Using sequential chains of regular n-gons in a row with one side touching, as for example, one triangle, two triangles, three triangles, and so on, students graph the length of the perimeter versus the number of n-gons and determine the functional relationship for different values of n. (MKR)

The material examines areas generated by combinations of: (1) Circles and Triangles; (2) Closely Packed Circles; and (3) Overlapping Circles. The presentation looks at examples of certain areas and at logical ways to generate the necessary algebra to clarify the problems and solve general cases. Ideas for extension are provided. (MP)

Three worksheets are provided to help secondary students explore relationships among the areas of a variety of similar figures constructed on the sides of right triangles. The activity is extended to include the relationship among the lengths of the sides of the right triangle. Included are several student worksheets. (DC)

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Presents a cooperative-learning lesson in which high school students visit stations equipped with different tools to establish the midpoint of a Pixy Stix, a brand of candy-filled straw. Provides solutions for two potential stations, suggestions to extend the activity, and two activity worksheets. (MDH)