Why do this problem?
based on the well-known story, opens the door to a whole realm of mathematical calculations that can be explored with or without a spreadsheet. It also gives opportunities for pupils to create further questions to answer.
If possible, it would be good to read a version of The Pied Piper of Hamlin with the children so that they are familiar with the story before starting this investigation.
On a second reading, you could use the story to talk about the number of legs at particular times. You could also pose some theoretical questions, such as asking the children to imagine you've opened the book at a page which had 10 legs on it in total. How many people and how many rats could there have been? Learners could work on this in pairs using mini-whiteboards and then you can talk
about the possiblities as a whole group. This will lead into a general chat about the number of animals/people and how the number of each affects the other.
You might also want to spend some time sharing ways of recording what the children are doing. Some might be drawing pictures or symbols for the rats/people, others might be recording numbers only. It is worth talking about the different ways and the advantages/disadvantages of each. You may find that after some discussion, a few children adopt a different way of recording to the one they
How many legs do your rats have?
What could you replace a rat with?
Can you tell me about the way you are working out so many possibilities?
(And for the pupils who have gone much further)
What have you noticed about all your results so far?
Can you explain why . . . . . has happened?
Look at animals with other numbers of legs and perhaps three types of different-legged animals at the same time - eg. birds, spiders and pigs.
Some models,toys or pictures representing the different animals may help some pupils to get started.