The plan here is to start with geometric figures and move to patterns and variables. Algebra and geometry are connected.

Important definition:

Regular Polygon: A polygon is "regular" if all its sides are equal in length and all its interior angles are also equal to each other.

 Time Estimate Activity Main Idea 15 min (:15) Discussion of polygons and regularity. Try drawing them. What do we need to know to draw a regular polygon? 5-10 min (:25) Discuss the troubles with drawing regular polygons of more than 4 sides. Why does it get more difficult? Squares and triangles are easier because you know, or have a good sense of, the interior angles.
Step-by-step guide

1. Give everyone paper and pencil and ruler. Ask them to draw a regular triangle
• A regular quadrilateral (a square)
• A regular pentagon
• A regular hexagon
• A regular heptagon
• A regular octagon and so on until they begin to have trouble.

2. Why does it get more difficult to draw the regular polygons as the number of sides increases? Answer: it’s harder to guess what the angle and the side length will be as the number of sides and angles increases.

3. What do you need to know to be able to draw the polygons correctly? Answer: You need to know what the interiors are. Since they are all equal, if you know one, you will know them all.

Possible Problems and Concerns
Students may not know what regular means. See the definition at the left.

Internet Resources

http://www.mste.uiuc.edu/m2t2/algebra/regs.gsp is a Geometer's Sketchpad file of regular polygons. Resources for this unit are available at http://www.mste.uiuc.edu/m2t2/algebra/