Complete Mental Math Strategies: Addition and Subtraction in Grade 1

Master mental math strategies for both addition and subtraction: number bonds, addition facts, subtraction techniques through comprehensive explanations and visual learning aids.

Mental Math Strategies: Addition Examples 1 to 3
1 Counting On Strategy for Addition
Addition Strategy 1
Counting On: Add by starting with the larger number and counting forward
Definition:

Counting On Strategy: Starting with the larger number and counting forward by the amount of the smaller number

Counting On Method:
  1. Identify the larger number (start number)
  2. Keep the larger number in your head
  3. Count forward by the smaller number
  4. Track each count with fingers or in your mind
Problem
7 + 4
Start with 7
7
Count 4 more
8, 9, 10, 11
Answer
11
Step 1: Identify the larger number

Between 7 and 4, 7 is larger, so we start with 7

Step 2: Keep 7 in your head

Think "7" and hold it in your mind

Step 3: Count forward 4 times

Count: 8 (that's 1), 9 (that's 2), 10 (that's 3), 11 (that's 4)

Counting On Strategy
🧠
Hold 7
7
➡️
Count 4 more
8, 9, 10, 11
✅
Final Answer
7 + 4 = 11
💡
Strategy
Start big, count small
0 2 4 6 8 10 12 14 16
7
8
9
10
11
7 + 4 = 11 (counting on: 7 → 8, 9, 10, 11)
7
1
1
1
1
7 + 4 = 11
Final answer:

7 + 4 = 11

Mental Math Tip:

Always start with the bigger number when counting on. It's faster and easier to count a small number forward than a large number!

2 Making Tens Strategy for Addition
Addition Strategy 2
Making Tens: Use 10 as a benchmark number to simplify addition
Definition:

Making Tens Strategy: Using the benchmark number 10 to simplify addition by breaking apart numbers strategically

Problem
8 + 6
Make 10
8 + 2 = 10
Remaining
6 = 2 + 4
Answer
10 + 4 = 14
Step 1: Identify what's needed to make 10

From 8, we need 2 more to make 10

Step 2: Break apart the second number

Split 6 into 2 and 4 (because 2 + 4 = 6)

Step 3: Complete the calculation

(8 + 2) + 4 = 10 + 4 = 14

Making Tens Strategy
🎯
Goal
Make 10
8️⃣
Start with 8
Need 2 more
🔄
Break 6
2 + 4
✅
Answer
10 + 4 = 14
8 + 6 = (8 + 2) + 4 = 10 + 4 = 14
8
2
4
8 + 6 = 14
Final answer:

8 + 6 = 14

Mental Math Tip:

Practice number bonds to 10 until they become automatic. Knowing pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5) will make this strategy fast and effective!

3 Doubles Plus One Strategy for Addition
Addition Strategy 3
Doubles Plus One: Use known doubles facts to solve nearby problems
Definition:

Doubles Plus One Strategy: Using known doubles facts to solve problems where one number is one more than the other

Problem
5 + 6
Think
5 + 5 + 1
Doubles Fact
5 + 5 = 10
Add One
10 + 1 = 11
Step 1: Recognize the relationship

6 is one more than 5, so we can use 5 + 5 and add 1

Step 2: Recall the doubles fact

5 + 5 = 10 (this should be memorized)

Step 3: Add the extra one

10 + 1 = 11

Doubles Plus One Strategy
🎲
Doubles
5 + 5 = 10
➕
Plus One
10 + 1 = 11
🎯
Original
5 + 6 = 11
💡
Strategy
Use known facts
5 + 6 = 5 + 5 + 1 = 10 + 1 = 11
5
5
1
10
1
5 + 6 = 11
Final answer:

5 + 6 = 11

Mental Math Tip:

Memorize doubles facts (1+1, 2+2, 3+3, etc.) as they form the foundation for many other mental math strategies!

Mental Math Strategies: Complete Summary
Comprehensive Mental Math Guide
Key Definitions

Mental Math: Performing mathematical calculations in your head without writing anything down or using tools.

Number Bonds: Pairs of numbers that add up to a specific total, especially 10.

Strategies: Different approaches to solving math problems mentally.

Core Principles

• Use Benchmarks: Use 10 as a reference point since it's easy to work with

• Start Big: Begin with the larger number when adding

• Break Down: Split numbers into smaller, more manageable parts

Mental Math Strategies

Addition:

1. Counting On: Start with the larger number and count forward

2. Making Tens: Use 10 as a benchmark for addition

3. Doubles Plus One: Use doubles facts to solve nearby problems

Subtraction:

4. Counting Back: Start with the larger number and count backward

5. Adding Up: Think of subtraction as finding a missing addend

6. Breaking Down: Decompose numbers for easier subtraction

Practice Techniques

Flashcards: Practice basic facts daily

Number Talks: Discuss different ways to solve problems

Games: Use math games to make practice fun

Common Challenges

• Getting overwhelmed with larger numbers

• Forgetting steps in multi-step problems

• Mixing up addition and subtraction

Success Factors

• Regular practice with basic facts

• Understanding the "why" behind strategies

• Flexibility in choosing approaches

Daily Mental Math Routine:

