Download Polygons

Polygons
Math Alliance
October 5, 2010
Kevin McLeod
Chris Guthrie
S
Session Goals
S Review/finalize our definition of triangle
S Deepen our understanding of polygons, including the
definition of polygon, and characteristics of polygons
Triangles
S At your tables, review your definition(s) of triangle.
Definition of Triangle
(O’Daffer et al.)
S 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
Definition of Triangle (Contd.)
S Do you think there is anything missing from O’Daffer’s
definition?
S 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.)
S 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
S Choose a recorder for your table
S One person removes a card from the envelope
S Sort the quadrilateral shapes by the criterion on the card
S Record the sort and discussion on the recording sheet
S Scramble the shapes, pass the envelope to the next person,
and repeat
Sorting Criteria
S All right angles
S At least one right angle
S Both pairs of opposite sides congruent
S Both pairs of opposite sides parallel
S Both pairs of opposite angles congruent
Sorting Criteria (Contd.)
S Congruent diagonals
S Diagonals bisect each other
S At least one pair of parallel sides
S Exactly one pair of parallel side
What Did You Discover?
S Did any of the sorting criteria pose greater challenges than
others?
S Did you notice any patterns, or relationships between the
different sorts?
van Hiele Levels
S Thinking about the van Hiele levels, where might this
sorting activity fit?