Mental Math Strategies for Addition in Grade 2

Master mental addition strategies: counting on, making tens, doubles, near doubles, and compensation methods through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting On Strategy
Exercise 1
Solve: 8 + 3 using the counting on strategy
Definition:

Counting on: Start with the larger number and count up by the smaller number

Strategy: Counting On

This strategy works best when adding a small number (1, 2, or 3) to a larger number.

Start with the larger number and count up: 8, then count 3 more: 9, 10, 11

8
→
9
→
10
→
11
Step 1: Identify the larger number

Between 8 and 3, the larger number is 8

Step 2: Count up from the larger number

Start at 8, then count: 9, 10, 11

Step 3: The final number is your answer

After counting 3 more from 8, we reach 11

8 + 3 = 11
Final answer:

8 + 3 = 11

Applied rules:

• Counting on: Start with the larger number and count up

• Efficiency: This is faster than starting from 1

• Pattern recognition: Helps develop number sense

2 Making Tens Strategy
Exercise 2
Solve: 9 + 5 using the making tens strategy
Definition:

Making tens: Break apart one number to make a ten with the other

9
1
2
3
4
Strategy: Making Tens

Think: 9 needs 1 more to make 10

Break 5 into 1 and 4

Add 9 + 1 = 10, then add the remaining 4

Original
9 + 5
Break apart
9 + (1 + 4)
Make ten
(9 + 1) + 4
Final
10 + 4 = 14
Step 1: Look for numbers close to 10

9 is just 1 away from 10, so take 1 from 5

Step 2: Make the ten

9 + 1 = 10

Step 3: Add the remainder

We took 1 from 5, leaving 4, so 10 + 4 = 14

9 + 5 = 14
Final answer:

9 + 5 = 14

Applied rules:

• Associative property: (a + b) + c = a + (b + c)

• Ten combinations: Know pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5)

• Breaking apart: Decompose numbers strategically

3 Doubles Strategy
Exercise 3
Solve: 6 + 6 using the doubles strategy
Definition:

Doubles: Adding the same number twice (like 6 + 6)

Strategy: Doubles

Doubles facts are easy to remember because you're adding the same number twice.

Memorize doubles: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, etc.

1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
6+6=12
7+7=14
8+8=16
9+9=18
10+10=20
Expression
6 + 6
Doubles fact
6 × 2
Result
12
Step 1: Recognize the pattern

This is a doubles fact: 6 + 6 means 6 groups of 2

Step 2: Recall the doubles fact

6 + 6 = 12 (memorized fact)

Step 3: Verify with counting

Count: 6, 7, 8, 9, 10, 11, 12 (counting 6 more from 6)

6 + 6 = 12
Final answer:

6 + 6 = 12

Applied rules:

• Doubles pattern: n + n = 2n

• Memorization: Doubles facts are foundational

• Building blocks: Doubles help with near doubles

Mental Math Addition Strategies & Methods
Counting On: a + b = Start with a, count b more
Counting On Strategy
Making Tens
8 + 5 = 8 + (2 + 3) = (8 + 2) + 3 = 10 + 3 = 13
Break to make 10
Doubles
n + n = 2n
Add same number twice
Near Doubles
n + (n+1) = 2n + 1
One more than doubles
Key definitions:

Counting on: Starting with the larger number and counting up

Making tens: Breaking apart numbers to form a ten

Doubles: Adding the same number twice

Near doubles: Adding consecutive numbers (like 6 + 7)

Compensation: Adjusting one number and compensating with the other

Complete methodology:
  1. Look at the numbers: Identify which strategy fits best
  2. Choose the strategy: Counting on, making tens, doubles, etc.
  3. Apply the method: Follow the steps of your chosen strategy
  4. Check your work: Verify with a different method if needed
Tip 1: For adding 1, 2, or 3, use counting on.
Tip 2: Numbers close to 10 (like 8 or 9) work well with making tens.
Tip 3: Memorize doubles facts to use for near doubles.
Tip 4: Practice with visual aids like ten frames and number lines.
Common errors: Forgetting to start with the larger number, miscounting, not recognizing doubles.
Key patterns: Know that 10 + anything is easy, doubles are fast, and making tens simplifies problems.
Mental Math Strategies to Remember:

• Counting on: Start with larger number, count up

• Making tens: Break numbers to form 10

• Doubles: n + n = 2n

• Near doubles: Use doubles + 1 or - 1

• Compensation: Adjust and balance numbers

Solution: Exercises 4 to 5
4 Near Doubles Strategy
Exercise 4
Solve: 7 + 8 using the near doubles strategy
Definition:

Near doubles: Adding numbers that are close together (consecutive numbers)

Strategy: Near Doubles

Think of 7 + 8 as 7 + 7 + 1 (double 7 and add 1)

Or think of it as 8 + 8 - 1 (double 8 and subtract 1)

Both approaches use known doubles facts.

