Solved Exercises on Mental Addition Tricks in Grade 2

Master mental addition: counting on, making tens, breaking apart, compensation, and friendly numbers through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting On Method
Exercise 1
Solve mentally: 34 + 7
Definition:

Counting On Method: Start with the larger number and count forward by the smaller number.

Counting On Method:
  1. Start with the addend (the first number)
  2. Count forward one number at a time for the second addend
  3. Keep track of each count until you finish counting the second addend
  4. The number you land on is the sum
Problem
34 + 7
Count on
35, 36, 37, 38, 39, 40, 41
Answer
41
Step 1: Start with 34

We begin our count at the first addend: 34

Step 2: Count forward 7 numbers

34 → 35 → 36 → 37 → 38 → 39 → 40 → 41

Step 3: Count each step

Step 1: 34+1=35, Step 2: 35+1=36, ..., Step 7: 40+1=41

34 + 7 = 41
Final answer:

34 + 7 = 41

Applied rules:

• Counting On: Add by counting forward from the starting number

• Number Sense: Understanding that addition means moving right on the number line

• Sequential Counting: Each count represents adding 1

2 Making Tens Method
Exercise 2
Solve mentally: 28 + 6
Definition:

Making Tens Method: Use number bonds to make a ten, then add the remainder.

Problem
28 + 6
Make 10
28 + 2 = 30
Add remainder
30 + 4 = 34
Step 1: Look for how much is needed to make a ten from the first number

28 needs 2 more to make 30 (which is 3 tens)

Step 2: Break the second number into parts

6 = 2 + 4 (2 to make 30, and 4 more to add)

Step 3: Add to make the ten first

28 + 2 = 30

Step 4: Add the remaining part

30 + 4 = 34

28 + 6 = 34
Final answer:

28 + 6 = 34

Applied rules:

• Number Bonds: Understanding pairs that make 10 (8 + 2 = 10)

• Partial Addition: Adding in manageable chunks

• Place Value: Using knowledge of tens to simplify calculations

3 Breaking Apart Method
Exercise 3
Solve mentally: 45 + 27
Definition:

Breaking Apart Method: Break the second addend into tens and ones, then add in parts.

Problem
45 + 27
Break 27
20 + 7
Add in parts
45+20=65, 65+7=72
Step 1: Break the second addend (27) into tens and ones

27 = 20 + 7

Step 2: Add the tens first

45 + 20 = 65

Step 3: Add the remaining ones

65 + 7 = 72

Step 4: Combine the results

45 + 27 = 72

45 + 27 = 72
Final answer:

45 + 27 = 72

Applied rules:

• Decomposition: Breaking numbers into smaller, easier-to-handle parts

• Partial Addition: Adding in manageable chunks

• Place Value: Using knowledge of tens and ones to simplify calculations

Rules and methods, laws,...
Counting On: 34 + 7 = 34, 35, 36, 37, 38, 39, 40, 41
Counting On Method
Method 1
Counting On
Start at the first addend and count forward
Method 2
Making Tens
Use number bonds to make tens for easier addition
Method 3
Breaking Apart
Separate tens and ones for easier addition
Key definitions:

Addend: The numbers being added together (in 34 + 7, both 34 and 7 are addends)

Sum: The result of addition (in 34 + 7 = 41, 41 is the sum)

Number Bonds: Pairs of numbers that combine to make another number (like 8 + 2 = 10)

Complete methodology:
  1. Analyze the numbers: Look at the addends to determine which method works best
  2. Choose the method: Counting on for small addends, making tens for numbers that complement to 10, breaking apart for larger addends
  3. Apply the method: Follow the steps of the chosen technique
  4. Verify the result: Check your answer by using a different method
Tip 1: Use counting on for additions where the second number is less than 10.
Tip 2: For numbers ending in 8 or 9, try making tens (add 2 to 8, or 1 to 9).
Tip 3: Practice with a number line to visualize the addition process.
Tip 4: Always check your answer by using a different method.
Common errors: Forgetting to adjust when using compensation, miscounting when counting on, forgetting place value when breaking apart.
Key strategies: Recognize patterns, use known facts, break problems into smaller steps.
Mental addition strategies:

• Counting On: Good for small numbers (adding 1-9)

• Making Tens: Use number bonds to create friendly numbers (e.g., 28 + 6 = 28 + 2 + 4)

• Breaking Apart: Separate tens and ones (e.g., 45 + 27 = 45 + 20 + 7)

• Number Line Jumps: Visualize movement on a number line

• Doubles Plus One: Use doubles facts to help (e.g., 7 + 8 = 7 + 7 + 1)

Solution: Exercises 4 to 5
4 Compensation Method
Exercise 4
Solve mentally: 58 + 29
Definition:

Compensation Method: Round one number to make the calculation easier, then adjust the answer.

Problem
58 + 29
Round 29 to 30
58 + 30
Adjust result
88 - 1 = 87
Step 1: Round the second addend to a friendly number

29 is close to 30, which is easier to add to 58

Step 2: Perform the easier addition

58 + 30 = 88

Step 3: Adjust for the rounding

We added 1 too many (30 instead of 29), so subtract 1: 88 - 1 = 87

Step 4: Verify the result

87 - 29 = 58, so our answer is correct

58 + 29 = 87
Final answer:

58 + 29 = 87

Applied rules:

• Rounding: Making numbers friendlier for mental calculation

• Compensation: Adjusting the result to account for rounding

• Verification: Checking that the answer makes sense

5 Doubles Plus One Method
Exercise 5
Solve mentally: 7 + 8
Definition:

Doubles Plus One Method: Use known doubles facts and add one more.

