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LAB 2.3 Tangram Polygons Name(s) Equipment: Tangrams • Make geometric figures, using any number of tangram pieces from one set. • Keep track of your figures by checking boxes in the chart below. • On the left side of the chart, add the names of other geometric figures you make, then check the box for the number of pieces you used in making them. Triangle Square Parallelogram How many pieces you used 1 2 3 4 5 6 7 Discussion A. Which of the puzzles cannot be solved For example, a one-piece, nonsquare rectangle is impossible.Are there others Mark those puzzles with an X. B. Explain why a six-piece square is impossible. 30 Section 2 Tangrams Geometry Labs © 1999 Henri Picciotto, www.MathEducationPage.org
LAB 2.4 Symmetric Polygons Name(s) Equipment: Tangrams This tangram polygon By adding a small ...or rotationally symmetric: is not symmetric: tangram triangle, it can be made mirror symmetric: 1. Add one or more tangram pieces to each tangram pair below to make mirrorsymmetric polygons. Sketch your solutions on the figures. 2. Repeat Problem 1, making rotationally symmetric polygons. 3. Create your own symmetric tangram polygons. Sketch them on the back of this sheet. Discussion A. In Problems 1 and 2, is it more elegant to create symmetric figures by adding as few additional pieces as possible, or as many additional pieces as possible B. Create your own puzzles in the style of Problems 1 and 2. C. Is it possible for a tangram polygon to exhibit both mirror and rotational symmetry Geometry Labs Section 2 Tangrams 31 © 1999 Henri Picciotto, www.MathEducationPage.org
Page 1: GEOMETRY Henri Picciotto LABS ACTIV
Page 4 and 5: Project Editor: Editorial Assistant
Page 7 and 8: Contents Introduction .............
Page 9 and 10: 9 Distance and Square Root ........
Page 11 and 12: Introduction About This Book This b
Page 13 and 14: • Manipulatives can motivate stud
Page 15 and 16: If you have access to computers, I
Page 17 and 18: 1 Angles An essential foundation of
Page 19 and 20: LAB 1.1 Angles Around a Point Name(
Page 21 and 22: LAB 1.2 Angle Measurement (continue
Page 23 and 24: LAB 1.4 Angles of Pattern Block Pol
Page 25 and 26: LAB 1.5 Angles in a Triangle Name(s
Page 27 and 28: LAB 1.6 The Exterior Angle Theorem
Page 29 and 30: LAB 1.6 The Exterior Angle Theorem
Page 31 and 32: LAB 1.7 Angles and Triangles in a C
Page 33 and 34: LAB 1.8 The Intercepted Arc (contin
Page 35 and 36: LAB 1.10 Soccer Angles Name(s) Equi
Page 37 and 38: LAB 1.10 Soccer Angles (continued)
Page 39 and 40: LAB 1.10 Soccer Angles (continued)
Page 41 and 42: 2 Tangrams Tangram puzzles are quit
Page 43 and 44: LAB 2.1 Meet the Tangrams (continue
Page 45: LAB 2.2 Tangram Measurements (conti
Page 49 and 50: 3 Polygons In the first two labs, t
Page 51 and 52: LAB 3.1 Triangles from Sides (conti
Page 53 and 54: LAB 3.2 Triangles from Angles (cont
Page 55 and 56: LAB 3.3 Walking Convex Polygons (co
Page 57 and 58: LAB 3.4 Regular Polygons and Stars
Page 59 and 60: LAB 3.5 Walking Regular Polygons (c
Page 61 and 62: LAB 3.6 Walking Nonconvex Polygons
Page 63 and 64: LAB 3.8 Sum of the Angles in a Poly
Page 65 and 66: LAB 3.9 Triangulating Polygons (con
Page 67 and 68: 4 Polyominoes Polyominoes are a maj
Page 69 and 70: LAB 4.1 Finding the Polyominoes Nam
Page 71 and 72: LAB 4.2 Polyominoes and Symmetry Na
Page 73 and 74: LAB 4.3 Polyomino Puzzles Name(s) E
Page 75 and 76: LAB 4.4 Family Trees (continued) Na
Page 77 and 78: LAB 4.5 Envelopes (continued) Name(
Page 79 and 80: LAB 4.7 Minimum Covers Name(s) Equi
Page 81 and 82: LAB 4.9 Polytans Name(s) Equipment:
Page 83 and 84: LAB 4.10 Polyrectangles (continued)
Page 85 and 86: 5 Symmetry Many of the activities i
Page 87 and 88: LAB 5.1 Introduction to Symmetry (c
Page 89 and 90: LAB 5.2 Triangle and Quadrilateral
Page 91 and 92: LAB 5.3 One Mirror Name(s) Equipmen
Page 93 and 94: LAB 5.4 Two Mirrors Name(s) Equipme
Page 95 and 96: LAB 5.4 Two Mirrors (continued) Nam
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LAB 5.5 Rotation Symmetry (continue
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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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Triangles and 6Quadrilaterals The c
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LAB 6.1 Noncongruent Triangles (con
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LAB 6.2 Walking Parallelograms (con
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LAB 6.4 Making Quadrilaterals from
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7 Tiling In this section, we addres
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LAB 7.1 Tiling with Polyominoes Nam
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LAB 7.2 Tiling with Pattern Blocks
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LAB 7.4 Tiling with Regular Polygon
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8 Perimeter and Area This section s
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LAB 8.1 Polyomino Perimeter and Are
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LAB 8.2 Minimizing Perimeter Name(s
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LAB 8.3 A Formula for Polyomino Per
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LAB 8.4 Geoboard Area Name(s) Equip
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LAB 8.5 Geoboard Squares Name(s) Eq
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LAB 8.6 Pick’s Formula (continued
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Distance and 9Square Root This chap
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LAB 9.1 Taxicab Versus Euclidean Di
