Doubles and Near Doubles Strategies in Grade 1

Comprehensive guide to doubles and near doubles strategies: methods, techniques, and practice exercises for mathematical reasoning.

Strategy Activities 1-3
1 Doubles Strategy
Doubles Strategy: 6 + 6
1
Identify that both numbers are the same (doubles pattern)
2
Recall the doubles fact: 6 + 6 = 12
3
Alternatively, multiply: 6 × 2 = 12
Definition:

Doubles Strategy: Using known facts where both addends are identical to solve addition problems efficiently

6 + 6
→
12
1. Recognize the doubles pattern
2. Apply the doubles fact
3. Verify the result
Memory Trick:

"Doubles are twins - they're exactly the same! When you see two of the same number, just double it!"

Application:

This strategy works for all doubles facts: 1+1, 2+2, 3+3, up to 10+10. Memorizing these facts makes addition much faster!

Strategy Rules:

• Pattern Recognition: Both addends must be identical

• Efficiency: Use memorized facts for quick recall

• Verification: Check by counting or using manipulatives

2 Near Doubles Strategy
Near Doubles Strategy: 7 + 8
1
Recognize that 7 and 8 are consecutive numbers (near doubles)
2
Use the doubles fact: 7 + 7 = 14
3
Add one more: 14 + 1 = 15
Definition:

Near Doubles Strategy: Using known doubles facts to solve problems with consecutive addends

7 + 8
→
7 + 7 + 1
→
14 + 1 = 15
Method 1

Use smaller doubles: 7 + 7 = 14, then add 1

Method 2

Use larger doubles: 8 + 8 = 16, then subtract 1

1. Identify consecutive numbers
2. Choose the easier doubles fact
3. Adjust by 1 (add or subtract)
Memory Trick:

"Near doubles are neighbors - they live next door! Use the doubles fact and add/subtract 1."

Application:

This strategy works for all consecutive number pairs: 1+2, 2+3, 3+4, etc. It builds on known doubles facts!

Strategy Rules:

• Pattern Recognition: Numbers must be consecutive (differ by 1)

• Foundation: Requires knowledge of basic doubles facts

• Adjustment: Always add or subtract 1 from the doubles result

3 Strategy Comparison
Comparing Strategies: 5 + 5 vs 5 + 6
1
5 + 5 is a doubles fact: 5 + 5 = 10
2
5 + 6 is a near doubles fact: 5 + 6 = 11
3
Notice: 5 + 6 = (5 + 5) + 1 = 10 + 1 = 11
Definition:

Strategy Comparison: Analyzing the relationship between doubles and near doubles to understand the connection

Problem Type Strategy Result
4 + 4 Doubles Direct recall 8
4 + 5 Near Doubles 4 + 4 + 1 9
6 + 6 Doubles Direct recall 12
6 + 7 Near Doubles 6 + 6 + 1 13
Doubles: n + n = 2n
→
Near Doubles: n + (n+1) = 2n + 1
1. Understand the relationship between strategies
2. Recognize that near doubles build on doubles
3. Apply the appropriate strategy based on pattern
Memory Trick:

"Doubles are the foundation - near doubles just add one more brick to the tower!"

Application:

Understanding the relationship helps choose the most efficient strategy and reinforces mathematical connections.

Strategy Rules:

• Relationship: Near doubles are doubles plus or minus 1

  • Efficiency: Choose the strategy that uses the easiest known fact
  • Connection: Both strategies build number sense and fluency
    • Core Strategy Concepts
    n + n = 2n
    Doubles Formula
    Doubles
    n + n
    Same number twice
    Near Doubles
    n + (n+1)
    Consecutive numbers
    Strategy
    Use known facts
    Build on foundations
    Key Definitions:

    Strategy: A planned approach to solving mathematical problems efficiently and accurately.

    Doubles Strategy: Using known facts where both addends are identical to solve addition problems quickly.

    Near Doubles Strategy: Using doubles facts as a foundation to solve problems with consecutive addends.

    Strategy Development Process:
    1. Pattern Recognition: Identify the type of problem (doubles or near doubles)
    2. Strategy Selection: Choose the most appropriate approach
    3. Execution: Apply the chosen strategy systematically
    4. Verification: Check the result using alternative methods
    Doubles
    1+1=2
    Doubles
    2+2=4
    Doubles
    3+3=6
    Doubles
    4+4=8
    Near Doubles
    1+2=3
    Near Doubles
    2+3=5
    Near Doubles
    3+4=7
    Near Doubles
    4+5=9
    Tip 1: Memorize all doubles facts (0+0 to 10+10) for maximum efficiency.
    Tip 2: Practice recognizing the patterns quickly.
    Tip 3: Use visual models to reinforce the strategies.
    Tip 4: Connect strategies to real-world applications.
    Benefits: Builds number sense, increases fluency, develops strategic thinking.
    Outcomes: Faster computation, better problem-solving, stronger mathematical reasoning.
    Strategy Principles:

    • Each strategy serves a specific purpose based on the problem structure

    • Strategies build upon each other and connect mathematical concepts

    • Efficient strategies reduce cognitive load and improve accuracy

    • Regular practice strengthens strategy selection and application

    n + (n+1) = (n+n) + 1
    Near Doubles Formula
    Advanced Strategy Applications 4-5
    4 Flexible Strategy Use
    Flexible Strategy Application: 8 + 9
    1
    Recognize as near doubles (consecutive numbers)
    2
    Option A: Use 8 + 8 = 16, then add 1 → 17
    3
    Option B: Use 9 + 9 = 18, then subtract 1 → 17
    4
    Choose the easier option based on known facts
    Definition:

    Flexible Strategy Use: Adapting and choosing the most efficient approach based on the specific problem and known facts

    Approach 1

    8 + 9 = (8 + 8) + 1 = 16 + 1 = 17

    Uses the smaller doubles fact

    Approach 2

    8 + 9 = (9 + 9) - 1 = 18 - 1 = 17

    Uses the larger doubles fact

    8 + 9
    →
    Either approach = 17
    1. Analyze the problem structure
    2. Consider multiple approaches
    3. Select the most efficient path
    4. Execute and verify the solution
    Memory Trick:

    "Be flexible! You can go up from the smaller number or down from the bigger number - both roads lead to the same answer!"

