# Mathematical Modelling - November 2007, Stage 2&3

## Problems

### Simple Train Journeys

##### Age 5 to 11 Challenge Level:

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?

### Reef and Granny

##### Age 7 to 11 Challenge Level:

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?

### Turning Granny

##### Age 7 to 11 Challenge Level:

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?

### Twisting and Turning

##### Age 11 to 14 Challenge Level:

Take a look at the video and try to find a sequence of moves that will take you back to zero.

### More Twisting and Turning

##### Age 11 to 14 Challenge Level:

It would be nice to have a strategy for disentangling any tangled ropes...

### Turning Tangles

##### Age 11 to 14 Challenge Level:

Look carefully at the video of a tangle and explain what's happening.

### All Tangled Up

##### Age 11 to 14 Challenge Level:

Can you tangle yourself up and reach any fraction?

### Cola Can

##### Age 11 to 14 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?