Solved Exercises on Subtraction Word Problems in 1st Grade

Master subtraction word problems: take-away, comparison, and missing addend problems through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Take-Away Problem
Exercise 1
Solve the take-away problem:
"Emma had 7 stickers. She gave 3 to her friend. How many stickers does Emma have left?"
Definition:

Take-Away Problem: A subtraction problem where something is physically removed from a group. The total decreases as items are taken away.

Take-away method:
  1. Identify the starting amount
  2. Identify the amount taken away
  3. Subtract the taken amount from the starting amount
  4. Check if the answer is less than the starting amount
"Emma had 7 stickers. She gave 3 to her friend. How many stickers does Emma have left?"
1
Starting amount: Emma had 7 stickers
2
Taken away: She gave 3 stickers
3
Equation: 7 - 3 = ?
4
Solution: 7 - 3 = 4
Start with 7
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Gave away 3
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Remain 4
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Step 1: Identify the starting amount

Emma started with 7 stickers

Step 2: Identify what was taken away

She gave away 3 stickers to her friend

Step 3: Set up the subtraction

7 - 3 = ?

\(7 - 3 = 4\)
Final answer:

Emma has 4 stickers left.

Applied rules:

• Take-away structure: Start amount - taken amount = remaining

• Keywords: "gave", "left" indicate subtraction

• Visual method: Cross out objects to show taking away

2 Comparison Problem
Exercise 2
Solve the comparison problem:
"Tom has 8 marbles. Jake has 5 marbles. How many more marbles does Tom have than Jake?"
Definition:

Comparison Problem: A subtraction problem that finds the difference between two amounts. It asks how much more or less one quantity is than another.

"Tom has 8 marbles. Jake has 5 marbles. How many more marbles does Tom have than Jake?"
1
Larger amount: Tom has 8 marbles
2
Smaller amount: Jake has 5 marbles
3
Equation: 8 - 5 = ?
4
Solution: 8 - 5 = 3
Tom: 8 marbles
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Jake: 5 marbles
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Difference: 3
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Step 1: Identify the two quantities

Tom has 8 marbles, Jake has 5 marbles

Step 2: Determine which is larger

Tom has more marbles than Jake

Step 3: Find the difference

8 - 5 = 3

\(8 - 5 = 3\)
Final answer:

Tom has 3 more marbles than Jake.

Applied rules:

• Comparison structure: Larger amount - smaller amount = difference

• Keywords: "more than", "less than", "difference" indicate comparison

• Visual method: Match objects to see the difference

3 Missing Addend Problem
Exercise 3
Solve the missing addend problem:
"Maya had some cookies. She ate 4 and now has 3 left. How many cookies did Maya have at first?"
Definition:

Missing Addend Problem: A subtraction problem where you know the result after subtraction and one of the numbers, but need to find the original amount.

"Maya had some cookies. She ate 4 and now has 3 left. How many cookies did Maya have at first?"
1
Amount taken away: Maya ate 4 cookies
2
Amount remaining: 3 cookies left
3
Original amount: ? - 4 = 3
4
Solution: 3 + 4 = 7
Started with ?
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Ate 4
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Left: 3
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Step 1: Identify what happened

Maya ate 4 cookies and has 3 left

Step 2: Set up the relationship

Original amount - 4 = 3

Step 3: Find the original amount

To find the original, add: 3 + 4 = 7

\(7 - 4 = 3\)
Final answer:

Maya had 7 cookies at first.

Applied rules:

• Missing addend structure: Original - taken = remaining

• Reverse operation: To find original, add remaining + taken

• Keywords: "at first", "some", "originally" indicate missing addend

Types of Subtraction Word Problems
\( \text{Take-Away} \mid \text{Comparison} \mid \text{Missing Addend} \)
Three Main Categories
Take-Away Type

Objects are physically removed from a group.

Structure: Start with X, take away Y, find what remains
Keywords: gave, took, ate, lost, sold, left, remained
Equation: X - Y = ?
"Sarah had 6 balloons. She gave 2 away. How many does she have left?"
Comparison Type

Finding the difference between two amounts.

Structure: Compare two quantities to find the difference
Keywords: more than, less than, difference, how many more, how many fewer
Equation: Larger - Smaller = Difference
"Tom has 7 toys. Amy has 4 toys. How many more toys does Tom have than Amy?"
Missing Addend Type

Finding the original amount when you know what was taken and what remains.

Structure: Unknown start, known taken, known remainder
Keywords: at first, originally, some, started with, how many did you have
Equation: ? - Y = Z, so ? = Z + Y
"I ate 3 cookies and have 4 left. How many did I have at first?"
Characteristics of Each Type:
Take-Away:

• Something is physically removed

• Focus on what remains after removal

• Most common in early grades

Comparison:

• Compares two different groups

• Finds the difference between amounts

• Uses comparative language

Missing Addend:

• Requires working backwards

• Connects subtraction to addition

• Builds foundation for algebra

Type Identification Tips:

• Take-away: Focuses on removing items from one group

• Comparison: Involves two separate groups being compared

• Missing addend: Requires finding the original amount

Problem Solving Strategies
\( \text{Read} \rightarrow \text{Identify} \rightarrow \text{Solve} \rightarrow \text{Check} \)
Four-Step Process
Step-by-Step Problem Solving Process
Step 1: Read the problem carefully - Understand the story and what's happening
Step 2: Identify key information - Find numbers and keywords that indicate subtraction
Step 3: Determine the problem type - Decide if it's take-away, comparison, or missing addend
Step 4: Set up and solve - Write the equation and calculate the answer
Step 5: Check your answer - Make sure it makes sense in the context of the problem
Key Word Identification

Recognize specific words that indicate subtraction operations.

