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Geometry-Labs.Pdf Henri Picciotto GEOMETRYGEOMETRY ACTIVITIES FOR GRADES 8–11 ° 120° B + C = 50 LABSLABS 120° 120° 30° 120° 150° 150° 120° 30° 120° Pmax = 2A + 2 120° ° 60° 120 120° ° 2 2 60 (a + b) - 2ab (a + b) - 2ab 60° 120° 60° 90° 90° ° 60° 90 90° 60° 60° BLACKLINE MASTERS www.MathEducationPage.org GL361_ M_509_L.qx 10/21/09 3:59 PM Page Geometry Labs Henri Picciotto GL361_ M_509_L.qx 10/21/09 3:59 PM Page Project Editor: Dan Bennett Editorial Assistant: James A. Browne Production Editor: Jason Luz Copy Editor: Paul Green Production and Manufacturing Manager: Diana Jean Parks Production Coordinator: Ann Rothenbuhler Text Designer: Kirk Mills Compositor: Ann Rothenbuhler Cover Designer and Illustrator: Diane Varner Technical Artist: Kirk Mills Prepress and Printer: Data Reproductions Executive Editor: John Bergez Original Publisher: Steven Rasmussen Reproduction Permission © 1999 by Henri Picciotto.Some rights reserved.Henri Picciotto grants the teacher who downloadsGeometry Labs the right to reproduce material for any non-commercial use. For more information on this license, see <www.MathEducationPage.org/rights.html>. ™CircleTrig Geoboard is a trademark of Key Curriculum Press.All other registered trademarks and trademarks in this book are the property of their respective holders. For more curriculum materials by Henri Picciotto, see <www.MathEducationPage.org>. GL361_ M_509_L.qx 10/21/09 3:59 PM Page Acknowledgments Many of these activities were developed at the Urban School of San Francisco. Special thanks to my students and colleagues there, particularly Richard Lautze and Kim Seashore. Thanks also to Joe Todaro.As the editor of an earlier version of this book, he contributed many ideas. These math teachers and professors helped develop my love for geometry, or offered insights which have no doubt found their way into this book: Cal Crabill, G. D. Chakerian, Lew Douglas, Phil Mallinson, Sherman Stein, and Joel Teller. Finally, I’d like to thank the authors of the Elementary Science Study at the Educational Development Center, whose math units Ta n g ra m s and Pattern Blocks awakened in me an interest in doing math with manipulatives when I was a beginning teacher, many years ago. Henri Picciotto Geometry Labs iii GL361_ M_509_L.qx 10/21/09 3:59 PM Page GL361_ M_509_L.qx 10/21/09 3:59 PM Page Contents Introduction ...................................................................................................ix 1 Angles ..........................................................................................................1 Lab 1.1 Angles Around a Point .................................................................3 Lab 1.2 Angle Measurement .....................................................................4 Lab 1.3 Clock Angles ................................................................................6 Lab 1.4 Angles of Pattern Block Polygons .................................................7 Lab 1.5 Angles in a Triangle ......................................................................9 Lab 1.6 The Exterior Angle Theorem .....................................................11 Lab 1.7 Angles and Triangles in a Circle ..................................................14 Lab 1.8 The Intercepted Arc ...................................................................16 Lab 1.9 Tangents and Inscribed Angles ....................................................18 Lab 1.10 Soccer Angles .............................................................................19 Soccer Angles Worksheet ...........................................................................21 Soccer Circles Worksheet ...........................................................................22 Soccer Discussion Sheet .............................................................................23 Soccer Goal Worksheet ..............................................................................24 2 Tang rams ...................................................................................................25 Lab 2.1 Meet the Tangrams .....................................................................26 Lab 2.2 Tangram Measurements ..............................................................28 Lab 2.3 Tangram Polygons ......................................................................30 Lab 2.4 Symmetric Polygons ...................................................................31 Lab 2.5 Convex Polygons .......................................................................32 3 Polygons ....................................................................................................33 Lab 3.1 Triangles from Sides ...................................................................34 Lab 3.2 Triangles from Angles .................................................................36 Lab 3.3 Walking Convex Polygons ..........................................................38 Lab 3.4 Regular Polygons and Stars ........................................................40 Lab 3.5 Walking Regular Polygons .........................................................42 Lab 3.6 Walking Nonconvex Polygons ....................................................44 Lab 3.7 Diagonals ...................................................................................46 Lab 3.8 Sum of the Angles in a Polygon .................................................47 Lab 3.9 Triangulating Polygons ...............................................................48 Geometry Labs v © 1999 Henri Picciotto, www.MathEducationPage.org GL361_ M_509_L.qx 10/21/09 3:59 PM Page 4 Polyominoes ...............................................................................................51 Lab 4.1 Finding the Polyominoes ............................................................53 Polyomino Names Reference Sheet ...........................................................54 Lab 4.2 Polyominoes and Symmetry .......................................................55 Lab 4.3 Polyomino Puzzles .....................................................................57 Lab 4.4 Family Trees ...............................................................................58 Lab 4.5 Envelopes ...................................................................................60 Lab 4.6 Classifying the Hexominoes .......................................................62 Lab 4.7 Minimum Covers .......................................................................63 Lab 4.8 Polycubes ...................................................................................64 Lab 4.9 Polytans ......................................................................................65 Lab 4.10 Polyrectangles .............................................................................66 5 Symmetry ..................................................................................................69 Lab 5.1 Introduction to Symmetry ..........................................................70 Lab 5.2 Triangle and Quadrilateral Symmetry .........................................73 Lab 5.3 One Mirror ................................................................................75 Lab 5.4 Two Mirrors ...............................................................................77 Lab 5.5 Rotation Symmetry ...................................................................80 Lab 5.6 Rotation and Line Symmetry .....................................................82 Lab 5.7 Two Intersecting Lines of Symmetry ..........................................84 Lab 5.8 Parallel Lines of Symmetry .........................................................86 6 Triangles and Quadrilaterals .......................................................................89 Lab 6.1 Noncongruent Triangles .............................................................90 Lab 6.2 Walking Parallelograms ...............................................................92 Lab 6.3 Making Quadrilaterals from the Inside Out ................................94 Lab 6.4 Making Quadrilaterals from Triangles .........................................95 Lab 6.5 Slicing a Cube ............................................................................96 7 Tiling .........................................................................................................97 Lab 7.1 Tiling with Polyominoes ............................................................99 Lab 7.2 Tiling with Pattern Blocks .......................................................101 Lab 7.3 Tiling with Triangles and Quadrilaterals ...................................102 Lab 7.4 Tiling with Regular Polygons ..................................................103 8 Perimeter and Area ..................................................................................105 Lab 8.1 Polyomino Perimeter and Area .................................................106 Lab 8.2 Minimizing Perimeter ..............................................................109 Lab 8.3 A Formula for Polyomino Perimeter ........................................111 Lab 8.4 Geoboard Area .........................................................................113 Lab 8.5 Geoboard Squares .....................................................................115 Lab 8.6 Pick’s Formula ..........................................................................116 vi Geometry Labs © 1999 Henri Picciotto, www.MathEducationPage.org GL361_ M_509_L.qx 10/21/09 3:59 PM Page 9 Distance and Square Root ........................................................................119
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