We present FoldMecha, a computer-aided design (CAD) system for exploratory construction of mechanical papercraft. FoldMecha enables students to design their own movements with simple mechanisms by modifying parameters and build physical prototypes. This paper describes the system, as well as associated prototyping methods that make the construction process easier and more adaptable to widely different creations. The paper also discusses a week-long workshop that we held with six teenagers using FoldMecha. The teens successfully designed and built their own mechanisms, and adapted them to a variety of creations. Throughout the workshop, they progressively achieved an advanced level of skill and understanding about mechanical movements.