The four main forms of carbon--diamond, graphite, buckyballs, and carbon nanotubes (CNTs)--are an excellent vehicle for teaching fundamental principles of chemical bonding, material structure, and properties. Carbon atoms form a variety of structures that are intrinsically connected to the properties they exhibit. Educators can take advantage of this striking relationship between atomic structure and material properties to address several Physical Science Standards, including Structure of Atoms and Structure and Properties of Matter. This article discusses two new allotropes of carbon that are important for nanotechnology--buckyballs and CNTs--and related activities for the classroom. (Contains 7 figures.)