 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 3, Part A:
Hidden Polygons

In This Part: Identifying Polygons | Finding Polygons

Each corner of a polygon, where two sides meet, is called a vertex. The plural of vertex is vertices. Labeling vertices with capital letters makes it easy to refer to a polygon by name. For example, this figure contains two triangles and one quadrilateral: To name one of the polygons in the figure, list its vertices in order as you move around it in either direction. One name for the shaded triangle is Triangle ABC. Other names are possible, including BCA and ACB. One name for the white triangle is Triangle ADC.

The quadrilateral in the figure could be named Quadrilateral ABCD, BCDA, DCBA, or DABC. All of these names list the vertices in order as you move around the quadrilateral. The name ACBD is not correct.

In the following activities, you will search for polygons in several figures. You'll calculate a score for each figure by adding the following:

 a. 3 points for each triangle b. 4 points for each quadrilateral c. 5 points for each pentagon d. 6 points for each hexagon

As you work, try to discover a systematic way to find and list all the polygons in a figure.

Be careful to give only one name for each polygon. You may want to record your work for each problem in a table like this one, which shows the result for this figure.   Polygon Names Score      Triangle ABC, ADC 6 Quadrilateral ABCD 4 Pentagon None - Hexagon None - Total Score 10  Problem A2 How many polygons can you find in the following figure?   Here's a sample strategy for counting: Count triangles and quadrilaterals, and then look for their "complements." So YXWZV is everything in the shape except triangle YVZ. Another strategy would be to choose one vertex (e.g., X). Count all of the triangles that contain X. Then count all of the quadrilaterals that contain X, and so on. Next, count all of the triangles that contain vertex Y but not X, and so on.   Close Tip Here's a sample strategy for counting: Count triangles and quadrilaterals, and then look for their "complements." So YXWZV is everything in the shape except triangle YVZ. Another strategy would be to choose one vertex (e.g., X). Count all of the triangles that contain X. Then count all of the quadrilaterals that contain X, and so on. Next, count all of the triangles that contain vertex Y but not X, and so on. Problem A3 How many polygons can you find in the following figure?  Problem A4 How many polygons can you find in the following figure?    Video Segment In this video segment, Ric and Michelle discuss their strategies for finding polygons in various figures. Watch this segment after you have completed Problems A2-A4, and compare your strategies with those of the onscreen participants. What kinds of strategies did Ric and Michelle use to find polygons in their figures? Did you use any other strategies? If you are using a VCR, you can find this segment on the session video approximately 6 minutes and 46 seconds after the Annenberg Media logo.      Session 3: Index | Notes | Solutions | Video