Complete Mental Math Strategies Bridging 1st to 3rd Grade

Master foundational mental math strategies: number bonds, addition facts, and subtraction techniques that prepare for 3rd grade complexity through comprehensive explanations and visual learning aids.

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

Advanced Counting On Strategy: Starting with the larger number and counting forward by the amount of the smaller number, preparing for larger numbers in 3rd grade

Advanced 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
  5. Begin practicing with numbers up to 20
Example
12 + 5
Start with 12
12
Count 5 more
13, 14, 15, 16, 17
Answer
17
Step 1: Identify the larger number

Between 12 and 5, 12 is larger, so we start with 12

Step 2: Keep 12 in your head

Think "12" and hold it in your mind

Step 3: Count forward 5 times

Count: 13 (that's 1), 14 (that's 2), 15 (that's 3), 16 (that's 4), 17 (that's 5)

Advanced Counting On Strategy
🧠
Hold 12
12
➡️
Count 5 more
13, 14, 15, 16, 17
✅
Final Answer
12 + 5 = 17
🎓
3rd Grade Prep
Larger numbers
10 12 14 16 18 20 22 24 26
12
13
14
15
16
17
12 + 5 = 17 (advanced counting on: 12 → 13, 14, 15, 16, 17)
10
2
5
17
3rd Grade Connection:

This strategy prepares you for adding even larger numbers like 23 + 8 or 45 + 6.

12 + 5 = 17
Final answer:

12 + 5 = 17

Mental Math Tip:

Always start with the bigger number when counting on. This strategy will help you with larger numbers in 3rd grade!

2 Expanded Making Tens Strategy
Strategy 2
Expanded Making Tens: Use 10 as a benchmark with larger numbers
Definition:

Expanded Making Tens Strategy: Using the benchmark number 10 to simplify addition with larger numbers, preparing for 3rd grade place value understanding

Example
14 + 8
Make 10
14 + 6 = 20
Remaining
8 = 6 + 2
Answer
20 + 2 = 22
Step 1: Identify what's needed to make the next 10

From 14, we need 6 more to make 20

Step 2: Break apart the second number

Split 8 into 6 and 2 (because 6 + 2 = 8)

Step 3: Complete the calculation

(14 + 6) + 2 = 20 + 2 = 22

Expanded Making Tens Strategy
🎯
Goal
Make Next 10
1️⃣4️⃣
Start with 14
Need 6 more to 20
🔄
Break 8
6 + 2
✅
Answer
20 + 2 = 22
14 + 8 = (14 + 6) + 2 = 20 + 2 = 22
10
4
6
2
20
2
3rd Grade Connection:

This strategy introduces place value concepts that will be essential in 3rd grade.

14 + 8 = 22
Final answer:

14 + 8 = 22

Mental Math Tip:

As you advance to 3rd grade, you'll use this strategy with hundreds and thousands too!

3 Advanced Counting Back Strategy
Strategy 3
Advanced Counting Back: Subtract by starting with larger numbers and counting backward
Definition:

Advanced Counting Back Strategy: Starting with the larger number and counting backward by the amount of the smaller number, preparing for larger subtractions in 3rd grade

Example
18 - 6
Start with 18
18
Count back 6
17, 16, 15, 14, 13, 12
Answer
12
Step 1: Start with the larger number

Begin with 18

Step 2: Count backward 6 times

Count: 17 (that's 1), 16 (that's 2), 15 (that's 3), 14 (that's 4), 13 (that's 5), 12 (that's 6)

Step 3: The result is the answer

18 - 6 = 12

Advanced Counting Back Strategy
🧠
Hold 18
18
⬅️
Count back 6
17, 16, 15, 14, 13, 12
✅
Final Answer
18 - 6 = 12
🎓
3rd Grade Prep
Larger numbers
18 - 6 = 12 (advanced counting back: 18 → 17, 16, 15, 14, 13, 12)
10
8
6
12
3rd Grade Connection:

This strategy will help you subtract numbers in the hundreds by 3rd grade.

18 - 6 = 12
Final answer:

18 - 6 = 12

Mental Math Tip:

For subtraction, count backward from the starting number. This skill will be essential for 3rd grade!