Expression
7 + 8
As near double
7 + (7 + 1)
Simplify
(7 + 7) + 1 = 14 + 1 = 15
Step 1: Recognize near doubles pattern

7 and 8 are consecutive numbers (differ by 1)

Step 2: Use the doubles fact

7 + 7 = 14 (known doubles fact)

Step 3: Add the extra amount

Since 8 is 1 more than 7, add 1 to the doubles fact

14 + 1 = 15

Step 4: Alternative approach

8 + 8 = 16, then subtract 1: 16 - 1 = 15

7 + 8 = 15
Final answer:

7 + 8 = 15

Applied rules:

• Near doubles pattern: n + (n+1) = 2n + 1

• Using known facts: Build on memorized doubles

• Flexibility: Can use either number as the base

5 Compensation Strategy
Exercise 5
Solve: 29 + 6 using the compensation strategy
Definition:

Compensation: Adjust one number to make the calculation easier, then adjust back

Strategy: Compensation

Rounding 29 to 30 makes the addition easier

Add 30 + 6 = 36, then subtract the 1 we added to 29

36 - 1 = 35

Original
29 + 6
Compensate
(30 - 1) + 6
Rearrange
30 + 6 - 1 = 36 - 1 = 35
Step 1: Look for easy numbers

29 is close to 30, which is easier to add

Step 2: Round and add

Round 29 up to 30: 30 + 6 = 36

Step 3: Adjust back

We added 1 too many (since 29 = 30 - 1), so subtract 1

36 - 1 = 35

Step 4: Verify with another method

Using making tens: 29 + 1 = 30, then 30 + 5 = 35 ✓

29 + 6 = 35
Final answer:

29 + 6 = 35

Applied rules:

• Compensation principle: a + b = (a + c) + (b - c)

• Rounding: Round to nearest ten or hundred

• Adjustment: Compensate for the rounding

Mental Math Addition Rules, Methods, and Definitions
n + (n+1) = 2n + 1
Near Doubles Formula
Key definitions:

Mental math: Calculating in your head without writing

Number sense: Understanding how numbers relate to each other

Strategic thinking: Choosing the best method for each problem

Complete methodology:
  1. Scan the problem: Look for patterns (near doubles, tens, etc.)
  2. Select strategy: Choose most efficient method
  3. Execute: Apply the chosen strategy
  4. Verify: Check using a different method
Tip 1: Practice daily with small problems to build speed.
Tip 2: Use finger counting initially, then move to mental only.
Tip 3: Games and timed challenges help with fluency.
Tip 4: Explain your thinking to reinforce understanding.
Common errors: Counting from wrong number, forgetting to compensate, misapplying strategies.
Success habits: Regular practice, checking work, flexibility in approach.
Mental Math Fundamentals:

• Counting on: Best for small addends (1-3)

• Making tens: For numbers close to 10

• Doubles: Memorize facts 1+1 through 10+10

• Near doubles: Use doubles + 1 or - 1

• Compensation: Round to friendly numbers

Questions & Answers

Question: I don't understand when to use making tens versus counting on. How do I decide which strategy is better?

Answer: Great question! Here's how to decide:

  • Use counting on when: Adding a small number (1, 2, or 3) to a larger number
  • Use making tens when: One number is close to 10 (like 8, 9) and you can break the other to make 10

Examples:

• 7 + 2 → Counting on (start at 7, count 2 more: 8, 9)

• 9 + 4 → Making tens (take 1 from 4 to make 10: 9 + 1 = 10, then 10 + 3 = 13)

The key is looking at the numbers and seeing which approach feels easier mentally!

Question: Why do we learn different strategies instead of just one way to add?

Answer: Learning multiple strategies gives you flexibility! Different problems work better with different approaches:

  • Some problems are fastest with counting on
  • Others are easier with making tens
  • Having choices helps you solve problems more efficiently
  • It builds number sense and mathematical thinking

Think of it like having different tools in a toolbox - you want the right tool for each job!

Question: My child is struggling with mental math. How can I help them practice at home?

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

  • Play math games during car rides or meals
  • Use everyday situations: "We have 8 cookies and bought 5 more, how many now?"
  • Practice for just 5-10 minutes daily rather than long sessions
  • Encourage explaining their thinking out loud
  • Use manipulatives like counters or fingers initially

The key is keeping it fun and low-pressure while building confidence gradually!