Subtraction Within 20 Using Ten Frames for 1st Grade

Visual subtraction learning: ten frames, counting strategies, and hands-on activities for mastering subtraction within 20.

Ten Frame Subtraction Activities 1 to 3
1 Single Ten Frame Subtraction
Activity 1
Use a single ten frame to visualize subtraction problems within 10.
Example: 8 - 3, fill 8 circles and cross out 3.
Definition:

Ten Frame: A visual tool with 10 boxes arranged in 2 rows of 5, used to represent numbers and operations.

Ten Frame Subtraction Method:
  1. Fill the ten frame with the minuend number of counters
  2. Cross out the subtrahend number of counters
  3. Count the remaining filled boxes
  4. Record the difference
Start: 8
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Subtract: 3
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Result: 5
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Visual Process:

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Fill 8 boxes with counters (●)
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Cross out 3 boxes (●)
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Count remaining filled boxes: 5
Step 1: Set up the ten frame

Represent the minuend (8) by filling boxes

Step 2: Remove counters

Cross out the subtrahend (3) number of boxes

Step 3: Count remaining

Count how many boxes are still filled

Final answer:

8 - 3 = 5

Applied rules:

• Visual Representation: Concrete visualization of abstract concepts

• Part-Whole Relationship: See how parts combine to form the whole

• Counting Strategy: Physical removal reinforces the concept

2 Double Ten Frame Subtraction
Activity 2
Use two ten frames to visualize subtraction problems between 10 and 20.
Example: 15 - 7, fill 15 boxes across two frames and cross out 7.
Definition:

Double Ten Frame: Two connected ten frames used to represent numbers 11-20 and model subtraction.

Start: 15
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Subtract: 7
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Result: 8
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Step 1: Fill both ten frames

First frame: 10 counters, Second frame: 5 counters (total 15)

Step 2: Cross out 7 counters

Remove from left to right, starting with first frame

Step 3: Count remaining counters

8 counters remain in the frames

Final answer:

15 - 7 = 8

Applied rules:

• Place Value Understanding: See tens and ones clearly

• Decomposition: Break into 10 + 5 to make subtraction easier

• Visual Strategy: Concrete representation of larger numbers

3 Manipulative Practice
Activity 3
Use physical counters on ten frames to practice subtraction problems.
Example: 13 - 6, place 13 counters and remove 6.
Definition:

Manipulative Practice: Using physical objects to represent mathematical concepts and operations.

Hands-On Practice Guide:

1
Place 13 counters on the ten frames (fill first completely, then 3 on second)
2
Remove 6 counters, starting from the second frame
3
Count remaining counters to find the answer
Step 1: Represent the minuend

Place 13 counters on the ten frames (10 in first, 3 in second)

Step 2: Remove the subtrahend

Take away 6 counters from the frames

Step 3: Count the remainder

Count how many counters remain

Step 4: Record the difference

Write down the answer

Final answer:

13 - 6 = 7

Applied rules:

• Tactile Learning: Physical interaction enhances understanding

• Concrete to Abstract: Move from physical objects to mental math

• Multiple Representations: Connect physical, visual, and symbolic

Ten Frame Learning Methods and Strategies
Minuend - Subtrahend = Difference
Subtraction Structure
Method 1
Single Frame
Numbers 1-10
Method 2
Double Frame
Numbers 11-20
Method 3
Manipulatives
Physical objects
Key definitions:

Ten Frame: A visual tool with 10 boxes used to represent numbers and operations

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

Manipulatives: Physical objects used to represent mathematical concepts

Ten Frame Subtraction Strategies:
  1. Visual Representation: Use filled and empty boxes to show numbers
  2. Counting Strategy: Count remaining boxes after removal
  3. Decomposition: Break numbers into tens and ones
  4. Place Value Understanding: Recognize tens and ones in numbers
  5. Pattern Recognition: Identify number relationships
  6. Concrete Manipulation: Use physical objects for tactile learning
Tip 1: Start with single ten frames before moving to double frames.
Tip 2: Use different colored counters to distinguish minuend and subtrahend.
Tip 3: Practice with manipulatives before moving to drawn representations.
Tip 4: Connect ten frame representations to number sentences.
Benefits: Builds number sense, develops place value understanding, provides concrete visualization, enhances spatial reasoning.
Key Concepts: Subtraction as taking away, part-whole relationships, base-10 structure, visual pattern recognition.
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
Ten Frame Subtraction 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.

Ten Frame: A visual tool with 10 boxes arranged in 2 rows of 5, used to represent numbers and operations.

Double Ten Frame: Two connected ten frames used to represent numbers 11-20.

Manipulatives: Physical objects used to represent mathematical concepts and operations.

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

Ten Frame Subtraction Methods:
  1. Single Frame Method: Use one ten frame for numbers 1-10
  2. Double Frame Method: Use two ten frames for numbers 11-20
  3. Manipulative Method: Use physical counters on ten frames
  4. Visual Crossing Method: Cross out counters to represent subtraction
  5. Counting Strategy: Count remaining filled boxes
  6. Place Value Method: Recognize tens and ones in numbers
Step-by-Step Ten Frame Process:
  1. Identify the minuend and subtrahend in the problem
  2. Choose appropriate ten frame (single or double)
  3. Fill the ten frame with the minuend number of counters
  4. Cross out or remove the subtrahend number of counters
  5. Count the remaining filled boxes
  6. Record the difference as the answer
  7. Verify by adding the difference to the subtrahend
Basic Ten Frame Examples:

5 - 2 = 3 (fill 5 boxes, cross out 2, count 3 remaining)

