Explaining, convincing and proving

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Can you find the hidden factors which multiply together to produce each quadratic expression?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Have you ever wondered what it would be like to race against Usain Bolt?

When two closely matched teams play each other, what is the most likely result?

Simple additions can lead to intriguing results...

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?