Addition Practice Within 20: Complete Guide for 1st Graders

Master addition within 20 through 5 detailed exercises covering counting strategies, number bonds, mental math, and visual representations.

Solution: Exercises 1 to 3
1 Counting Strategy
Exercise 1
Solve: 8 + 5 = ?
Use counting strategy starting from 8
Definition:

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

Addition method:
  1. Identify the larger number (8 in this case)
  2. Start counting from that number
  3. Count up by the amount of the smaller number (5)
  4. Keep track of each count
Problem
8 + 5
Counting
8, 9, 10, 11, 12, 13
Answer
13
Step 1: Identify larger number

Between 8 and 5, 8 is larger, so we start counting from 8

Step 2: Count up 5 more numbers

8 → 9 → 10 → 11 → 12 → 13 (that's 5 counts)

Step 3: Final result

We counted 5 numbers starting from 8, ending at 13

8 + 5 = 13
Final answer:

8 + 5 = 13

Applied rules:

• Counting Rule: Always start from the larger number

• Sequential Counting: Count one number at a time

• Tracking: Keep count of how many numbers you've added

2 Number Bonds
Exercise 2
Solve: 7 + 6 = ?
Break down using number bonds to make 10
Definition:

Number Bonds: Breaking numbers to make 10, then adding the remainder

Problem
7 + 6
Make 10
7 + 3 = 10
Remainder
6 - 3 = 3
Total
10 + 3 = 13
Step 1: See how much needed to make 10

From 7, we need 3 more to make 10 (7 + 3 = 10)

Step 2: Break down the second number

6 = 3 + 3 (the 3 goes with 7 to make 10, leaving 3)

Step 3: Add the remaining part

10 + 3 = 13

7 + 6 = 13
Final answer:

7 + 6 = 13

Applied rules:

• Make 10 Rule: Look for combinations that make 10

• Decomposition: Break numbers into parts

• Compensation: Adjust and balance the equation

3 Doubles Plus One
Exercise 3
Solve: 6 + 7 = ?
Use doubles fact: 6 + 6 = 12
Definition:

Doubles Plus One: When numbers are consecutive, use the smaller double and add 1

Problem
6 + 7
Doubles Fact
6 + 6 = 12
Add One More
12 + 1 = 13
Step 1: Recognize consecutive numbers

6 and 7 are consecutive (one apart)

Step 2: Use the smaller double

6 + 6 = 12 (memorized doubles fact)

Step 3: Add the difference

Since 7 is one more than 6, add 1 to the doubles answer

Step 4: Final calculation

12 + 1 = 13

6 + 7 = 13
Final answer:

6 + 7 = 13

Applied rules:

• Doubles Rule: Memorize doubles facts (5+5, 6+6, etc.)

• Consecutive Numbers: For n+(n+1), use 2n+1

• Pattern Recognition: Spot number relationships

Addition Strategies and Methods
Counting: 8 + 5 = 8,9,10,11,12,13 = 13
Counting Strategy
Make 10
7 + 6 = 7 + 3 + 3 = 10 + 3 = 13
Number Bonds Method
Doubles + 1
6 + 7 = 6 + 6 + 1 = 12 + 1 = 13
Consecutive Numbers
Doubles
5 + 5 = 10, 6 + 6 = 12
Memorized Facts
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

Addition strategies:
  1. Counting On: Start with the larger number and count up
  2. Make 10: Break numbers to form 10, then add remainder
  3. Doubles: Memorize doubles facts (5+5, 6+6, etc.)
  4. Doubles Plus One: Use doubles for consecutive numbers
  5. Number Line: Move forward on a visual number line
Tip 1: Always start counting from the larger number.
Tip 2: Memorize doubles facts - they make many problems easier.
Tip 3: Making 10 is often the fastest way to solve addition.
Tip 4: Draw dots or use fingers if you need to visualize.
Common errors: Starting from 1 instead of the larger number, miscounting, forgetting to add the final count.
Practice focus: Master doubles facts, practice making 10, work on counting accuracy.
Important addition facts to know:

• 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

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

• Commutative Property: 3+5 = 5+3 (order doesn't matter)

• Identity Property: Any number + 0 = that number

• Adding 1: Any number + 1 = the next number

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

Making 10 Strategy: Break apart one number to combine with the other to make 10

Problem
9 + 4
Make 10
9 + 1 = 10
Remainder
4 - 1 = 3
Total
10 + 3 = 13
Step 1: See how much needed to make 10

From 9, we need 1 more to make 10 (9 + 1 = 10)

Step 2: Break apart the second number

4 = 1 + 3 (the 1 goes with 9 to make 10, leaving 3)

