Using Doubles Facts to Subtract - Grade 1 Mathematics

Master using doubles facts to subtract: doubles, near doubles, strategies, and mental math techniques through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Doubles Subtraction
Exercise 1
Use doubles facts to solve: 8 - 4
Definition:

Doubles subtraction: Subtraction facts where the minuend is double the subtrahend

Doubles subtraction method:
  1. Recognize that the minuend (8) is double the subtrahend (4)
  2. Think: "What number added to itself equals the minuend?"
  3. Since 4 + 4 = 8, then 8 - 4 = 4
Expression
8 - 4
Doubles relation
4 + 4 = 8
Result
4
Step 1: Identify the doubles relationship

8 is double 4 (4 + 4 = 8), so 8 - 4 = 4

Step 2: Apply the doubles subtraction strategy

If 4 + 4 = 8, then taking away one 4 leaves the other 4

Step 3: Verify the result

Check: 4 + 4 = 8, so 8 - 4 = 4 ✓

8 - 4 = 4
Final answer:

8 - 4 = 4

Applied rules:

• Doubles relationship: If n + n = 2n, then 2n - n = n

• Fact families: Addition and subtraction are inverse operations

• Mental math: Use known addition facts for subtraction

2 Doubles Subtraction with Larger Numbers
Exercise 2
Use doubles facts to solve: 12 - 6
Definition:

Larger doubles subtraction: When working with doubles facts beyond 10

Expression
12 - 6
Doubles fact
6 + 6 = 12
Result
6
Step 1: Recognize the doubles pattern

12 is double 6, since 6 + 6 = 12

Step 2: Apply the doubles subtraction rule

If 6 + 6 = 12, then 12 - 6 = 6

Step 3: Count to verify

Start at 12 and count back 6: 11, 10, 9, 8, 7, 6

12 - 6 = 6
Final answer:

12 - 6 = 6

Applied rules:

• Doubles subtraction: For 2n - n = n, use doubles facts

• Number sense: Understand relationships between numbers

• Verification: Check answers using counting or addition

3 Near Doubles Subtraction
Exercise 3
Use doubles facts to solve: 11 - 6
Definition:

Near doubles subtraction: When the minuend is close to a doubles fact

Expression
11 - 6
Related doubles
12 - 6 = 6
Adjustment
6 - 1 = 5
Step 1: Identify the near doubles relationship

11 is one less than 12, and 12 is double 6 (6 + 6 = 12)

Step 2: Use the related doubles fact

Since 12 - 6 = 6, and 11 is one less than 12

Step 3: Adjust for the difference

11 - 6 = (12 - 6) - 1 = 6 - 1 = 5

Step 4: Verify the result

Check: 5 + 6 = 11 ✓

11 - 6 = 5
Final answer:

11 - 6 = 5

Applied rules:

• Near doubles: Use closest doubles fact and adjust

• Adjustment strategy: Add or subtract the difference

• Fact families: Use addition to check subtraction

Rules and methods, laws,...
2n - n = n
Basic Doubles Subtraction
Doubles Subtraction
4-2=2, 6-3=3, 8-4=4
Basic doubles facts
Larger Doubles
10-5=5, 12-6=6, 14-7=7
Extended doubles facts
Near Doubles
9-4=5 (since 8-4=4, +1)
Adjusting from doubles
Key definitions:

Doubles Subtraction: Subtraction facts where the minuend is double the subtrahend

Near Doubles Subtraction: Subtraction where minuend is close to a doubles fact

Mental Math: Strategies for solving problems without physical counting

Complete methodology:
  1. Recognize the pattern: Identify if it's doubles or near doubles
  2. Recall the doubles fact: Remember the corresponding addition fact
  3. Apply the strategy: Use doubles relationship for subtraction
  4. Verify the result: Check using addition or counting
Tip 1: Remember that subtraction is the opposite of addition.
Tip 2: Use addition facts to help with subtraction.
Tip 3: Practice doubles facts (addition) to strengthen subtraction skills.
Tip 4: Use visual models like number lines or counters to see the relationship.
Common errors: Forgetting to use the doubles relationship, counting incorrectly.
Memory aids: Sing doubles songs, use rhymes, practice daily.
Facts to know by heart:

• Basic doubles subtraction: 2-1=1, 4-2=2, 6-3=3, 8-4=4, 10-5=5

• More doubles: 12-6=6, 14-7=7, 16-8=8, 18-9=9, 20-10=10

• Strategy: Use addition doubles facts to derive subtraction facts

Solution: Exercises 4 to 5
4 Advanced Near Doubles Subtraction
Exercise 4
Use doubles facts to solve: 15 - 8
Definition:

Advanced near doubles subtraction: Working with larger numbers and greater differences

Expression
15 - 8
Related doubles
16 - 8 = 8
Adjustment
8 - 1 = 7
Step 1: Identify the relationship

15 is one less than 16, and 16 is double 8 (8 + 8 = 16)

Step 2: Use the related doubles fact

Since 16 - 8 = 8, and 15 is one less than 16

Step 3: Adjust for the difference

15 - 8 = (16 - 8) - 1 = 8 - 1 = 7

Step 4: Verify using addition

Check: 7 + 8 = 15 ✓

15 - 8 = 7
Final answer:

15 - 8 = 7

Applied rules:

• Advanced near doubles: Use closest doubles fact and adjust

• Subtraction as difference: Find how much to add to subtrahend

• Verification: Always check with addition

5 Mixed Doubles Subtraction Practice
Exercise 5
Use doubles facts to solve: 14 - 7
Definition:

Mixed doubles practice: Combining various doubles subtraction strategies

Expression
14 - 7
Doubles fact
7 + 7 = 14
Result
7
Step 1: Recognize the doubles relationship

14 is double 7, since 7 + 7 = 14

Step 2: Apply the doubles subtraction rule

If 7 + 7 = 14, then 14 - 7 = 7

Step 3: Alternative approach

You could think: "What number added to 7 gives 14?" Answer: 7

Step 4: Verify the result

Check: 7 + 7 = 14 ✓

14 - 7 = 7
Final answer:

14 - 7 = 7

Applied rules:

• Doubles subtraction: 2n - n = n

• Multiplicative relationship: Understanding doubling

• Inverse operations: Addition and subtraction are opposites

Complete Guide to Using Doubles Facts for Subtraction
2n - n = n
Doubles Subtraction Formula
Key definitions:

Doubles Subtraction: Subtraction facts where the minuend is double the subtrahend (e.g., 8 - 4)

Near Doubles Subtraction: Subtraction where minuend is close to a doubles fact (e.g., 9 - 4)

Mental Math: Computational strategies performed mentally without physical aids

Complete methodology:
  1. Pattern Recognition: Identify if the problem involves doubles or near doubles
  2. Fact Retrieval: Recall the corresponding doubles addition fact
  3. Relationship Application: Use the addition fact to solve subtraction
  4. Adjustment: Modify for near doubles situations
  5. Verification: Confirm the answer using addition
Tip 1: Practice doubles addition facts to strengthen subtraction skills.
Tip 2: Use visual representations like dominoes or dice patterns.
Tip 3: Connect doubles to real-world scenarios (wheels on cars, eyes on faces).
Tip 4: Encourage multiple approaches to verify answers.
Common errors: Misidentifying near doubles, incorrect adjustments from doubles facts.
Teaching strategies: Use manipulatives, visual models, and repeated practice.
Core facts and formulas:

• Basic doubles subtraction: 2-1=1, 4-2=2, 6-3=3, 8-4=4, 10-5=5

• Extended doubles: 12-6=6, 14-7=7, 16-8=8, 18-9=9, 20-10=10

• Near doubles: Use closest doubles fact and adjust (+/- difference)

• Mental strategy: Use known addition facts to derive subtraction facts

Doubles Subtraction Patterns: Understanding Relationships
Exercise 6: Doubles Subtraction Pattern Recognition
Explore the pattern of doubles subtraction facts:
2-1=1, 4-2=2, 6-3=3, 8-4=4, 10-5=5
12-6=6, 14-7=7, 16-8=8, 18-9=9, 20-10=10

Pattern Analysis: Doubles subtraction facts show a direct relationship where the result equals the subtrahend.

  • Each result equals the number being subtracted (the subtrahend)
  • This demonstrates the inverse relationship between addition and subtraction
  • Near doubles follow predictable adjustment patterns

Questions & Answers

Question: My child understands doubles addition but struggles with doubles subtraction. How can I help them make the connection?

Answer: Making the connection between addition and subtraction requires explicit teaching of inverse relationships:

  • Fact families: Show how 4 + 4 = 8 connects to 8 - 4 = 4
  • Physical models: Use counters or objects to demonstrate "putting together" vs "taking apart"
  • Verbal connections: Say "If 4 and 4 make 8, then 8 take away 4 leaves 4"
  • Visual representations: Draw circles showing the whole and parts

Practice with concrete objects first, then move to abstract numbers. Reinforce that addition and subtraction are opposite operations!

Question: Why do we learn to use doubles facts for subtraction? Can't I just count backwards?

Answer: Great question! Learning doubles facts for subtraction makes math faster and easier:

  • Speed: Instead of counting backwards 14 - 7 = 13, 12, 11, 10, 9, 8, 7, you instantly know it's 7
  • Foundation: Doubles help with harder problems and multiplication later
  • Confidence: Knowing facts makes math feel easier and more fun
  • Brain efficiency: It frees up brain power for solving complex problems

Think of doubles facts like knowing your phone number - it saves time and helps you get to the right answer quickly!

Question: How can I assess if my students truly understand using doubles facts for subtraction rather than just memorizing them?

Answer: Assess conceptual understanding with these strategies:

  • Ask for explanation: "How did you solve 12 - 6? What doubles fact helped you?"
  • Variety of problems: Mix doubles, near doubles, and unrelated problems randomly
  • Visual representation: Have students draw or model their thinking with manipulatives
  • Fact family connections: Ask students to show the related addition fact

Look for students who can explain their reasoning, connect to other math concepts, and apply the strategy flexibly to new situations. True understanding shows in their ability to teach the concept to others.