A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

Learn how to use Excel to create triangular arrays.

Use Excel to investigate the effect of translations around a number grid.

This spreadsheet highlights multiples of numbers up to 20 in Pascal's triangle. What patterns can you see?

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree. . . .

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?