Newspaper
a flat page becomes a thing.
fold a sheet of newsprint into the hat, the plane, the fan -- the print folds with the paper
A fold is a mirror: everything on one side of the crease reflects across it. The crease is the perpendicular bisector of your drag, and the object is judged only on its finished outline.
Concepts: folding, geometry, symmetry.
An interactive you play with one thumb, on Wundr.