Compass Constructions: Activities for Using a Compass & Straightedge (Grades 5-8)

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9781593633165: Compass Constructions: Activities for Using a Compass & Straightedge (Grades 5-8)
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Extend your geometry curriculum with hands-on geometric drawing lessons that involve the use of a compass and straightedge. Compass Constructions activities supplement advanced geometry lessons for students in grades 5–8.

Students will enjoy activities that apply fundamental geometric concepts studied in class, such as the definitions and properties of altitudes, angle bisectors, perpendicular bisectors, parallel lines with transversals, parallelograms, and other quadrilaterals. Students will broaden their knowledge by completing construction activities such as Construction Arithmetic, The Infinitesimal and the Golden Ratio, Proofs of Properties, Hilbert’s Theorem, and more.

Not only will this book provide students with challenging activities, it also will prepare students for success in formal, proof-oriented geometry that will present itself later in students’ mathematics education.

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About the Author:

Christopher Freeman holds a BA in math and an MAT in math education from the University of Chicago. He teaches math to grades 6 through 12 at the University of Chicago Laboratory Schools. Chris 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 Chris’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.

Mathematical reasoning has two essential components: inductive and deductive. Deductive reasoning begins with fundamental causes and ascertains their effects. School mathematics classes generally stress deductive reasoning, as when students learn to follow algorithms to answer multiplication or division problems, to solve equations, or to prove theorems. Students generally have less opportunity to practice inductive reasoning—to examine the effects and surmise their fundamental governing principles. Students in Chris’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.

Chris 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 two books with Prufrock, Nim: Variations and Strategies and Drawing Stars and Building Polyhedra.

Review:

No basic mathematics curriculum can be considered complete without the inclusion of geometry. Geometry is best taught in drawing lessons that incorporate the use of a compass and a straightedge. An ideal curriculum supplement specific to the compass and the straightedge is Compass Constructions: Activities for Using a Compass and Straightedge by Christopher M. Freeman. Offering “hands-on” geometric drawing lessons and ready-to-use reproducible handouts, Compass Constructions covers Lines and Arcs; Kites and Basic Constructions; Centers of a Triangle; Perpendiculars and Rectangles; Parallels and Parallelograms; Constructing Triangles; The Infinitesimal and the Golden Ratio; Similar Triangles; Circles and Tangents; and Construction Arithmetic. The three appendices offer high school level geometry problems that will demonstrate the application of the previous lessons. The answers to all the problems and assignments comprising Compass Constructions are provided in the “Answers” section at the end of the book. Compass Constructions is a thoroughly “user friendly” compilation and is strongly recommended for both classroom math class curriculums—and self-instruction as well as home schooling math curriculums. --
    —James A.Cox, Editor-in-Chief, Midwest Book Review

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