Problem
7 + 8
Think: 7 + 7
7 + 7 = 14
Add one more
14 + 1 = 15
Step 1: Recognize that 7 and 8 are consecutive numbers

8 is 1 more than 7, so we can use the double of 7 and add 1

Step 2: Recall the double fact

7 + 7 = 14

Step 3: Add the extra amount

Since 8 is 1 more than 7, add 1 more to the double: 14 + 1 = 15

Step 4: Calculate the final answer

7 + 8 = 15

Step 5: Verify the result

15 - 8 = 7, confirming our answer is correct

7 + 8 = 15
Final answer:

7 + 8 = 15

Applied rules:

• Number Relationships: Recognizing consecutive numbers

• Known Facts: Using memorized doubles facts

• Compensation: Adjusting for the difference from the double

Mental Addition Strategies and Techniques
Counting On: 34 + 7 = 34, 35, 36, 37, 38, 39, 40, 41 = 41
Counting On Strategy
Key definitions:

Addition: The operation of combining two or more numbers to find their total

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

Friendly Numbers: Numbers that are easy to work with mentally (like multiples of 10)

Number Bonds: Pairs of numbers that combine to make another number (like 7 + 3 = 10)

Complete methodology:
  1. Look at the numbers: Examine the addends to choose the best strategy
  2. Select the method: Counting on for small addends, making tens for numbers that complement to 10, breaking apart for larger addends
  3. Execute the method: Follow the specific steps for your chosen technique
  4. Verify the result: Check your answer by using a different method
Tip 1: For adding 9, add 10 and subtract 1 back (e.g., 45 + 9 = 45 + 10 - 1 = 54)
Tip 2: Use doubles facts to help with near-doubles (if 6 + 6 = 12, then 6 + 7 = 13)
Tip 3: When adding across tens (like 38 + 5), break it into parts (38 + 2 + 3)
Tip 4: Practice with visual aids like number lines or counters before going mental
Common errors: Forgetting to adjust when using compensation, miscounting when counting on, forgetting place value when breaking apart.
Success habits: Regular practice, checking answers, visualizing the process, recognizing patterns.
Mental addition strategies:

• Counting On: Good for small numbers (adding 1-9)

• Making Tens: Use number bonds to create friendly numbers (e.g., 28 + 6 = 28 + 2 + 4)

• Breaking Apart: Separate tens and ones (e.g., 45 + 27 = 45 + 20 + 7)

• Compensation: Round one number and adjust (e.g., 58 + 29 = 58 + 30 - 1)

• Doubles Plus/Minus: Use doubles facts for near-doubles (e.g., 7 + 8 = 7 + 7 + 1)

• Place Value: Add tens and ones separately (e.g., 34 + 45 = 30 + 40 + 4 + 5)

Mental Addition Workflow

🔢
Step-by-Step Process
1
Look at the numbers
2
Choose a method
3
Calculate mentally
4
Check answer
Number Line Visualization
Mental addition involves visualizing movement along a number line, starting from the first addend and moving forward by the value of the second addend.
Practice Daily for Mental Math Mastery!

Questions & Answers

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

Answer: Great question! The choice depends on the numbers you're adding:

  • Counting On: Best when adding small numbers (usually 1-9). It's quick and straightforward. Example: 34 + 7 = 34, 35, 36, 37, 38, 39, 40, 41 = 41
  • Making Tens: Better when one number can easily combine with part of the other to make a ten. Example: 28 + 6 = 28 + 2 + 4 = 30 + 4 = 34

Think of it this way: if the second number is small, counting on is like taking a few steps forward. If you see that adding part of the second number will make a round number (like 10, 20, 30), making tens is often easier!

Both methods are valuable - try both with the same problem to see which feels easier for you!

Question: My child struggles with mental math. How can I help them practice these addition tricks at home?

Answer: Here are effective ways to practice mental addition at home:

  • Use everyday situations: While cooking, ask "If we have 28 cookies and bake 6 more, how many will we have?"
  • Number line walks: Draw a number line on paper or floor tape, have your child physically move forward to visualize addition
  • Playing cards: Draw two cards and practice adding them together
  • Story problems: Create fun stories like "Emma has 45 stickers, her friend gives her 27 more, how many does she have now?"

Start with smaller numbers and gradually increase difficulty. Make it a game - perhaps a race to see who can solve it faster!

Encourage your child to explain their thinking. This helps reinforce the concepts and reveals any misunderstandings.

Question: Why do we need different methods? Can't I just add normally?

Answer: Different methods make addition easier in different situations! Think of it like having different tools:

  • Some problems are easier with counting on (like 34 + 3)
  • Others are easier when you make tens (like 28 + 6)
  • Some are easier with compensation (like 58 + 29, which becomes 58 + 30 - 1)

Having multiple methods gives you flexibility. You can choose the one that makes the most sense for each problem. It's like having a toolbox - sometimes you need a hammer, sometimes a screwdriver!

As you practice, you'll develop number sense and automatically choose the best method for each problem.