🌡️ Negative numbers
Below zero
There are numbers below zero, and you’ve seen them in every winter weather forecast.
Someone once told you that you can’t take 7 from 3.
That’s only true if you stop counting at zero.
Keep counting past zero and you’ll find the answer below it.
The puzzle
Counting carries on past zero
Picture a thermometer. Warm temperatures are near the top and cold ones further down, with 0° in the middle. Think of zero as a doorway: if you go straight down through it, the counting carries on, but now each number has a minus sign in front.
Your turn. Grab the mercury and drag it up and down, then push it through zero and watch the readout keep counting.
18°
Watch the readout as you cross zero. The counting keeps going, but now with a minus sign. −1° means one degree below zero.
Which is colder: −5° or −2°?
Now, which is the smaller number?
The trap
Is 5 always bigger than 2?
Answer both questions before you look at the number line, and stick with your answers.
Which is colder: −5° or −2°?
And which number is smaller: −5 or −2?
The further left a number is on the line, the smaller it is. 5 is bigger than 2, but a minus sign turns that round. The bigger the number after a minus sign, the further below zero you are, so −5 < −2.
When you subtract, you walk left.
Zero is just one spot along the way, and you can keep walking past it.
The why
Walking 3 − 7 along the line
To subtract, walk left along the line. Start at 3 and take 7 steps left. You’ll walk past zero and keep going until you land on −4. Pick your own start and number of steps and try it.
Doing the sums
Temperature sums
You can think of any negative-number sum as a change in temperature. Set a starting temperature and choose how much it rises or drops. You’ll see the tempting wrong answer next to the right one, with the working.
Your number line goes down below zero.
It can go left of zero too.
Put the two together and every point on the map gets its own address.
The whole map
Two number lines make a map
Put one number line across and another up and down, and you get a full map. Every spot has an address: you give the across number first, then the up-or-down number, always in that order. Across, minus means left. Up and down, minus means down. Drag the dot around, then try the four challenges.
You can always keep counting past zero.
The numbers keep going down below it.
Once you know about minus numbers, you’ll spot them on freezers, in overdrafts and on a lift’s floor −1.
One more thing
Negative numbers turn up all over the place. Your freezer runs at −18°. An overdrawn bank account is a balance below zero. In a lift, the floors under the ground floor are often numbered −1 and −2. The shore of the Dead Sea is more than 400 metres below sea level, so its height is a negative number.
And next time someone tells you that you can’t take 7 from 3, show them a thermometer. If it’s 3° and the temperature drops 7°, it ends up at −4°. If you can walk them along the line to −4, you really understand it.