The Giant Triangles are brightly colored lightweight, 1 meter edge length, equilateral triangles, which can quickly be assembled and reassembled into polyhedra. This workshop activity was developed in an urban teacher preparation program for students with little or no prior exposure to conceptual or investigative learning approaches. It involves groups building their own creations with the triangles which are to be `beautiful and interesting' and then explaining why their creation is beautiful and interesting. Taking each creation in turn, we will discuss how to bring out the inherent mathematics and identify key teaching opportunities in whole group discussions.