Mental Math Strategies for Grade 1

Master mental math strategies for grade 1: counting on, making tens, doubles, and basic addition/subtraction through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting On Strategy
Exercise 1
Calculate: 7 + 4 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 (7) and count up 4 more: 8, 9, 10, 11

7
→
8
→
9
→
10
→
11
Step 1: Identify the larger number

Between 7 and 4, the larger number is 7

Step 2: Count up from the larger number

Start at 7, then count: 8, 9, 10, 11

Step 3: The final number is your answer

After counting 4 more from 7, we reach 11

7 + 4 = 11
Final answer:

7 + 4 = 11

Applied rules:

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

• Efficiency: This is faster than starting from 1

• Number sense: Helps develop understanding of quantity relationships

2 Making Tens Strategy
Exercise 2
Calculate: 8 + 5 using the making tens strategy
Definition:

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

Strategy: Making Tens

Think: 8 needs 2 more to make 10

Break 5 into 2 and 3

Add 8 + 2 = 10, then add the remaining 3

1
2
3
4
5
6
7
8
9
10
Original
8 + 5
Break apart
8 + (2 + 3)
Make ten
(8 + 2) + 3
Final
10 + 3 = 13
Step 1: Look for numbers close to 10

8 is just 2 away from 10, so take 2 from 5

Step 2: Make the ten

8 + 2 = 10

Step 3: Add the remainder

We took 2 from 5, leaving 3, so 10 + 3 = 13

8 + 5 = 13
Final answer:

8 + 5 = 13

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
Calculate: 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

Grade 1 Mental Math 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
Complete Grade 1 Mental Math Summary
Key Definitions:

Addition: Combining two or more numbers to find the total

Subtraction: Taking away or finding the difference between numbers

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

Near doubles: Adding consecutive numbers

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
  4. Near Doubles: Use doubles + 1 or - 1
  5. Counting Back: For subtraction
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.
Tip 4: Practice daily for 10-15 minutes to build fluency.
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
Calculate: 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 Counting Back Strategy (Subtraction)
Exercise 5
Calculate: 12 - 5 using the counting back strategy
Definition:

Counting back: Start with the larger number and count backwards by the smaller number

Strategy: Counting Back

Start at 12 and count back 5 numbers: 11, 10, 9, 8, 7

The final number is your answer: 7

12
←
11
←
10
←
9
←
8
←
7
Expression
12 - 5
Count back
12 → 11 → 10 → 9 → 8 → 7
Result
7
Step 1: Start with the larger number

Begin at 12

Step 2: Count backwards

Count back 5 numbers: 11, 10, 9, 8, 7

Step 3: The final number is your answer

After counting back 5 from 12, we reach 7

Step 4: Verify with related facts

Check: 7 + 5 = 12 ✓

12 - 5 = 7
Final answer:

12 - 5 = 7

Applied rules:

• Counting back: Start with the larger number and count backwards

• Subtraction as inverse: 12 - 5 = ? means 5 + ? = 12

• Verification: Add to check subtraction

Grade 1 Mental Math Practice Worksheet
Practice Problems
Problem
Strategy
Answer
6 + 3
Counting On
9
7 + 4
Making Tens
11
5 + 5
Doubles
10
8 + 9
Near Doubles
17
11 - 4
Counting Back
7
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 and subtract numbers up to 20 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!