tip 2: Use visual imagery of number lines or base-10 blocks
Tip 3: Always start with the larger number when counting on
Tip 4: Round numbers to make calculations easier, then adjust
Common errors: Forgetting to carry over, miscounting, mixing up addition and subtraction.
Practice focus: Work on fluency with numbers up to 100, memorize basic facts, practice multiple strategies.
Mental Math Techniques to Master:

• Breaking Apart: 47 + 26 = (40 + 20) + (7 + 6) = 60 + 13 = 73

• Compensation: 53 - 28 = 53 - 30 + 2 = 23 + 2 = 25

• Counting On: 65 + 17 = 65 + 10 + 7 = 75 + 7 = 82

• Making Tens: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13

• Doubles Plus One: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

Solution: Exercises 4 to 5
4 Making Tens Strategy
Exercise 4
Solve mentally: 74 - 37 = ?
Definition:

Making Tens Strategy: Use knowledge of how numbers combine to make tens and hundreds to simplify subtraction. Think: How much to get from 37 to 74?

Original
74 - 37
Think
37 + ? = 74
Break Down
37 + 3 + 30 + 4 = 74
Result
3 + 30 + 4 = 37
Step 1: Think addition instead of subtraction

What number added to 37 gives 74?

Step 2: Go from 37 to the next ten

37 + 3 = 40 (add 3 to get to 40)

Step 3: Go from 40 to 70

40 + 30 = 70 (add 30 to get to 70)

Step 4: Go from 70 to 74

70 + 4 = 74 (add 4 to get to 74)

Step 5: Add up the amounts added

3 + 30 + 4 = 37

74 - 37 = 37
Final answer:

74 - 37 = 37

Applied rules:

• Relationship between addition and subtraction: a - b = c means b + c = a

• Sequential counting: Break the distance into manageable parts

• Verification: Check by adding the result to the subtracted number

5 Doubles Plus/Minus Strategy
Exercise 5
Solve mentally: 46 + 48 = ?
Definition:

Doubles Plus/Minus Strategy: Use known doubles facts and adjust. 46 + 48 is close to 47 + 47 = 94, so 46 + 48 = 94.

Original
46 + 48
Think
47 + 47 = 94
Since
46 = 47 - 1, 48 = 47 + 1
Result
94
Step 1: Notice the numbers are near each other

46 and 48 are both close to 47

Step 2: Express each number in relation to the middle

46 = 47 - 1 and 48 = 47 + 1

Step 3: Rewrite the addition

46 + 48 = (47 - 1) + (47 + 1) = 47 + 47 - 1 + 1 = 47 + 47 = 94

Step 4: Use the double fact

47 + 47 = 94 (double 47)

Step 5: Verify the result

94 - 48 = 46 ✓

46 + 48 = 94
Final answer:

46 + 48 = 94

Applied rules:

• Near Doubles: When numbers are close, use a known double

• Algebraic Thinking: (a - 1) + (a + 1) = 2a

• Verification: Always check your result by reversing the operation

Mental Math Laws, Methods, Rules, and Key Concepts
Breaking: 47 + 26 = (40 + 20) + (7 + 6) = 60 + 13 = 73
Mental Addition
Key definitions:

Place Value: Understanding that in 47, the 4 represents 40 (4 tens) and the 7 represents 7 ones

Mental Math: Performing calculations in your head without physical aids

Compensation: Adjusting numbers to make calculations easier, then correcting the result

Number Bonds: Pairs of numbers that add up to a specific total (like 3 + 7 = 10)

Complete Mental Math Methodology:
  1. Identify the strategy: Look for patterns that suggest a particular method
  2. Apply the method: Follow the steps of your chosen mental math technique
  3. Calculate mentally: Perform the operations in your head
  4. Verify: Check your answer using estimation or reverse operation
Tip 1: Practice with visual models like base-10 blocks to build number sense.
Tip 2: Memorize doubles facts (6+6, 7+7, etc.) as building blocks.
Tip 3: Use number lines in your mind to visualize addition and subtraction.
Tip 4: Estimate first to check if your answer makes sense.
Common errors: Misplacing tens and ones, forgetting to carry/borrow, rushing calculations.
Success strategies: Daily practice, using multiple strategies, checking work, building fluency with basic facts.
Mental Math Strategies to Know:

