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PolygonsMath Alliance
October 5, 2010
Kevin McLeodChris Guthrie
Session Goals
Review/finalize our definition of triangle
Deepen our understanding of polygons, including the definition of polygon, and characteristics of polygons
Triangles
At your tables, review your definition(s) of triangle.
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.
A
B
C
Definition of Triangle (Contd.)
Do you think there is anything missing from O’Daffer’s definition?
Is there anything surprising about it?
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)?
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.
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
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
Sorting Criteria (Contd.)
Congruent diagonals
Diagonals bisect each other
At least one pair of parallel sides
Exactly one pair of parallel side
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?
van Hiele Levels
Thinking about the van Hiele levels, where might this sorting activity fit?
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