    Application:

    This flexibility allows students to adapt their approach based on which doubles facts they know best.

    Flexibility Rules:

    • Multiple Paths: There's often more than one correct approach

    • Personal Choice: Students can select the approach that feels most comfortable

    • Efficiency: Choose the path that uses the most familiar facts

    5 Strategic Problem Solving
    Strategic Problem Solving: Word Problem Context
    1
    "Tom has 6 marbles and his friend gives him 7 more. How many does he have?"
    2
    Identify the operation: 6 + 7
    3
    Recognize as near doubles: 6 + 7
    4
    Apply strategy: 6 + 6 + 1 = 12 + 1 = 13
    Definition:

    Strategic Problem Solving: Applying mathematical strategies within real-world contexts and word problems

    Problem Analysis

    Tom starts with 6, gets 7 more → 6 + 7

    Strategy Application

    6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

    6 marbles
    +
    7 marbles
    →
    13 marbles
    1. Read and understand the problem
    2. Identify the mathematical operation needed
    3. Recognize the type of addition fact
    4. Apply the appropriate strategy
    Memory Trick:

    "Word problems are just stories about math! Find the numbers and the action, then use your strategy!"

    Application:

    These strategies transfer to real-world situations, making math meaningful and applicable to everyday life.

    Problem-Solving Rules:

    • Context Recognition: Identify the mathematical operation within the story

    • Strategy Transfer: Apply learned strategies to new situations

    • Verification: Check that the answer makes sense in the context

    Complete Strategy Summary: Doubles and Near Doubles
    n + n = 2n
    Doubles Formula
    Comprehensive definitions:

    Doubles Strategy: An efficient method for solving addition problems where both addends are identical (e.g., 3+3, 8+8). This strategy relies on memorizing doubles facts and recognizing the pattern instantly.

    Near Doubles Strategy: A method that uses known doubles facts to solve problems with consecutive addends (e.g., 4+5, 7+8). This strategy builds on the foundation of doubles facts and adds or subtracts 1.

    Strategic Thinking: The ability to recognize patterns, select appropriate methods, and apply mathematical knowledge flexibly to solve problems efficiently.

    Core methodologies:
    1. Pattern Recognition: Identifying whether a problem involves doubles or near doubles
    2. Strategy Selection: Choosing the most appropriate method based on the problem structure
    3. Knowledge Application: Using memorized facts to solve new problems
    4. Verification: Checking work using alternative methods or estimation
    Strategy Pattern Formula Example
    Doubles Same numbers n + n 5 + 5 = 10
    Near Doubles Consecutive numbers n + (n+1) 5 + 6 = 11
    Tip 1: Practice doubles facts daily until they become automatic.
    Tip 2: Use visual models like counters or drawings to reinforce the strategies.
    Tip 3: Be flexible - use the doubles fact that feels most comfortable.
    Tip 4: Connect the strategies to real-world situations for better understanding.
    Common misconceptions: Thinking all addition problems require counting from 1, not recognizing the efficiency of using known facts.
    Success indicators: Quick recognition of patterns, efficient problem-solving, accurate results.
    Fundamental principles and formulas:

    • Doubles principle: n + n = 2n (always results in an even number)

    • Near doubles principle: n + (n+1) = (n+n) + 1 (always results in an odd number)

    • Strategy principle: Use known facts to solve unknown problems efficiently

    • Flexibility principle: Multiple approaches can lead to the same correct answer

    Strategic Thinking Benefits:
    • Builds strong number sense and mathematical reasoning
    • Increases computational fluency and speed
    • Develops problem-solving skills and confidence
    • Creates connections between mathematical concepts
    • Prepares students for more complex mathematical thinking

    Questions & Answers

    Question: How can I help my students develop flexibility in choosing between different strategies? Some seem to get stuck using one approach.

    Answer: Developing strategic flexibility involves:

    1. Explicit instruction: Teach multiple approaches and discuss when each is most efficient
    2. Guided practice: Provide problems where different strategies work best
    3. Student choice: Allow students to select their preferred approach
    4. Reflection: Discuss why certain strategies work well for specific problems

    For example, with 9 + 8, some students might prefer 8 + 8 + 1, while others prefer 9 + 9 - 1. Both are valid!

    Question: My child knows some doubles facts but struggles with near doubles. How can I support this at home?

    Answer: Here are effective home support strategies:

    • Strengthen doubles: Practice known doubles facts until they're automatic
    • Use visual aids: Counters, fingers, or drawings to show the "add one more" concept
    • Connect the dots: Show how 5 + 5 = 10 leads to 5 + 6 = 11
    • Make it fun: Games and activities that involve doubles and near doubles

    The key is ensuring your child sees near doubles as "doubles plus one" rather than a completely new concept.

    Question: How do I know which strategy to use for 7 + 8? It's confusing!

    Answer: Great question! Here's how to figure it out for 7 + 8:

    1. Look at the numbers: Are they the same? No, they're 7 and 8
    2. Are they neighbors?: Yes, 7 and 8 come one after the other when counting
    3. So it's a near doubles problem!

    You can solve it as 7 + 7 + 1 = 14 + 1 = 15, or as 8 + 8 - 1 = 16 - 1 = 15. Both work!