Graphene's unique combination of exceptional mechanical, electronic, and thermal properties makes this material a promising candidate to enable next-generation technologies in a wide range of fields, including electronics, energy, and medicine. However, educational activities involving graphene have been limited due to the high expense and complexity associated with fabricating and characterizing graphene. Here, we demonstrate an economical, safe, and simple technique to synthesize multilayer graphene films via chemical vapor deposition in 30-45 min in a classroom setting. Raman spectroscopy indicates that the graphene is of high quality, scanning electron microscopy shows that the films are continuous over large areas, and oxidation studies demonstrate graphene's high impermeability. The films are also transferred to insulating, optically transparent substrates, which enables measurement of the high electrical conductivity of graphene and direct visualization of several layers of atoms. This graphene synthesis has been successfully implemented in diverse settings with students ranging in education level from 5th grade to undergraduate. In addition to reinforcing fundamental concepts at the core of chemical education, this experiment introduces students to cutting-edge nanotechnology research.