Complete Guide to Addition Within 20 Strategies in Grade 1

Master all addition within 20 strategies: counting on, making ten, doubles facts, and number line methods with detailed examples and visual representations.

Addition Within 20 Strategies Overview
1 Counting On Strategy
Counting On Strategy
Start with the larger number and count up by the smaller number. Example: 7 + 3 = 7, 8, 9, 10
Definition:

Counting On: A strategy where you start with the larger number in an addition problem and count up by the smaller number.

Counting On Method:
  1. Identify the larger number in the addition problem
  2. Start counting from that number (don't count it again)
  3. Count up by the smaller number of times
  4. The final number you land on is your answer
Problem
7 + 3
Strategy
Count on from 7
Solution
7, 8, 9, 10
Step 1: Identify the larger number

Between 7 and 3, 7 is the larger number

Step 2: Start counting from the larger number

Begin counting from 7: 7 (don't count this again)

Step 3: Count up by the smaller number

Count 3 more: 8, 9, 10

Step 4: Identify the final answer

The last number counted is 10, so 7 + 3 = 10

Step 5: Verify the answer

Check: 7 + 3 = 10, which is less than 20, so it's within our range

7 + 3 = 10
Final answer:

7 + 3 = 10 using the counting on strategy.

Key Rules:

• Always start with the larger number to make counting faster

• Don't count the starting number again - only count up

• This strategy works best when the second number is small (1-5)

2 Making Ten Strategy
Making Ten Strategy
Adjust numbers to create sums of 10, which are easier to work with. Example: 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14
Definition:

Making Ten: A strategy that uses the fact that adding to 10 is easier, so we adjust one number to make 10 and add the remainder.

Problem
8 + 6
Strategy
Make 10 from 8
Solution
8 + 2 + 4 = 14
Step 1: Identify how much is needed to make 10

From 8, we need 2 more to make 10

Step 2: Take that amount from the second number

Take 2 from 6, leaving 4

Step 3: Add to make 10 and then add the remainder

8 + 2 = 10, then add the remaining 4: 10 + 4 = 14

Step 4: Write the complete solution

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

Step 5: Verify the answer

Check: 8 + 6 = 14, which is less than 20, so it's within our range

8 + 6 = 14
Final answer:

8 + 6 = 14 using the making ten strategy.

Key Rules:

• Works best when one number is close to 10 (8, 9)

• Memorize pairs that make 10: 1+9, 2+8, 3+7, 4+6, 5+5

• Adjust numbers strategically to create easier sums

3 Doubles Facts Strategy
Doubles Facts Strategy
Use known doubles facts (like 5+5=10) and adjust. Example: 5 + 6 = 5 + 5 + 1 = 11
Definition:

Doubles Facts: Addition facts where both numbers are the same (like 2+2, 5+5, 8+8), which are often memorized first.

Problem
5 + 6
Strategy
Use 5+5 and add 1
Solution
5 + 5 + 1 = 11
Step 1: Identify the closest doubles fact

5 + 5 = 10 is the closest doubles fact to 5 + 6

Step 2: Determine the difference

6 is 1 more than 5, so we need to add 1 more

Step 3: Apply the doubles plus one strategy

5 + 6 = 5 + 5 + 1 = 10 + 1 = 11

Step 4: Write the complete solution

5 + 6 = 11 using doubles facts

Step 5: Verify the answer

Check: 5 + 6 = 11, which is less than 20, so it's within our range

5 + 6 = 11
Final answer:

5 + 6 = 11 using the doubles facts strategy.

