This activity uses the familiar environment of a swimming pool to introduce negative numbers, and is designed to be accessible to primary pupils at Key Stages 1 and 2.
Detailed teachers' notes for this activity are available on our NRICH website.
When you start learning about swimming it may be that you will go
down the steps carefully to reach the bottom, or use the ladder
from the side of the pool.
Here's a picture of a set of steps and the ladder.
You'll probably notice that I've coloured the steps.
The first step into the water is light green, the second step is
purple, the third red and so on.
The same is true of the ladder.
Later, I'll be thinking about numbering these coloured steps.
1. Suppose your friend puts you on step $4$ and you only want to go
a little way into the water so you head for the red step. Stepping
down carefully, one step at a time, how many steps will you have to
2. Now the next time you want to go into the water your friend
takes you to step $2$ and you're going to step down carefully to
the blue step at the bottom. How many steps down do you have to
3. When you have finished swimming you take yourself to the yellow
step and meet your friend on step $5$. How many steps, one at a
time, do you have to take?
Maybe it's time to number these coloured steps.
I think I'll go for numbering them down from the water
Can you invent your own way of numbering the steps which go under
When you've numbered your steps in some way perhaps you'd like to
send in the pictures?
If you're finding hard to get started, try looking at this hint.
Detailed teachers' notes for this activity are available on our NRICH website, where you can also find thousands more mathematical resources including problems, investigations and games for all ages from 5 to 19.