If I have the chance I will think of a few provocations on the fly. Not all of the will be good, but just to keep them coming:
• Create a concertina secret mini book about a secret. A mini book you can keep hidden.
• Invent a folded paper object. Can you show someone else how to make it?
• Stab some scissors through a sheet of white paper or newspaper. Now cut a landscape with trees and animals into the centre of the page, in negative space.