- Page 1: GEOMETRY Henri Picciotto LABS ACTIV
- Page 5: Acknowledgments Many of these activ
- Page 8 and 9: 4 Polyominoes .....................
- Page 10 and 11: © 1999 Henri Picciotto, www.MathEd
- Page 12 and 13: In some cases, I included lessons w
- Page 14 and 15: has a tendency to dominate our thin
- Page 16 and 17: Cubes: Cubes are useful as multi-pu
- Page 18 and 19: about their measures. If you are co
- Page 20 and 21: LAB 1.2 Angle Measurement Name(s) E
- Page 22 and 23: LAB 1.3 Clock Angles Name(s) What a
- Page 24 and 25: LAB 1.4 Angles of Pattern Block Pol
- Page 26 and 27: LAB 1.5 Angles in a Triangle (conti
- Page 28 and 29: LAB 1.6 The Exterior Angle Theorem
- Page 30 and 31: LAB 1.7 Angles and Triangles in a C
- Page 32 and 33: LAB 1.8 The Intercepted Arc Name(s)
- Page 34 and 35: LAB 1.9 Tangents and Inscribed Angl
- Page 36 and 37: LAB 1.10 Soccer Angles (continued)
- Page 38 and 39: LAB 1.10 Soccer Angles (continued)
- Page 40 and 41: LAB 1.10 Soccer Angles (continued)
- Page 42 and 43: LAB 2.1 Meet the Tangrams Name(s) E
- Page 44 and 45: LAB 2.2 Tangram Measurements Name(s
- Page 46 and 47: LAB 2.3 Tangram Polygons Name(s) Eq
- Page 48 and 49: LAB 2.5 Convex Polygons Name(s) Equ
- Page 50 and 51: LAB 3.1 Triangles from Sides Name(s
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LAB 3.2 Triangles from Angles Name(
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LAB 3.3 Walking Convex Polygons Nam
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LAB 3.4 Regular Polygons and Stars
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LAB 3.5 Walking Regular Polygons Na
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LAB 3.6 Walking Nonconvex Polygons
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LAB 3.7 Diagonals Name(s) Definitio
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LAB 3.9 Triangulating Polygons Name
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© 1999 Henri Picciotto, www.MathEd
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the traditional curriculum, but the
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These are the standard polyomino na
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LAB 4.2 Polyominoes and Symmetry (c
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LAB 4.4 Family Trees Name(s) Equipm
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LAB 4.5 Envelopes Name(s) Equipment
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LAB 4.6 Classifying the Hexominoes
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LAB 4.8 Polycubes Name(s) Equipment
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LAB 4.10 Polyrectangles Name(s) Equ
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© 1999 Henri Picciotto, www.MathEd
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LAB 5.1 Introduction to Symmetry Na
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LAB 5.1 Introduction to Symmetry (c
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LAB 5.2 Triangle and Quadrilateral
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LAB 5.3 One Mirror (continued) Name
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LAB 5.4 Two Mirrors (continued) Nam
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LAB 5.5 Rotation Symmetry Name(s) E
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LAB 5.6 Rotation and Line Symmetry
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LAB 5.7 Two Intersecting Lines of S
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LAB 5.8 Parallel Lines of Symmetry
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© 1999 Henri Picciotto, www.MathEd
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LAB 6.1 Noncongruent Triangles Name
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LAB 6.2 Walking Parallelograms Name
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LAB 6.3 Making Quadrilaterals from
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LAB 6.5 Slicing a Cube Name(s) Equi
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students, or groups of students, as
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LAB 7.1 Tiling with Polyominoes (co
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LAB 7.3 Tiling with Triangles and Q
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LAB 7.4 Tiling with Regular Polygon
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LAB 8.1 Polyomino Perimeter and Are
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LAB 8.1 Polyomino Perimeter and Are
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LAB 8.2 Minimizing Perimeter (conti
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LAB 8.3 A Formula for Polyomino Per
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LAB 8.4 Geoboard Area (continued) N
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LAB 8.6 Pick’s Formula Name(s) Eq
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© 1999 Henri Picciotto, www.MathEd
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In the course of these lessons, I h
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LAB 9.1 Taxicab Versus Euclidean Di
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LAB 9.2 The Pythagorean Theorem (co
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LAB 9.3 Simplifying Radicals (conti
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LAB 9.5 Area Problems and Puzzles N
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LAB 9.6 Taxicab Geometry (continued
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The other central idea of this sect
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LAB 10.1 Scaling on the Geoboard (c
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LAB 10.2 Similar Rectangles (contin
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LAB 10.3 Polyomino Blowups (continu
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LAB 10.4 Rep-Tiles Name(s) Equipmen
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LAB 10.5 3-D Blowups (continued) Na
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LAB 10.6 Tangram Similarity (contin
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LAB 10.7 Famous Right Triangles (co
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we introduce the tangent ratio in t
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LAB 11.1 Angles and Slopes (continu
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LAB 11.2 Using Slope Angles (contin
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LAB 11.3 Solving Right Triangles (c
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LAB 11.4 Ratios Involving the Hypot
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LAB 11.5 Using the Hypotenuse Ratio
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LAB 11.6 The Unit Circle Name(s) Eq
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LAB 11.7 Name(s) Perimeters and Are
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LAB 11.8 “ ” for Regular Polygo
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© 1999 Henri Picciotto, www.MathEd
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This activity should help students
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d. Answers will vary. One angle sho
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3. 25°. Explanations will vary. 4.
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Discussion Answers A. They have the
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Problems 1 and 2 offer a good oppor
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Discussion Answers A. No. It’s on
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4. Every Star or Number Angle p-th
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Lab 3.6: Walking Nonconvex Polygons
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• Adding a side vertex adds one t
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2, 3. 4. 2 × 2 2 × 3 2 × 4 3 ×
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It is not crucial that students fin
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Plastic SuperTangrams are available
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Answers 1. a. Answers will vary. b.
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By placing the mirror on an equilat
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have the advantage that the mirrors
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encouraging students to select care
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4. No triangles; the sum of angles
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Make sure your students notice the
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may remind them of (or supply them
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what you know about the angles of a
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8 Perimeter and Area Lab 8.1: Polyo
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8.1 C 50 Perimeter 45 40 35 30 25 2
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D. There is no greatest area. See N
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Lab 8.6: Pick’s Formula Prerequis
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4. In a right triangle, the sum of
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Answers 1. 10 10 101 226 109 229 55
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Geoboards are likely to be too smal
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d. 6. Taxi- 4 7. The centers are at
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(3, 4) (6, 8) (4, 3) (8, 6) (3, 5)
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. c. 226 Notes and Answers Geometry
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. 7. Only the parallelograms (inclu
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3. The scaling factors are as follo
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the angle between -90° and 90° fo
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that, as it is possible to solve an
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2. Tangent 5. The cosines of the tw
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is about 2.94; is about 2.38. P A L
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240 1-Centimeter Dot Paper Geometry
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242 1/5-Inch Graph Paper Geometry L
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Instructions: Trace the figure onto
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246 Isometric Dot Paper Geometry La
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Bibliography Alexanderson, G.L. and