Conjecturing and generalising

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

How much of the square is coloured blue? How will the pattern continue?

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Engage in a little mathematical detective work to see if you can spot the fakes.

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Try entering different sets of numbers in the number pyramids. How does the total at the top change?