Mental Math Strategies for Addition - Lesson 1

Learn the basics of mental addition: counting on, making tens, doubles, and simple compensation through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting On Strategy
Exercise 1
Solve: 5 + 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 is the easiest strategy for small additions.

Start with the bigger number (5) and count up 3 more: 6, 7, 8

5
→
6
→
7
→
8
Step 1: Identify the larger number

Between 5 and 3, the larger number is 5

Step 2: Count up from the larger number

Start at 5, then count: 6, 7, 8

Step 3: The final number is your answer

After counting 3 more from 5, we reach 8

5 + 3 = 8
Final answer:

5 + 3 = 8

Applied rules:

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

• Efficiency: This is faster than starting from 1

• Number sense: Builds understanding of quantity relationships

2 Making Tens Strategy
Exercise 2
Solve: 7 + 3 using the making tens strategy
Definition:

Making tens: Recognize when two numbers add up to 10

Strategy: Making Tens

7 and 3 are partners that make 10

When you see 7 + 3, you know immediately: 10

7
3
Expression
7 + 3
Tens partner
7 + 3 = 10
Step 1: Recognize the tens partners

7 and 3 are friends that make 10 together

Step 2: Recall the fact

7 + 3 = 10 (memorized fact)

Step 3: Practice with other tens partners

1+9, 2+8, 3+7, 4+6, 5+5

7 + 3 = 10
Final answer:

7 + 3 = 10

Applied rules:

• Ten partners: Know pairs that sum to 10

• Instant recall: These facts should be automatic

• Foundation: Makes harder problems easier

3 Doubles Strategy
Exercise 3
Solve: 4 + 4 using the doubles strategy
Definition:

Doubles: Adding the same number twice (like 4 + 4)

Strategy: Doubles

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

Think: "4 and 4 make 8" or "4 doubled is 8"

1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
Expression
4 + 4
Doubles fact
4 × 2
Result
8
Step 1: Recognize the pattern

This is a doubles fact: 4 + 4 means 4 groups of 2

Step 2: Recall the doubles fact

4 + 4 = 8 (memorized fact)

Step 3: Verify with counting

Count: 4, 5, 6, 7, 8 (counting 4 more from 4)

4 + 4 = 8
Final answer:

4 + 4 = 8

Applied rules:

• Doubles pattern: n + n = 2n

• Memorization: Doubles facts are foundational

• Building blocks: Doubles help with near doubles

Lesson 1: Mental Math Addition Concepts
Counting On: a + b = Start with a, count b more
Counting On Strategy
Making Tens
7 + 3 = 10
Tens partners
Doubles
n + n = 2n
Add same number twice
Addition Property
a + b = b + a
Order doesn't matter
Complete Lesson 1 Summary
Key Definitions:

Addition: Combining two or more numbers to find the total

Mental math: Calculating in your head without writing

Counting on: Starting with the larger number and counting up

Tens partners: Two numbers that add up to 10

Doubles: Adding the same number twice

Core Methods:
  1. Counting On: Start with larger number, count up
  2. Making Tens: Know pairs that sum to 10
  3. Doubles: Memorize same-number additions
Tip 1: Always start with the bigger number when counting on.
Tip 2: Practice tens partners until they're automatic.
Tip 3: Use your fingers or objects to visualize problems.
Counting On
Start big, count up
Making Tens
Partners to 10
Doubles
Same number twice
Check Work
Count backwards
Essential Rules for Grade 1:

• Always start with the larger number when counting on

• Memorize tens partners (1+9, 2+8, 3+7, 4+6, 5+5)

• Know doubles facts up to 5+5

• Check your work by counting backwards

• Practice regularly to build fluency

Solution: Exercises 4 to 5
4 Near Doubles Strategy
Exercise 4
Solve: 5 + 6 using the near doubles strategy
Definition:

Near doubles: Adding numbers that are next to each other (consecutive numbers)

Strategy: Near Doubles

Think of 5 + 6 as 5 + 5 + 1 (double 5 and add 1)

Or think of it as 6 + 6 - 1 (double 6 and subtract 1)

Both approaches use known doubles facts.

