Solved Exercises on Mental Addition and Subtraction Strategies in Grade 2

Master mental math strategies: counting on, making tens, decomposing numbers, compensation method, and number line strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting On Strategy
Exercise 1
Solve mentally: 27 + 5 = ?
Use the counting on strategy.
Definition:

Counting On Strategy: Start with the larger number and count up by the smaller number. This works well when adding small numbers (1, 2, 3, 4, or 5).

Step-by-step method:
  1. Identify the larger number (27) and the smaller number (5)
  2. Start counting from the larger number: 27
  3. Count up by the smaller number: 28, 29, 30, 31, 32
  4. The final number is the answer: 32
Start
27
Count Up
+5
Result
32
Step 1: Identify numbers

27 is the larger number, 5 is the smaller number

Step 2: Start with larger number

Start counting from 27

Step 3: Count up by smaller number

27 → 28 → 29 → 30 → 31 → 32 (count 5 numbers)

Step 4: Record the final number

The last number counted is the answer: 32

27 + 5 = 32
Final answer:

27 + 5 = 32

Applied rules:

• Counting On: Start with the larger number to minimize counting

• Sequential Counting: Add one number at a time

• Small Numbers: Best used when adding 1-5

2 Making Tens Strategy
Exercise 2
Solve mentally: 38 + 6 = ?
Use the making tens strategy.
Definition:

Making Tens Strategy: Break apart one number to make a ten with the other number, then add the remaining amount.

Original
38 + 6
Make Ten
38 + 2 + 4
Simplify
40 + 4 = 44
Step 1: Identify how many needed to make a ten

From 38, we need 2 more to reach 40 (the next ten)

Step 2: Break apart the second number

Break 6 into 2 + 4 (so we can make 10 with 38)

Step 3: Add to make the ten

38 + 2 = 40

Step 4: Add the remaining amount

40 + 4 = 44

38 + 6 = 44
Final answer:

38 + 6 = 44

Applied rules:

• Ten Complements: Know how many more to make the next ten

• Decomposition: Break apart numbers strategically

• Easy Addition: Adding multiples of 10 is easier

3 Decomposing Numbers
Exercise 3
Solve mentally: 46 + 27 = ?
Use the decomposing numbers strategy.
Definition:

Decomposing Numbers: Break apart both numbers into tens and ones, add the tens together, add the ones together, then combine the results.

Original
46 + 27
Decompose
40+6 + 20+7
Result
60+13 = 73
Step 1: Decompose each number

46 = 40 + 6 (4 tens and 6 ones)

27 = 20 + 7 (2 tens and 7 ones)

Step 2: Add the tens together

40 + 20 = 60

Step 3: Add the ones together

6 + 7 = 13

Step 4: Combine the sums

60 + 13 = 73

46 + 27 = 73
Final answer:

46 + 27 = 73

Applied rules:

• Place Value: Separate tens and ones

• Group Like Terms: Add tens with tens, ones with ones

• Regrouping: If ones sum to 10 or more, add to tens

Mental Math Strategies, Laws, and Methods
Counting On: Start with larger number
Strategy 1
Making Tens
38 + 6 = 38 + 2 + 4 = 40 + 4
Break apart to make 10
Decomposing
46 + 27 = 40+6 + 20+7 = 60+13
Separate tens and ones
Compensation
59 + 18 = 60 + 17 = 77
Round and adjust
Key definitions:

Mental Math: Calculating in your head without paper or tools

Decomposing: Breaking numbers into parts (tens and ones)

Compensation: Adjusting numbers to make calculations easier

Complete methodology:
  1. Look at the numbers: Identify which strategy might work best
  2. Choose the method: Counting on, making tens, decomposing, or compensation
  3. Apply the strategy: Follow the steps of the chosen technique
  4. Combine results: Put the pieces back together
Tip 1: Always start with the larger number when counting on.
Tip 2: Practice complements to 10 (like 7 needs 3 to make 10).
Tip 3: Decompose both numbers to add tens and ones separately.
Tip 4: Round difficult numbers to make them easier to work with.
Common errors: Forgetting to count the starting number, miscounting, adding instead of subtracting when compensating.
Exam preparation: Practice with number bonds to 10, memorize basic facts, practice decomposing numbers.
Solution: Exercises 4 to 5
4 Compensation Method
Exercise 4
Solve mentally: 59 + 18 = ?
Use the compensation method.
Definition:

Compensation Method: Round one number to make it easier to work with, then adjust the answer by the amount you changed.

Original
59 + 18
Round Up
60 + 17
Result
77
Step 1: Look for numbers near tens

59 is close to 60 (just 1 away)

Step 2: Round one number up

Add 1 to 59 to make it 60

Step 3: Adjust the other number

Subtract 1 from 18 to keep the total the same: 18 - 1 = 17

Step 4: Add the rounded numbers

60 + 17 = 77

59 + 18 = 77
Final answer:

59 + 18 = 77

Applied rules:

• Compensation: When you add to one number, subtract from the other

• Rounding: Make numbers easier by rounding to nearest ten

• Balancing: Keep the equation balanced by adjusting both sides

5 Mental Subtraction Strategy
Exercise 5
Solve mentally: 63 - 8 = ?
Use the counting back or compensation strategy.
Definition:

Mental Subtraction: Use counting back, making tens, or compensation to subtract without paper.

