Adding Numbers Within 20

Master adding numbers within 20: strategies, visual representations, and practice for 1st grade students.

Adding Numbers Within 20 Exercises
1 Counting On Strategy
Exercise 1
\(8 + 5 = ?\)
Definition:

Counting on: Starting with the larger number and counting up

Solution method:
  1. Start with the larger number (8)
  2. Count up 5 more: 9, 10, 11, 12, 13
  3. The answer is 13
Start with
\(8\)
Count up 5
\(9, 10, 11, 12, 13\)
Step 1: Identify the larger number

We start with 8 (the larger number)

Step 2: Count up from the larger number

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

Step 3: Identify the final number

The last number counted is the answer

\(8 + 5 = 13\)
Final answer:

8 + 5 = 13

Applied rules:

• Counting on strategy: Start with the larger number

• Sequential counting: Count each number in sequence

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

2 Making Ten Strategy
Exercise 2
\(9 + 4 = ?\)
Definition:

Making ten: Breaking apart one number to make 10 with the other

Break apart 4
\(9 + 1 + 3\)
Make 10
\(10 + 3 = 13\)
Step 1: Look for numbers close to 10

9 is close to 10, needing 1 more

Step 2: Break apart the second number

4 = 1 + 3 (so we can make 10 with 9)

Step 3: Add to make 10, then add remainder

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

Step 4: Calculate the final answer

10 + 3 = 13

\(9 + 4 = 13\)
Final answer:

9 + 4 = 13

Applied rules:

• Making ten strategy: Use 10 as a benchmark

• Decomposition: Break apart numbers strategically

• Associative property: Group numbers differently

3 Doubles Plus One
Exercise 3
\(6 + 7 = ?\)
Definition:

Doubles plus one: Using a doubles fact and adding one more

Double fact
\(6 + 6 = 12\)
Plus one more
\(12 + 1 = 13\)
Step 1: Identify the doubles fact

6 + 7 is close to 6 + 6

Step 2: Recall the doubles fact

6 + 6 = 12

Step 3: Add the extra one

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

Step 4: Calculate the final answer

12 + 1 = 13

\(6 + 7 = 13\)
Final answer:

6 + 7 = 13

Applied rules:

• Doubles plus one strategy: Use known doubles facts

• Near doubles: Numbers that differ by 1

• Pattern recognition: See relationships between numbers

More Addition Within 20 Practice
4 Commutative Property
Exercise 4
\(5 + 8 = ?\)
Definition:

Commutative property: Order of addends doesn't change the sum

Rearrange
\(8 + 5\)
Count on
\(9, 10, 11, 12, 13\)
Step 1: Use commutative property

5 + 8 = 8 + 5 (start with the larger number)

Step 2: Count up from the larger number

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

Step 3: Identify the final number

The last number counted is the answer

Step 4: Calculate the final answer

5 + 8 = 13

\(5 + 8 = 13\)
Final answer:

5 + 8 = 13

Applied rules:

• Commutative property: a + b = b + a

• Efficiency: Start with the larger number

• Counting on: Sequential counting strategy

5 Decomposition Strategy
Exercise 5
\(7 + 6 = ?\)
Definition:

Decomposition: Breaking numbers into parts to make addition easier

Break apart 6
\(7 + 3 + 3\)
Make 10
\(10 + 3 = 13\)
Step 1: Look for parts that make 10

7 needs 3 more to make 10

Step 2: Break apart the second number

6 = 3 + 3 (so we can make 10 with 7)

Step 3: Add to make 10, then add remainder

(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 strategy: Break numbers into helpful parts

• Make 10 strategy: Use 10 as a benchmark number

• Associative property: Group numbers differently

6 Number Line Strategy
Exercise 6
\(4 + 9 = ?\)
Definition:

Number line: Visual tool to represent addition as movement

Start at 4
\(4\)
Jump 9 places
\(4 \rightarrow 13\)
Step 1: Start at the first number

Begin at 4 on the number line

Step 2: Move forward the second number

Move 9 places to the right

Step 3: Identify the landing spot

The number where you land is the answer

Step 4: Calculate the final answer

4 + 9 = 13

\(4 + 9 = 13\)
Final answer:

