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Negative numbers and the number line
Years 4 to 8
Numbers below zero live on the left of the number line, and adding and subtracting are moves along it.
For learners
Numbers can go below zero. On a cold day the temperature might be −3°C. We say 'minus three'.
On a number line, zero is in the middle. Positive numbers go to the right. Negative numbers go to the left.
Adding moves you right. Taking away moves you left. 2 − 5 means start at 2 and move 5 to the left. You land on −3.
A worked example
What is ?
- Start at −3 on the number line.
- Move 8 to the right: −3 to 0 is 3 steps, then 5 more.
- You land on 5.
For grown-ups
A number line or a thermometer is the best model. Count down to zero first, then carry on below zero. Later, the rules for multiplying two negatives come from patterns, not tricks.
Common mistakes
- Thinking −5 is bigger than −2 because 5 is bigger than 2. −2 is closer to zero, so it is bigger.
- Dropping the minus sign when subtracting a negative: goes up to 7.
- Treating two minuses next to each other as 'cancel' without understanding the move.
Why it matters
Negative numbers are used in temperatures, money owed, heights below sea level, and in all of algebra and graphs.
Topics in quarter that use this
- Negative numbers
- Calculating with negative numbers
- Counting through zero
- Substituting negative numbers