Drawing Stars and 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.