Mathematical Modelling - November 2007, Stage 1&2

Problems

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How Many Pieces?

Stage: 1 Challenge Level: Challenge Level:1

How many loops of string have been used to make these patterns?

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How Many Pieces This Time?

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

How many pieces of string have been used in these patterns? Can you describe how you know?

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Train Routes

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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Simple Train Journeys

Stage: 1 and 2 Challenge Level: Challenge Level:1

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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Reef and Granny

Stage: 2 Challenge Level: Challenge Level:1

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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Turning Granny

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?