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Where should runners start the 200m race so that they have all run the same distance by the finish?

Can you find triangles on a 9-point circle? Can you work out their angles?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

We usually use squares to measure area, but what if we use triangles instead?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

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?