Explaining, convincing and proving

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?

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?