Instructions
- Read the instructions for each section carefully.
- Complete the tasks using your knowledge of positive and negative numbers (rational numbers).
- Use the symbols: > (greater than), < (less than), or = (equal to) when comparing numbers.
- For sections requiring justification, use clear, complete sentences that reference the real-world context.
Section 1: Comparing Integers (The Basics)
Activity 1: True or False?
Determine if the inequality statement is True (T) or False (F).
| Comparison | T / F |
|---|---|
| 1. -5 > 2 | F |
| 2. -10 < -8 | |
| 3. 0 > -15 | |
| 4. -25 = 25 | |
| 5. 1 > -100 |
Activity 2: Fill in the Blank
Use the correct symbol (>, <, or =).
- -14 ____ -2
- 7 ____ -7
- -30 ____ 0
- -4 ____ -4.0
Section 2: Real-World Scenarios
Scenario A: Winter Temperatures
| City | Temperature (˚C) |
|---|---|
| Anchorage | -15 |
| Boston | -2 |
| Denver | 4 |
| Chicago | -8 |
-
Which city is colder: Chicago or Anchorage?
Comparison (Use < or >): -8 ____ -15
Answer: ____ is colder.
-
Explain why the city you chose is colder, referencing the number line. (Hint: Colder temperatures are farther left from zero).
Explanation:
-
Boston’s temperature (-2˚C) is warmer than which two other cities listed? Write two separate inequalities to show this.
a) -2˚C > __ ˚C b) -2˚C > __ ˚C
Scenario B: Ocean Depth
Depth below sea level is represented by negative numbers (e.g., 50 feet below sea level is -50 ft). The larger the negative number's absolute value, the deeper the object.
| Item | Depth (ft) |
|---|---|
| Submarine | -800 |
| Reef | -40 |
| Anglerfish | -2500 |
-
Which object is closer to the surface: The Submarine or the Anglerfish?
Comparison (Use < or >): -800 ____ -2500
Answer: ____ is closer to the surface.
-
Write an inequality that compares the Reef's depth to the Submarine's depth and explain what the inequality means in terms of distance from the surface.
| Inequality | Explanation (What does the comparison mean in the real world?) |
|---|---|
| Example: -100 < -50 | -100 ft is farther below the surface than -50 ft. |
Section 3: Ordering Rational Numbers
Task 1: Financial Records
A financial analyst is tracking the status of five accounts. Negative numbers represent debt (money owed).
Order the account balances from Least (most debt/worst balance) to Greatest (most savings/best balance).
| Account | Balance ($) |
|---|---|
| A | -500 |
| B | 150 |
| C | 0 |
| D | -125 |
| E | 200 |
Order (Least to Greatest):
Task 2: Altitude Data
Order the following altitudes (in miles relative to a central planetary landmark) from Highest to Lowest.
| Altitude Data Set (miles) |
|---|
| -15, 8, -2, 0, 10, -5 |
Order (Highest to Lowest):
Section 4: Critical Thinking Challenge
-
An engineer observes two pipes being installed underground. Pipe A is located at -12 feet. Pipe B is located at -16 feet.
The engineer states, "Pipe A is at a greater depth than Pipe B."
Is the engineer correct? (Circle one: YES / NO)
Justify your answer: Write an inequality comparing the two depths, and then explain why the inequality proves the engineer right or wrong.
-
Creation Task: Create a real-world scenario (like temperature, golf scores, or debt) that requires comparing the following three numbers: -12, 5, -20.
a. Write two sentences explaining what the positive and negative numbers represent in your scenario.
Scenario Context:
b. Order them from least to greatest based on the scenario's meaning.
Order (Least to Greatest):
Answer Key
Section 1: Quick Comparisons
| Comparison | T / F |
|---|---|
| 1. -5 > 2 | F |
| 2. -10 < -8 | T |
| 3. 0 > -15 | T |
| 4. -25 = 25 | F |
| 5. 1 > -100 | T |
Activity 2: Fill in the Blank
- -14 < -2
- 7 > -7
- -30 < 0
- -4 = -4.0
Section 2: Real-World Scenarios
-
Comparison: -8 > -15. Answer: Anchorage is colder.
-
Explanation: Anchorage (-15˚C) is colder than Chicago (-8˚C) because -15 is farther to the left of zero on the number line, meaning it represents a smaller, colder value.
-
a) -2˚C > -8 ˚C (Chicago) b) -2˚C > -15 ˚C (Anchorage)
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Comparison: -800 > -2500. Answer: The Submarine is closer to the surface.
-
Inequality Explanation (What does the comparison mean in the real world?) Example: -100 < -50 -100 ft is farther below the surface than -50 ft. -40 > -800 The Reef is closer to the surface than the Submarine because -40 is a greater number (less far below zero) than -800.
Section 3: Ordering Rational Numbers
Task 1: Financial Records Order: -500, -125, 0, 150, 200
Task 2: Altitude Data (Highest to Lowest) Order: 10, 8, 0, -2, -5, -15
Section 4: Critical Thinking Challenge
-
Is the engineer correct? (Circle one: NO)
Justify your answer: The inequality is -12 > -16. Pipe A (-12 ft) is a greater number, which means it is numerically closer to zero (the surface). Therefore, Pipe B (-16 ft) is at a greater depth (farther below the surface) than Pipe A. The engineer is incorrect.
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Creation Task: (Accept any logical scenario, such as golf scores or temperature, where negative numbers represent a lower/worse value and positive numbers represent a higher/better value.)
Example Scenario Context: These numbers represent golf scores relative to par. 5 is 5 strokes over par. -12 is 12 strokes under par. -20 is 20 strokes under par.
Order (Least to Greatest): -20, -12, 5 (This represents the best score to the worst score).