Examples of Mental Math Strategies for 1st Grade

Master essential mental math strategies for addition and subtraction with visual examples, step-by-step guidance, and practical exercises.

Mental Math Strategy Exercises & Solutions
1 Counting On Strategy
Exercise 1
Solve: 5 + 3 = ?
Definition:

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

Method:
  1. Identify the larger number (start here)
  2. Count forward by the smaller number
  3. Keep track of the counts
5
+
3
=
8
1
Start at 5
2
Count 6, 7, 8
3
Answer: 8
Step 1: Identify larger number

Between 5 and 3, start with 5 (the larger number)

Step 2: Count forward

Count 3 more: 5 → 6 → 7 → 8

Step 3: State the answer

5 + 3 = 8

5 + 3 = 8
Final answer:

5 + 3 = 8

Applied rules:

• Counting on: Start with the larger number to minimize counting

• Efficiency: Counting forward is faster than starting from 1

• Visualization: Use fingers or mental number line

2 Making Ten Strategy
Exercise 2
Solve: 8 + 5 = ?
Definition:

Making ten: Break apart one number to make a ten, then add the remainder

8
+
5
=
13
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 5 into 2 + 3

Step 3: Add to make 10, then add remainder

8 + 2 = 10, then 10 + 3 = 13

1
8 + 2 = 10
2
5 = 2 + 3
3
10 + 3 = 13
8 + 5 = 13
Final answer:

8 + 5 = 13

Applied rules:

• Decomposition: Break apart numbers strategically

• Ten as benchmark: Use 10 as a friendly number

• Regrouping: Reorganize numbers for easier computation

3 Doubles Plus One Strategy
Exercise 3
Solve: 6 + 7 = ?
Definition:

Doubles plus one: Use a known double fact and add one more

6
+
7
=
13
Step 1: Recognize the near-double

6 + 7 is close to 6 + 6 (a double fact)

Step 2: Use the double fact

6 + 6 = 12

Step 3: Add one more

Since 7 is one more than 6, add 1 to the double

12 + 1 = 13

1
6 + 6 = 12
2
7 = 6 + 1
3
12 + 1 = 13
6 + 7 = 13
Final answer:

6 + 7 = 13

Applied rules:

• Known facts: Use memorized doubles to solve near-doubles

• Relationships: Understand number relationships

• Efficiency: Leverage known facts for new computations

Mental Math Strategies Overview
Counting On
Start with the larger number and count forward
Example: 7 + 3 → Start at 7, count 8, 9, 10 → Answer: 10
Making Ten
Break apart numbers to make a ten, then add remainder
Example: 9 + 4 → 9 + 1 = 10, then 10 + 3 = 13
Doubles Plus/Minus One
Use known doubles and adjust by one
Example: 5 + 6 → 5 + 5 = 10, then 10 + 1 = 11
Using Doubles
Know double facts automatically
Example: 4 + 4 = 8 (memorized)
🔢
Counting On
🔟
Making Ten
⚡
Near Doubles
🎯
Doubles
Key benefits:

Speed: Faster than counting from 1

Flexibility: Multiple pathways to solutions

Understanding: Builds number sense

When to use each strategy:
  1. Counting on: When one number is small (≤3)
  2. Making ten: When numbers are close to 10
  3. Near doubles: When numbers are consecutive
  4. Doubles: When numbers are the same
Tip 1: Practice with concrete objects before mental math.
Tip 2: Encourage flexible thinking about numbers.
Tip 3: Use multiple strategies to verify answers.
Mental Math Concepts & Properties
Mental Math = Flexible Thinking
Strategy-Based Calculation
Definition:

Mental math strategies: Techniques for solving math problems in your head without paper or tools

Efficiency: Faster than traditional counting methods.
Flexibility: Multiple approaches to reach the same answer.
Number sense: Develops understanding of number relationships.
Foundation: Builds skills for advanced math concepts.
Teaching strategies:
  1. Model thinking: Verbalize thought processes aloud
  2. Multiple exposures: Practice same strategy with different numbers
  3. Strategy choice: Let students choose their preferred method
  4. Gradual release: Move from concrete to abstract
Key principles:

• Flexibility: Different problems may require different strategies

• Efficiency: Some strategies work better than others for specific problems

• Understanding: Know why the strategy works, not just how

• Practice: Regular practice builds fluency and confidence

Common mistake: Relying on counting from 1 for all problems.
Practice tip: Use daily "number talks" to discuss strategies.
Practice Activities & Tips
Practice Builds Fluency!
Mental Math Development
Practice activities:

Number strings: Series of related problems that build on each other

Flash cards: Quick recognition and response practice

Games: Engaging activities that reinforce strategies

Learning progression:
  1. Concrete: Use manipulatives and visual models
  2. Representational: Draw pictures and diagrams
  3. Abstract: Work with numbers only
  4. Fluent: Automatic recall and application
Tip 1: Practice 5-10 minutes daily for consistent improvement.
Tip 2: Discuss multiple ways to solve the same problem.
Tip 3: Connect strategies to real-life scenarios.
Tip 4: Encourage explanation of thinking process.
Assessment: Students should solve problems mentally within 5-10 seconds.
Connection: Mental math supports problem-solving and estimation skills.
Common core alignment:

• 1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

• 1.NBT.4: Add within 100, including adding a two-digit number and a one-digit number.

• 1.OA.1: Use addition and subtraction within 20 to solve word problems.

Detailed Summary & Key Takeaways
Key Concepts:

Mental math strategies: Techniques for solving math problems mentally without paper or tools

Flexible thinking: Multiple approaches to reach the same answer

Number relationships: Understanding how numbers connect and interact

Core Rules & Principles:
  1. Efficiency: Choose the fastest strategy for each problem
  2. Flexibility: Be able to use multiple strategies
  3. Understanding: Know why strategies work, not just how
  4. Practice: Regular practice builds fluency and automaticity
Examples (simple → advanced): Counting on (3+2), Making ten (8+5), Near doubles (6+7)
Memorization tip: Practice doubles facts first as they support other strategies
Common pitfall: Sticking to one strategy regardless of problem type
Application: Mental math strategies support estimation and problem-solving
Long-term benefits:

• Speed: Faster computational abilities

• Confidence: Increased mathematical self-assurance

• Understanding: Deeper comprehension of number relationships

• Foundation: Supports advanced mathematical concepts

Questions & Answers

Question: How do I know if my child is using mental math strategies effectively?

Answer: Effective mental math use shows in several ways:

  • Speed: Solves problems faster than counting from 1
  • Variety: Uses different strategies for different problems
  • Explanation: Can describe their thinking process
  • Accuracy: Gets correct answers consistently

Ask your child to "think aloud" while solving problems to observe their strategy use.

Question: Should I teach all strategies at once or introduce them gradually?

Answer: Introduce strategies gradually for best results:

  • Start with counting on: Most intuitive for beginners
  • Add making ten: Once students are comfortable with tens
  • Introduce doubles: After mastering basic facts
  • Combine strategies: As students gain confidence

Allow students to explore and choose their preferred strategies rather than mandating specific methods.

Question: What if a student struggles with mental math strategies?

Answer: For struggling students, try these approaches:

  • Return to concrete: Use manipulatives and visual models
  • Slow the pace: Focus on one strategy at a time
  • Provide scaffolding: Use number lines or hundreds charts
  • Build confidence: Start with easier numbers and build complexity

Some students may need more time to develop mental math skills, and that's perfectly normal.