Can you find out which 3D shape your partner has chosen before they work out your shape?

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?

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?

What is the shape of wrapping paper that you would need to completely wrap this model?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Various solids are lowered into a beaker of water. How does the water level rise in each case?