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Block 27

MA .8.G. 2.3 Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles, and the sum of angles in polygons. Block 27. Polygon Capture Game.

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Block 27

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  1. MA.8.G.2.3Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles, and the sum of angles in polygons Block 27

  2. Polygon Capture Game • In this activity, participants classify polygons according to more than one property at a time. In the context of a game, participants move from a simple description of shapes to an analysis of how properties are related. Note: Use activity if review of polygons is necessary If not, skip to slide 8 Teacher Quality Grant - AE - FAU

  3. Instructional Plan • The purpose of this game is to motivate students to examine relationships among geometric properties of polygons. • From the perspective of the Van Hiele model of geometry, the students move from recognition or description to analysis. • Middle school students rarely use more than one property to describe a polygon. • By having to choose figures according to a pair of properties, students go beyond simple recognition to an analysis of the properties and how they interrelate. Teacher Quality Grant - AE - FAU

  4. Pre-requisites for the Game • Knowledge of the properties of polygons that include angles, sides, diagonals • Use the special quadrilateral worksheet if a review is necessary • Familiarity with vocabulary: parallel, perpendicular, polygon, and classification of angles Teacher Quality Grant - AE - FAU

  5. Materials for the Game • Game Rules • Game Cards • Game Polygons Each group of two needs one set of Cards and one copy of the polygons Teacher Quality Grant - AE - FAU

  6. Extensions • The Polygon Capture game cards can also be used to generate figures. As in the game, students turn over two cards. Instead of capturing polygons, they use a geoboard or dot paper to make a figure that has the two properties. Rather than a game, this is simply an activity to help students learn to coordinate the features of a polygon. Teacher Quality Grant - AE - FAU

  7. Discussions • Will students find difficult to coordinate two properties at a time? • How could this game by adapted for different students? • Is this game best suited for advanced students? • Could this game be used as a review of the lesson? Teacher Quality Grant - AE - FAU

  8. Interior Angle Sum of Polygons • Distribute worksheet Triangulation of polygons • Participants, in small groups, work on the worksheet • Whole group discussion on patterns seen in the worksheet Teacher Quality Grant - AE - FAU

  9. Exterior Angle Sum of Polygons • Is there an exterior angle sum? • Open a new GeoGebra file • Draw a large polygon • Extend its sides to form a set of exterior angles • Measure all the interior angles • Use the Linear Pair Conjecture to calculate the measure of each interior angle • Calculate the sum of the measures of the exterior angles • Share your results with group members Open the GeoGebra file exterior angles, to show the exterior angle sum conjecture. Notice what happens to the exterior angles when the vertices get closer to the point in the center. Teacher Quality Grant - AE - FAU

  10. Star Polygons A star polygon is formed by extending pairs of sides of a convex polygon that are connected by a third side. Regular Star Pentagon Teacher Quality Grant - AE - FAU

  11. Regular Star Pentagon What is the sum of the angles in the “points of the star? Teacher Quality Grant - AE - FAU

  12. Non-regular star pentagon Hint: What is the sum of the angles of the shaded polygon? Look at quadrilateral ABCJ How many quadrilaterals can we have like that? Teacher Quality Grant - AE - FAU

  13. What is the sum of the angles in the points of the star hexagon? Hint: Each point of the star hexagon is part of a pentagon Teacher Quality Grant - AE - FAU

  14. Could we generalize? • Could we have used a star triangle? • Could we have used a star quadrilateral? • What is the pattern? • Is it possible to find a general formula? Teacher Quality Grant - AE - FAU

  15. General formula • If a star polygon is from from an n-sided polygon (n ≥ 5) • (the sum of the measures of the points of the star polygon) + (n-2)(sum of the measures of the angles of the n-gon) = n(n-3)180° Teacher Quality Grant - AE - FAU

  16. Extension How does the sum of the internal angles of a {7, 3} star compare to a {7, 2} star? {7, 2} star {7, 3} star Teacher Quality Grant - AE - FAU

  17. Extension: • How does the sum of the internal angles of a {7, 3} star compare to a {7, 2} star? Teacher Quality Grant - AE - FAU

  18. What about the exterior angles? Teacher Quality Grant - AE - FAU

  19. Regular polygons and Tessellations • Do all regular polygons tessellate? • Which ones do and which ones don’t? • Why? • Can an explanation be given based on the interior angles? Open the GeoGebra file polygon tessellation to very your answers Teacher Quality Grant - AE - FAU

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