Grade: Grade 6 Subject: Mathematics Unit: Integers SAT: Algebra ACT: Math

Integer Word Problems

Apply your integer skills to solve real-world problems involving temperature, money, elevation, and more.

Integers in the Real World

Why Word Problems Matter

Integers are everywhere! Understanding how to apply integer operations to real situations is a key skill for everyday life and standardized tests.

Common Real-World Contexts for Integers

🌡️

Temperature

Temperatures below zero are negative. Changes in temperature use addition/subtraction.

-5°F rises 12°F = 7°F
💰

Money & Debt

Debt and withdrawals are negative. Deposits and earnings are positive.

-$50 debt + $75 = $25 balance
🏔️

Elevation

Below sea level is negative. Above sea level is positive.

-400 ft to +200 ft = 600 ft change
🏈

Sports

Yards lost are negative. Yards gained are positive.

-5 yards + 12 yards = 7 yards

Problem-Solving Strategy

  • Read carefully - identify what you need to find
  • Identify integers - what numbers are positive? negative?
  • Choose the operation - add, subtract, multiply, or divide?
  • Solve and check - does your answer make sense?

Worked Examples

🌡️ Temperature Problem

At 6 AM, the temperature in Minneapolis was -8°F. By noon, the temperature had risen 15°F. What was the temperature at noon?
Find: Temperature at noon
1
Identify the integers:
Starting temperature: -8°F (negative)
Change: +15°F (positive, because it rose)
2
Set up the equation:
-8 + 15 = ?
3
Solve (different signs, subtract):
15 - 8 = 7, and 15 > 8, so positive.
-8 + 15 = 7
The temperature at noon was 7°F

💰 Money Problem

Maria has $45 in her account. She writes a check for $72. What is her new account balance?
Find: New account balance
1
Identify the integers:
Starting balance: $45 (positive)
Check written: -$72 (negative, money going out)
2
Set up the equation:
45 + (-72) = ? (or 45 - 72 = ?)
3
Solve (different signs, subtract):
72 - 45 = 27, and 72 > 45, so negative.
45 - 72 = -27
Maria's new balance is -$27 (she is $27 overdrawn)

🏔️ Elevation Problem

A submarine is at -350 feet (below sea level). It rises 120 feet, then dives 85 feet. What is its final depth?
Find: Final depth of the submarine
1
Identify the integers:
Starting depth: -350 feet
First change: +120 feet (rises = positive)
Second change: -85 feet (dives = negative)
2
Set up the equation:
-350 + 120 + (-85) = ?
3
Solve step by step:
-350 + 120 = -230 (different signs: 350-120=230, negative)
-230 + (-85) = -315 (same signs: 230+85=315, negative)
The submarine's final depth is -315 feet (315 feet below sea level)

🏈 Sports Problem

In 4 plays, a football team gained the following yards: -3, +8, -2, +12. What was their total yardage for these 4 plays?
Find: Total yards gained or lost
1
Add all the integers:
-3 + 8 + (-2) + 12
2
Group positives and negatives:
Positives: 8 + 12 = 20
Negatives: -3 + (-2) = -5
3
Combine:
20 + (-5) = 15
The team gained a total of 15 yards

Practice Problems

Apply what you have learned to solve these word problems!

Problem 1: Temperature

The temperature at midnight was -12°F. By 8 AM, it had risen 18°F. What was the temperature at 8 AM?

Problem 2: Money

Jake has $120 in his savings account. He withdraws $85, then deposits $40. What is his new balance?

Problem 3: Elevation

A hiker starts at an elevation of 250 feet above sea level. She descends 400 feet into a canyon. What is her new elevation?

Problem 4: Football

A running back's rushing yards for 5 carries were: +6, -2, +15, -4, +8. What was his total rushing yards?

Problem 5: Temperature Change

The temperature dropped 5°F each hour for 6 hours. What was the total temperature change?

Problem 6: Debt

Lisa owes $180 on her credit card (debt = -180). She makes 3 equal payments to pay it off completely. How much is each payment?

Problem 7: Sea Level

A scuba diver is at -45 feet. She needs to reach -80 feet. How many more feet must she descend?

Problem 8: Stock Market

A stock lost $8 per share each day for 5 days, then gained $15 per share on the 6th day. What was the overall change per share?

Check for Understanding

Word Problem Tips:
  • "Rises," "gains," "deposits," "above" usually mean positive
  • "Falls," "loses," "withdraws," "below" usually mean negative
  • Always check if your answer makes sense in the context
  • Drawing a number line can help visualize the problem

Key Takeaways

  • Read the problem carefully to identify which numbers are positive or negative
  • Translate words into mathematical operations
  • Solve step by step and check your answer
  • Context helps you understand if your answer is reasonable

Next Steps

  • Practice identifying integers in everyday situations
  • Create your own word problems to share with classmates
  • Move on to learn about common mistakes to avoid!