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Diagonal Trace


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Rail Network


Delia's Routes


Why do this problem?

This problem has a story line that will encourage learners to become involved in Delia's nocturnal adventures. To answer the question How many days before Delia has to take the same route again? requires the children to find all of the possibilities. Given the number of pathways, this problem could be ongoing asking the children if they could find another three or four routes each day over a couple of weeks. This sheet gives 6 copies of Delia's garden plan.

Key questions

How many tiles along and how many tiles up must Delia go on each journey?
Can you think of a way to record all the different pathways Delia could take?
How many ways can you go when you get to this junction?
Which tiles can Delia not run along because they go into the pond?

Possible extension

Learners could repeat the problem with a differently-sized pond and/or garden.

Possible support

Suggest using different colours to find different routes on this sheet.