Key Rules:

• Memorize doubles facts from 1+1 to 10+10

• Use doubles ± 1 for numbers that are close to each other

• Build on known facts to solve unknown problems

Addition Within 20: Comprehensive Strategy Guide
\(a + b = c\) where \(a + b ≤ 20\)
Addition Within 20
Commutative Property
\(a + b = b + a\)
Order doesn't matter
Identity Property
\(a + 0 = a\)
Adding zero changes nothing
Associative Property
\((a + b) + c = a + (b + c)\)
Grouping doesn't matter
Key definitions:

Addition: Combining two or more numbers to find their total

Sum: The result of adding numbers together

Strategy: A method or technique used to solve mathematical problems efficiently

Counting On: Starting with one number and counting up by another number

Making Ten: Adjusting numbers to create sums of 10 for easier calculation

Doubles Facts: Addition facts where both numbers are identical

Complete Addition Strategies:
  1. Counting On: Start with the larger number and count up
  2. Making Ten: Adjust numbers to create sums of 10
  3. Using Doubles: Know doubles facts and adjust (+1, +2)
  4. Number Line: Jump forward on a number line
  5. Visual Models: Use drawings or manipulatives
  6. Decomposition: Break apart numbers to make addition easier
Tip 1: Start with the larger number when counting on to make addition faster.
Tip 2: Memorize doubles facts (1+1 through 10+10) as building blocks.
Tip 3: Use the "making ten" strategy when one number is 8 or 9.
Tip 4: Practice number bonds that make 10 (1+9, 2+8, 3+7, 4+6, 5+5).
Tip 5: Use fingers or manipulatives to visualize addition problems.
Common errors: Counting the starting number again, misapplying strategies, forgetting to check answers.
Success strategies: Practice regularly, use multiple methods, verify answers.
Important Properties:

• Commutative Property: Order doesn't affect the sum

• Identity Property: Adding zero keeps the number the same

• Associative Property: Grouping doesn't change the sum

• Compensation: Adjusting numbers while maintaining the same sum

Advanced Addition Strategies & Practice
4 Number Line Strategy
Number Line Strategy
Use a number line to jump forward. Example: 9 + 4 → Start at 9, jump 4 spaces → Land on 13
Definition:

Number Line Strategy: A visual method where you represent addition as jumps forward on a number line.

Problem
9 + 4
Strategy
Jump on number line
Solution
9 → 10 → 11 → 12 → 13
Step 1: Start at the first number

Begin at 9 on the number line

Step 2: Make jumps equal to the second number

Jump forward 4 spaces: 9 → 10 → 11 → 12 → 13

Step 3: Identify the landing point

You land on 13, which is the answer

Step 4: Verify the answer

Check: 9 + 4 = 13, which is less than 20, so it's within our range

9 + 4 = 13
Final answer:

9 + 4 = 13 using the number line strategy.

Key Rules:

• Start at the first number on the number line

• Jump forward the number of spaces equal to the second number

• The landing point is your answer

5 Decomposition Strategy
Decomposition Strategy
Break apart numbers into tens and ones. Example: 13 + 6 = (10 + 3) + 6 = 10 + 9 = 19
Definition:

Decomposition: Breaking numbers into smaller parts (tens and ones) to make addition easier.

Problem
13 + 6
Strategy
Decompose 13
Solution
(10 + 3) + 6 = 19
Step 1: Break apart the larger number

13 = 10 + 3 (tens and ones)

Step 2: Add the ones to the second number

3 + 6 = 9

Step 3: Add the tens to the result

10 + 9 = 19

Step 4: Write the complete solution

13 + 6 = (10 + 3) + 6 = 10 + (3 + 6) = 10 + 9 = 19

Step 5: Verify the answer

Check: 13 + 6 = 19, which is less than 20, so it's within our range

13 + 6 = 19
Final answer:

13 + 6 = 19 using the decomposition strategy.

Key Rules:

• Separate tens and ones to simplify addition

• Add the ones first then add to the tens

• This strategy helps understand place value

Addition Within 20: Complete Learning Summary
\(a + b = c\) where \(a + b ≤ 20\)
Addition Within 20
Key definitions:

Addition: The mathematical operation of combining two or more numbers to find their total sum.

Sum: The result obtained when numbers are added together.

Strategy: A planned method or approach used to solve mathematical problems efficiently.

Counting On: A mental math strategy where you start with the larger number and count up by the smaller number.

Making Ten: A strategy that uses number combinations that sum to 10 as a foundation for solving other problems.

Doubles Facts: Addition facts where both addends are the same number (e.g., 3+3, 7+7).

