GEOMETRY LABS ACTIVITIES FOR GRADES 8–11

[Pages:266]GEOMETRY Henri Picciotto

LABS

ACTIVITIES FOR GRADES 8?11

120?

120?

B + C = 50?

30? 150?

150? 30?

120? 120?

120? 120?

Pmax = 2A + 2

120?

60?

60?

120?

(a + b) 2 - 2ab

120? 60?

120?

60?

(a + b) 2 - 2ab

90?

90?

60?

60?

60?

90?

90?

BLACKLINE MASTERS



Geometry Labs

Henri Picciotto

Project Editor: Editorial Assistant: Production Editor: Copy Editor: Production and Manufacturing Manager: Production Coordinator: Text Designer: Compositor: Cover Designer and Illustrator: Technical Artist: Prepress and Printer:

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Reproduction Permission

? 1999 by Henri Picciotto. Some rights reserved.Henri Picciotto grants the teacher who downloads Geometry Labs the right to reproduce material for any non-commercial use.

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TMCircleTrig Geoboard is a trademark of Key Curriculum Press. All other registered trademarks and trademarks in this book are the property of their respective holders.

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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 Tangrams and Pattern Blocks awakened in me an interest in doing math with manipulatives when I was a beginning teacher, many years ago.

Henri Picciotto

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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 Tangrams ...................................................................................................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

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? 1999 Henri Picciotto,

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

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Geometry Labs

? 1999 Henri Picciotto,

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