Visualising and representing

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

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

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

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Where should runners start the 200m race so that they have all run the same distance by the finish?

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

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...