Being curious

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

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

What's the largest volume of box you can make from a square of paper?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Use your skill and judgement to match the sets of random data.

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.