Solved Exercises on Addition Within 20 Story Problems in Grade 1

Master addition within 20 story problems: understanding word problems, identifying key words, and solving step-by-step through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Apples Story Problem
Exercise 1
Sarah has 8 red apples. Her mom gives her 5 green apples. How many apples does Sarah have altogether?
Definition:

Addition Story Problems: Word problems that require combining two or more quantities to find the total amount.

Problem Solving Method:
  1. Read the problem carefully - Understand what is being asked
  2. Identify key words - Look for words like "altogether", "total", "sum", "more", "added"
  3. Find the numbers - Identify the quantities to add
  4. Write the number sentence - Create the addition equation
  5. Solve the problem - Add the numbers together
  6. Check your answer - Make sure it makes sense
Problem
Sarah has 8 red apples + 5 green apples
Number Sentence
8 + 5 = ?
Solution
8 + 5 = 13
Step 1: Identify what we know

Sarah starts with 8 red apples and gets 5 more green apples

Step 2: Identify what we need to find

We need to find the total number of apples (altogether)

Step 3: Identify the operation

The key word "altogether" tells us to add the two amounts together

Step 4: Write the number sentence

8 + 5 = 13

Step 5: Solve using counting strategies

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

Step 6: Check the answer

8 + 5 = 13, which is less than 20, so it's reasonable

Sarah has 13 apples altogether
Final answer:

Sarah has 13 apples altogether.

Applied rules:

• Key Words: "altogether" signals addition

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

• Make Ten Strategy: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13

2 Fish Tank Problem
Exercise 2
There are 12 goldfish in a tank. Tom adds 6 more goldfish to the tank. How many goldfish are in the tank now?
Definition:

Addition Story Problems: Word problems that involve combining groups or adding to a quantity.

Problem
12 goldfish + 6 more goldfish
Number Sentence
12 + 6 = ?
Solution
12 + 6 = 18
Step 1: Identify the starting amount

There are 12 goldfish in the tank initially

Step 2: Identify what is added

Tom adds 6 more goldfish to the tank

Step 3: Identify the key word

"Adds" indicates we need to perform addition

Step 4: Write the number sentence

12 + 6 = 18

Step 5: Solve using the make ten strategy

Break 6 into 8 and -2: 12 + 6 = 12 + 8 - 2 = 20 - 2 = 18

Or think: 12 + 6 = (10 + 2) + 6 = 10 + 8 = 18

Step 6: Verify the answer

12 + 6 = 18, which is less than 20, so it's within our range

There are 18 goldfish in the tank now
Final answer:

There are 18 goldfish in the tank now.

Applied rules:

• Key Words: "adds" signals addition

• Decomposition: Breaking numbers to make tens

• Place Value: Understanding that 12 = 10 + 2

3 Books Story Problem
Exercise 3
Emma has 9 books on her shelf. She gets 7 more books from the library. How many books does Emma have in total?
Definition:

Addition Story Problems: Real-world scenarios that require finding the sum of two or more quantities.

Problem
9 books + 7 more books
Number Sentence
9 + 7 = ?
Solution
9 + 7 = 16
Step 1: Identify the initial amount

Emma starts with 9 books on her shelf

Step 2: Identify the additional amount

She gets 7 more books from the library

Step 3: Recognize the key word

"Total" indicates we need to add the two amounts

Step 4: Write the number sentence

9 + 7 = 16

Step 5: Solve using the make ten strategy

Take 1 from 7 to make 9 into 10: 9 + 7 = (9 + 1) + 6 = 10 + 6 = 16

Step 6: Confirm the answer

9 + 7 = 16, which is less than 20, so it's within our limit

Emma has 16 books in total
Final answer:

Emma has 16 books in total.

