National Aeronautics and Space Administration (NASA) Engineers at Marshall Space Flight Center, Dryden Flight Research Center, and their partners at other NASA centers and in private industry are currently developing X-33, a prototype to test technologies for the next generation of space transportation. This single-stage-to-orbit reusable launch vehicle (SSTO RLV) may replace the Space Shuttle Orbiter and greatly reduce the cost of putting people, satellites, and scientific experiments into space. This guide is divided into several sections: (1) National Science Education Standards; (2) Math Connections; (3) Thinking Skills; (4) Background material; (5) Preparation for the challenge; (6) Day-by-day procedures; (7) Detailed materials list; (8) Extensions; (9) Resources; and (10) Masters. (Contains a list of 5 resources and 19 online resources.) [This Design Challenge was designed by TERC, Cambridge, MA and was sponsored by NASA Marshall Space Flight Center and NASA Dryden Flight Research Center.]