• Breaking Apart: 47 + 26 = (40 + 20) + (7 + 6) = 60 + 13 = 73

• Compensation: 53 - 28 = 53 - 30 + 2 = 23 + 2 = 25

• Counting On: 65 + 17 = 65 + 10 + 7 = 75 + 7 = 82

• Making Tens: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13

• Near Doubles: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

• Adding by Place: 46 + 48 = (40 + 40) + (6 + 8) = 80 + 14 = 94

Mental Math Strategies Visualization
Mental Math Strategies Comparison
Different approaches to solve: 38 + 27
• Breaking Apart: (30 + 8) + (20 + 7) = 50 + 15 = 65
• Compensation: 38 + 30 - 3 = 68 - 3 = 65
• Counting On: 38 + 20 + 7 = 58 + 7 = 65

Analysis: Different mental math strategies lead to the same result. Students should choose the method that feels most comfortable.

  • Breaking Apart: Separates tens and ones
  • Compensation: Rounds one number then adjusts
  • Counting On: Starts with one number and counts up

Questions & Answers

Question: I don't understand how to break apart numbers like 47 and 26. Can you explain how to separate tens and ones?

Answer: Great question! Breaking apart numbers helps us understand place value:

  • In 47, the 4 is in the tens place, so it represents 40 (4 groups of 10)
  • In 47, the 7 is in the ones place, so it represents 7 individual units
  • So 47 = 40 + 7

Similarly, 26 = 20 + 6 because:

  • The 2 is in the tens place, so it represents 20
  • The 6 is in the ones place, so it represents 6

Visual tip: Imagine 47 as 4 bags of 10 cubes and 7 single cubes. This makes 40 + 7 = 47!

Question: When my child solves 53 - 28 using compensation, why do we add 2 back after subtracting 30?

Answer: The compensation strategy works like this:

  • We want to subtract 28, but 28 is close to 30
  • It's easier to subtract 30 than 28, so we subtract 30 instead
  • But wait! We subtracted 2 too many (since 30 - 28 = 2)
  • So we need to add back those 2 to balance out the equation

Example: 53 - 28 = 53 - 30 + 2 = 23 + 2 = 25

Think of it like this: If you took $30 when someone owed you $28, you'd need to give back $2!

Question: My students struggle with deciding which mental math strategy to use. How can I help them choose?

Answer: Here's a decision guide for choosing mental math strategies:

  1. Breaking Apart: Use when both numbers have tens and ones (like 47 + 26)
  2. Compensation: Use when one number is close to a round number (like 28 is close to 30)
  3. Counting On: Use when adding a small number to a large one (like 65 + 17)
  4. Near Doubles: Use when numbers are close together (like 46 + 48)

Encourage students to look at the numbers first and ask: "Which strategy makes these numbers easier to work with?"

Practice with number talks where students share different approaches to the same problem!

Question: How do I know if my mental math answer is correct without using paper?

Answer: Here are mental verification strategies:

  • Estimation: Round numbers and see if your answer is reasonable. For 47 + 26, estimate 50 + 30 = 80. Your answer of 73 is close to 80, so it's likely correct.
  • Reverse Operation: For addition, subtract your answer by one of the numbers. For 47 + 26 = 73, check 73 - 26 = 47 ✓
  • Alternative Method: Try solving the same problem with a different strategy to see if you get the same answer

These verification skills are just as important as getting the answer!

Question: Why do we learn different ways to do the same math problem? Isn't there just one way?

Answer: Just like there are different ways to get to school (walking, biking, taking the bus), there are different ways to solve math problems! Here's why:

  • Some methods work better for certain numbers: 53 - 28 is easier with compensation, but 45 + 32 might be easier with breaking apart
  • Different minds work differently: Some students find one method easier than another
  • Flexibility builds understanding: Knowing multiple methods helps you understand numbers better
  • Real-world problem solving: Life problems often have multiple solutions

Learning multiple strategies makes you a stronger, more flexible mathematician!