Take-Away Words: gave, took, ate, lost, sold, used, drank, broke
Comparison Words: more than, less than, fewer than, difference, how many more
Missing Addend Words: at first, originally, started with, some, how many did you have
Tip 1: Draw pictures to visualize the problem situation.
Tip 2: Use your fingers or counters to help solve the problem.
Tip 3: Always check if your answer is smaller than the starting number.
Tip 4: Reread the problem after solving to make sure your answer makes sense.
Common errors: Adding instead of subtracting, misidentifying the problem type, not checking the answer.
Success strategies: Circle key words, underline numbers, draw pictures, check answers.
Problem-solving concepts:

• Subtraction means taking away or finding the difference

• Always check if your answer makes sense in the story

• Some problems have multiple steps requiring several operations

• Words like "left" or "remains" usually mean subtract

Detailed Summary: Subtraction Word Problems
Complete Learning Guide
Definition of Subtraction Word Problems: Mathematical problems presented in a story format that require subtraction to solve. These problems connect real-world situations to mathematical operations, helping students understand the practical applications of subtraction.
Key Terms:
  • Take-Away Problem: Problems where objects are removed from a single group
  • Comparison Problem: Problems that find the difference between two separate groups
  • Missing Addend Problem: Problems where you find the original amount when you know what was taken and what remains
  • Keywords: Words that indicate which operation to use
  • Problem-Solving: The process of analyzing and solving mathematical problems
Core Rules of Subtraction Word Problems:
  • Take-Away: Start with a group, remove some, find what remains (X - Y = ?)
  • Comparison: Compare two groups, find the difference (Larger - Smaller = Difference)
  • Missing Addend: Know the result, find the original (X - Y = Z, so X = Z + Y)
  • Keyword Recognition: Different words indicate different problem types
Three Main Problem Types:
  1. Take-Away: Something is physically removed from a group (e.g., "gave", "ate", "lost")
  2. Comparison: Finding the difference between two amounts (e.g., "more than", "less than", "difference")
  3. Missing Addend: Finding the original amount (e.g., "at first", "originally", "started with")
Examples (Simple to Advanced):
  • Take-Away: "I had 5 apples and ate 2. How many are left?" (5 - 2 = 3)
  • Comparison: "Tom has 7 toys. Amy has 4 toys. How many more does Tom have?" (7 - 4 = 3)
  • Missing Addend: "I ate 3 cookies and have 4 left. How many did I have at first?" (4 + 3 = 7)
Tips and Tricks:
  • Read the question part first to understand what's being asked
  • Look for keywords that indicate the problem type
  • Sketch a picture to visualize the problem structure
  • Check that your answer makes sense in the context
  • Remember that missing addend problems require addition to solve
Common Pitfalls:
  • Misidentifying the problem type and using the wrong operation
  • Forgetting that missing addend problems require addition to solve
  • Not recognizing comparison problems that use subtraction
  • Ignoring context and focusing only on numbers
Memory Aids:
  • "Take-away: Something is removed from one group"
  • "Comparison: Two groups, find the difference"
  • "Missing addend: Work backwards, use addition"
  • Practice identifying keywords for each type
Checking Your Work: Always verify your answer makes sense in the story context and matches the problem type you identified.

Questions & Answers

Question: I understand take-away problems, but comparison problems confuse me. How do I know if it's asking for the difference between two groups?

Answer: Great question! Comparison problems are different from take-away because they involve two separate groups:

  • Look for two subjects: Comparison problems mention two different people, animals, or groups
  • Key phrases: Look for "more than", "less than", "fewer than", "how many more", "how many fewer"
  • Two amounts: You'll see two different numbers representing separate groups
  • Question focus: The question asks about the difference between the two amounts

Example: "Sarah has 6 dolls. Emma has 4 dolls. How many more dolls does Sarah have than Emma?"

This is comparison because: 1) Two people (Sarah and Emma), 2) Two different amounts (6 and 4), 3) Question asks "how many more"

To solve: Always subtract the smaller number from the larger number!

Question: Missing addend problems seem backwards. If it's a subtraction problem, why do I need to add to solve it?

Answer: You're right that it seems backwards! Think of it this way:

  • Subtraction happened: Something was taken away from an unknown starting amount
  • You know the result: You see what's left after the subtraction
  • Work backwards: To find what you started with, you do the opposite operation
  • Opposite operations: Addition undoes subtraction

Example: "I ate 3 cookies and have 4 left. How many did I have at first?"

The math sentence is: ? - 3 = 4

To find the question mark, add: 4 + 3 = 7

Check: 7 - 3 = 4 ✓

Missing addend problems prepare you for algebra where you solve for unknowns!

Question: Sometimes I see words like "more" in take-away problems. How do I know which type it is?

Answer: Words can be tricky! Context is more important than individual words:

  • Take-away with "more": "I had 5 apples and got 2 more" (addition) vs "I had 5 apples and ate 2" (subtraction)
  • Look at the action: What is happening to the objects?
  • Compare groups: Are there two different groups being compared?
  • Check the question: What is the problem asking you to find?

Example of comparison: "Tom has 6 toys. Sarah has 4 toys. How many more toys does Tom have?" → This is comparison because it compares two groups

Example of take-away: "I had 6 cookies and ate 2. How many more do I need to eat to finish them all?" → This is take-away followed by another question

Always consider the full context, not just keywords!