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

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Can you find a way to identify times tables after they have been shifted up?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference is divisible by 6. What if one of the terms is 3?

A story for students about adding powers of integers - with a festive twist.

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

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

Cellular is an animation that helps you make geometric sequences composed of square cells.