Understanding Integers Worksheet

Name:

Date:

Number line with positive and negative integers

📊 Part 1: Ordering and Basic Operations

1. Order these integers from smallest to largest: 7, -3, 0, -8, 2, -1

Answer: _____, _____, _____, _____, _____, _____

2. Use the number line to solve -4 + 6. Show your working by describing your steps.

Answer: _____

3. Calculate using two-sided counters or number line method:

a) -7 + 3 = _____

b) 5 - 8 = _____

c) -2 - 4 = _____

4. Which statement about multiplying integers is correct?

Positive × Positive = Negative

Negative × Negative = Positive

Positive × Negative = Positive

Negative × Positive = Positive

🌡️ Part 2: Real-Life Applications

5. Temperature Problem: The temperature in Queenstown was 3°C at noon. It dropped by 8°C by midnight. What was the temperature at midnight?

Answer: _____°C

6. Financial Problem: Sarah's bank account had $45. She made the following transactions:

• Withdrew $60 (overdraft fee of $5 applied)

• Deposited $30

• Withdrew $15

What is her final account balance?

Answer: $_____

7. Elevation Problem: A submarine starts at sea level (0 metres). It descends 45 metres, then rises 20 metres, then descends another 15 metres. What is its final position relative to sea level?

Answer: _____ metres

8. Calculate these integer operations:

a) (-3) × 4 = _____

b) (-24) ÷ (-6) = _____

c) 7 × (-2) = _____

d) (-15) ÷ 3 = _____

💭 Part 3: Problem Solving and Reflection

9. Challenge Problem: In a quiz game, correct answers earn 5 points and incorrect answers lose 3 points. If Tom answered 8 questions correctly and 4 questions incorrectly, what was his final score?

Answer: _____ points

10. Explain in your own words why (-4) × (-3) = 12. Use an example or pattern to justify your answer.

11. Reflection Questions:

a) What was the most challenging part of working with integers today?

b) Describe one real-life situation where you might use negative numbers that wasn't mentioned in this worksheet.

c) What strategy helped you most when adding or subtracting integers?

Number line method

Two-sided counters

Memorising rules

Other: ________________