Week 3 · Negative numbers, opposites, comparing, and the families of numbers · 3 lessons
1
Negative numbers and opposites on the number line
Discover Mathematics P6: Term 1, Unit 2, Lessons 1–3
GoalRead and write negative numbers in real situations, and find the opposite of a number.
New words
negative number · a number less than 0, written with a minus sign, like −3positive number · a number greater than 0opposites · two numbers the same distance from 0 on opposite sideszero · the starting point; neither positive nor negative
Explanation
On a number line, numbers to the right of 0 are positive and numbers to the left of 0 are negative. We use negative numbers for things that are below a starting point: a temperature below 0 °C, a depth below sea level, a floor below the ground, or money that is owed. We write −3 and say negative 3. On a vertical number line, up is positive and down is negative. Zero is neither positive nor negative. Two numbers that are the same distance from 0 but on opposite sides are opposites: 4 and −4 are opposites. The opposite of 0 is 0, and the opposite of −7 is 7.
Worked examples
On a cold winter night the thermometer on the mountain shows 4 degrees below zero. We write −4 °C. The liquid is below the 0 mark.
Points A and B are both 3 steps from 0. A is 3 and B is −3, so they are opposites. The opposite of 3 is −3, and the opposite of −3 is 3.
Situation
Number
A diver 12 m below the sea surface
−12
The second basement of a car park
−2
Mina owes her brother 30 LE
−30
A kite 12 m above the ground
12
Real situations as numbers. Starting points are 0: sea level, ground level, nothing owed.
Class activity
Weather hunt. Look up the temperatures of three cities in a newspaper or on a phone, for example a cold mountain town and two warm cities. Write each as a number with its sign. Which is the lowest? Draw a vertical number line and mark them.
Practice
1
Write a number for 8 degrees below zero.
−8 °C.
2
Write the opposite of each number: 9, −15, 0.
−9, 15 and 0.
3
Which number does point P show?
−5, because P is 5 steps to the left of 0.
4
A bird is 7 m above the sea and a fish is 7 m below it. Write both positions as numbers. How are they related?
The bird is 7 and the fish is −7. They are opposites.
5
Is 0 positive or negative? What is the opposite of the opposite of −6?
Zero is neither. The opposite of −6 is 6, and the opposite of 6 is −6 again.
