Hands-on Geometry: Constructions With a Straightedge and Compass

Put compasses into your students' hands and behold the results! Hands-On Geometry teaches students to draw accurate constructions of equilateral triangles, squares, and regular hexagons, octagons, and dodecagons; to construct kites and use their diagonals to construct altitudes, angle bisectors, perpendicular bisectors, and the inscribed and circumscribed circles of any triangle; to construct perpendicular lines and rectangles, parallel lines, and parallelograms; and to construct a regular pentagon and a golden rectangle.

Students will enjoy fulfilling high standards of precision with these hands-on activities. Hands-On Geometry provides the background students need to become exceptionally well prepared for a formal geometry class. The book provides an easy way to differentiate instruction: Because the lessons are self-explanatory, students can proceed at their own pace, and the finished constructions can be assessed at a glance.

Grades 4-6

Christopher Freeman holds a bachelor's degree in math and a master's degree in math education from the University of Chicago. He teaches math to grades 6-12 at the University of Chicago Laboratory Schools. Freeman also teaches math enrichment classes in the Worlds of Wisdom and Wonder and Project programs for gifted children in the Chicago area, sponsored by the Center for Gifted at National-Louis University. His books are the fruits of curricula he has developed for gifted children in these programs and in the regular classroom.

All of Freeman's activities involve students in inductive thinking. Students are presented with an intriguing situation or set of special cases, and they formulate conjectures about the fundamental mathematical properties that govern them. Students in Freeman's classes practice inductive thinking when they find winning strategies for math games, formulate conjectures about the structure of many-pointed stars, or figure out which polygons can fit together to form polyhedra―and why.

Freeman is a regular presenter at the annual conventions of the National Association for Gifted Children. He contributed a chapter on math curriculum in the NAGC publication Designing and Developing Programs for Gifted Students, edited by Joan Franklin Smutny. He has published three books with Prufrock Press, Nim: Variations and Strategies, Drawing Stars and Building Polyhedra, and Compass Constructions.