Solved Exercises on Mental Addition and Subtraction in Grade 2

Master mental addition and subtraction: number bonds, place value, and mental math strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Adding tens and ones
Exercise 1
Calculate mentally:
\(34 + 25\)
Definition:

Place value: In 34, 3 represents 30 (3 tens) and 4 represents 4 ones

Mental addition method:
  1. Add the tens together (30 + 20 = 50)
  2. Add the ones together (4 + 5 = 9)
  3. Combine the results (50 + 9 = 59)
Expression
\(34 + 25\)
Separate tens and ones
\(30 + 4 + 20 + 5\)
Result
\(59\)
Step 1: Break down into tens and ones

\(34 = 30 + 4\) and \(25 = 20 + 5\)

Step 2: Add tens together

\(30 + 20 = 50\)

Step 3: Add ones together

\(4 + 5 = 9\)

Step 4: Combine the results

\(50 + 9 = 59\)

\(34 + 25 = 59\)
Final answer:

\(34 + 25 = 59\)

Applied rules:

• Place value: Separate tens and ones to make mental calculation easier

• Associative property: Group tens with tens and ones with ones

• Combining: Add the partial sums together

2 Subtracting by counting up
Exercise 2
Calculate mentally:
\(72 - 48\)
Definition:

Counting up strategy: Instead of subtracting, count up from the smaller number to the larger number

Expression
\(72 - 48\)
Counting up
\(48 + ? = 72\)
Result
\(24\)
Step 1: Start from 48

Think: "How much do I need to add to 48 to get 72?"

Step 2: Count up by tens first

\(48 + 20 = 68\)

Step 3: Count up the remaining ones

\(68 + 4 = 72\)

Step 4: Add the amounts counted up

\(20 + 4 = 24\)

\(72 - 48 = 24\)
Final answer:

\(72 - 48 = 24\)

Applied rules:

• Counting up: An alternative to direct subtraction that can be easier mentally

• Breaking into parts: Add in chunks (tens first, then ones)

• Verification: Check that \(48 + 24 = 72\)

3 Using number bonds
Exercise 3
Calculate mentally:
\(56 + 37\)
Definition:

Number bonds: Pairs of numbers that add up to a specific total (like 10, 100)

Expression
\(56 + 37\)
Adjust to make tens
\(56 + 4 + 33\)
Result
\(93\)
Step 1: Look for ways to make tens

\(56 + 37\): Notice that adding 4 to 56 makes 60

Step 2: Take 4 from 37

\(37 = 4 + 33\), so \(56 + 37 = 56 + 4 + 33\)

Step 3: Add the round number first

\(56 + 4 = 60\)

Step 4: Add the remaining amount

\(60 + 33 = 93\)

\(56 + 37 = 93\)
Final answer:

\(56 + 37 = 93\)

Applied rules:

• Number bonds: Use knowledge of number pairs that make tens or hundreds

• Compensation: Adjust one number to make a round number, then adjust the other

• Breaking apart: Split numbers to make calculations easier

Mental Addition and Subtraction Strategies
\(34 + 25 = (30 + 20) + (4 + 5) = 50 + 9 = 59\)
Place Value Strategy
Strategy 1
Break Apart Numbers
Separate tens and ones
Strategy 2
Count Up
Instead of subtracting, count up
Strategy 3
Make Tens
Use number bonds to make tens
Key definitions:

Place value: Understanding that digits represent different values based on their position

Number bonds: Pairs of numbers that add up to a specific total (like 6 + 4 = 10)

