On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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