Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Epidemic Modelling

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

Designing Table Mats

Stage: 3 and 4 Challenge Level:

The photo on the right shows a table mat made from a coiled rope.

Chris wants to produce and sell sets of table mats like this.  Her initial plan is to make them by coiling a thin rope into a rectangular pattern, sewing each layer to the next with 'thread' made of a strand of the material the rope is made from.  Measuring a mat she already has, she decides that 30cm x 24 cm is a good size to aim for.

• Is this size possible using this method - coiling a length of rope as in this image?
• How might she rethink the design so she can make a bigger range of lengths and widths of mat?
This problem is asking you to create a mathematical model for the design of a table mat.

You will need to make sensible assumptions about the thickness of the rope, and the construction of the mat including the length of the starting section of rope in the centre of the mat.  Write down all the assumptions you make so you can revisit them and decide if they are acceptable.