Conjecturing and generalising

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?

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

Can you do a little mathematical detective work to figure out which number has been wiped out?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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

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

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?