Word Problems: Addition and Subtraction

For Elementary Students

What Is a Word Problem?

A word problem is a math problem told as a story!

Think about it like this: Instead of seeing "5 + 3 = ?", you read "Anna has 5 apples and gets 3 more. How many does she have now?"

Your job: Turn the story into a math problem!

The Secret: Look for Clue Words!

Certain words tell you which operation to use!

Addition Clue Words

These words mean ADD (+):

Common clues:

• total ("What's the total?")
• altogether ("How many altogether?")
• in all ("How many in all?")
• sum ("Find the sum")
• combined ("Combined amount")
• more ("She gets 5 more")
• increase ("Increase by 10")
• gain ("He gained 8 points")

Example: Addition Problem

Problem: "Maria has 12 stickers. Her friend gives her 8 more stickers. How many stickers does Maria have in all?"

Step 1: Find the clue words

• "more" = addition
• "in all" = we want the total

Step 2: Write the equation

12 + 8 = ?

Step 3: Solve

12 + 8 = 20

Answer: Maria has 20 stickers! ✓

Subtraction Clue Words

These words mean SUBTRACT (−):

Common clues:

• left ("How many left?")
• remaining ("How many remaining?")
• difference ("What's the difference?")
• fewer ("5 fewer than")
• less ("3 less than")
• lost ("He lost 7")
• gave away ("She gave away 4")
• ate/used ("They ate 6")

Example: Subtraction Problem

Problem: "There were 30 cookies on a plate. The students ate 18 cookies. How many cookies are left?"

Step 1: Find clue words

• "ate" = subtraction (taking away)
• "left" = we want what remains

Step 2: Write the equation

30 − 18 = ?

Step 3: Solve

30 − 18 = 12

Answer: 12 cookies are left! ✓

"How Many More" Problems (Tricky!)

These problems compare two amounts. You subtract to find the difference!

Example: "Tom read 14 books. Mia read 9 books. How many more books did Tom read?"

Think about it: Tom has MORE books than Mia. How much more?

14 − 9 = 5

Answer: Tom read 5 more books ✓

Another way to think: Mia needs 5 more books to catch up to Tom!

The 4-Step Strategy

Step 1: READ the whole problem carefully

• Read it twice if needed!

Step 2: IDENTIFY what you're looking for

• Underline or circle the question

Step 3: PICK the operation

• Look for clue words
• Decide: add or subtract?

Step 4: SOLVE and check

• Do the math
• Does your answer make sense?

Example with All 4 Steps

Problem: "A toy store had 45 toy cars. They sold 17 toy cars today. How many toy cars does the store have now?"

Step 1: READ

• A store starts with 45, sells 17, wants to know how many now

Step 2: IDENTIFY

• Question: "How many toy cars does the store have now?"

Step 3: PICK

• "sold" = gave away = subtraction
• Start with 45, take away 17

Step 4: SOLVE

45 − 17 = 28

• Check: 28 + 17 = 45 ✓ Makes sense!

Answer: 28 toy cars ✓

Watch Out for Extra Information!

Some problems give you numbers you DON'T need!

Example: "A classroom has 25 students and 30 chairs. 7 students are absent today. How many students are present?"

Numbers given:

• 25 students (NEED)
• 30 chairs (DON'T NEED!)
• 7 absent (NEED)

Equation:

25 − 7 = 18

Answer: 18 students present ✓

Tip: Read the question carefully to know which numbers to use!

Make It Real!

Draw a picture! It helps you see what's happening!

Problem: "5 birds on a tree. 3 more birds land. How many birds now?"

🐦🐦🐦🐦🐦  (5 birds)
   +
  🐦🐦🐦      (3 more)
   =
🐦🐦🐦🐦🐦🐦🐦🐦  (8 total!)

Quick Practice

Problem 1: "Emma had 20 candies. She ate 6. How many left?"

Clue word: "left" = subtraction
20 − 6 = 14 candies ✓

Problem 2: "There are 15 red balloons and 12 blue balloons. How many altogether?"

Clue word: "altogether" = addition
15 + 12 = 27 balloons ✓

For Junior High Students

Understanding Word Problems

Word problems require translating verbal descriptions into mathematical equations, then solving those equations.

Purpose:

• Apply math to real-world contexts
• Develop problem-solving skills
• Practice reading comprehension in a mathematical context

Key skill: Identifying the mathematical operation implied by the language.

Systematic Approach

1. Read and comprehend:

• Read the entire problem without rushing
• Identify the given information
• Determine what is being asked

2. Analyze:

• Identify relevant data
• Discard irrelevant information
• Look for keywords indicating operations

3. Formulate:

• Translate words into mathematical expressions
• Set up an equation

4. Solve:

• Perform the calculation
• Show all work

5. Verify:

• Check if the answer makes sense in context
• Verify units are correct
• Consider if the magnitude is reasonable

Addition Keywords and Context

Direct addition indicators:

• Total: "Find the total cost"
• Sum: "What is the sum of..."
• Combined: "The combined weight"
• Altogether: "How many altogether?"
• In all: "How many students in all?"

