Addition Within 20 Worksheets Printable: Mastering Basic Addition for 1st Graders

Complete educational exercises with solutions: visual counting methods, number lines, fact families, and step-by-step strategies for addition within 20.

Solution: Exercises 1 to 3
1 Counting On Method
Exercise 1
Solve: 8 + 5 = ?
Use the counting on method starting from 8.
Definition:

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

Addition method:
  1. Identify the larger number (start point)
  2. Count up by the smaller number
  3. Keep track of each count
  4. The final number is the answer
8 + 5 = ?
→
8
9
10
11
12
13
Step 1: Start at the larger number

Start counting from 8 (the larger number)

Step 2: Count up by the smaller number

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

Step 3: Record the final number

We land on 13

8 + 5 = 13
Final answer:

8 + 5 = 13

Applied rules:

• Counting On: Start with the larger number for efficiency

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

• Sequential Counting: Numbers increase by 1 each time

2 Making Ten Strategy
Exercise 2
Solve: 7 + 6 = ?
Use the making ten strategy.
Definition:

Making Ten: Break apart the smaller number to make 10 with the larger number.

7 + 6 = ?
+
Step 1: Identify how many more to make 10

From 7, we need 3 more to make 10

Step 2: Break apart the second number

6 = 3 + 3 (we take 3 to make 10 with 7)

Step 3: Add to make 10, then add remaining

(7 + 3) + 3 = 10 + 3 = 13

Step 4: Calculate the final answer

10 + 3 = 13

7 + 6 = 13
Final answer:

7 + 6 = 13

Applied rules:

• Decomposition: Break apart numbers to make 10

• Associative Property: Group numbers differently

• Number Bonds: Understand how numbers combine to 10

3 Doubles Plus One
Exercise 3
Solve: 5 + 6 = ?
Use the doubles plus one strategy.
Definition:

Doubles Plus One: Use known doubles facts and add one more.

5 + 6 = ?
+
Step 1: Identify the nearest double

5 + 5 = 10 (double of 5)

Step 2: Recognize the relationship

6 is one more than 5, so 5 + 6 = (5 + 5) + 1

Step 3: Apply the doubles fact

5 + 6 = 10 + 1 = 11

Step 4: Verify the answer

Count to confirm: 5, 6, 7, 8, 9, 10, 11

5 + 6 = 11
Final answer:

5 + 6 = 11

Applied rules:

• Doubles Facts: Know basic doubles (1+1, 2+2, etc.)

• Near Doubles: Use doubles + 1 or doubles - 1

• Pattern Recognition: Identify when numbers are consecutive

Rules and methods, laws,...
a + b = c
Basic Addition
Counting On
Start with larger number, count up
Example: 8 + 3 → 9, 10, 11
Making Ten
Break apart to make 10
Example: 7 + 5 → (7 + 3) + 2 = 12
Doubles Facts
Numbers added to themselves
Example: 4 + 4 = 8
Key definitions:

Addition: Combining two or more numbers to find their total

Sum: The result of adding numbers together

Addends: The numbers being added together

Addition strategies:
  1. Counting All: Count all objects from the beginning
  2. Counting On: Start with the larger number and count up
  3. Making Ten: Break numbers to make 10 first
  4. Doubles: Use known doubles facts
  5. Number Line: Jump forward on a number line
Tip 1: Always start counting from the larger number.
Tip 2: Memorize doubles facts (1+1, 2+2, 3+3, etc.).
Tip 3: Use fingers or objects to visualize addition.
Tip 4: Practice making 10 with different combinations.
Common errors: Starting from 1 instead of the larger number, miscounting, forgetting to count the starting number.
Success strategies: Use multiple methods, check work, practice regularly, use visual aids.
Properties of Addition:

• Commutative: a + b = b + a

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

• Identity: a + 0 = a

Solution: Exercises 4 to 5
4 Number Bond Method
Exercise 4
Solve: 9 + 4 = ?
Use number bonds to 10.
Definition:

Number Bonds: Pairs of numbers that add up to a specific number.

9 + 4 = ?
+
Step 1: Identify what goes with 9 to make 10

9 + 1 = 10, so we take 1 from the 4

Step 2: Break apart the second number

4 = 1 + 3

Step 3: Make 10 first, then add remaining

(9 + 1) + 3 = 10 + 3 = 13

Step 4: Calculate the final sum

10 + 3 = 13

9 + 4 = 13
Final answer:

9 + 4 = 13

Applied rules:

• Number Bonds: Know pairs that make 10

• Decomposition: Break apart numbers strategically

• Associative Property: Regroup for easier calculation

5 Fact Families
Exercise 5
Solve: 6 + 8 = ?
Use fact family relationships.
Definition:

Fact Family: A set of related addition and subtraction facts using the same numbers.

