Addition and Subtraction Within 20 Strategies - Grade 1 Mathematics

Master addition and subtraction within 20 strategies: counting on, counting back, number bonds, and mental math techniques through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Count On Strategy
Exercise 1
Use count on strategy: 7 + 6 = ?
Definition:

Count on: Starting with the first number and counting forward by the second number

Count on method:
  1. Start with the larger number
  2. Count forward by the amount of the second number
  3. Keep track of each count
Expression
7 + 6
Count on
8, 9, 10, 11, 12, 13
Result
13
Step 1: Start with the first number

Begin counting from 7

Step 2: Count forward by the second number

Count 6 more: 8, 9, 10, 11, 12, 13

Step 3: Identify the final number

We land on 13, so 7 + 6 = 13

7 + 6 = 13
Final answer:

7 + 6 = 13

Applied rules:

• Count on strategy: Start with first number and count forward

• Addition: Combining quantities

• Number sequence: Each number is one more than the previous

2 Count Back Strategy
Exercise 2
Use count back strategy: 14 - 5 = ?
Definition:

Count back: Starting with the first number and counting backward by the second number

Expression
14 - 5
Count back
13, 12, 11, 10, 9
Result
9
Step 1: Start with the first number

Begin counting from 14

Step 2: Count backward by the second number

Count 5 less: 13, 12, 11, 10, 9

Step 3: Identify the final number

We land on 9, so 14 - 5 = 9

14 - 5 = 9
Final answer:

14 - 5 = 9

Applied rules:

• Count back strategy: Start with first number and count backward

• Subtraction: Taking away quantities

• Number sequence: Each number is one less than the previous

3 Number Bonds Strategy
Exercise 3
Use number bonds: 8 + 7 = ?
Definition:

Number bonds: Using known combinations to solve problems

Expression
8 + 7
Think
8 + 2 + 5 = 10 + 5
Result
15
Step 1: Break down the second number

Think of 7 as 2 + 5

Step 2: Use number bonds to 10

8 + 2 = 10

Step 3: Add the remaining amount

10 + 5 = 15

Step 4: Verify the answer

Count: 8, 9, 10, 11, 12, 13, 14, 15

8 + 7 = 15
Final answer:

8 + 7 = 15

Applied rules:

• Number bonds to 10: Using 10 as a benchmark number

• Decomposition: Breaking numbers into parts

• Compensation: Making numbers easier to work with

Rules and methods, laws,...
Count On: a + b = a, a+1, a+2, ..., a+b
Count On Strategy
Count On
7+6=7→8→9→10→11→12→13
Move forward
Count Back
14-5=14→13→12→11→10→9
Move backward
Number Bonds
8+7=(8+2)+5=15
Make 10 first
Key definitions:

Count On: Starting with a number and counting forward to add

Count Back: Starting with a number and counting backward to subtract

Number Bonds: Pairs of numbers that combine to make a specific total

Complete methodology:
  1. Identify the operation: Determine if addition or subtraction
  2. Choose the strategy: Count on for addition, count back for subtraction, number bonds for both
  3. Execute the method: Count the appropriate number of steps
  4. Verify the result: Check if the answer makes sense
Tip 1: Use fingers to keep track of counting steps.
Tip 2: Practice number bonds to 10 to make addition easier.
Tip 3: Start with smaller numbers and gradually increase difficulty.
Tip 4: Use visual models like number lines to reinforce strategies.
Common errors: Counting the starting number, going in wrong direction, losing track.
Memory aids: "Count ON for ADDition, Count BACK for suBTraction".
Facts to know by heart:

• Count on: Addition problems (a + b, start at a, count b more)

• Count back: Subtraction problems (a - b, start at a, count b back)

• Number bonds to 10: 1+9, 2+8, 3+7, 4+6, 5+5

• Number bonds to 20: 10+10, 11+9, 12+8, 13+7, 14+6, 15+5

• Mental math: Strategies build number sense and fluency

Solution: Exercises 4 to 5
4 Doubles Plus One Strategy
Exercise 4
Use doubles plus one: 6 + 7 = ?
Definition:

Doubles plus one: Using known doubles facts and adding one more

Expression
6 + 7
Think
6 + 6 + 1 = 12 + 1
Result
13
Step 1: Identify the relationship

7 is one more than 6, so think of 6 + 6 + 1

Step 2: Use the doubles fact

6 + 6 = 12

Step 3: Add the extra one

12 + 1 = 13

Step 4: Verify the answer

Check: 6 + 7 = 13 ✓

6 + 7 = 13
Final answer:

6 + 7 = 13

Applied rules:

• Doubles plus one: Use closest doubles fact and add 1

• Known facts: Build on memorized doubles

• Number relationships: Recognize consecutive numbers

5 Choosing the Right Strategy
Exercise 5
Solve: 15 - 8 and 9 + 8 using appropriate strategies
Definition:

Strategy selection: Choosing the most efficient method for each problem

Subtraction
15 - 8 = 7
Addition
9 + 8 = 17
Strategies
Count back, Doubles + 1
Step 1: Identify the operations

15 - 8 (subtraction) and 9 + 8 (addition)

Step 2: Apply count back for subtraction

Start at 15, count 8 back: 14, 13, 12, 11, 10, 9, 8, 7

Step 3: Apply doubles plus one for addition

Think 8 + 8 + 1 = 16 + 1 = 17

Step 4: Verify both answers

Check: 15 - 8 = 7 and 9 + 8 = 17

15 - 8 = 7, 9 + 8 = 17
Final answer:

15 - 8 = 7 and 9 + 8 = 17

Applied rules:

• Strategy selection: Choose the most efficient method for each problem

• Operation identification: Recognize + vs - signs

• Flexible thinking: Use different strategies for different problems

Complete Guide to Addition and Subtraction Strategies Within 20
Count On: a + b → a, a+1, a+2, ..., a+b
Counting Strategies Formula
Key definitions:

Count On: Starting with a number and counting forward to perform addition

Count Back: Starting with a number and counting backward to perform subtraction

Number Bonds: Pairs of numbers that combine to make a specific total

Complete methodology:
  1. Problem Analysis: Identify whether to add or subtract
  2. Strategy Selection: Choose the most efficient method
  3. Execution: Apply the chosen counting strategy
  4. Verification: Check that the answer is reasonable
Tip 1: Always start counting from the first number given.
Tip 2: Don't count the starting number itself when counting on/back.
Tip 3: Use visual aids like number lines or fingers to stay organized.
Tip 4: Practice regularly to build fluency and confidence.
Common errors: Counting the starting number, going in wrong direction, losing track of counts.
Teaching strategies: Use manipulatives, visual models, and real-world connections.
Core facts and principles:

• Count on: For addition, move forward on the number line

• Count back: For subtraction, move backward on the number line

• Number bonds to 10: 1+9, 2+8, 3+7, 4+6, 5+5

• Doubles facts: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, etc.

• Mental math foundation: Builds number sense and fluency

Strategy Effectiveness Visualization: Comparing Different Approaches
Exercise 6: Strategy Comparison
Compare different strategies for the same problems:
8 + 7: Count on (8→9→10→11→12→13→14→15) vs Number bonds (8+2+5=15)
13 - 6: Count back (13→12→11→10→9→8→7) vs Fact families (6+7=13, so 13-6=7)

Pattern Analysis: Different strategies may be more efficient depending on the numbers involved.

  • Count on: Good for small additions
  • Number bonds: Efficient when making 10
  • Doubles: Quick when numbers are close
  • Strategy choice depends on the specific problem

Questions & Answers

Question: My child sometimes counts the starting number when using count on/count back. How can I help them understand they shouldn't count the starting number?

Answer: This is a very common issue! Here are strategies to help:

  • Physical cues: Have your child touch the starting number, then count the jumps separately
  • Verbal prompts: Say "start at 7" then "jump 6 more" (not "count 7, 8, 9, 10...")
  • Visual aids: Use arrows or circles to show the starting point vs the jumps
  • Practice with smaller numbers: Start with +1 and -1 problems first

Emphasize that the starting number is the "home base" - we don't count it, we count FROM it!

Question: Why do we need to learn different strategies? Can't I just count everything?

Answer: Great question! Different strategies are helpful shortcuts:

  • Speed: Instead of counting 7, 8, 9, 10, 11, 12, 13 for 7 + 6, you start at 7 and count 8, 9, 10, 11, 12, 13
  • Mental math: These strategies help you solve problems in your head
  • Foundation: They build skills for harder math later
  • Efficiency: Some strategies work better for certain problems

Think of strategies like different tools - each one works best for different jobs!

Question: How can I help students choose the most efficient strategy for each problem?

Answer: Help students develop strategic thinking by:

  • Pattern recognition: Teach them to notice when numbers are close to 10
  • Practice with comparison: Try the same problem with different strategies
  • Discussion: Ask "Which strategy was fastest for this problem?"
  • Guided discovery: Let them explore which strategies work best for different problems

Create strategy reference charts and encourage students to reflect on which methods work best for different types of problems!