• Spend 5-10 minutes daily practicing mental math

• Start with easy problems and gradually increase difficulty

• Use multiple strategies to solve the same problem

Building Speed:

• Focus on accuracy first, then work on speed

• Practice number bonds until they become automatic

• Use visual imagery to help with calculations

Counting On
Start with larger number, count forward
Making Tens
Use 10 as benchmark number
Counting Back
Start with larger number, count backward
Doubles Plus One
Use doubles facts for nearby problems
Tip 1: Use your fingers when starting out, but gradually move to mental visualization.
Tip 2: Practice "number talks" - explain your thinking out loud.
Tip 3: Use real-life situations: "If I have 6 cookies and eat 2, how many are left?"
Tip 4: Check your mental math by using a different strategy.
Tip 5: Celebrate progress - mental math skills develop over time!
\(a + b = \text{mental calculation}\)
Where mental calculation uses strategies like counting on, making tens, or counting back
Mental Math Strategies: Subtraction Examples 4 to 5
4 Counting Back Strategy for Subtraction
Subtraction Strategy 1
Counting Back: Subtract by starting with the larger number and counting backward
Definition:

Counting Back Strategy: Starting with the larger number and counting backward by the amount of the smaller number

Problem
11 - 4
Start with 11
11
Count back 4
10, 9, 8, 7
Answer
7
Step 1: Start with the larger number

Begin with 11

Step 2: Count backward 4 times

Count: 10 (that's 1), 9 (that's 2), 8 (that's 3), 7 (that's 4)

Step 3: The result is the answer

11 - 4 = 7

Counting Back Strategy
🧠
Hold 11
11
⬅️
Count back 4
10, 9, 8, 7
✅
Final Answer
11 - 4 = 7
💡
Strategy
Subtract by counting back
11 - 4 = 7 (counting back: 11 → 10, 9, 8, 7)
10
1
4
7
11 - 4 = 7
Final answer:

11 - 4 = 7

Mental Math Tip:

For subtraction, count backward from the starting number. For addition, count forward!

5 Adding Up Strategy for Subtraction
Subtraction Strategy 2
Adding Up: Think of subtraction as finding the missing addend
Definition:

Adding Up Strategy: Thinking about subtraction as finding the missing addend in an addition problem

Problem
13 - 8
Think
8 + ? = 13
Add to 10
8 + 2 = 10
Then to 13
10 + 3 = 13
Answer
2 + 3 = 5
Step 1: Change subtraction to addition

Instead of 13 - 8, think "what plus 8 equals 13?"

Step 2: Use making tens strategy

From 8, add 2 to make 10, then add 3 more to reach 13

Step 3: Add the amounts together

2 + 3 = 5, so 13 - 8 = 5

Adding Up Strategy
❓
Think
8 + ? = 13
🎯
Make 10
8 + 2 = 10
➡️
To 13
10 + 3 = 13
✅
Answer
2 + 3 = 5
13 - 8 = 5 (think: 8 + 5 = 13)
8
2
3
13 - 8 = 5
Final answer:

13 - 8 = 5

Mental Math Tip:

This strategy works well for subtraction problems where the numbers are close together. It's often easier than traditional subtraction!

Questions & Answers

Question: My child seems confused about when to use addition strategies versus subtraction strategies. How can I help them choose the right one?

Answer: Here's how to help your child distinguish between operations:

  • Look for keywords: Addition words include "more," "total," "altogether," "combined"; subtraction words include "take away," "left," "difference," "less than"
  • Context matters: If something is being added or combined, use addition strategies; if something is being taken away or compared, use subtraction strategies
  • Practice both: Mix addition and subtraction problems so your child practices identifying the operation
  • Visual cues: Draw pictures or use objects to show what's happening in the problem

The key is helping them understand the story in the problem, not just the numbers!

Question: How can I teach my students to be flexible with both addition and subtraction mental math strategies?

Answer: Build flexibility through mixed practice:

  • Number talks: Discuss different strategies for the same problem
  • Mixed operations: Present problems that require both addition and subtraction
  • Strategy comparison: Compare efficiency of different approaches
  • Pattern recognition: Help students notice when certain strategies work best

Create anchor charts showing both addition and subtraction strategies. Flexibility develops with exposure to different problem types!

Question: Sometimes I forget whether to count forward or backward. How can I remember?

Answer: Here's a memory trick to help you remember:

  • Plus sign (+): Addition means getting bigger, so count forward (up the number line)
  • Minus sign (-): Subtraction means getting smaller, so count backward (down the number line)
  • Think of it like stairs: Adding goes up stairs, subtracting goes down stairs
  • Check your answer: Does it make sense? If you subtract and get a bigger number, you probably counted the wrong direction!

Practice with small numbers first until you feel confident with the direction!