Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 1, Session 2: Characteristics of Polygons, Regular and Irregular Polygons,Classifying Polygons, a Hierarchy for Polygons1. What are the important concepts?a) Polygons are closed 2-dimensional shapes formed by line segments that meet at a"corner" or vertex.b) A polygon is named by the number of its sides.c) If all sides of a polygon are equal, their interior angles are equal, and thus theshape is termed a regular polygon.d) The shape of a polygon depends not only on its side lengths, but also on themeasures of its interior angles.e) Polygons can be classified according to their side length and angle attributes.2. How do children think about these concepts?a) When considering triangles, most young children think of an equilateral trianglestanding on its base. If the same triangle is rotated so that a vertex is pointeddownward, they often do not "see" it as a triangle.Similarly, if shown a scalene triangle, with three different side lengths, they alsomight not perceive it as a triangle. This is because they have equated their concept ofa triangle with a single model. They have not yet discovered that a triangle is any 3-sided closed figure.b) Quadrilaterals can be organized into a hierarchy, from an irregular quadrilateral tothe most specialized quadrilateral, a square.Most youngsters do not realize that a square is also both a rectangle and a rhombus, aswell as a parallelogram. Just as with triangles, this can be because they have not hadexperience discussing the characteristics of quadrilaterals.However, they also lack the vocabulary and terminology (such as parallel andopposite) as well as the idea of angle measurement. Thus, once they realize a polygonhas four equal sides but doesn't "look" square they may think of it as a "squashedsquare" where two of the vertices look "pointier" than the other two. This informaldescription of a rhombus is a starting point from where the teacher can begin toformalize how to describe the shape's characteristics.c) Children may assume that any closed figure is a polygon, or that an open figurecomposed of line segments is a polygon. Thus it is important to offercounterexamples such as those below so that students can begin to refine theirdefinition of a polygon's required characteristics.