Mental math: Calculating in your head without writing anything down

Mental math methodology:
  1. Analyze the numbers: Look for patterns, tens, or easy combinations
  2. Choose the best strategy: Place value, counting up, making tens, or compensation
  3. Execute the strategy: Follow the mental steps of the chosen technique
  4. Verify the result: Check if your answer makes sense
Tip 1: To add 9, add 10 and subtract 1. Example: 23 + 9 = 23 + 10 - 1 = 32.
Tip 2: To subtract 9, subtract 10 and add 1. Example: 54 - 9 = 54 - 10 + 1 = 45.
Tip 3: Look for doubles facts. If you know 8 + 8 = 16, then 8 + 9 = 17.
Tip 4: Practice number bonds to 10: 1+9, 2+8, 3+7, 4+6, 5+5.
Common errors: Forgetting to regroup, miscounting when counting up, confusing addition and subtraction.
Exam preparation: Practice daily mental math, memorize number bonds, master place value concepts.
Mental math strategies to know:

• Place value: \(34 + 25 = (30 + 20) + (4 + 5) = 50 + 9 = 59\)

• Counting up: \(72 - 48\) means "what added to 48 equals 72?" Answer: 24

• Make tens: \(56 + 37 = 56 + 4 + 33 = 60 + 33 = 93\)

• Compensation: \(48 + 35 = 50 + 33 = 83\) (added 2 to 48, so subtracted 2 from 35)

Solution: Exercises 4 to 5
4 Compensation strategy
Exercise 4
Calculate mentally:
\(63 - 29\)
Definition:

Compensation strategy: Adjust numbers to make calculations easier, then compensate for the adjustment

Expression
\(63 - 29\)
Adjust to round number
\(63 - 30 + 1\)
Result
\(34\)
Step 1: Round the subtrahend

\(29\) is close to \(30\), so we'll subtract \(30\) and add back \(1\)

Step 2: Subtract the rounded number

\(63 - 30 = 33\)

Step 3: Compensate for the adjustment

We subtracted \(1\) too many (since \(30 - 29 = 1\)), so we add \(1\)

Step 4: Calculate the final result

\(33 + 1 = 34\)

\(63 - 29 = 34\)
Final answer:

\(63 - 29 = 34\)

Applied rules:

• Compensation: Make calculations easier by rounding, then adjusting

• Adjustment: If you subtract more than needed, add back the difference

• Verification: Check that \(34 + 29 = 63\)

5 Doubles plus or minus one
Exercise 5
Calculate mentally:
\(38 + 36\)
Definition:

Doubles plus/minus: Use known doubles facts to solve nearby problems

Expression
\(38 + 36\)
Use doubles fact
\(37 + 37 + 1 - 1\)
Result
\(74\)
Step 1: Recognize the relationship

\(38\) and \(36\) are each one away from \(37\), so we can use the double of \(37\)

Step 2: Rewrite using doubles

\(38 + 36 = (37 + 1) + (37 - 1) = 37 + 37 + 1 - 1 = 37 + 37\)

Step 3: Calculate the double

\(37 + 37 = 74\)

Step 4: Verify the result

\(38 + 36 = 74\), and checking: \(37 + 37 = 74\) ✓

\(38 + 36 = 74\)
Final answer:

\(38 + 36 = 74\)

Applied rules:

• Doubles facts: Know doubles like \(37 + 37\) to solve nearby problems

• Adjustment: If numbers are close to a common value, use that value's double

• Verification: Always check your mental calculation

Mental Math Laws, Methods, and Definitions
\(34 + 25 = (30 + 20) + (4 + 5) = 50 + 9 = 59\)
Place Value Decomposition
Key definitions:

Mental addition: Adding numbers in your head using strategies like place value decomposition

Mental subtraction: Taking away numbers mentally using techniques like counting up

Number bonds: Pairs of numbers that combine to make a specific total (like 10, 20, 100)

