Chapter 1.1 (Mathematics 8th)

# Identifying Integers in Different Situations. Re­pre­senting Integers on a Number Line

By the end of the lesson, the learner should be able:

• to identify integers in different situations;
• to represent integers on a number line.

## Activities

### Activity 1

1. Mark a reference point on a level ground.
2. Make five steps from the reference point, marking each step.
3. From the same reference point, make and mark five steps in the opposite direction.
4. Using (0) as the reference point, assign a positive sign (+ve) to each of the number of steps made forward and negative sign (–ve) to each of the number of steps made backward.
5. Discuss and share your work with other groups.

#### Note:

Consider moving forward as a positive direction whereas moving backward as a negative direction.

### Activity 2

1. Choose a reference point (O) on a level ground.
2. Write numbers on cards to represent positive steps or negative steps.
3. In groups, pick a card and make steps from the reference point according to the number of steps indicated.

### Learning Point

Positive whole numbers, negative whole numbers and zero are called integers.

### Activity 3

Consider the following integers:
​–5, –1, +4, –3, 0, +1, +3, +2, +5, –4, –2

1. Represent the integers on a number line.
2. Discuss and share with other groups.

### Learning Point

• All integers to the left of zero are negative while the ones to the right of zero are positive.
• On a number line, an integer is less than all other integers to the right of it and greater than all those to the left of it.

## Example 1

Use greater than (>) and less than (<) signs to compare the following integers:

1. (–2) and (+2)
2. (–1) and (–7)
3. (+3) and (–4)

Solution

(–2) is on the left of (+2)
​(–2) is less than (+2)

• ​(–2) < (+2)

(–7) is to the left of (–1)
​(–7) is less than (–1)

• (–7) < (–1)

(+3) is on the right of (–4)
​(+3) is greater than (–4)

• (+3) > (–4)

## Exercise 1

Use a number line in the exercise.

1. Greater is
• (–3)
• (+3)
1. Greater is
• (+5)
• (+11)
1. Greater is
• (–11)
• (+2)
1. Smaller is
• (–2)
• (–8)
1. Smaller is
• (+4)
• (–9)
1. Smaller is
• (+1)
• (–1)
1. (–4)(–7)
2. (+2)(–9)
3. (+3)(+5)
1. (+8)(–8)
2. (–5)(+2)
3. (–12)(–15)
1.
• (+5)
• (–7)
• (–4)
• (+1)
• (–3)
• (–1)
1.
• (–5)
• (+2)
• (–2)
• (+8)
• (–3)
• (+6)
1.
• (–7)
• (+9)
• (+3)
• (–2)
• (–9)
• (+7)