Solved Exercises on Addition Facts Within 20 in Grade 2

Master addition facts within 20: counting on, doubles, near doubles, make 10 strategy, addition properties through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting on strategy
Exercise 1
Solve 8 + 5 using the counting on strategy.
Definition:

Counting on: Starting with the larger number and counting forward by the smaller number.

Counting on method:
  1. Identify the larger number (start here)
  2. Count forward by the smaller number
  3. Keep track of counts
8
→
9
→
10
→
11
→
12
→
13
Step 1: Start with the larger number

Start with 8 (the larger number)

Step 2: Count on by the smaller number

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

Step 3: Record the final number

8 + 5 = 13

Counting on: 8 + 5

Start at 8, count 5 more: 9, 10, 11, 12, 13

8 + 5 = 13
Final answer:

8 + 5 = 13 using the counting on strategy.

Applied rules:

• Start with larger: Begin counting from the larger addend

• Count forward: Move forward by the number of counts equal to the smaller addend

• Track counts: Keep count of each step to ensure accuracy

2 Doubles facts
Exercise 2
Solve 6 + 6 using the doubles fact.
Definition:

Doubles facts: Adding the same number to itself (e.g., 6 + 6, 7 + 7).

6
6
6
6
6
6
6
6
6
6
6
6
Step 1: Recognize the doubles pattern

6 + 6 means the same number added to itself

Step 2: Apply the doubles rule

Any number added to itself is double that number

6 + 6 = 2 × 6 = 12

Step 3: Verify the result

Count: 6 + 6 = 12 ✓

Doubles fact: 6 + 6

Same number added to itself = double the number

6 + 6 = 12
Final answer:

6 + 6 = 12 using the doubles fact.

Applied rules:

• Doubles principle: n + n = 2n

• Memorization: Doubles facts should be memorized for fluency

• Pattern recognition: Same numbers added together

3 Near doubles
Exercise 3
Solve 7 + 8 using the near doubles strategy.
Definition:

Near doubles: Adding numbers that are one apart (e.g., 7 + 8, 5 + 6).

7
7
7
7
7
7
7
8
8
8
8
8
8
8
Step 1: Recognize near doubles pattern

7 + 8 are consecutive numbers (one apart)

Step 2: Use the doubles fact

7 + 7 = 14 (double 7)

Step 3: Adjust for the difference

Since 8 is 1 more than 7, add 1 more

14 + 1 = 15

Step 4: Write the final answer

7 + 8 = 15

Near doubles: 7 + 8

7 + 7 = 14, then add 1 more = 15

7 + 8 = 15
Final answer:

7 + 8 = 15 using the near doubles strategy.

Applied rules:

• Near doubles principle: n + (n+1) = (n + n) + 1

• Pattern building: Use known doubles to solve near doubles

• Adjustment strategy: Add or subtract the difference

Addition Facts Within 20 Rules and Methods
8 + 5 = 13
Counting On
Strategy 1
Counting On
Start with larger number
Strategy 2
Doubles Facts
n + n = 2n
Strategy 3
Near Doubles
n + (n+1) = (n+n)+1
Key definitions:

Addition facts: Basic addition equations with sums within 20

Counting on: Starting with the larger number and counting forward

Doubles facts: Adding the same number to itself (e.g., 5 + 5)

Near doubles: Adding consecutive numbers (e.g., 5 + 6)

Make 10 strategy: Breaking apart numbers to make 10 first

Complete methodology:
  1. Counting on: Start with larger number, count forward by smaller number
  2. Doubles: Memorize same number + same number facts
  3. Near doubles: Use doubles and adjust by 1
  4. Make 10: Break apart to reach 10 first
Tip 1: Always start counting from the larger number to save time.
Tip 2: Practice doubles facts until they become automatic.
Tip 3: Use fingers or counters to visualize the addition.
Tip 4: Look for patterns in near doubles to use known doubles.
Common errors: Counting from 1 instead of starting number, forgetting to stop at the right count, miscounting near doubles.
Memory aid: "Start big, count small" for counting on strategy.
Rules to remember:

• Step 1: Identify the addition strategy to use

• Step 2: Apply the chosen strategy methodically

• Step 3: Verify the result by checking

• Step 4: Practice regularly for fluency

9 + 4 = 13
Example Addition
Solution: Exercises 4 to 5
4 Make 10 strategy
Exercise 4
Solve 9 + 6 using the make 10 strategy.
Definition:

Make 10 strategy: Breaking apart one number to make 10 with the other number.

9
9
9
9
9
9
9
9
9
6
6
6
Step 1: Identify what's needed to make 10

9 needs 1 more to make 10

Step 2: Break apart the second number

Break 6 into 1 and 5

Step 3: Make 10 first

9 + 1 = 10

Step 4: Add the remaining part

10 + 5 = 15

Make 10: 9 + 6

9 + 1 = 10, then 10 + 5 = 15

9 + 6 = 15
Final answer:

9 + 6 = 15 using the make 10 strategy.

Applied rules:

• Make 10 principle: Break one number to complement the other to 10

• Decomposition: Break apart the second addend strategically

• Addition sequence: Make 10 first, then add remainder

5 Fact families
Exercise 5
Show the fact family for 7 + 8 = 15.
Definition:

Fact family: A group of related addition and subtraction facts using the same three numbers.