Complete Problem-Solving Process:
  1. Recognize the Problem: Identify that addition is needed
  2. Choose a Strategy: Select the most efficient method for the numbers involved
  3. Execute the Strategy: Apply the chosen method step by step
  4. Verify the Answer: Check that the answer is reasonable and within the range
  5. Reflect: Consider if another strategy might be more efficient next time
Tip 1: Practice all strategies regularly to develop flexibility in problem-solving.
Tip 2: Some problems are easier with specific strategies - learn to recognize which strategy works best.
Tip 3: Visual aids like number lines and ten frames help cement understanding.
Tip 4: Regular practice with varied problems builds fluency and confidence.
Common challenges: Transitioning from counting all to counting on, applying the right strategy, memorizing basic facts.
Success keys: Consistent practice, understanding multiple strategies, connecting to real-world applications.
Essential Addition Facts to Memorize:

• Doubles: 1+1 to 10+10

• Near Doubles: 1+2, 2+3, 3+4, etc.

• Making Ten: 1+9, 2+8, 3+7, 4+6, 5+5

• Plus One: Any number + 1

• Plus Two: Any number + 2

Visual Representation: Addition Strategy Effectiveness
Addition Strategy Effectiveness Chart
Different approaches to solve addition problems within 20:
Counting On, Making Ten, Using Doubles, Number Line, Decomposition

Analysis: The chart shows different addition strategies and their effectiveness for solving problems within 20.

  • Counting On: Most effective for small second numbers (1-3)
  • Making Ten: Most effective when one number is 8 or 9
  • Using Doubles: Most effective for consecutive numbers
  • Number Line: Good visual tool for all problems
  • Decomposition: Builds understanding of place value

Questions & Answers

Question: How do I help my first-grader decide which addition strategy to use for different problems? They seem to struggle with choosing the right method.

Answer: This is a common challenge! Here's how to help students choose the right strategy:

  • Counting On: Best when the second number is small (1-3). Example: 7 + 2, 12 + 3
  • Making Ten: Best when one number is 8 or 9. Example: 8 + 5, 9 + 4
  • Using Doubles: Best when numbers are the same or consecutive. Example: 6 + 6, 7 + 8
  • Number Line: Good for visual learners and all problems
  • Decomposition: Helpful for problems with teen numbers. Example: 14 + 5

Start by explicitly teaching each strategy separately. Then, provide mixed practice where students identify which strategy would work best for each problem. Over time, they'll develop intuition for choosing the most efficient method.

Encourage them to try different strategies and compare which feels easiest for them. The goal is flexibility, not rigid adherence to one method.

Question: My child still counts on their fingers for every addition problem. Should I discourage this and push them toward mental math strategies?

Answer: Finger counting is actually a positive sign! It shows your child is actively trying to solve problems. Don't discourage it completely, but gradually introduce more efficient strategies:

  • Accept finger counting as a transitional tool
  • Introduce mental strategies alongside finger counting
  • Compare efficiency: "Let's try counting on from the bigger number - is that faster?"
  • Gradually encourage mental math for easier problems
  • Celebrate progress when they use strategies without fingers

Finger counting provides a concrete foundation. As children gain confidence with strategies like counting on or making ten, they'll naturally move away from finger counting. The key is to offer better tools while acknowledging that finger counting is a valid problem-solving approach.

Focus on understanding first, then efficiency. Rushing away from finger counting too early can cause anxiety and hinder conceptual understanding.

Question: Why do I need to learn so many different ways to add? Isn't it enough to just count?

Answer: Great question! Learning different ways to add is like having different tools in a toolbox:

  • Some problems are easier with certain strategies: Like how it's faster to do 9 + 4 by thinking "9 + 1 = 10, then 10 + 3 = 13" than counting 9, 10, 11, 12, 13
  • They help your brain grow stronger: Just like exercise makes your muscles stronger, using different strategies makes your math brain stronger
  • You can check your work: If you get the same answer using two different strategies, you know it's probably right
  • Some strategies work better for different types of problems: Like how doubles facts (5+5) are really fast to remember

Think of it like having different routes to get to school - sometimes one path is faster, sometimes another. Having choices makes you a more flexible thinker!

Start with the strategy that feels easiest, then try others. Soon you'll have a favorite that works best for you!