Explaining, convincing and proving

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

How can we make sense of national and global statistics involving very large numbers?

Match the cumulative frequency curves with their corresponding box plots.

Is it possible to find the angles in this rather special isosceles triangle?

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Can you work out the dimensions of the three cubes?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Two ladders are propped up against facing walls. At what height do the ladders cross?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?