Why do this problem?
can be used as a starting point for introducing, and raising children's awareness of, negative numbers.
The first part of the problem is effectively counting along a number line in different directions, but in this case it is vertical rather than the more usual horizontal orientation, so that we are moving up and down rather than right and left. The final part of the activity encourages children to be creative and invent their own way of numbering the steps below the water level. This will
undoubtedly provide some interesting points for discussion amongst the whole class. You may want to share a few of their ways with everyone, asking the relevant children to explain why they think their way works well. There could be some debate about which ways might work best.
At this stage, you could specifically introduce the idea of negative numbers. One way to do this is to ask children whether they know of any number scales which are vertical and this might make them think of a thermometer. It would be great to have a thermometer to hand and then you could look together at the negative parts of the scale, talking about what they mean. You could then transfer
this negative number scale to the swimming pool. At a higher level, the next stage would be to revisit the swimming pool problem here and discuss numerical differences between negative and positive numbers.
Can you tell me about how you are working these out?
Some pupils could move away from the swimming pool situation and be given other situations to find the numerical difference between two numbers - one positive and one negative.
Pupils may find it helpful to have a small vertical number line going from the negative to the positive. It may be necessary to have some discussion about the place of zero.