Let's solve each problem one by one and explain the reasoning step-by-step.
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1. FOOTBALL
*A team gained 5 yards on their first play of the game. Then they lost 6 yards. Find the total change in yardage.*
Solution:
- Gain of 5 yards → +5
- Loss of 6 yards → –6
- Total change = 5 + (–6) =
–1 yard
✔ Answer: –1 yard
This means the team is
1 yard behind where they started.
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2. CHECKING
*Your checking account is overdrawn by $50. You write a check for $20. What is the balance in your account?*
Solution:
- Overdrawn by $50 → current balance =
–$50
- Writing a check for $20 means you subtract another $20:
–50 – 20 =
–$70
✔ Answer: –$70
The account is now
$70 overdrawn.
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3. TEMPERATURE
*The average temperature in Calgary, Canada, is 22°C in July and –11°C in January. Find the range of the highest and lowest temperatures in Calgary.*
Solution:
- Highest temperature = 22°C
- Lowest temperature = –11°C
- Range = Highest – Lowest = 22 – (–11) = 22 + 11 =
33°C
✔ Answer: 33°C
This is the difference between the hottest and coldest average temperatures.
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4. ROLLER COASTER
*A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent.*
Solution:
- Starting height = 90 feet
- Descends 105 feet → subtract 105
- New height = 90 – 105 =
–15 feet
Negative height means it’s
15 feet below ground level.
✔ Answer: –15 feet
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5. SAVINGS
*Sonia has $235 in her savings account. She withdraws $45. What is left in her savings account?*
Solution:
- Initial amount = $235
- Withdrawal = $45
- Remaining = 235 – 45 =
$190
✔ Answer: $190
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6. BEACH
*Wai and Kuri were digging in the sand at the beach. Wai dug a hole that was 15 inches below the surface and Kuri dug a hole that was 9 inches below the surface. Find the difference in the depths of their holes.*
Solution:
- Wai’s depth = –15 inches (below surface)
- Kuri’s depth = –9 inches
- Difference = |–15| – |–9| = 15 – 9 =
6 inches
Alternatively:
Difference = –9 – (–15) = –9 + 15 =
6 inches
✔ Answer: 6 inches
Wai’s hole is 6 inches deeper than Kuri’s.
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✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1. Football | –1 yard |
| 2. Checking | –$70 |
| 3. Temperature | 33°C |
| 4. Roller Coaster | –15 feet |
| 5. Savings | $190 |
| 6. Beach | 6 inches |
Let me know if you'd like these explained in simpler terms or with diagrams!
Parent Tip: Review the logic above to help your child master the concept of free integer word problems worksheet.
