Being resourceful

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Here are two games you can play. Which offers the better chance of winning?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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?