Drawing Stars & Building Polyhedra

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9781593630669: Drawing Stars & Building Polyhedra

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-D 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 reproducible handouts 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.

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About the Author:

Christopher Freeman holds a bachelor's degree in math and an 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.

Review:

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 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 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. --Tina Forester, TEMPO, Texas Association for the Gifted and Talented, Spring 2004

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Book Description Prufrock Press, United States, 2005. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. 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. Students develop a definition of star and find a procedure for drawing stars with seven, eight, nine, or more points. Students assemble equilateral triangles, squares, pentagons, hexagons, octagons, and decagons to form symmetrical 3-dimensional solids called polyhedra. 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. Bookseller Inventory # APC9781593630669

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Book Description Prufrock Press, United States, 2005. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.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. Students develop a definition of star and find a procedure for drawing stars with seven, eight, nine, or more points. Students assemble equilateral triangles, squares, pentagons, hexagons, octagons, and decagons to form symmetrical 3-dimensional solids called polyhedra. 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. Bookseller Inventory # APC9781593630669

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Book Description Prufrock Press. Paperback. Book Condition: New. Paperback. 64 pages. Dimensions: 10.7in. x 8.1in. x 0.2in.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-D solids called polyhedra. This book allows students to experiment for themselves: Some combinations dont 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 reproducible handouts 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9781593630669

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