Applied rules:

• Key Words: "total" signals addition

• Make Ten Strategy: Adjust numbers to make tens

• Compensation: Adding and subtracting the same amount

Addition Within 20: Rules and Methods
\(a + b = c\)
Addition Formula
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

Story Problem: A real-world situation expressed in words requiring mathematical operations

Addition Strategies:
  1. Counting On: Start with the larger number and count up
  2. Make Ten: Adjust numbers to create easier sums
  3. Using Doubles: Know doubles facts (5+5, 6+6) and adjust
  4. Number Line: Jump forward on a number line
  5. Finger Counting: Use fingers to represent numbers
Tip 1: Look for key words like "total", "altogether", "sum", "more", "added", "combined".
Tip 2: Start counting with the larger number to make addition faster.
Tip 3: Use the "make ten" strategy when one number is close to 10.
Tip 4: Always check if your answer is reasonable and less than 20.
Common errors: Misreading key words, counting incorrectly, forgetting to add all parts of the problem.
Success tips: Draw pictures, use manipulatives, read the problem twice, circle important numbers.
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

• Making Tens: Adjust numbers to create easier additions

Solution: Exercises 4 to 5
4 Pets Story Problem
Exercise 4
Jake has 11 dogs at his house. His friend brings 8 more dogs to play. How many dogs are playing together?
Definition:

Addition Story Problems: Problems that involve combining groups of objects or people.

Problem
11 dogs + 8 more dogs
Number Sentence
11 + 8 = ?
Solution
11 + 8 = 19
Step 1: Identify the starting number

Jake has 11 dogs at his house initially

Step 2: Identify the additional number

His friend brings 8 more dogs to play

Step 3: Find the key phrase

"Playing together" suggests we need to combine both groups

Step 4: Write the number sentence

11 + 8 = 19

Step 5: Solve using decomposition strategy

Break 8 into 9 and -1: 11 + 8 = 11 + 9 - 1 = 20 - 1 = 19

Or use the fact that 11 + 8 = (10 + 1) + 8 = 10 + 9 = 19

Step 6: Verify the answer

11 + 8 = 19, which is less than 20, so it's within our limit

19 dogs are playing together
Final answer:

19 dogs are playing together.

Applied rules:

• Combination: "Playing together" means combining groups

• Decomposition: Breaking numbers to make calculations easier

• Place Value: Understanding that 11 = 10 + 1

5 Stickers Story Problem
Exercise 5
Mia has 14 stickers in her collection. She buys 6 more stickers at the store. How many stickers does Mia have now?
Definition:

Addition Story Problems: Problems that model real-life situations involving combining quantities.

Problem
14 stickers + 6 more stickers
Number Sentence
14 + 6 = ?
Solution
14 + 6 = 20
Step 1: Identify the initial amount

Mia starts with 14 stickers in her collection

Step 2: Identify the amount added

She buys 6 more stickers at the store

Step 3: Recognize the action

Buying more stickers means adding to her collection

Step 4: Write the number sentence

14 + 6 = 20

Step 5: Solve using the make ten strategy

Take 6 from 14 to make 10: 14 + 6 = (10 + 4) + 6 = 10 + 10 = 20

Or think: 14 + 6 = 14 + 6 = 20 (since 4 + 6 = 10)

Step 6: Check the answer

14 + 6 = 20, which equals our maximum (within 20), so it's correct

Mia has 20 stickers now
Final answer:

Mia has 20 stickers now.

Applied rules:

• Real-World Context: Connecting math to everyday situations

• Make Ten Strategy: Using knowledge of number pairs that make 10

• Maximum Limit: Understanding that our focus is addition within 20

Addition Within 20 Story Problems: Comprehensive Guide
\(a + b = c\) where \(a + b ≤ 20\)
Addition Within 20
Key definitions:

Addition Story Problems: Word problems that require combining two or more quantities where the sum is 20 or less

Key Words: Words that indicate addition such as "total", "altogether", "sum", "more", "added", "combined", "in all"

Number Sentence: A mathematical statement showing the relationship between numbers using symbols

