Can you have backwards numbers?


Numbers are useful for counting and measuring things. We use them all the time, even when we’re not thinking about maths. For example, I use them every day, for telling the time, cooking, exercising and driving my car.

Normally when we count, we start at zero and count upwards in whole numbers: one, two, three, and so on… But what happens if we count down from a bigger number – do we have to stop when we get back to zero?

When my daughters started to learn their numbers, we counted with them up to ten over and over again. We practised these numbers until they had learnt them in the right order. And for a long time, I think my girls thought that these were the only numbers in the world because we always started with one (1) and stopped at ten (10).

We can arrange the numbers in a row called a number line, like this:

0   1   2   3   4   5   6   7   8   9   10

A number line is a useful tool for sorting numbers into the correct order. It also helps us to work out adding and subtracting (taking away) sums and to look for number patterns.

But counting doesn’t stop at the number ten. As I explained in a post about the biggest number, counting and numbers can go on and on for ever! And we don’t always have to count the numbers from smallest to largest – we can count them in the other direction as well, simply by working back down the number line.

But what happens when we get to zero?

Well, what if I told you that, instead of being at the beginning of the number line, zero is the number that sits right in the very middle? That means that there is the same number of numbers on each side of zero in a number line that stretches on an on for ever in both directions! So, the number line actually looks more like this:

-10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0   1   2   3   4   5   6   7   8   9   10


The numbers on the right-hand-side of zero are the ‘counting up’ numbers that you will be used to. These are the numbers that we start off learning and they are the ones that we use in every day life.

The numbers on the left-hand-side of zero look a little bit different. They use the same digits (like 1 and 5) but they have a special maths minus (or take-away) symbol in front of them to show that they are different. They are called ‘negative numbers’ and they are smaller than zero. This means that they aren’t very useful for counting everyday things (like sweets or pencils). But negative numbers are good for measuring, especially for measuring things change.

For example, negative numbers can describe how a car slows down when the driver presses the brake pedal. Or how much colder the winter weather gets compared to the temperature at which water freezes into ice.

We can add and subtract and multiply negative numbers in the same way that we use positive numbers but sometimes the answers are a little bit surprising. To find out more about counting positive and negative numbers, check out [this webpage] which is all about the number line (!

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