Subtraction Within 20 Strategies for 1st Grade

Comprehensive subtraction strategies: counting back, number line, fact families, and multiple problem-solving methods for mastering subtraction within 20.

Subtraction Strategies 1 to 3
1 Counting Back Strategy
Strategy 1
Start with the larger number and count backward by the smaller number.
Example: 15 - 7, start at 15 and count back 7 numbers.
Definition:

Counting Back: A subtraction strategy where you start with the minuend and count backward by the number of steps equal to the subtrahend.

Counting Back Method:
  1. Identify the minuend (starting number) and subtrahend (number to subtract)
  2. Start counting from the minuend
  3. Count backward by the number of steps equal to the subtrahend
  4. The number you land on is the difference

Counting Back

Start at minuend, count back by subtrahend

15
←
14
←
13
←
12
←
11
←
10
←
9
←
8
Step 1: Identify the numbers

Minuend = 15, Subtrahend = 7

Step 2: Start at the minuend

Begin counting at 15

Step 3: Count back 7 steps

15 → 14 → 13 → 12 → 11 → 10 → 9 → 8

Final answer:

15 - 7 = 8

Applied rules:

• Sequential Counting: Each step reduces the number by 1

• Accurate Counting: Count each step individually

• Verification: Check by adding the difference to the subtrahend

2 Number Line Strategy
Strategy 2
Use a number line to visualize subtraction as movement to the left.
Example: 18 - 9, start at 18 and move 9 spaces to the left.
Definition:

Number Line: A visual representation of numbers in order, used to show subtraction as movement to the left.

Number Line

Move left on the number line by subtrahend

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
←
←
←
←
←
←
←
←
←
9
Step 1: Locate the minuend

Find 18 on the number line

Step 2: Move left by subtrahend

Move 9 spaces to the left

Step 3: Identify the landing point

Where you land is the answer

Final answer:

18 - 9 = 9

Applied rules:

• Directional Movement: Subtraction moves left on the number line

• Consistent Spacing: Each step represents one unit

• Visual Confirmation: See the distance between numbers

3 Fact Family Strategy
Strategy 3
Use related addition facts to solve subtraction problems.
Example: For 16 - 8, think "8 + ? = 16".
Definition:

Fact Family: A group of related addition and subtraction facts using the same three numbers.

Fact Family

Use addition to solve subtraction

Fact Family for 8, 8, 16:

8 + 8 = 16

8 + 8 = 16

16 - 8 = 8

16 - 8 = 8

Step 1: Identify the fact family

For 16 - 8, the numbers are 8, 8, and 16

Step 2: Use addition fact

Since 8 + 8 = 16, then 16 - 8 = 8

Step 3: Verify the relationship

Check: 8 + 8 = 16, so 16 - 8 = 8

Step 4: Complete the family

Know all 4 related facts

Final answer:

16 - 8 = 8

Applied rules:

• Inverse Operations: Addition and subtraction are opposites

• Part-Part-Whole: Three numbers relate as parts and whole

• Verification: Use addition to check subtraction answers

Subtraction Strategy Methods and Approaches
Minuend - Subtrahend = Difference
Subtraction Structure
Strategy 1
Counting Back
Start with larger number
Strategy 2
Number Line
Visual representation
Strategy 3
Fact Families
Use related facts
Key definitions:

Subtraction: The operation of taking away one number from another to find the difference

Minuend: The number being subtracted from

Subtrahend: The number being subtracted

Difference: The result of subtraction

Strategy: A method or approach used to solve mathematical problems

Fact Family: Related addition and subtraction facts using the same numbers

Additional Subtraction Strategies:
  1. Think Addition: For 13 - 8, think "what + 8 = 13?"
  2. Decompose Numbers: Break apart numbers to make subtraction easier
  3. Doubles Strategy: Use doubles facts to solve near-doubles (14 - 7 = 7)
  4. Compensation: Adjust numbers to make subtraction easier
  5. Pattern Recognition: Use known facts to derive unknown ones
  6. Visual Models: Use drawings or manipulatives to represent problems
Tip 1: Choose the strategy that feels easiest for each problem.
Tip 2: Practice multiple strategies to become flexible.
Tip 3: Use manipulatives when first learning a strategy.
Tip 4: Check answers by adding the difference to the subtrahend.
Benefits: Builds number sense, develops multiple approaches, strengthens problem-solving skills, increases flexibility.
Key Concepts: Subtraction as taking away, part-whole relationships, inverse relationship with addition.
Important Subtraction Facts:

• Any number minus itself equals zero: n - n = 0

• Any number minus zero equals itself: n - 0 = n

• Subtraction is the inverse of addition: a - b = c means c + b = a

• Fact families: 3 numbers create 4 related facts (e.g., 5, 3, 8 → 5+3=8, 3+5=8, 8-5=3, 8-3=5)

Detailed Summary and Key Concepts
4 Comprehensive Summary
Subtraction Strategy Definitions:

Subtraction: The operation of taking away one number from another to find the difference.

Minuend: The number from which another number is subtracted (the first number in a subtraction problem).

Subtrahend: The number that is subtracted (the second number in a subtraction problem).

Difference: The result of a subtraction problem.

Strategy: A planned approach or method for solving mathematical problems.

Counting Back: Starting with the minuend and counting backward by the subtrahend.

Number Line: A visual tool showing numbers in order to represent mathematical operations.

Fact Family: A group of related addition and subtraction facts using the same numbers.

Core Subtraction Rules:

• Identity Property: n - 0 = n (subtracting zero doesn't change the number)

• Zero Property: n - n = 0 (any number minus itself equals zero)

• Inverse Relationship: If a - b = c, then c + b = a

• Order Matters: Subtraction is not commutative (a - b ≠ b - a)

• Subtraction Facts: Know basic facts from 0-20 fluently

Subtraction Strategy Methods:
  1. Counting Back: Start with the minuend and count backward by the subtrahend
  2. Number Line: Move left on a number line from the minuend
  3. Fact Families: Use related addition facts to solve subtraction
  4. Think Addition: For 13 - 8, think "8 plus what equals 13?"
  5. Decompose Numbers: Break apart numbers to make subtraction easier
  6. Doubles Strategy: Use doubles facts to solve near-doubles (14 - 7 = 7)
Step-by-Step Strategy Selection Process:
  1. Read the subtraction problem carefully
  2. Identify the minuend and subtrahend
  3. Consider which strategy might be most efficient
  4. Apply the chosen strategy
  5. Verify the answer using another method
  6. Record the difference
Basic Strategy Examples:

5 - 2 = 3 (counting back: 5, 4, 3)

10 - 4 = 6 (think addition: 4 + ? = 10)

8 - 8 = 0 (zero property)

7 - 0 = 7 (identity property)

Intermediate Strategy Examples:

15 - 7 = 8 (fact family: 7 + 8 = 15)

18 - 9 = 9 (doubles relationship)

16 - 8 = 8 (halving relationship)

14 - 6 = 8 (think addition: 6 + 8 = 14)

Advanced Strategy Examples:

17 - 8 = 9 (think: 8 + 9 = 17)

14 - 6 = 8 (decompose: 14 - 4 - 2 = 8)

19 - 12 = 7 (counting back or addition thinking)

13 - 5 = 8 (pattern recognition: 10 - 5 = 5, so 13 - 5 = 8)

Common Mistakes: Counting the starting number when counting back, subtracting in wrong order, rushing and making careless errors, forgetting to check answers.
Memory Tricks: Use doubles facts, think addition, practice fact families regularly, look for patterns.
Key Takeaways:
  • Multiple strategies provide flexibility and deeper understanding
  • Choosing the right strategy depends on the specific problem
  • Practice with multiple approaches strengthens number sense
  • Verification by addition builds confidence
  • Strategy fluency leads to computational efficiency
5 Strategy Selection and Application
Strategy Application Elements:

Strategy Selection: Choosing the most appropriate method based on problem characteristics

Efficiency: Selecting the fastest and most accurate approach

Flexibility: Adapting approach based on problem complexity

Verification: Checking answers using alternative methods

Strategy Selection Criteria:
  1. Problem Difficulty: Easier problems might use direct facts
  2. Number Relationships: Use fact families for related numbers
  3. Personal Preference: Choose the most comfortable method
  4. Time Constraints: Select the most efficient approach
  5. Context: Consider the problem's real-world application
Application Guidelines:

• Practice each strategy individually before combining

• Recognize which problems suit each strategy

• Build fluency with multiple approaches

• Verify answers using different methods

• Transition from concrete to abstract representations

Strategy Mastery Indicators:

• Quick identification of the most efficient strategy

• Accurate application of chosen method

• Flexibility to switch strategies when needed

• Consistent verification of answers

Advanced Strategy Applications and Mastery
A - B = C
Basic Subtraction
Extended definitions:

Subtraction Fluency: The ability to recall subtraction facts within 20 instantly and accurately.

Computational Efficiency: Using the most efficient strategy for each particular problem.

Mental Math: Performing calculations mentally without relying on physical tools.

Transfer Skills: Applying subtraction knowledge to solve more complex problems.

Strategic Flexibility: Adapting approach based on problem characteristics.

Metacognitive Awareness: Understanding one's own thinking and learning processes.

Problem-Solving: Applying mathematical strategies to solve real-world situations.

Advanced Strategy Techniques:
  1. Compensation: Adjusting numbers to make subtraction easier (15 - 9 = 16 - 10 = 6)
  2. Decomposition: Breaking numbers into parts (14 - 6 = 14 - 4 - 2 = 8)
  3. Relationship Recognition: Using known facts to derive unknown ones
  4. Pattern Application: Extending recognized patterns to new problems
  5. Verification Techniques: Checking answers through addition
  6. Self-Explanation: Articulating the reasoning behind each step
  7. Strategic Choice: Selecting the most efficient method for each problem
Tip 1: Create personalized sets of challenging problems for targeted practice.
Tip 2: Use multiple strategies to verify answers and build confidence.
Tip 3: Practice subtraction in context (word problems, real-world applications).
Tip 4: Monitor which strategies work best for different types of problems.
Common misconceptions: Thinking one strategy fits all problems, believing memorization is sufficient without understanding, ignoring the importance of multiple approaches.
Long-term benefits: Foundation for advanced math, improved problem-solving skills, enhanced cognitive flexibility, better number sense.
Subtraction Properties and Relationships:

• Commutative Property does NOT apply: a - b ≠ b - a

• Associative Property does NOT apply: (a - b) - c ≠ a - (b - c)

• Compensation Principle: If you add the same amount to both numbers, the difference stays the same

• Connection to Addition: Every subtraction problem can be checked with addition

• Decomposition: Breaking numbers into parts to simplify calculations

Questions & Answers

Question: Why do I need so many different ways to subtract? Can't I just use one way?

Answer: Great question! Having multiple strategies is like having different tools in a toolbox:

  • Different Problems: Some strategies work better for certain problems
  • Flexibility: If one way doesn't work, you have others to try
  • Deeper Understanding: Multiple approaches help you understand the math better
  • Efficiency: Some strategies are faster for certain problems
  • Verification: You can check your answer using a different method

It's like having different routes to school - sometimes one is faster, sometimes another is better!

Question: My child seems confused by all the different strategies. How can I help them choose the right one?

Answer: Start by focusing on one strategy at a time:

  • Master One: Let your child become comfortable with one method first
  • Gradual Introduction: Add one new strategy at a time
  • Practice Both: Use both strategies to solve the same problems
  • Compare Results: Show that different strategies lead to the same answer
  • Let Them Choose: Allow your child to pick the strategy that feels easiest
  • Real-World Context: Practice with word problems that connect to real life

Remember: the goal is understanding, not just getting the right answer!

Question: What if I get confused and mix up the strategies? Is that okay?

Answer: It's completely normal to get confused when learning new strategies! Here's what to do:

  • Slow Down: Take your time to think through each step
  • Practice One at a Time: Focus on one strategy until it feels easy
  • Use Manipulatives: Counters or drawings can help visualize
  • Ask for Help: Teachers and parents are there to support you
  • Check Your Work: Add your answer to the smaller number to verify
  • Be Patient: Learning takes time and practice

Mistakes help your brain learn better! Each error teaches you something new.