Mental math methodology:
  1. Look for patterns: Identify if numbers are close to tens, doubles, or complements
  2. Choose the best strategy: Place value, counting up, making tens, or compensation
  3. Execute mentally: Follow the mental steps of the chosen technique
  4. Verify quickly: Check if your answer seems reasonable
Tip 1: To add near doubles, find the double and adjust. Example: 7 + 8 = double 7 + 1 = 14 + 1 = 15.
Tip 2: For subtracting across zeros, like 100 - 7, think: 100 - 10 + 3 = 93.
Tip 3: Practice with number lines in your head. Jump by tens, then by ones.
Tip 4: When adding 3 numbers, look for pairs that make 10 first. Example: 4 + 7 + 6 = 4 + 6 + 7 = 17.
Common errors: Forgetting to adjust after rounding, mixing up addition and subtraction, miscalculating place values.
Success strategies: Practice number bonds daily, visualize numbers, use finger counting initially.
Mental math formulas and strategies:

• Place value decomposition: \(34 + 25 = (30 + 20) + (4 + 5) = 50 + 9 = 59\)

• Counting up: \(72 - 48\) means counting from 48 to 72: \(48 + 20 = 68\), \(68 + 4 = 72\), so answer is \(24\)

• Making tens: \(56 + 37 = 56 + 4 + 33 = 60 + 33 = 93\)

• Compensation: \(63 - 29 = 63 - 30 + 1 = 33 + 1 = 34\)

• Doubles ±1: \(7 + 8 = 7 + 7 + 1 = 14 + 1 = 15\)

Exercise with Visualization: Mental Math Strategies
Exercise 6: Mental Math Visualization
Consider the following mental math strategies:
\(f_1(x) = x + 10\) (Adding tens)
\(f_2(x) = x + 9 = x + 10 - 1\) (Adding nines)
\(f_3(x) = x - 10\) (Subtracting tens)

Analysis: The chart shows the behavior of different mental math operations.

  • \(f_1(x) = x + 10\) (Adding tens strategy)
  • \(f_2(x) = x + 9 = x + 10 - 1\) (Adding nines using compensation)
  • \(f_3(x) = x - 10\) (Subtracting tens strategy)

Questions & Answers

Question: I'm confused about when to use the "counting up" strategy versus regular subtraction. Can you explain the difference?

Answer: Great question! The counting up strategy is especially helpful when subtracting numbers that are close together:

  • Regular subtraction: Take away the smaller number from the larger number
  • Counting up: Find the distance between two numbers by starting from the smaller number

For example, with 72 - 48:

  • Regular subtraction might require borrowing: 72 - 48 = ?
  • Counting up: Start at 48 and count up to 72: 48 → 50 (+2), 50 → 70 (+20), 70 → 72 (+2), total = 24

Counting up is often easier mentally because it avoids borrowing and works with positive additions. Try both methods and see which feels more natural!

Question: When I need to add 38 + 36, how do I know to use the doubles strategy instead of just adding normally?

Answer: To decide which strategy to use, look at the numbers:

  • If the numbers are close to each other (like 38 and 36), consider the doubles strategy
  • If the numbers are round numbers (like 40 and 30), place value decomposition works well
  • If one number is close to a round number (like 39), consider compensation

In your example 38 + 36: Both numbers are close to 37, and since 38 = 37 + 1 and 36 = 37 - 1, we get (37 + 1) + (37 - 1) = 37 + 37 = 74.

This is faster than adding 30 + 30 = 60, then 8 + 6 = 14, then 60 + 14 = 74.

Tip: With practice, you'll automatically recognize which strategy works best for different number pairs!

Question: My child struggles with mental math. Are there games or activities to make practicing more fun?

Answer: Absolutely! Here are engaging ways to practice mental math:

  • Math War: Use a deck of cards. Each player flips two cards and adds/subtracts them. Highest answer wins the round.
  • Number Bond Games: "I say 7, you say the number that makes 10" (answer: 3)
  • Real-life scenarios: While shopping, ask "If apples cost $2 and oranges cost $3, how much for both?"
  • Counting challenges: Count by 2s, 5s, or 10s while walking, jumping, or doing chores

Make it a game: Set a timer for 1 minute and see how many mental math problems they can solve. Or create a point system with small rewards.

Remember: Keep sessions short (5-10 minutes) and positive. Success builds confidence!