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, Δ ABC, is the union of three segments AB, AC and BC determined by three non-collinear points A, B and C. A B C

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 1. At most two segments meet at one endpoint, and 1. 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

12. 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?

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