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LAB 9.2 The Pythagorean Theorem Nam
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LAB 9.3 Simplifying Radicals Name(s
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LAB 9.4 Distance from the Origin Na
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LAB 9.6 Taxicab Geometry Name(s) Eq
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10 Similarity and Scaling Similarit
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LAB 10.1 Scaling on the Geoboard Na
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LAB 10.2 Similar Rectangles Name(s)
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LAB 10.3 Polyomino Blowups Name(s)
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LAB 10.3 Polyomino Blowups (continu
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LAB 10.5 3-D Blowups Name(s) Equipm
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LAB 10.6 Tangram Similarity Name(s)
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LAB 10.7 Famous Right Triangles Nam
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11 Angles and Ratios This section p
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LAB 11.1 Angles and Slopes Name(s)
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LAB 11.2 Using Slope Angles Name(s)
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LAB 11.3 Solving Right Triangles Na
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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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Trigonometry Reference Sheet The pa
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LAB 11.6 The Unit Circle (continued
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LAB 11.7 Name(s) Perimeters and Are
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LAB 11.8 “” for Regular Polygon
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1 Angles Lab 1.1: Angles Around a P
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For this pattern block hexagon, add
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Theorems: triangle sum theorem, iso
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Answers 1-5. See student work. 6. T
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7. Answers will vary. Discussion An
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compass and straightedge.You may al
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3. Answers will vary. Here are some
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which Question B hints at, is that
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To make an algebra connection, you
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Answers 1. See Polyomino Names Refe
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Answers 1. C. F, N, P D. Only the W
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Lab 4.7: Minimum Covers This lab is
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5. Discussion Answers A. Polyominoe
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information in the relevant cells o
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Discussion Answers A. Pentagons and
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other. Students can make rubber sta
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draw the lines and duplicate them y
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5. Answers will vary. Here are some
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Or students could analyze: • poss
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For Problem 2, make sure the studen
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2 hexagons, 2 triangles 1 hexagon,
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4. P max 2A 2 5. Answers will vary.
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This shows that 2 A⎤ 2n, and sinc
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Lab 8.5: Geoboard Squares Prerequis
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Answers 1. a. 11 b. 10 c. 4 d. 6.4
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3. Discussion Answers A. √5 5 √
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If your students enjoy Problem 6, a
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4. a. 5. a. (0, 0) (6, 0) (0, 0) (0
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congruent to each other and similar
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2. (In the Perimeter table, numbers
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Discussion Answers A. They are the
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Discussion Answers A. Each individu
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3. Triangle c: 1, 3, 2 4. Triangles
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type of slope triangle will work fo
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Discussion Answers A. Answers will
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8. sin 2 cos 2 1. It is the Pythago
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Geometry Labs Geoboard Paper 239 ©
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Geometry Labs 1-Centimeter Grid Pap
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Geometry Labs Circle Geoboard Paper
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To make the radius of this circle e
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Geometry Labs Unit Circles 247 © 1
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GEOMETRY LABS Geometry Labs are han
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