Step 3: Add the remaining part to 10

10 + 3 = 13

9 + 4 = 13
Final answer:

9 + 4 = 13

Applied rules:

• Make 10 Rule: Look for combinations that make 10

• Decomposition: Break numbers into parts

• Associative Property: Grouping doesn't change the sum

5 Mental Math with Patterns
Exercise 5
Solve: 8 + 6 = ?
Use pattern recognition and known facts
Definition:

Mental Math Patterns: Using known facts and patterns to solve quickly

Problem
8 + 6
Known Fact
8 + 2 = 10
Remaining
6 - 2 = 4
Total
10 + 4 = 14
Step 1: Recognize how to make 10

8 needs 2 more to make 10 (8 + 2 = 10)

Step 2: Break 6 into 2 and 4

6 = 2 + 4 (use 2 to make 10 with 8)

Step 3: Combine 10 with remaining 4

10 + 4 = 14

Step 4: Verify the result

8 + 6 = 14, which matches our pattern recognition

8 + 6 = 14
Final answer:

8 + 6 = 14

Applied rules:

• Pattern Recognition: Identify familiar number relationships

• Breaking Down: Decompose numbers strategically

• Building Up: Use known facts to reach the answer

Addition Properties and Key Facts
Commutative: a + b = b + a
Addition Property
Key definitions:

Addition: The operation of combining quantities

Sum: The total when numbers are added

Addend: Each number being added

Complete methodology:
  1. Look at the numbers: Identify if they are doubles, consecutive, or close to 10
  2. Choose the best strategy: Counting, making 10, using doubles, or mental math
  3. Apply the method: Follow the steps of your chosen strategy
  4. Verify the result: Check your answer using a different method
Tip 1: Practice doubles facts daily - they're the foundation for many addition problems.
Tip 2: Making 10 is usually the fastest method for numbers that add up close to 10.
Tip 3: Use your fingers or draw pictures if you need to visualize the addition.
Tip 4: Always check your answer by counting or using a different method.
Common errors: Starting from 1 instead of larger number, miscounting, forgetting to add final number.
Success patterns: Master doubles, practice making 10, develop number sense.
Addition facts to memorize:

• 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

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

• Adding 1: 1+1=2, 2+1=3, 3+1=4, 4+1=5, 5+1=6, 6+1=7, 7+1=8, 8+1=9, 9+1=10, 10+1=11

• Commutative Property: 3+5 = 5+3 (order doesn't matter)

• Identity Property: Any number + 0 = that number

Questions & Answers

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

Answer: Great question! Starting from the bigger number is a smart shortcut that saves time and reduces mistakes.

Example comparison:

  • To solve 8 + 5 by starting from 1: Count 1,2,3,4,5,6,7,8,9,10,11,12,13 (13 counts!)
  • To solve 8 + 5 by starting from 8: Count 8,9,10,11,12,13 (just 5 counts!)

Starting from the bigger number means you only count up by the amount of the smaller number. It's like taking a shortcut - you get to the same answer faster and with less chance of losing track!

Think of it like climbing stairs - if you're on step 8 and need to go up 5 more steps, you don't go back to step 1, you just climb 5 more steps from where you are!

Question: My child is struggling with making 10. How can I help them understand this strategy better?

Answer: The "making 10" strategy is foundational for mental math! Here's how to teach it:

Visual approach:

  • Use 10 fingers - show 8 fingers up, ask "How many more to make 10?" (Answer: 2)
  • Use counters or small toys to physically group numbers
  • Create a "ten frame" (grid of 10 boxes) to see how many spaces are filled vs. empty

Practice patterns:

  • Focus on pairs that make 10: 1+9, 2+8, 3+7, 4+6, 5+5
  • Play games like "What goes with 7 to make 10?" (Answer: 3)
  • Use flashcards with these pairs

Once they know these "partners of 10," solving 8 + 5 becomes: "8 needs 2 more to make 10, so I take 2 from the 5, leaving 3. That gives me 10 + 3 = 13."

Question: Why do we learn doubles facts? They seem easy but I don't see why they're important.

Answer: Doubles facts are super important because they're building blocks for harder problems!

Examples of how doubles help:

  • Doubles + 1: If you know 6+6=12, then 6+7 is just one more: 13!
  • Doubles - 1: If you know 5+5=10, then 5+4 is just one less: 9!
  • Quick recognition: When you see 8+8, you instantly know it's 16

Think of doubles like secret codes - once you know them, you can solve many more problems quickly. If someone asks you 7+8, you can think "7+7=14, so 7+8 is 15!"

It's like having a calculator in your head for these special number pairs!