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

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

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

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

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

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

Transition to 3rd Grade:

These strategies will expand to include multiplication, division, and working with numbers up to 1,000!

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 15 cookies and eat 7, 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: Examples 4 to 5
4 Advanced Doubles Plus One Strategy
Strategy 4
Advanced Doubles Plus One: Use known doubles facts for larger numbers
Definition:

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

Example
11 + 12
Think
11 + 11 + 1
Doubles Fact
11 + 11 = 22
Add One
22 + 1 = 23
Step 1: Recognize the relationship

12 is one more than 11, so we can use 11 + 11 and add 1

Step 2: Recall the doubles fact

11 + 11 = 22 (double the tens and double the ones)

Step 3: Add the extra one

22 + 1 = 23

Advanced Doubles Plus One Strategy
🎲
Doubles
11 + 11 = 22
➕
Plus One
22 + 1 = 23
🎯
Original
11 + 12 = 23
🎓
3rd Grade Prep
Larger numbers
11 + 12 = 11 + 11 + 1 = 22 + 1 = 23
10
1
10
1
1
20
2
1
3rd Grade Connection:

This strategy will help you with multiplication facts in 3rd grade!

11 + 12 = 23
Final answer:

11 + 12 = 23

Mental Math Tip:

Memorize doubles facts as they form the foundation for many other mental math strategies and multiplication in 3rd grade!

5 Advanced Strategy Selection
Strategy 5
Advanced Strategy Selection: Choose the most efficient approach for larger numbers
Definition:

Advanced Strategy Selection: Choosing the most efficient mental math strategy based on larger numbers involved, preparing for 3rd grade complexity

Example
16 + 7
Best Strategy
Making Tens
Calculation
(16 + 4) + 3 = 23
Answer
23
Step 1: Analyze the numbers

16 + 7: Since 16 is close to 20, making tens is efficient

Step 2: Apply the making tens strategy

16 needs 4 more to make 20, so split 7 into 4 + 3

Step 3: Complete the calculation

(16 + 4) + 3 = 20 + 3 = 23

Advanced Strategy Selection
📊
Analyze
16 + 7
🎯
Make Tens
16 + 4 = 20
🔄
Break Apart
7 = 4 + 3
✅
Answer
20 + 3 = 23
16 + 7 = (16 + 4) + 3 = 20 + 3 = 23
10
6
4
3
20
3
3rd Grade Connection:

These decision-making skills will help you choose the best method for complex problems!

16 + 7 = 23
Final answer:

16 + 7 = 23

Mental Math Tip:

With practice, you'll automatically select the most efficient strategy. This skill will be essential in 3rd grade!

Questions & Answers

Question: My child is learning these advanced strategies now, but they're still in 1st grade. Is this too challenging?

Answer: These "advanced" strategies are designed to gently prepare your child for 3rd grade while staying within 1st grade concepts:

  • Gradual introduction: We're extending familiar concepts to slightly larger numbers
  • Foundation building: These skills will make 3rd grade much easier
  • Flexible pacing: Move at your child's comfort level
  • Review emphasis: Continue reinforcing basic strategies alongside advanced ones

The goal is preparation, not pressure. If your child finds these too challenging, focus on mastering basic strategies first.

Question: How do I balance teaching advanced strategies while ensuring students master basic ones?

Answer: Balance is key when preparing for future grades:

  • 80/20 rule: 80% of time on mastering basics, 20% on extension
  • Assessment first: Ensure mastery of basic strategies before introducing advanced ones
  • Differentiated instruction: Offer advanced strategies to ready students only
  • Connection emphasis: Show how advanced strategies build on basic ones

The advanced strategies should feel like natural extensions of what students already know, not entirely new concepts.

Question: Why are we learning "3rd grade" stuff when I'm still in 1st grade? Isn't that confusing?

Answer: Great question! We're not skipping grades - we're building a strong foundation:

  • Like training wheels: Learning these skills now makes future math easier
  • Building blocks: Each math skill builds on the previous one
  • No pressure: We're just introducing ideas, not expecting mastery yet
  • Fun challenge: Some students enjoy the extra challenge

Think of it like learning to ride a bike with training wheels that help you get ready for riding without them!