Solved Exercises on Addition Within 20 for Grade 1

Master addition within 20: counting strategies, number bonds, and visual representations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Strategy
Exercise 1
Solve: 7 + 5 = ?
Definition:

Counting Strategy: Start with the larger number and count up by the smaller number

Addition method:
  1. Identify the larger number (7)
  2. Count up by the smaller number (5)
  3. Count: 8, 9, 10, 11, 12
  4. Result: 12
7
+
5
=
12
Step 1: Start with the larger number

We start counting from 7

Step 2: Count up by 5

7 → 8 → 9 → 10 → 11 → 12

Step 3: Record the final number

The answer is 12

7 + 5 = 12
Final answer:

7 + 5 = 12

Applied rules:

• Start with larger number: More efficient counting

• Count up: Move forward on the number line

• One-to-one correspondence: Each count represents one unit

2 Number Bonds
Exercise 2
Solve: 8 + 6 = ?
Definition:

Number Bonds: Breaking numbers into parts to make addition easier (like making 10)

8
+
6
=
14
Step 1: Break down the second number

6 = 2 + 4 (so that 8 + 2 = 10)

Step 2: Make 10 first

8 + 2 = 10

Step 3: Add the remaining part

10 + 4 = 14

Step 4: Combine the results

8 + 6 = 8 + 2 + 4 = 10 + 4 = 14

8 + 6 = 14
Final answer:

8 + 6 = 14

Applied rules:

• Make 10 strategy: Use 10 as a benchmark number

• Decomposition: Break numbers into friendly parts

• Associative property: Group numbers differently

3 Doubles Plus One
Exercise 3
Solve: 6 + 7 = ?
Definition:

Doubles Plus One: When adding consecutive numbers, use the doubles fact and add one more

6
+
7
=
13
Step 1: Identify the doubles fact

6 + 6 = 12 (the closest doubles fact)

Step 2: Recognize the relationship

7 is one more than 6, so we add one more to the doubles fact

Step 3: Calculate the result

6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

Step 4: Verify the answer

Count: 6, 7, 8, 9, 10, 11, 12, 13

6 + 7 = 13
Final answer:

6 + 7 = 13

Applied rules:

• Doubles facts: Memorized sums of identical numbers

• Consecutive numbers: Numbers that follow each other

• Compensation strategy: Adjust one number and compensate

Addition Strategies and Methods
a + b = c
Basic Addition
Counting On
Start with larger number, count up
7 + 3 = 7, 8, 9, 10
Make 10
Break numbers to make 10 first
8 + 6 = 8 + 2 + 4 = 14
Doubles + 1
Use doubles facts for consecutive numbers
5 + 6 = 5 + 5 + 1 = 11
Key definitions:

Addition: Combining two or more numbers to find their total

Sum: The result of an addition problem

Addends: The numbers being added together

Number line: Visual representation of numbers in order

Addition strategies:
  1. Counting on: Start with the larger number and count up
  2. Make 10: Break numbers to create 10 as a benchmark
  3. Doubles facts: Memorize sums of identical numbers
  4. Doubles plus/minus 1: Use doubles for consecutive numbers
Tip 1: Always start counting with the larger number to be more efficient.
Tip 2: Practice doubles facts (2+2, 3+3, etc.) until they're automatic.
Tip 3: Use fingers or objects to visualize the addition process.
Tip 4: Check your work by counting backwards from your answer.
Common errors: Counting from 1 instead of the larger number, miscounting, forgetting to include the starting number.
Memorization aids: Sing songs about doubles, use flashcards, play addition games.
Properties to remember:

• Commutative property: a + b = b + a (order doesn't matter)

• Identity property: a + 0 = a (adding zero doesn't change the number)

• Associative property: (a + b) + c = a + (b + c)

Solution: Exercises 4 to 5
4 Making 10 Strategy
Exercise 4
Solve: 9 + 5 = ?
Definition:

Making 10 Strategy: Break apart the second number to make 10 with the first number, then add the remainder

9
+
5
=
14
Step 1: Identify how many needed to make 10

9 + ? = 10 → We need 1 more to make 10

Step 2: Break apart the second number

5 = 1 + 4 (we take 1 to make 10, leaving 4)

Step 3: Add to make 10 first

9 + 1 = 10

Step 4: Add the remaining amount

10 + 4 = 14

Step 5: Write the complete equation

9 + 5 = 9 + 1 + 4 = 10 + 4 = 14

9 + 5 = 14
Final answer:

9 + 5 = 14

Applied rules:

• Make 10 strategy: Use 10 as a benchmark for easier addition

• Number decomposition: Break numbers into helpful parts

• Sequential addition: Add in parts to reach the final sum

5 Mixed Strategies
Exercise 5
Solve: 7 + 8 = ?
Definition:

Mixed Strategies: Using multiple approaches depending on the numbers involved

7
+
8
=
15
Step 1: Identify the approach

These are consecutive numbers (7 and 8), so we can use doubles plus one

Step 2: Find the nearest doubles fact

7 + 7 = 14 (or 8 + 8 = 16, but 7 + 7 is closer)

Step 3: Apply the doubles plus one strategy

Since 8 = 7 + 1, we have: 7 + 8 = 7 + 7 + 1 = 14 + 1 = 15

Step 4: Alternative approach - making 10

7 + 8 = 7 + 3 + 5 = 10 + 5 = 15

Step 5: Verify with counting strategy

Starting from 8: 8, 9, 10, 11, 12, 13, 14, 15 (counting 7 more)

7 + 8 = 15
Final answer:

7 + 8 = 15

Applied rules:

• Flexibility: Multiple strategies can solve the same problem

• Doubles facts: Use known facts to derive new ones

• Verification: Check answers using different methods

Key Addition Concepts and Strategies
a + b = c
Addition Equation
Key definitions:

Addition: The operation of combining two or more quantities to find their total

Sum: The result obtained when numbers are added together

Addends: The numbers that are being added in an addition problem

Number bond: A visual representation showing how numbers are related in addition

Complete methodology:
  1. Examine the numbers: Look for patterns (doubles, near doubles, making 10)
  2. Choose a strategy: Select the most efficient method for the given numbers
  3. Apply the method: Follow the steps of the chosen strategy
  4. Verify the result: Check using a different method or counting
Tip 1: Memorize doubles facts (1+1=2, 2+2=4, ..., 10+10=20) as building blocks.
Tip 2: Numbers that add to 10 (1+9, 2+8, 3+7, etc.) are crucial for mental math.
Tip 3: Use your hands to represent numbers when visualizing addition.
Tip 4: Practice regularly with small increments to build fluency.
Common errors: Starting to count from 1 instead of the larger number, losing track while counting, misremembering basic facts.
Success strategies: Use visual aids, practice with manipulatives, connect to real-world situations.
Addition facts to know by heart:

• Doubles: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20

• Ten pairs: 1+9=10, 2+8=10, 3+7=10, 4+6=10, 5+5=10

• Adding zero: Any number + 0 = itself

• Adding one: Any number + 1 = next number

Questions & Answers

Question: I don't understand why we need to start counting from the bigger number. Why can't I just start from 1 every time?

Answer: Great question! Starting from the bigger number makes addition faster and reduces mistakes:

  • For 3 + 8: If you start from 1, you count 1,2,3,4,5,6,7,8,9,10,11 - that's 11 counts!
  • But if you start from 8, you count 8,9,10,11 - that's only 4 counts!
  • This strategy uses the commutative property: 3 + 8 = 8 + 3

Think of it like climbing stairs - if you're on the 8th floor and want to go up 3 more floors, you start counting from 8, not from the ground floor!

Question: My child gets confused with the "making 10" strategy. How can I help them understand it better?

Answer: The "making 10" strategy is powerful once understood! Try these approaches:

  • Use physical objects: Have your child take 9 blocks and 5 blocks, then rearrange to make a group of 10
  • Visual aids: Draw circles to represent numbers, then group 10 together
  • Practice number bonds to 10: Show how numbers combine to make 10 (1+9, 2+8, etc.)

For 9 + 5: Take 1 from the 5 to make 10 with the 9, leaving 4. So 10 + 4 = 14.

This strategy builds a strong foundation for mental math and future place value understanding.

Question: I sometimes forget my doubles facts. How can I remember them better?

Answer: Doubles facts are like building blocks for other addition facts! Here are memory tricks:

  • Make rhymes: "2 + 2 = 4, that's for sure!" or "6 + 6 = 12, let's all do it again!"
  • Use your fingers: Hold up 3 fingers on each hand, count them all (3 + 3 = 6)
  • Draw pictures: Draw 4 dots twice to show 4 + 4 = 8

Practice a little each day - start with 1+1, 2+2, 3+3 and gradually add more. Once you know doubles, you can easily figure out doubles plus one!

Remember: 5 + 5 = 10 is like having both hands full!