Complete Problem-Solving Method:
  1. Read carefully: Understand the situation described
  2. Identify key information: Circle numbers and underline key words
  3. Determine the operation: Decide if you need to add or subtract
  4. Draw a picture: Visualize the problem with objects or drawings
  5. Write the number sentence: Translate the words into math
  6. Solve: Use an appropriate strategy to find the answer
  7. Check: Verify your answer makes sense in the context
Tip 1: Use manipulatives like counters or blocks to physically combine groups.
Tip 2: When adding numbers close to 10, use the "make ten" strategy.
Tip 3: Practice doubles facts (like 5+5, 6+6) to build fluency.
Tip 4: Read the problem twice to ensure you understand what's being asked.
Common errors: Adding the wrong numbers, missing key information, not reading carefully.
Success strategies: Drawing pictures, using number lines, checking answers.
Addition Strategies to Know:

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

• Making Ten: Adjust numbers to create sums of 10

• Using Doubles: Know doubles and adjust (e.g., 6+7 = 6+6+1)

• Number Line: Jump forward on a number line

• Decomposition: Break apart numbers to make addition easier

Visual Representation: Addition Strategies
Addition Within 20 Strategies
Different approaches to solve addition problems with sums up to 20:
Counting On, Making Ten, Using Doubles, Number Line

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

  • Counting On: Starting with the larger number and counting up
  • Making Ten: Adjusting numbers to create sums of 10
  • Using Doubles: Applying known doubles facts
  • Number Line: Moving along a number line to add

Questions & Answers

Question: My first-grader struggles with identifying whether to add or subtract in story problems. What strategies can help them distinguish between the two operations?

Answer: This is a common challenge for first-graders! Here are effective strategies:

  • Focus on Action Words: Teach them to look for specific keywords. Addition words include "altogether," "total," "sum," "more," "added," "combined," "in all." Subtraction words include "left," "remaining," "less," "take away," "fewer," "difference."
  • Act Out Problems: Have them physically act out the problem with objects like blocks or counters.
  • Draw Pictures: Encourage drawing simple sketches to visualize what's happening.
  • Ask Questions: "Are we putting things together?" (addition) or "Are we taking some away?" (subtraction)

Example: "Sarah had 8 apples. She ate 3. How many are left?" The word "ate" and "left" suggest subtraction. "Tom has 5 cars. His mom gave him 3 more. How many does he have now?" The word "more" suggests addition.

Practice with consistent language and gradually increase complexity as they master the basics.

Question: My child seems overwhelmed by story problems and often doesn't know where to start. How can I help them break down the problem?

Answer: Story problems can indeed be overwhelming for young learners. Here's a systematic approach:

  • Read Together: Read the problem aloud slowly, then have your child read it back to you.
  • Circle Numbers: Have them circle or highlight all the numbers in the problem.
  • Underline Key Words: Help them identify and underline important words like "altogether," "total," "more," etc.
  • Draw a Picture: Encourage them to sketch a simple drawing representing the problem.
  • Write the Number Sentence: Help them translate the words into a math equation.
  • Solve Step-by-Step: Use counting strategies like counting on or making ten.

Example: For "There are 7 birds on a tree. 4 more fly in. How many birds are there altogether?":

  • Circle: 7, 4
  • Underline: "more," "altogether"
  • Draw: 7 circles + 4 more circles
  • Equation: 7 + 4 = ?

Consistent practice with this routine will build confidence and reduce overwhelm.

Question: I don't like story problems because they take too long to solve. Can't I just add the numbers without reading everything?

Answer: It might seem faster to just add the numbers, but reading the whole problem is actually the quicker way to get the right answer! Here's why:

  • You might add the wrong numbers: Some problems include extra numbers that aren't needed for the answer.
  • You might use the wrong operation: Without reading, you might add when you should subtract.
  • Understanding builds skills: Reading carefully helps you get better at math over time.

Think of it like a treasure hunt - the words in the problem are clues that help you find the right answer. If you skip the clues, you might end up looking in the wrong place!

Here's a quick strategy: Read once for fun, then read again to find the numbers and the question. This way, you'll be faster and more accurate!