Contextual addition:

• More: "He received 5 more" (increase)
• Gain: "The team gained 12 yards"
• Increase: "Increased by 15%"
• Join: "Two groups joining together"

Example 1: "A store sold 132 items in the morning and 89 items in the afternoon. How many items were sold in total?"

Analysis:

• Given: 132 (morning), 89 (afternoon)
• Asked: total sold
• Operation: addition (keyword: "total")

Solution:

132 + 89 = 221 items

Verification: 221 is greater than either individual value ✓

Example 2: "Sarah's savings increased by $45 this month. She previously had $230. How much does she have now?"

Solution:

230 + 45 = 275 dollars

Contextual check: "increased" suggests addition ✓

Subtraction Keywords and Context

Direct subtraction indicators:

• Difference: "What is the difference?"
• Remaining: "How many remaining?"
• Left: "How many left?"
• Fewer: "5 fewer than..."
• Less: "10 less than..."

Contextual subtraction:

• Lost: "He lost 7 points"
• Gave away: "She gave away 3 books"
• Sold: "The store sold 20 units"
• Decreased: "Decreased by 8"
• Ate/Used/Spent: Actions that remove quantity

Example 1: "A theater has 240 seats. 186 tickets were sold. How many seats remain?"

Analysis:

• Total: 240 seats
• Sold: 186
• Asked: remaining
• Operation: subtraction

Solution:

240 − 186 = 54 seats

Verification: 186 + 54 = 240 ✓

Example 2: "The temperature was 72°F and decreased by 15°F. What is the new temperature?"

Solution:

72 − 15 = 57°F

Context check: "decreased" means subtract ✓

Comparison Problems

"How many more" / "How many fewer" problems compare two quantities.

Structure: Find the difference between two amounts.

Example: "Jake scored 85 points and Lily scored 92 points. How many more points did Lily score?"

Analysis:

• Lily: 92 (larger)
• Jake: 85 (smaller)
• Asked: difference

Solution:

92 − 85 = 7 points

Interpretation: Lily scored 7 more points than Jake

Alternative phrasing: "How many fewer points did Jake score?"

Same calculation: 92 − 85 = 7
Answer: Jake scored 7 fewer points

Identifying Irrelevant Information

Strategy: Determine which data points are necessary to answer the specific question asked.

Example: "A classroom has 28 students, 32 desks, and 4 windows. If 5 students are absent, how many students are present?"

Analysis:

• Relevant: 28 students, 5 absent
• Irrelevant: 32 desks, 4 windows (not asked about)

Solution:

28 − 5 = 23 students present

Skill: Distinguish between contextual information and operational data.

Setting Up Equations

General forms:

Addition:

a + b = ?
"a and b combined equals what?"

Subtraction:

a − b = ?
"a decreased by b equals what?"

Example: "Emma had 45 marbles. She gave 17 to her friend. How many does Emma have now?"

Translation:

Starting amount − given away = remaining
45 − 17 = x
x = 28 marbles

Real-Life Applications

Shopping: "A shirt costs $32 and pants cost $48. What is the total?"

32 + 48 = 80 dollars

Banking: "Account balance is $450. After a $125 withdrawal, what remains?"

450 − 125 = 325 dollars

Inventory: "Store had 200 units. Received 75 more. How many total?"

200 + 75 = 275 units

Travel: "Drove 285 miles. Destination is 420 miles away. How far remaining?"

420 − 285 = 135 miles

Common Mistakes

Mistake 1: Using wrong operation

❌ "There are 5 fewer than 20" → 5 + 20 = 25 ✓ "Fewer" means subtract: 20 − 5 = 15

Mistake 2: Subtracting in wrong order

❌ "How many more is 50 than 30?" → 30 − 50 = −20 ✓ Larger − smaller: 50 − 30 = 20

Mistake 3: Using irrelevant numbers

❌ Including all numbers mentioned without checking relevance ✓ Only use numbers that answer the specific question

Mistake 4: Not checking reasonableness

❌ Getting an answer and moving on without verification ✓ Ask: "Does this make sense in the context?"

Tips for Success

Tip 1: Read the entire problem before attempting to solve

Tip 2: Underline or highlight key information and the question

Tip 3: Circle numbers that are relevant to the solution

Tip 4: Write out the equation before calculating

Tip 5: Include units in your answer (dollars, students, meters, etc.)

Tip 6: Verify your answer makes sense contextually

Tip 7: Check your work by working backwards when possible

Verification Strategies

1. Inverse operation:

• Used addition? Check with subtraction
• Used subtraction? Check with addition

Example: Solved 132 + 89 = 221

• Check: 221 − 89 = 132 ✓
• Check: 221 − 132 = 89 ✓

2. Contextual reasonableness:

• Is the answer larger/smaller as expected?
• Do the units make sense?
• Is the magnitude reasonable?

3. Estimation:

• Round and estimate before solving
• Compare exact answer to estimate

Example: 132 + 89 ≈ 130 + 90 = 220

• Actual: 221 ✓ (close to estimate)

Problem-Solving Checklist

Before solving:

• Read the entire problem
• Identify what is being asked
• Determine given information
• Identify operation needed

While solving:

• Set up the equation
• Perform calculation
• Include units

After solving:

• Check reasonableness
• Verify with inverse operation
• Ensure you answered the question asked

Practice