This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects. Included are materials ranging from simple demonstrations of mathematical problems or principles that the teachers had assigned as classroom learning experiences to complex, sophisticated exhibits intended for fairs and competitions. The first chapter, "Developing a Mathematics Project," discusses choosing a project, research methods, construction methods, responsibilities and guidance, and evaluation criteria. The second chapter, "Looking for Ideas," lists possible project titles and ideas for high school and junior high school. The third chapter, "General Topics," provides examples of how a project can be chosen and developed. Chapter 4, "Resources," provides an annotated bibliography and names and addresses of publishers and periodicals. A total of 193 references are listed in the last chapter. Appendices include: (1) "Mathematics Project Progress Report;" and (2) "Tips for Oral Presentation of Projects." (YP)