Mental Math Strategies PDF Guide for Grade 1

Master mental math strategies: counting on, making tens, doubles, compensation, and place value through these 5 detailed exercises. Download our comprehensive PDF guide for continued practice.

Solution: Exercises 1 to 3
1 Counting On Strategy
Exercise 1
Calculate: 8 + 5 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 (8) and count up 5 more: 9, 10, 11, 12, 13

8
→
9
→
10
→
11
→
12
→
13
Step 1: Identify the larger number

Between 8 and 5, the larger number is 8

Step 2: Count up from the larger number

Start at 8, then count: 9, 10, 11, 12, 13

Step 3: The final number is your answer

After counting 5 more from 8, we reach 13

8 + 5 = 13
Final answer:

8 + 5 = 13

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: 7 + 6 using the making tens strategy
Definition:

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

Strategy: Making Tens

Think: 7 needs 3 more to make 10

Break 6 into 3 and 3

Add 7 + 3 = 10, then add the remaining 3

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

7 is just 3 away from 10, so take 3 from 6

Step 2: Make the ten

7 + 3 = 10

Step 3: Add the remainder

We took 3 from 6, leaving 3, so 10 + 3 = 13

7 + 6 = 13
Final answer:

7 + 6 = 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: 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.

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

Mental Math Strategies & Methods
Counting On: a + b = Start with a, count b more
Counting On Strategy
Making Tens
7 + 6 = 7 + (3 + 3) = (7 + 3) + 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

Download Complete PDF Guide

Click below to download the full mental math strategies PDF with all exercises, tips, and practice problems.

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

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

Strategy: Near Doubles

Think: 5 + 6 = 5 + (5 + 1) = (5 + 5) + 1 = 10 + 1 = 11

Or think: 6 + 6 - 1 = 12 - 1 = 11

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

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 Compensation Strategy
Exercise 5
Calculate: 19 + 4 using the compensation strategy
Definition:

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

Strategy: Compensation

Round 19 up to 20 (add 1)

Add 20 + 4 = 24

Then subtract the 1 we added: 24 - 1 = 23

Original
19 + 4
Compensate
(20 - 1) + 4
Rearrange
20 + 4 - 1 = 24 - 1 = 23
Step 1: Look for easy numbers

19 is close to 20, which is easier to add

Step 2: Round and add

Round 19 up to 20: 20 + 4 = 24

Step 3: Adjust back

We added 1 too many (since 19 = 20 - 1), so subtract 1

24 - 1 = 23

19 + 4 = 23
Final answer:

19 + 4 = 23

Applied rules:

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

• Adjustment: Add same amount to both numbers

• Difference preservation: The difference stays the same

Grade 1 Mental Math Practice Worksheet
Practice Problems
Problem
Strategy
Answer
3 + 4
Counting On
7
6 + 4
Making Tens
10
5 + 5
Doubles
10
4 + 5
Near Doubles
9
18 + 3
Compensation
21
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 don't understand when to use making tens versus counting on. How do I decide?

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 or 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: 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 rather than long sessions
  • Encourage explaining their thinking out loud
  • Use manipulatives like counters or fingers initially
  • Make it fun with songs or math rhymes

Consistent practice in small doses works better than infrequent long sessions!

Question: What if I make a mistake? Should I try again or ask for help?

Answer: Making mistakes is part of learning! Here's what to do:

  • First, try to catch your mistake by checking with a different strategy
  • If you're stuck, ask for help - teachers and parents want to assist you
  • Write down your error to learn from it
  • Practice similar problems to strengthen that skill

Remember, every mathematician makes mistakes - what matters is learning from them!