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Polygons

Polygons. Math Alliance October 5, 2010. Kevin McLeod Chris Guthrie. Session Goals. Review/finalize our definition of triangle Deepen our understanding of polygons, including the definition of polygon , and characteristics of polygons. Triangles.

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Polygons

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  1. Polygons Math Alliance October 5, 2010 Kevin McLeod Chris Guthrie

  2. Session Goals • Review/finalize our definition of triangle • Deepen our understanding of polygons, including the definition of polygon, and characteristics of polygons

  3. Triangles • At your tables, review your definition(s) of triangle.

  4. Definition of Triangle (O’Daffer et al.) • A triangle, ΔABC, is the union of three segments AB, AC and BC determined by three non-collinear points A, B and C. B C A

  5. Definition of Triangle (Contd.) • Do you think there is anything missing from O’Daffer’s definition? • Is there anything surprising about it?

  6. What is a polygon? Discuss at your tables: What would be a definition of polygon that was appropriate in third grade? How (if at all) would this definition be different from a definition that was appropriate for older students (or adults)?

  7. Definition of Polygon(O’Daffer et al.) • A polygon is a closed curve created from the union of segments meeting only at endpoints, such that • At most two segments meet at one endpoint, and • Each segment meets exactly two other segments at their endpoints.

  8. Quadrilateral Sort • Choose a recorder for your table • One person removes a card from the envelope • Sort the quadrilateral shapes by the criterion on the card • Record the sort and discussion on the recording sheet • Scramble the shapes, pass the envelope to the next person, and repeat

  9. Sorting Criteria • All right angles • At least one right angle • Both pairs of opposite sides congruent • Both pairs of opposite sides parallel • Both pairs of opposite angles congruent

  10. Sorting Criteria (Contd.) • Congruent diagonals • Diagonals bisect each other • At least one pair of parallel sides • Exactly one pair of parallel side

  11. What Did You Discover? • Did any of the sorting criteria pose greater challenges than others? • Did you notice any patterns, or relationships between the different sorts?

  12. van Hiele Levels • Thinking about the van Hiele levels, where might this sorting activity fit?

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