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?