### Sponge Sections

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

### Bands and Bridges: Bringing Topology Back

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

### Triangles in the Middle

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

# Auditorium Steps

### Why do this problem?

This activity is specially designed for the highest-attaining pupils that you ever come across. It acts as a further extension to Wrapping Presents. It's an activity that is intended to give opportunities for those pupils to explore deeply using their intuition, flair and risk-taking skills.

### Possible approach

As this is designed for the highest attaining, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. This discussion could determine what kind of start suits the learner, for example it may be a model needs to be constructed, it may be a conversation about imagining it in the head, it may be a $2$D representation.