6 + 8 = ?
+
Step 1: Think of the commutative property

6 + 8 = 8 + 6 (same result, easier to count from 8)

Step 2: Use counting on from the larger number

Start at 8, count 6 more: 9, 10, 11, 12, 13, 14

Step 3: Verify with a known fact

Think: 5 + 5 = 10, so 6 + 8 = (5 + 1) + (5 + 3) = 10 + 4 = 14

Step 4: Confirm the answer

Count all: 6 + 8 = 14

6 + 8 = 14
Final answer:

6 + 8 = 14

Applied rules:

• Commutative Property: Order doesn't matter in addition

• Fact Families: Related facts help solve problems

• Multiple Strategies: Use different methods to verify

Key Addition Concepts and Strategies for 1st Grade Students
a + b = c
Addition Fundamentals
Key definitions:

Addition: Combining two or more numbers to find their total amount

Sum: The result obtained when numbers are added together

Addends: The numbers that are being added together

Number Bonds: Pairs of numbers that combine to make another number

Complete methodology:
  1. Visualize the Problem: Use objects, fingers, or drawings to represent numbers
  2. Choose a Strategy: Counting all, counting on, making ten, or using doubles
  3. Execute the Strategy: Follow the chosen method step-by-step
  4. Verify the Answer: Check using a different method or counting back
Tip 1: Always start counting from the larger number to be more efficient.
Tip 2: Practice "making ten" with number bonds: 1+9, 2+8, 3+7, 4+6, 5+5.
Tip 3: Memorize doubles facts (1+1, 2+2, 3+3, etc.) as they're building blocks.
Tip 4: Use a number line to physically move forward when adding.
Common errors: Starting from 1 instead of the larger number, miscounting, forgetting to count the starting number, not understanding the concept of combining.
Success strategies: Use multiple representations (objects, drawings, number lines), practice regularly, check work with a different method, build confidence with simpler problems first.
Addition Properties to Remember:

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

• Associative Property: (a + b) + c = a + (b + c) (grouping doesn't matter)

• Identity Property: a + 0 = a (adding zero changes nothing)

Addition Strategies for Within 20:

• Counting On: Start with the larger number and count up

• Making Ten: Break apart numbers to make 10 first

• Doubles Plus/Minus One: Use known doubles facts

• Number Line: Jump forward on a number line

• Facts to 20: Memorize basic addition facts

Questions & Answers

Question: I'm confused about when to use the "making ten" strategy versus counting on. Can you explain when to use each method?

Answer: Great question! Here's how to choose the right strategy:

  • Counting On: Best when one number is small (1, 2, or 3) and you're comfortable counting up. Example: 14 + 2 → count 15, 16.
  • Making Ten: Best when one number is close to 10 or when the numbers can easily combine to make 10. Example: 8 + 6 → take 2 from 6 to make 10 + 4 = 14.

The key is recognizing number relationships. If you see 9 + 5, think "I need 1 more to make 10 with 9," so it becomes 10 + 4 = 14. This is faster than counting 9, 10, 11, 12, 13, 14.

Try both methods initially to see which feels easier for each problem. With practice, you'll develop intuition for which strategy works best!

Question: My child gets frustrated with addition and counts from 1 every time. How can I help them learn to start from the larger number?

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

  • Use Visual Aids: Show two groups of objects, circle the larger group, and say "Let's start counting from here."
  • Physical Movement: Have your child touch the larger number first, then count the rest.
  • Make it Fun: Call the larger number "the big number" and make a big gesture when pointing to it.
  • Practice Comparison: Before adding, ask "Which number is bigger?" to build number sense.

Start with very simple problems where the difference is obvious (like 2 + 9), and gradually work up. Celebrate when they remember to start from the larger number!

Be patient - this skill develops over time with consistent practice and positive reinforcement.

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

Answer: That's a smart question! Here's why different methods help:

  • Speed: Counting on is faster than counting all (8 + 3 is quicker as 9, 10, 11 than 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11).
  • Bigger Numbers: Counting all becomes hard with larger numbers (try counting 15 + 6 objects!)
  • Understanding: Different methods help you understand how numbers work together.
  • Flexibility: Some problems are easier with one method, others with another.

Think of it like having different tools - sometimes you need a hammer, sometimes a screwdriver. Learning different addition methods makes you a stronger math problem-solver!

As you practice, you'll naturally choose the method that works best for each problem.