Being curious

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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?

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?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Simple additions can lead to intriguing results...

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

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?