Author: Christopher M. Freeman
Product Code: 662
ISBN: 9781593630669
Pages: 64
Availability: In stock.

Using this book, students learn to draw stars with seven, eight, or more points, and formulate conjectures about their mathematical structure. They also assemble polygons into 3-D polyhedra and develop spatial intuition.

Drawing Stars: Students develop a definition of star and find a procedure for drawing stars with seven, eight, nine, or more points. They also use stars to illustrate multiplication: for example, 2 x 4 = 8 describes two overlapping squares that form an 8-pointed star. Students discern mathematical properties of stars. They distinguish continuous stars (which can be drawn without lifting pencil from paper) from stars that consist of overlapping copies of simpler stars. Students formulate a conjecture that uses the Greatest Common Factor to predict whether a particular star will be continuous or overlapping.

Building Polyhedra: Students assemble equilateral triangles, squares, pentagons, hexagons, octagons, and decagons to form symmetrical 3-dimensional solids called polyhedra. This book allows students to experiment for themselves: Some combinations don’t work, but students enjoy discovering the combinations that do fit together. Students develop spatial intuition that applies to the structure of molecules, to playground climbing equipment, and to geodesic domes. The book provides blackline masters of polygons to photocopy onto colored paper. Students cut out the polygons, fold the flaps, and attach them with small staplers. Completed polyhedra make an attractive wall display.

These activities meet four distinct NCTM standards.

Grades 4–7


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Review by: Tina Forester, Texan Association for the Gifted and Talented - May 1, 2004
Polyhedra are three-dimensional figures with flat polygonal surfaces. You probably know them as solids. Christopher Freeman knows them as the door to mathematical motivation and imagination. As both a teacher and a student of concept mathematics, and a proponent of three-dimensional problem solving, I fully agree.

The workbook size, Drawing Stars and Building Polyhedra, expands the mathematical drawing of star patterns into three-dimensional constructions while guiding students to inductively develop definitions, test conjectures, and analyze properties of geometric shapes. NCTM standards in the areas of numbers and operations, geometry, reasoning and proof, and connections are clearly addressed in the introduction section to each unit. Lessons are open-ended and allow for more advanced students to work independently on more difficult lessons; a real plus for the regular education classroom teacher with multiple mathematics groups.

Drawing Stars and Building Polyhedra exhibits a level of creative giftedness often lacking in mathematics instruction. The interdisciplinary connections and problem solving opportunities these forms present are limited only by the imagination. This is a thinking book for student and teacher alike.

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