Expression
5 + 6
As near double
5 + (5 + 1)
Simplify
(5 + 5) + 1 = 10 + 1 = 11
Step 1: Recognize near doubles pattern

5 and 6 are consecutive numbers (differ by 1)

Step 2: Use the doubles fact

5 + 5 = 10 (known doubles fact)

Step 3: Add the extra amount

Since 6 is 1 more than 5, add 1 to the doubles fact

10 + 1 = 11

Step 4: Alternative approach

6 + 6 = 12, then subtract 1: 12 - 1 = 11

5 + 6 = 11
Final answer:

5 + 6 = 11

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 Simple Compensation Strategy
Exercise 5
Solve: 9 + 2 using the compensation strategy
Definition:

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

Strategy: Compensation

Round 9 up to 10 (add 1)

Add 10 + 2 = 12

Then subtract the 1 we added: 12 - 1 = 11

Original
9 + 2
Compensate
(10 - 1) + 2
Rearrange
10 + 2 - 1 = 12 - 1 = 11
Step 1: Look for easy numbers

9 is close to 10, which is easier to add

Step 2: Round and add

Round 9 up to 10: 10 + 2 = 12

Step 3: Adjust back

We added 1 too many (since 9 = 10 - 1), so subtract 1

12 - 1 = 11

Step 4: Verify with counting on

Start at 9, count 2 more: 10, 11 ✓

9 + 2 = 11
Final answer:

9 + 2 = 11

Applied rules:

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

• Rounding: Round to nearest ten for easier calculation

• Adjustment: Compensate for the rounding

Lesson 1 Practice Worksheet
Basic Addition Facts
Problem
Strategy
Answer
3 + 4
Counting On
7
6 + 4
Making Tens
10
3 + 3
Doubles
6
4 + 5
Near Doubles
9
8 + 3
Compensation
11
Key Concepts for Grade 1:

Number sense: Understanding how numbers relate to each other

Strategic thinking: Choosing the best method for each problem

Memorization: Building automatic recall of basic facts

Verification: Checking answers using different methods

Problem-Solving Steps:
  1. Look: Examine the numbers for patterns
  2. Choose: Select the best strategy
  3. Calculate: Perform the mental computation
  4. Check: Verify using a different method
Tip 1: Practice with small numbers first, then increase difficulty.
Tip 2: Use your fingers or objects to visualize problems.
Tip 3: Practice daily for 10-15 minutes to build fluency.
Grade 1 Mental Math Goals:

• Add numbers up to 10 mentally

• Use multiple strategies flexibly

• Build computational fluency

• Develop number sense

• Verify solutions independently

Questions & Answers

Question: I sometimes forget which number to start with when counting on. What should I do?

Answer: Great question! Here's the rule:

  • Always start with the bigger number
  • Count up by the smaller number

Examples:

• 3 + 5 → Start at 5, count 3 more: 6, 7, 8

• 7 + 2 → Start at 7, count 2 more: 8, 9

Starting with the bigger number makes counting easier and faster!

Question: How can I help my child practice mental math at home?

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

  • Use everyday situations: "We have 3 apples and buy 4 more, how many now?"
  • Play math games with dice or cards
  • Practice for just 10-15 minutes daily
  • Encourage using fingers or small objects to visualize
  • Make it fun with songs or rhymes about math facts
  • Celebrate progress and effort, not just correct answers

Short, consistent practice sessions work better than long, infrequent ones!

Question: What if I can't remember the answer? Should I count from 1?

Answer: It's okay to count if you need to! Here's what to do:

  • Don't count from 1 - that takes too long
  • Use the counting on strategy: start with the bigger number
  • Practice the facts regularly until they become automatic
  • Use visual aids like fingers or drawings if helpful

Remember, everyone learns at their own pace - keep practicing and you'll get faster!