8 - 3 = 5 (fill 8 boxes, cross out 3, count 5 remaining)

10 - 4 = 6 (fill 10 boxes, cross out 4, count 6 remaining)

7 - 7 = 0 (fill 7 boxes, cross out all 7, count 0 remaining)

Intermediate Ten Frame Examples:

12 - 5 = 7 (fill first frame completely, 2 in second, cross out 5, count 7 remaining)

15 - 8 = 7 (fill first frame completely, 5 in second, cross out 8, count 7 remaining)

18 - 9 = 9 (fill first frame completely, 8 in second, cross out 9, count 9 remaining)

14 - 6 = 8 (fill first frame completely, 4 in second, cross out 6, count 8 remaining)

Advanced Ten Frame Examples:

17 - 9 = 8 (use decomposition: 17 = 10 + 7, then 10 - 9 = 1, 1 + 7 = 8)

16 - 7 = 9 (visualize: 16 counters, remove 7, 9 remain)

19 - 12 = 7 (double frame: first full, 9 in second, remove 12, 7 remain)

13 - 5 = 8 (manipulative approach: place 13, remove 5, count 8)

Common Mistakes: Forgetting to cross out the correct number of boxes, miscounting remaining boxes, confusing minuend and subtrahend.
Memory Tricks: Use color coding, practice with manipulatives, connect to number sentences.
Key Takeaways:
  • Ten frames provide concrete visualization of abstract concepts
  • Physical manipulation enhances understanding and retention
  • Visual patterns help develop number sense
  • Connection between concrete and symbolic representations builds fluency
  • Place value understanding is reinforced through ten frame use
5 Implementation Strategies
Implementation Elements:

Progressive Complexity: Starting with simple problems and increasing difficulty

Multiple Representations: Connecting physical, visual, and symbolic forms

Assessment Integration: Evaluating learning through visual demonstrations

Differentiated Instruction: Adapting activities for various learning needs

Ten Frame Implementation Strategies:
  1. Start Concrete: Begin with physical manipulatives
  2. Build Gradually: Progress from single to double ten frames
  3. Connect Representations: Link visual frames to number sentences
  4. Encourage Exploration: Let students discover patterns independently
  5. Regular Practice: Consistent exposure for memory consolidation
  6. Combine Approaches: Mix ten frames with other strategies
Teaching Guidelines:

• Align activities with curriculum standards

• Balance concrete and abstract representations

• Include diverse problem types

• Provide scaffolding for struggling students

• Allow for individual and group practice

Success Indicators:

• Accurate use of ten frame representations

• Correct identification of minuend and subtrahend

• Consistent application of subtraction strategies

• Ability to transition from concrete to abstract thinking

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

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

Visual-Spatial Reasoning: Using visual patterns to understand mathematical concepts.

Place Value Understanding: Recognizing the value of digits based on their position.

Transfer Skills: Applying ten frame knowledge to solve more complex problems.

Abstract Thinking: Moving from concrete representations to mental math.

Pattern Recognition: Identifying and utilizing numerical relationships.

Advanced Ten Frame Strategies:
  1. Compensation: Adjusting numbers to make subtraction easier using ten frames
  2. Decomposition: Breaking numbers into tens and ones for easier subtraction
  3. Relationship Recognition: Using known facts to derive unknown ones
  4. Pattern Application: Extending recognized patterns to new problems
  5. Verification Techniques: Checking answers using addition
  6. Self-Explanation: Articulating the reasoning behind each step
Tip 1: Create personalized ten frame sets targeting specific weak areas.
Tip 2: Use ten frames to explore fact families and inverse relationships.
Tip 3: Practice subtraction in context through story problems with ten frames.
Tip 4: Use ten frames to build confidence in students who struggle with traditional methods.
Common misconceptions: Thinking ten frames are only for beginners; believing visual methods are less rigorous; ignoring the connection to abstract mathematics.
Long-term benefits: Foundation for advanced math, improved number sense, enhanced visual-spatial skills, stronger mathematical reasoning.
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 we use ten frames for subtraction? Can't I just count in my head?

Answer: Great question! Ten frames are like training wheels for your brain:

  • Visual Learning: Seeing the numbers helps your brain understand what's happening
  • Concrete Understanding: You can actually see the taking away process
  • Pattern Recognition: You notice helpful patterns that make math easier
  • Memory Building: Visuals help your brain remember facts longer
  • Confidence Builder: You can check your work easily

Once you understand subtraction with ten frames, counting in your head becomes much easier!

Question: My child understands subtraction with ten frames but struggles when the frames aren't there. How do I help bridge this gap?

Answer: This is a normal part of learning! Here's how to help:

  • Gradual Reduction: Start with ten frames, then draw them, then visualize them
  • Verbal Connections: Have your child explain the ten frame process out loud
  • Partial Removal: Use ten frames for harder problems, mental math for easier ones
  • Pattern Recognition: Point out the patterns that emerge from ten frame work
  • Regular Practice: Consistent practice builds automatic recall
  • Patience: Trust the process - visual foundations lead to strong mental math

The ten frame work creates strong neural pathways that eventually become automatic!

Question: What if I don't like using ten frames? Can I still learn subtraction?

Answer: Absolutely! Ten frames are just one tool among many:

  • Number Lines: Hop backwards to subtract
  • Counting Back: Count backwards from the starting number
  • Fact Families: Use addition facts to solve subtraction
  • Think Addition: For 13 - 8, think "what + 8 = 13?"
  • Fingers: Use your fingers to represent numbers
  • Manipulatives: Use any small objects to represent problems

Try ten frames for a while - they might grow on you! But if not, there are many other great ways to learn subtraction.