I. Introductive Activity:
Concept Attainment with Exemplars. Listing positive and negative exemplars, have students hypothesize and make a connection between the positive exemplars utilizing the negative exemplars for contrast to clarify or qualify the concept.
Example: Positive Examples Negative Examples
*How are shapes alike?
*How are shapes different?
Classification Scheme:
1. Number of sides
2. Number of sides
3. Equilateral only
4. Convexity
5. Concavity
6. Equiangular only
7. Regular
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II. Defining the Concept: Once the students have discovered the concept and shared their prior knowledge of that concept, they will agree on a definition of the concept.
In this lesson the appropriate responses would center around the fact that the positive exemplars are true polygons "a closed plane figure" whose sides are segments that intersect only at their endpoints. No two sides with a common endpoint are collinear."
III. Refining the Concept: Next the students will break into research groups. Each group is assigned a different polygon. Students work in their groups, discuss possible classifications for their shape, enter their discoveries into the database, then sketch those shapes. Their task is to find the facts to a list of questions (all groups will answer the same questions). Students will enter the facts into a database as their reporting device. Groups are as follows:
1. Triangle
2. Quadrilateral
3. Pentagon
4. Heptagon
5. Octagon
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IV. Redefining the Concept: The class will examine the database, reexamine the definition of the concept and arrive at a final definition of the concept. Students will also discuss the characteristics, consequences, and influences of the concept.
V. Curriculum Content: Students will enter math curriculum content that is grade level appropriate. Accompanying the unit are the traditional book or worksheet activities as well as Internet activities for discovering polygons in nature. A field trip to collect leaves may be used to identify different polygons in the natural environment.
VI. Closure/Beyond: To close the unit, the teacher will conduct a syntaktikos activity that will lead the students to developing a series of polygons representing ones found in nature.
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