What are integers? Explain their characteristics, uses, and how to represent them on a number line.

3. Questions about integers

a) I need the sentences from Question 2 to identify the key words.

b) Characteristics found in the positive column are numbers greater than zero.

c) Characteristics found in the negative column are numbers less than zero.

d) Characteristics of integers:

• Integers are whole numbers (no fractions or decimals).
• They can be positive, negative, or zero.

e) Integers are used in everyday life for:

• Temperature: $-5^\circ \text{C}$ (five degrees below freezing).
• Bank balances: $-\text{R}150$ (a debt of 150 Rand).
• Elevation: $-100 \text{ m}$ (100 meters below sea level).
• Sports scores: $-2$ (two points behind).
• Stock market changes: $-30$ points (a drop of 30 points).

4. Complete these number lines.

a) The number line increases by 1. $\dots, -2, -1, 0, 1, 2, \dots$ b) The number line increases by 5. $\dots, -15, -10, -5, 0, 5, 10, \dots$ c) The number line increases by 2. $\dots, -4, -2, 0, 2, 4, 6, \dots$ d) The number line increases by 10. $\dots, -20, -10, 0, 10, 20, \dots$ e) The number line increases by 1. $\dots, -3, -2, -1, 0, 1, \dots$ f) The number line increases by 3. $\dots, -6, -3, 0, 3, 6, \dots$

5. Complete the following:

a) The sequence decreases by 1. $\{3; 2; 1; 0; \boxed{-1}; \boxed{-2}; \boxed{-3}\}$ b) The sequence increases by 1. $\{-10; -9; -8; \boxed{-7}; \boxed{-6}; \boxed{-5}\}$ c) The sequence decreases by 2. $\{8; 6; 4; 2; \boxed{0}; \boxed{-2}; \boxed{-4}\}$ d) The sequence increases by 3. $\{-9; -6; -3; \boxed{0}; \boxed{3}; \boxed{6}\}$ e) The sequence decreases by 4. $\{12; 8; 4; \boxed{0}; \boxed{-4}; \boxed{-8}\}$

Problem solving

a) If we were to find five negative numbers in a newspaper, they might represent:

• $-\text{R}500$: A company's loss of 500 Rand.
• $-3^\circ \text{C}$: A temperature of 3 degrees below zero.
• $-10 \text{ points}$: A decrease of 10 points in a stock index.
• $-2 \text{ goals}$: A team's goal difference of minus 2.
• $-15 \text{ m}$: A depth of 15 meters below sea level.

b) The opposite numbers for the examples above would be:

• Opposite of $-\text{R}500$ is $\boxed{\text{R}500}$.
• Opposite of $-3^\circ \text{C}$ is $\boxed{3^\circ \text{C}}$.
• Opposite of $-10 \text{ points}$ is $\boxed{10 \text{ points}}$.
• Opposite of $-2 \text{ goals}$ is $\boxed{2 \text{ goals}}$.
• Opposite of $-15 \text{ m}$ is $\boxed{15 \text{ m}}$.