7 + 8 = 15
→
8 + 7 = 15
→
15 - 7 = 8
→
15 - 8 = 7
Step 1: Start with the given addition fact

7 + 8 = 15

Step 2: Write the related addition fact

8 + 7 = 15 (commutative property)

Step 3: Write the related subtraction facts

15 - 7 = 8 and 15 - 8 = 7

Step 4: Verify all facts are correct

Check: 7 + 8 = 15 ✓, 8 + 7 = 15 ✓, 15 - 7 = 8 ✓, 15 - 8 = 7 ✓

Fact family: 7, 8, 15

Two addition facts and two subtraction facts

7 + 8 = 15, 8 + 7 = 15
Final answer:

The fact family for 7 + 8 = 15 includes: 7 + 8 = 15, 8 + 7 = 15, 15 - 7 = 8, 15 - 8 = 7.

Applied rules:

• Fact family principle: Three numbers create four related facts

• Commutative property: Order doesn't matter in addition

• Relationship principle: Addition and subtraction are inverse operations

Addition Facts Within 20 Laws, Methods, and Definitions
a + b = b + a
Commutative Property
Key definitions:

Addition facts: Basic addition equations with sums within 20 that should be memorized

Counting on: A strategy starting with the larger number and counting forward by the smaller number

Doubles facts: Addition facts where both addends are the same (e.g., 4 + 4, 6 + 6)

Near doubles: Addition facts where addends are consecutive numbers (e.g., 4 + 5, 6 + 7)

Make 10 strategy: Breaking apart one number to make 10 with the other number

Fact family: A set of related addition and subtraction facts using the same three numbers

Complete methodology:
  1. Counting on: Start with larger addend, count forward by smaller addend
  2. Doubles: Memorize n + n facts for fluency
  3. Near doubles: Use doubles + 1 or doubles - 1
  4. Make 10: Break one number to make 10 with the other
  5. Verification: Always check the answer using a different method
Tip 1: Practice doubles facts daily until they become automatic.
Tip 2: Use the make 10 strategy when one addend is close to 10.
Tip 3: Count on from the larger number to save time and effort.
Tip 4: Recognize patterns in near doubles to use known facts.
Common errors: Counting from 1 instead of the larger number, forgetting to stop at the correct count, confusing near doubles patterns.
Memory aids: "Start big, count small" for counting on, "same numbers make doubles" for doubles facts.
Essential laws and rules:

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

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

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

• Counting on rule: Start with larger addend, count forward by smaller addend

• Doubles principle: n + n = 2n

5 + 7 = 12
Example Addition
Visual representation: Using counters or fingers helps students understand the concept of combining quantities.
Real-world connection: Addition represents combining groups of items together.

Questions & Answers

Question: Why do we start counting from the bigger number? Why not start from 1?

Answer: Great question! Starting from the bigger number is faster and easier:

  • Counting on: If you have 8 + 5, start at 8 and count 5 more: 9, 10, 11, 12, 13
  • Counting from 1: You'd have to count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

Starting from the bigger number saves you time - you only count the number of steps you need to add!

It's like walking from house number 8 to house number 13 - you don't walk past all the houses before 8, you just walk 5 more houses!

Question: What are doubles facts and why are they important?

Answer: Doubles facts are when you add the same number to itself:

  • 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

They're important because:

  • They're easier to remember and become automatic
  • They help with near doubles (like 5 + 6 = 5 + 5 + 1 = 11)
  • They build confidence in addition skills

Practice doubles until you can say them without thinking!

Question: My child struggles with the "make 10" strategy. How can I help them understand it?

Answer: The make 10 strategy can be taught step-by-step:

  • Step 1: Look for numbers close to 10 (like 9, 8, 7)
  • Step 2: Figure out what's needed to make 10 (9 needs 1 more)
  • Step 3: Break the other number to provide what's needed
  • Step 4: Add the leftover part to 10

For 9 + 6:

  • 9 needs 1 more to make 10
  • Break 6 into 1 and 5
  • 9 + 1 = 10, then 10 + 5 = 15

Use physical objects like counters to demonstrate this visually.

Question: What's a fact family? I don't understand why we need four facts.

Answer: A fact family uses 3 numbers to make 4 facts! It shows how addition and subtraction are connected:

  • With numbers 7, 8, and 15: 7 + 8 = 15 and 8 + 7 = 15
  • Also: 15 - 7 = 8 and 15 - 8 = 7

You need four facts because:

  • Addition can be done in either order (7 + 8 or 8 + 7)
  • Subtraction shows how to get back to the original numbers
  • This helps you understand the relationship between addition and subtraction

It's like having a family photo album - all the facts belong together!

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

Answer: Different strategies help you add faster and more accurately:

  • Counting on: Faster than counting from 1
  • Doubles: Once memorized, instant answers
  • Make 10: Easier mental math
  • Near doubles: Build on known facts

Think of it like having different tools for different jobs:

  • Counting from 1 is like walking everywhere (works but slow)
  • Using strategies is like riding a bike (faster and more efficient)

The more strategies you know, the faster and better you'll become at addition!