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Teacher Guide: Integer Word Problems

Learn to translate real-world situations into integer operations and solve them step by step.

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Printable worksheet

All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Negative Numbers. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Identify key words that indicate addition or subtraction
  • Translate word problems into integer expressions
  • Solve multi-step integer word problems
  • Interpret positive and negative results in context
Prerequisites
  • • Understanding of positive and negative numbers
  • • Adding and subtracting integers
  • • Locating integers on a number line
Discussion Starters
  • 1. Can you think of a job where you would use negative numbers every day?
  • 2. If you owe your friend 10 dollars and earn 15 dollars, how would you describe your situation using integers?
  • 3. Why might an elevator have a button for floor -2?
  • 4. A mountain climber goes from 200 meters to -50 meters. What happened?
Common Misconceptions

Thinking 'subtract' always makes numbers smaller

Remediation: Show that subtracting a negative makes numbers bigger: 5−(−3)=85 - (-3) = 8. Use the 'removing debt' analogy.

Treating 'difference' as always positive

Remediation: Explain that A−BA - B can be positive or negative depending on which is larger. The question context tells us which direction matters.

Differentiation Ideas

For Struggling Students:

  • • Start with one-step problems before multi-step
  • • Provide a number line for every problem
  • • Use a key word chart (gain → +, lose → -)

For On-Level Students:

  • • Solve two-step and three-step problems
  • • Compare final values in different scenarios
  • • Create their own word problems

For Advanced Students:

  • • Solve problems with unknowns (algebra preview)
  • • Analyze which changes have the greatest impact
  • • Work with larger integers and multiple operations
Standards Alignment
  • 7.NS.A.3 (CCSS.MATH.CONTENT.7.NS.A.3)

    Solve real-world and mathematical problems involving the four operations with rational numbers

  • 6.NS.C.5 (CCSS.MATH.CONTENT.6.NS.C.5)

    Understand that positive and negative numbers describe quantities having opposite directions or values

Lesson Resources
  • visualNumber Line Tool

    Students visualize integer operations on an interactive number line

  • activityReal-World Scenario Cards

    Students match word problems to correct expressions

  • worksheetMixed Integer Word Problems

    Practice with temperature, money, and elevation problems

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Integer word problems describe real-world situations using positive and negative whole numbers. To solve them, you need to:
  1. 1.Identify the quantities - What numbers are involved?
  2. 2.Determine the operation - Is it addition, subtraction, or comparison?
  3. 3.Translate to math - Write an expression with integers
  4. 4.Solve and interpret - Calculate and explain what the answer means
Key phrases to watch for:
  • *"below zero"* or *"under sea level"* → negative numbers
  • *"increased by"* or *"gained"* → addition
  • *"decreased by"* or *"lost"* → subtraction
  • *"how much more/less"* or *"difference"* → subtraction

Worked Examples

At 6 AM, the temperature was −8°C-8°C. By noon, it had risen by 1515 degrees. What was the temperature at noon?
1

Identify the starting value

The temperature at 6 AM was −8°C-8°C → Start: −8-8
2

Identify the change

"Risen by" means we add. The change is +15+15 → Change: +15+15
3

Write the expression

−8+15-8 + 15 → Expression set up
4

Calculate

Starting at −8-8, moving 1515 units right: −8+15=7-8 + 15 = 7
5

Interpret the answer

Positive 77 means above zero → 7°C7°C

Common Mistakes

Confusing 'how much deeper' with subtraction order

Why it's wrong: Students often subtract in the wrong order when comparing values.

Correct: To find how much deeper A is than B, calculate the distance: ∣(−120)−(−85)∣=35|(-120) - (-85)| = 35 meters. Or think: from −85-85 to −120-120 is 3535 meters down.

Ignoring negative signs in the answer

Why it's wrong: Students calculate correctly but forget to consider what a negative result means.

Correct: Always interpret: negative balance = debt, negative temperature = below zero, negative floor = basement level.

Adding when the problem says 'lost' or 'decreased'

Why it's wrong: Key words like 'lost,' 'dropped,' and 'fell' indicate subtraction, not addition.

Correct: Lost 10 points means subtract 10: if you had 55 points, now you have 5−10=−55 - 10 = -5 points.

Why It Matters

Integer word problems appear everywhere in daily life:
  • Weather: A temperature of −5°C-5°C rises by 1212 degrees
  • Finance: Your account has −50-50 dollars (debt), then you deposit 7575
  • Geography: A submarine at −200-200 meters descends 5050 more meters
  • Sports: A football team gains 88 yards then loses 1515 yards
Being able to translate words into math helps you solve real problems quickly and accurately!

Real World Applications

Weather Forecasting

Meteorologists calculate temperature changes using integers every day.

Example:

If tonight's low is −12°C-12°C and tomorrow's high is 8°C8°C, the temperature range is 8−(−12)=208 - (-12) = 20 degrees.

1Try It Yourself

The temperature at midnight was −7°C-7°C. It dropped 44 degrees by 3 AM, then rose 99 degrees by 9 AM.

What was the temperature at 9 AM?

Step 1: Write the mathematical expression

Calculate: −7+(−4)+9-7 + (-4) + 9

Football Yardage

Football teams track yards gained and lost throughout a game.

Example:

A team gains 1212 yards, loses 55, then gains 88. Net yardage: 12+(−5)+8=1512 + (-5) + 8 = 15 yards.

2Try It Yourself

A football team starts at the 30-yard line. They gain 15 yards, lose 8 yards, then lose 12 more yards.

What yard line are they on now?

Step 1: Write the mathematical expression

Calculate: 30+15+(−8)+(−12)30 + 15 + (-8) + (-12)

Scuba Diving Depth

Divers track their depth below sea level using negative numbers.

Example:

A diver at −15-15 meters descends 1010 more meters to reach −25-25 meters.

3Try It Yourself

A diver is at −30-30 meters. She ascends 1212 meters, rests, then descends 88 meters.

What is her final depth?

Step 1: Write the mathematical expression

Calculate: −30+12+(−8)-30 + 12 + (-8)

Key Takeaways

  • 1Read carefully to identify starting values, changes, and what the question asks
  • 2Translate key words: 'rise/gain/deposit' → add, 'fall/lose/withdraw' → subtract
  • 3Use negative numbers for values below zero (debt, basement floors, underwater depths)
  • 4After calculating, interpret what the answer means in the real-world context

Frequently Asked Questions

How do I know if an answer should be negative?

Think about the context: if someone owes money, is below sea level, or is at a temperature below freezing, the answer is negative. Your calculation will show this naturally if you set it up correctly.

What's the difference between 'decreased by 5' and 'is 5 less than'?

'Decreased by 5' means subtract 5 from a value: x−5x - 5. 'Is 5 less than' compares two values: if A is 5 less than B, then A=B−5A = B - 5.

Glossary

Integer
A whole number that can be positive, negative, or zero
Elevation
Height above or below sea level (sea level = 0)
Deposit
Money added to an account (increases balance)
Withdrawal
Money taken from an account (decreases balance)
Net change
The overall result after all increases and decreases

More in This Topic

Introduction to Negative Numbers

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Adding and Subtracting Integers

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Comparing Integers

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Ordering Integers

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