Integers
1.0 Numbers · 1.1 Integers
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.1 Integers (6 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Identify integers in different situations
- Represent integers on a number line
- Carry out operations of addition and subtraction of integers on the number line
- Reflect on the use of integers in real-life situations
Integers
A fridge in a shop shows −4 °C. A bank statement shows −500. Neither number is a mistake. Both describe something below an agreed starting point.
Integers are the whole numbers, their negatives, and zero.
a) Where you meet them
| Situation | What the negative means |
|---|---|
| Temperature | colder than freezing |
| Bank balance | money owed |
| Altitude | below sea level |
| Football | goals conceded against scored |
| Lift buttons | floors below the ground |
In every case there is an agreed zero, and the negative numbers sit below it.
Zero itself is an integer. It is neither positive nor negative.
Numbers with a fraction or a decimal part are not integers. So 3 is an integer, but 3.5 and ½ are not.
b) The number line
The line runs forever in both directions. Positive numbers sit to the right of zero and negative numbers to the left.
Every integer has exactly one place on the line, and the spacing between neighbours is always the same.
c) Comparing integers
The rule is simple: the number further to the right is the larger one.
Look at −5 and −2. On the line, −2 sits to the right, so −2 is larger.
This surprises most learners, because 5 is bigger than 2. With negatives it works the other way round. Think of temperature: −2 °C is warmer than −5 °C.
We write −2 > −5, or equally −5 < −2.
d) Adding on the number line
To add, start at the first number and move right.
Start at −4. Move 5 places right. You land on 1.
So −4 + 5 = 1.
Counting the jumps aloud helps. From −4 to −3 is one. To −2 is two, to −1 is three, to 0 is four, and to 1 is five.
e) Subtracting on the number line
To subtract, start at the first number and move left.
Start at 3. Move 5 places left. You land on −2.
So 3 − 5 = −2.
Notice that you can subtract a bigger number from a smaller one. The answer simply crosses zero into the negatives. Counting numbers alone cannot do this, which is the main reason integers exist.
f) A check that always works
Adding always moves right, so the answer is further right than where you started.
Subtracting always moves left, so the answer is further left.
If your answer sits on the wrong side of where you began, you have moved the wrong way.
g) Where this is used
A weather forecaster reports temperatures above and below zero. A bank shows a positive balance and an overdraft. A lift indicator counts floors up and down from the ground.
Words to know
- Integer -- a whole number that can be positive, negative, or zero, with no fractional or decimal part.
- Number line -- a straight line on which every integer has a fixed position, with zero at the centre, positive numbers to the right, and negative numbers to the left.
:::checkpoint Check yourself
- Which is larger, −7 or −3?
- Use a number line to work out −5 + 8.
- Use a number line to work out 2 − 6.
- Give one real-life situation where negative numbers are used. :::
Bridge to practice
Try the exercises below -- on identifying integers, representing them on a number line, and adding and subtracting them.