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'Simple Train Journeys' printed from http://nrich.maths.org/
, but it would be good to focus more on looking for patterns and generalising in this case. You might like to work on the different routes for four stations as a whole class then ask small groups to look at five
and six stations so that you can pool results. Ask the children how they are recording the different routes - using initial capitals to stand for the stations is a great help, but share any good ways the pupils have found.
In order to look for a pattern in the numbers of routes, it might be helpful to make a table, something like this:
|Number of station visits
||Number of different journeys
and so on ...
Encourage the class to look carefully at how the number of different journeys in each case is related to the number of different journeys for smaller numbers of station visits. Once they have identified the pattern, ask them to think about why the pattern occurs.
Making up their own rail networks and investigating them with similar questions would be a good next step. Alternatively, you could challenge them to devise networks with certain criteria.
Initially, this problem could be introduced in a similar way as is suggested in the notes for