Original
63 - 8
Compensate
63 - 10 + 2
Result
55
Step 1: Look for numbers near tens

8 is close to 10 (2 away)

Step 2: Subtract the round number

63 - 10 = 53

Step 3: Add back the difference

We subtracted 2 too many, so add 2 back: 53 + 2 = 55

Step 4: Verify the result

55 + 8 = 63 ✓

63 - 8 = 55
Final answer:

63 - 8 = 55

Applied rules:

• Compensation for Subtraction: Subtract more than needed, then add back

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

• Mental Flexibility: Choose the easiest strategy for the numbers

Mental Math Strategies, Laws, and Methods Guide
Counting On: 27 + 5 = 27 → 28 → 29 → 30 → 31 → 32
Strategy Overview
Key definitions:

Mental Math: Performing calculations in your head without paper or tools

Number Bonds: Pairs of numbers that add up to another number (like 7 and 3 bond to make 10)

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

Complete methodology:
  1. Analyze the numbers: Look for patterns, round numbers, or easy combinations
  2. Choose the strategy: Counting on, making tens, decomposing, or compensation
  3. Apply the method: Follow the specific steps for the chosen technique
  4. Verify the result: Check your answer by using another method or reversing the operation
Tip 1: Practice number bonds to 10 daily (pairs that make 10).
Tip 2: When adding, start with the larger number to minimize counting.
Tip 3: Round difficult numbers to the nearest ten for easier calculations.
Tip 4: Always verify your mental math by checking with a different method.
Tip 5: Practice regularly to build speed and accuracy.
Common errors: Forgetting to compensate properly, miscounting, confusing addition and subtraction steps.
Key memorizations: Number bonds to 10, doubles facts, place value understanding.
Advanced techniques: Using known facts to derive unknown facts, looking for patterns.
Mental Math Strategies Summary:

• Counting On: Start with larger number, count up by smaller number

• Making Tens: Break numbers to form a ten, then add remainder

• Decomposing: Separate into tens and ones, add separately

• Compensation: Round numbers to make calculation easier, adjust result

• Number Line: Visualize jumps forward or backward on a number line

Visualization: Mental Math Strategies Comparison
Comparing Mental Math Approaches
Different strategies for solving: 47 + 16
Counting On: 47 → 48 → 49... (16 counts)
Making Tens: 47 + 3 + 13 = 50 + 13 = 63
Decomposing: 40+7 + 10+6 = 50+13 = 63
Compensation: 50 + 13 = 63

Analysis: Different strategies offer varying levels of efficiency depending on the numbers involved.

  • Counting On: Simple but lengthy for larger additions
  • Making Tens: Efficient when one number is close to a ten
  • Decomposing: Systematic approach for any two-digit numbers
  • Compensation: Great for numbers near round figures

Questions & Answers

Question: I don't understand when to use making tens versus decomposing numbers. Can you explain the difference?

Answer: Great question! The key difference is in how you manipulate the numbers:

  • Making Tens: You break apart ONE number to combine with the other to make a ten. Example: For 38 + 6, you take 2 from 6 to make 38 into 40, leaving 4. So it becomes 40 + 4 = 44.
  • Decomposing: You break apart BOTH numbers into tens and ones. Example: For 46 + 27, you break 46 into 40+6 and 27 into 20+7, then add 40+20=60 and 6+7=13, finally 60+13=73.

When to use which:

  • Use Making Tens when one number is close to a multiple of 10 (like 38, 59, 87)
  • Use Decomposing when neither number is particularly close to a round number

Both strategies aim to make the math easier by working with friendlier numbers!

Question: Why is it better to start counting on from the bigger number? Doesn't it matter which one I start with?

Answer: Yes, it definitely matters! Starting from the bigger number makes mental math much easier because you have fewer numbers to count.

Example: Let's say you want to solve 7 + 24.

  • If you start from 7 and count on 24: 8, 9, 10, 11, 12... (24 counts!) - This is hard to keep track of!
  • If you start from 24 and count on 7: 25, 26, 27, 28, 29, 30, 31 - Much easier!

Starting with the larger number minimizes the amount of counting you need to do, which reduces the chance of making mistakes and helps you find the answer faster. It's all about efficiency in mental math!

Think of it like taking the shortest path - you want to do the least amount of work to get to your answer.

Question: My child struggles with the compensation method. How can I help them understand when to add versus subtract during compensation?

Answer: The compensation method can be tricky! Here's a simple rule to remember:

  • If you ADD to one number: SUBTRACT the same amount from the other number
  • If you SUBTRACT from one number: ADD the same amount to the other number

Example with addition: 59 + 18

  • I add 1 to 59 to make it 60
  • So I must subtract 1 from 18 to keep the total the same
  • Now I have 60 + 17 = 77

Example with subtraction: 63 - 8

  • I add 2 to 8 to make it 10 (easier to subtract)
  • So I must add 2 to 63 as well to keep the difference the same
  • Now I have 65 - 10 = 55

The key concept is keeping the equation balanced - whatever you do to one side, you must do to maintain equality.