Solved Exercises on Mental Math Subtraction Strategies in Grade 1

Master mental math subtraction: counting back, number bonds, compensation, doubles facts, and decomposing numbers through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Back Strategy
Exercise 1
Solve: 12 - 5 using the counting back strategy
Definition:

Counting Back: Start from the larger number and count backward by the amount of the smaller number

Counting back method:
  1. Start at the larger number (12)
  2. Count backward one number at a time
  3. Count the same number of steps as the subtracted number (5)
  4. The final number is the answer
Visual Number Line:
12
←
11
←
10
←
9
←
8
←
7

Counting back 5 steps: 12 → 11 → 10 → 9 → 8 → 7

Start
12
Count back
5 steps
Result
7
Step 1: Start at 12

Begin counting from the number being subtracted from

Step 2: Count back 5 times

12 - 1 = 11, 11 - 1 = 10, 10 - 1 = 9, 9 - 1 = 8, 8 - 1 = 7

Step 3: Identify the final number

After counting back 5 steps from 12, we land on 7

12 - 5 = 7
Final answer:

12 - 5 = 7

Applied rules:

• Counting Back: Move left on the number line

• Subtraction: Finding the difference between numbers

• Visualization: Use number line to support mental calculation

2 Number Bonds Strategy
Exercise 2
Solve: 15 - 8 using number bonds strategy
Definition:

Number Bonds: Using known addition facts to solve subtraction problems

Number Bond Relationship:

If: 8 + ? = 15, then: 15 - 8 = ?

Find the missing number that makes the equation true

8 dots + 7 dots = 15 dots total

Expression
15 - 8
Think
8 + ? = 15
Answer
7
Step 1: Think of the related addition fact

"What number added to 8 equals 15?"

Step 2: Use known facts

We know that 8 + 7 = 15

Step 3: Apply the inverse relationship

If 8 + 7 = 15, then 15 - 8 = 7

Step 4: Verify the answer

Check: 7 + 8 = 15 ✓

15 - 8 = 7
Final answer:

15 - 8 = 7

Applied rules:

• Addition-Subtraction Connection: Addition and subtraction are inverse operations

• Number Bonds: Numbers can be broken into parts that combine to make the whole

• Known Facts: Use memorized addition facts to solve subtraction

3 Compensation Strategy
Exercise 3
Solve: 16 - 9 using compensation strategy
Definition:

Compensation: Adjust the numbers to make the subtraction easier, then adjust the answer

Compensation Process:

Instead of 16 - 9, think of 16 - 10, then add 1 back

16 - 10 = 6, then 6 + 1 = 7

Original
16 - 9
Compensate
16 - 10
Adjust
6 + 1 = 7
Step 1: Round the subtracted number up

Change 9 to 10 (round up to the nearest ten)

Step 2: Subtract the rounded number

16 - 10 = 6

Step 3: Add back the difference

We subtracted 1 too many (10 - 9 = 1), so add 1 back

6 + 1 = 7

Step 4: Verify the answer

Check: 7 + 9 = 16 ✓

16 - 9 = 7
Final answer:

16 - 9 = 7

Applied rules:

• Compensation: Make numbers easier to work with

• Balance: Whatever you do to one part, compensate in the answer

• Rounding: Use round numbers to simplify calculations

Subtraction Strategies Overview
Subtraction = Minuend - Subtrahend = Difference
Basic Subtraction Structure
Mental Math Strategies:
  • Counting Back: Move backward on number line
  • Number Bonds: Use addition facts for subtraction
  • Compensation: Adjust numbers to make calculation easier
  • Doubles Facts: Use known doubles for related subtraction
  • Decomposing: Break apart numbers strategically
Key Insight: Subtraction finds how many more or less one number is compared to another.
Strategy Selection: Choose the easiest method for each specific problem.
Tip 1: Practice number bonds (addition facts) to strengthen subtraction skills.
Tip 2: Use physical objects or fingers when starting with new strategies.
Tip 3: Check your answer by adding the result to the subtracted number.
Tip 4: Start with smaller numbers and gradually increase difficulty.
Important Properties:

• Commutative Property: Does NOT apply to subtraction (a - b ≠ b - a)

• Associative Property: Does NOT apply to subtraction

• Identity Property: a - 0 = a

• Inverse Operations: Addition and subtraction undo each other

a - b = c means a = b + c
Subtraction-Addition Relationship
Solution: Exercises 4 to 5
4 Doubles Facts Strategy
Exercise 4
Solve: 14 - 7 using doubles facts strategy
Definition:

Doubles Facts: Use known doubles (like 7 + 7 = 14) to solve subtraction

Doubles Fact Recognition:

7 + 7 = 14, so 14 - 7 = 7

When you subtract one of the doubles from the total, you get the other double

Two equal groups of 7 make 14 total

Expression
14 - 7
Think
7 + 7 = 14
Answer
7
Step 1: Recognize the doubles fact

We know that 7 + 7 = 14

Step 2: Apply the inverse relationship

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

Step 3: Verify the answer

Check: 7 + 7 = 14 ✓

14 - 7 = 7
Final answer:

14 - 7 = 7

Applied rules:

• Doubles Facts: Memorize basic doubles (1+1, 2+2, ..., 10+10)

• Inverse Operations: Addition and subtraction are opposite operations

• Pattern Recognition: Identify when numbers are doubles

5 Decomposing Numbers Strategy
Exercise 5
Solve: 13 - 6 using decomposing numbers strategy
Definition:

Decomposing: Break apart the number being subtracted into smaller, easier-to-manage parts

Decomposition Process:

Break 6 into 3 and 3 (since 6 = 3 + 3)

Then subtract in steps: 13 - 3 - 3

First: 13 - 3 = 10, then: 10 - 3 = 7

Original
13 - 6
Decompose
6 = 3 + 3
Calculate
7
Step 1: Break apart the number being subtracted

Split 6 into two parts that are easy to subtract: 6 = 3 + 3

Step 2: Subtract the first part

13 - 3 = 10

Step 3: Subtract the second part

10 - 3 = 7

Step 4: Verify the answer

Check: 7 + 6 = 13 ✓

13 - 6 = 7
Final answer:

13 - 6 = 7

Applied rules:

• Decomposition: Break complex problems into simpler ones

• Associative Property: (a - b) - c = a - (b + c)

• Strategic Breaking: Choose parts that make subtraction easier

Complete Guide to Mental Math Subtraction
Minuend - Subtrahend = Difference
Subtraction Components
Key definitions:

Minuend: The number being subtracted from (the first number)

Subtrahend: The number being subtracted (the second number)

Difference: The result of the subtraction

Mental Math: Calculating in your head without writing

Complete methodology:
  1. Analyze the numbers: Look for relationships (doubles, near doubles, round numbers)
  2. Choose the strategy: Counting back, number bonds, compensation, doubles, or decomposition
  3. Apply the method: Follow the steps of the chosen technique
  4. Verify the result: Check by adding the difference to the subtrahend
Tip 1: Start with smaller numbers and use visual aids (fingers, objects) to build confidence.
Tip 2: Practice number bonds daily to strengthen addition/subtraction fluency.
Tip 3: Use compensation when subtracting numbers close to 10 (like 9, 8, 11, 12).
Tip 4: Always verify your answer by checking: difference + subtrahend = minuend.
Common errors: Counting incorrectly, forgetting to adjust in compensation, misidentifying number bonds.
Exam preparation: Master all five strategies, practice with various number combinations, focus on accuracy over speed.
Strategies to master:

• Counting Back: For small subtrahends (subtracting 1-5)

• Number Bonds: For problems with known addition facts

• Compensation: For numbers near 10 (9, 8, 11, 12)

• Doubles Facts: For doubles subtraction (like 12-6, 14-7)

• Decomposition: For breaking apart complex subtrahends

Strategy Selection Guide:
  • Subtracting 1-3: Use counting back
  • Subtracting 4-5: Counting back or number bonds
  • Subtracting 6-7: Number bonds or decomposition
  • Subtracting 8-9: Compensation (think 10 and adjust)
  • Doubles: Use doubles facts (12-6, 16-8)

Questions & Answers

Question: I get confused when doing 15 - 8. Should I count back or use number bonds? Which is faster?

Answer: Great question! For 15 - 8, number bonds is usually faster because 8 + 7 = 15, so 15 - 8 = 7. However, let's compare both methods:

  • Counting Back: 15 → 14 → 13 → 12 → 11 → 10 → 9 → 8 (7 steps) = 7
  • Number Bonds: Think "8 + ? = 15", answer is 7, so 15 - 8 = 7

Number bonds is faster once you know your addition facts! Practice both methods and use the one that feels easier for each specific problem. As you learn more addition facts, number bonds will become your go-to strategy.

Question: My child struggles with 14 - 6. How can I help them visualize the decomposing strategy?

Answer: Visualization helps tremendously! For 14 - 6, try this hands-on approach:

  • Use 14 objects (blocks, counters, etc.)
  • Show how 6 can be split into 4 and 2 (since 4 + 2 = 6)
  • First take away 4 from 14: 14 - 4 = 10
  • Then take away 2 from 10: 10 - 2 = 8

You can also draw it: Start with 14 circles, cross out 4, then cross out 2 more. Count what's left! This makes the abstract concept concrete and memorable.

Question: How do I teach students to choose the best strategy for each subtraction problem?

Answer: Help students develop strategy selection by teaching pattern recognition:

  • Small numbers (1-3): Counting back is often easiest
  • Doubles (like 12-6, 14-7): Use doubles facts
  • Near 10 (like 15-9, 13-8): Compensation works well
  • Known addition facts: Use number bonds
  • Complex numbers: Decompose into easier parts

Practice with a variety of problems and encourage students to think aloud: "I notice 15 and 9 are close to 10, so I'll use compensation..." This builds metacognitive awareness of their own thinking processes.