4 + 9 = 13

Applied rules:

• Number line strategy: Visual representation of addition

• Forward movement: Addition moves right on number line

• Sequential counting: Each jump represents one added

Visual Infographic: Adding Numbers Within 20
➕
🔢
🎯
💡

Adding Within 20

Strategies and Methods

8 + 5 = 13

Counting On: Start at 8, count 5 more

9 + 4 = 13

Making 10: 9 + 1 = 10, then 10 + 3 = 13

👉
Count On
🔟
Make 10
🎲
Doubles
↔️
Switch
Start Big
Always start with the larger number
Make 10
Use 10 as a benchmark
Check Sum
Never exceeds 20
💪

Practice Makes Perfect!

Summary: Adding Numbers Within 20
Complete Summary and Study Guide

This section provides a comprehensive overview of adding numbers within 20, including definitions, methods, strategies, and key concepts for 1st grade students.

Definitions

Addition: Combining numbers to find a total or sum.

Within 20: Problems where the answer is 20 or less.

Counting On: Starting with the larger number and counting up.

Making Ten: Breaking apart numbers to make 10 with one addend.

Core Rules

• Always start with the larger number when counting on

• Use 10 as a benchmark number for easier addition

• The sum of two numbers within 20 will never exceed 20

• Order doesn't matter (commutative property)

Addition Strategies

Counting On: Start with the larger number and count up

Making Ten: Break apart numbers to make 10 first

Doubles Plus One: Use known doubles facts

Number Line: Visual representation of addition

Examples

Counting On: 8 + 5 = start at 8, count 5: 9, 10, 11, 12, 13

Making Ten: 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13

Doubles Plus One: 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

Commutative: 5 + 8 = 8 + 5 = 13

Tips & Tricks

• Start with the larger number to minimize counting

• Practice doubles facts regularly (they help with near doubles)

• Use fingers or drawings if needed initially

• Look for numbers that are close to 10

Common Mistakes

• Starting to count from 1 instead of the larger number

• Miscounting when counting on

• Not recognizing opportunities to make 10

• Forgetting that order doesn't matter

Questions & Answers

Question: What does "within 20" mean? Does that mean the biggest number I can add is 20?

Answer: Great question! "Within 20" means that the answer (or sum) to your addition problem must be 20 or less.

For example:

  • 8 + 7 = 15 (this is within 20 because 15 is less than 20)
  • 12 + 6 = 18 (this is within 20 because 18 is less than 20)
  • But 15 + 8 = 23 (this is NOT within 20 because 23 is more than 20)

You can add numbers that are themselves bigger than 10, as long as the total doesn't go over 20. So you could add 11 + 8 = 19, which is within 20.

Think of "within 20" like a ceiling - nothing goes above 20!

Question: My child is still counting on their fingers for addition within 20. Should I be concerned, and how can I help them move beyond finger counting?

Answer: Finger counting is completely normal and appropriate for 1st graders! Don't worry - it shows your child is developing number sense.

Here are strategies to help transition from finger counting:

  • Use visual aids: Number lines, ten frames, or dot cards
  • Practice mental math: Start with very easy problems and gradually increase
  • Teach efficient strategies: Counting on from the larger number, making ten
  • Build fluency: Regular practice with doubles and near doubles
  • Gradual reduction: Encourage "just trying it in your head" for easier problems

Focus on building number relationships and strategies rather than rushing to eliminate finger counting. The mental strategies will develop naturally with practice and exposure to different approaches.

It typically takes several months of consistent practice to reduce reliance on finger counting.

Question: Why do we learn to "make 10"? Isn't it easier to just count everything?

Answer: Great question! Making 10 is actually much faster and easier once you get good at it!

Let's compare:

For 9 + 4:

  • Counting all: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 (13 counts!)
  • Making 10: 9 + 1 = 10, then 10 + 3 = 13 (just 2 steps!)

Making 10 is like having a shortcut. Also, knowing 10 facts really well helps you with bigger numbers later, like 19 + 4 or 29 + 4.

Think of 10 as a "friendly number" that makes addition easier. Once you practice enough, making 10 becomes automatic and much faster than counting everything!

It's like learning a secret code that makes math faster!