This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

How many different colours of paint would be needed to paint these pictures by numbers?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .

Which of these triangular jigsaws are impossible to finish?