Subtraction Questions Within 20 - Solved Exercises

Master subtraction within 20: counting back, number line method, and fact families through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Back Method
Exercise 1
Solve: 15 - 7 = ?
Definition:

Counting back: Start from the larger number and count backwards by the smaller number.

Counting back method:
  1. Start at the first number (15)
  2. Count back the number of steps equal to the second number (7)
  3. Land on the final number
Problem
15 - 7
Method
Count back 7
Answer
8
Step 1: Start at 15

Begin counting from 15

Step 2: Count back 7 steps

15 → 14 → 13 → 12 → 11 → 10 → 9 → 8

Step 3: Record the final number

After 7 steps back, we land on 8

15 - 7 = 8
Final answer:

15 - 7 = 8

Applied rules:

• Counting back: Move left on the number line

• Subtraction: Finding the difference between two numbers

• Verification: Check by adding: 8 + 7 = 15

2 Number Line Method
Exercise 2
Solve: 18 - 9 = ?
Definition:

Number line method: Start at the first number and move left by the second number.

Problem
18 - 9
Method
Move left 9
Answer
9
Step 1: Locate 18 on number line

Start at position 18

Step 2: Move 9 units to the left

Each step represents subtracting 1

Step 3: Land on the final position

After 9 moves left, we reach 9

18 - 9 = 9
Final answer:

18 - 9 = 9

Applied rules:

• Number line: Moving left represents subtraction

• Distance: The number of steps equals the subtrahend

• Verification: Check by adding: 9 + 9 = 18

3 Fact Family Method
Exercise 3
Solve: 14 - 6 = ?
Definition:

Fact family: Related addition and subtraction facts using the same numbers.

Problem
14 - 6
Fact Family
6 + ? = 14
Answer
8
Step 1: Think of the related addition

"What number added to 6 gives 14?"

Step 2: Solve the addition problem

6 + 8 = 14

Step 3: Apply to subtraction

If 6 + 8 = 14, then 14 - 6 = 8

Step 4: Verify the answer

8 + 6 = 14 ✓

14 - 6 = 8
Final answer:

14 - 6 = 8

Applied rules:

• Fact family: Addition and subtraction are inverse operations

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

• Verification: Check by adding: 8 + 6 = 14

Subtraction Rules and Methods
Minuend - Subtrahend = Difference
Basic Subtraction Structure
Counting Back
15 - 4 = 15→14→13→12→11
Move left on number line
Fact Family
If 5 + 3 = 8, then 8 - 5 = 3
Addition and subtraction relationship
Number Line
Start at minuend, move left by subtrahend
Visual representation of subtraction
Key Rule: Subtraction finds the difference between two numbers.
Commutative Property: Subtraction is NOT commutative (10-3 ≠ 3-10).
Subtraction Strategies:
  1. Counting Back: Start at first number, count backward
  2. Number Line: Visual movement on a line
  3. Fact Families: Use related addition facts
  4. Decomposition: Break apart numbers (e.g., 13-5 = 13-3-2)
Tip 1: Always check your answer by adding the difference to the subtrahend.
Tip 2: Use your fingers or draw dots to visualize small numbers.
Tip 3: Practice with number bonds to build fluency.
Tip 4: Remember: the answer in subtraction is called the "difference".
Key Concepts and Visual Guide
15 - 7 = 8
Minuend - Subtrahend = Difference
Key Terms:

Minuend: The number being subtracted from (15)

Subtrahend: The number being subtracted (7)

Difference: The result of subtraction (8)

Visualization Techniques:
  1. Objects: Use physical counters or drawings
  2. Number Lines: Show movement leftward
  3. Ten Frames: Fill and empty boxes
  4. Fingers: For problems up to 10
Common Mistake: Subtracting the larger number from the smaller one.
Memory Aid: "The answer is how many more you need."
Practice Strategy: Start with easier problems (within 10) first.
Verification: Always add difference + subtrahend to check.
Subtraction Properties: Order matters, zero property (n-0=n), n-n=0.
Within 20 Focus: Master facts up to 20 for future math success.
Essential Facts to Remember:

• Subtraction means taking away or finding the difference

• The minuend is always the largest number in basic subtraction

• Use addition to check subtraction: difference + subtrahend = minuend

• Practice makes fluency - aim for instant recall of facts

Subtraction Laws, Methods, and Key Expressions
a - b = c means b + c = a
Inverse Relationship
Key definitions:

Subtraction: Operation that finds the difference between two numbers

Minuend: Number being subtracted from

Subtrahend: Number being subtracted

Difference: Result of subtraction

Complete methodology:
  1. Identify parts: Recognize minuend, subtrahend, and unknown difference
  2. Choose strategy: Counting back, number line, or fact families
  3. Execute calculation: Follow chosen method systematically
  4. Verify result: Add difference to subtrahend to check
Tip 1: For numbers close together, count up instead of back.
Tip 2: Use doubles facts to help: 14-7 is half of 14.
Tip 3: Practice decomposing: 15-8 = 15-5-3 = 10-3 = 7.
Tip 4: Always verify by adding: difference + subtrahend = minuend.
Common errors: Reversing order, miscounting steps, forgetting to verify.
Success strategies: Multiple methods, visual aids, regular practice.
Key principles for subtraction within 20:

• Subtraction as take-away: physically removing objects

• Subtraction as comparison: finding how much more or less

• Subtraction as distance: measuring the gap between numbers

• Inverse relationship: subtraction undoes addition

• Zero property: any number minus itself equals zero

Questions & Answers

Question: My child gets confused when subtracting and sometimes subtracts the smaller number from the larger regardless of position. How can I help them understand the correct order?

Answer: This is a very common issue with beginning subtraction learners! Here are effective strategies:

  • Use concrete objects: "We have 12 apples and eat 5. How many are left?" This contextualizes the problem.
  • Emphasize vocabulary: Teach "take away," "how many are left," and "what's the difference" to connect to the concept.
  • Introduce the terms "start with" and "take away": "Start with 12, take away 5."
  • Use visual aids: Draw circles and cross out the ones being subtracted.

Example: For 12 - 5, say "I start with 12 and take away 5. That means I'll have fewer than 12 left." Never 5 - 12 in this context.

Practice with word problems before numeric expressions to build conceptual understanding.

Question: Some of my students struggle with subtraction facts within 20. What are the most effective methods to help them memorize these facts?

Answer: Building fact fluency requires multiple approaches:

  • Start with conceptual understanding before memorization. Students need to know WHAT subtraction means.
  • Use fact families to show relationships: knowing 6 + 4 = 10 helps with 10 - 6 = 4.
  • Focus on patterns: doubles (8 - 4), near doubles (9 - 4), and tens facts (10 - 7).
  • Incorporate games and timed practice once understanding is solid.

Effective sequence: Concrete (manipulatives) → Pictorial (drawings) → Abstract (numbers only).

Don't rush to memorization. Fluency comes naturally after understanding. Practice 5-10 minutes daily rather than longer sessions.

Question: How can I help students who rely too heavily on counting back and struggle with efficiency in solving subtraction problems?

Answer: Counting back is a valid starting strategy, but we want to build efficiency. Here's how to transition:

  • Introduce the "think addition" strategy: "What number plus 6 equals 14?" instead of counting back 14-6.
  • Teach decomposition: For 15-7, think 15-5-2 = 10-2 = 8.
  • Use number bonds: If students know 7+3=10, they can use this for 17-7=10.
  • Practice with missing addend problems to strengthen the connection.

The goal is flexible thinking. Some problems are easier with counting back (15-2), others with think-addition (15-8).

Encourage students to notice which strategy feels faster for different problems.