Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.

Students learn about the fundamental strength of different shapes, illustrating why structural engineers continue to use the triangle as the structural shape of choice. Examples from everyday life are introduced to show how this shape is consistently used for structural strength. Along with its associated activity, this lesson empowers students to explore the strength of trusses made with different triangular elements to evaluate the various structural properties.

Students work within constraints to construct model trusses and then test them to failure as a way to evaluate the relative strength of different truss configurations and construction styles. Each student group uses Popsicle sticks and hot glue to build a different truss configuration from a provided diagram of truss styles. Within each group, each student builds two exact copies of the team's truss configuration using his/her own construction method, one of which is tested under shear conditions and the other tested under compression conditions. Results are compiled and reviewed as a class to analyze the strength of different types of shapes and construction methods under the two types of loads. Students make and review predictions, and normalize strengths. Teams give brief presentations to recap their decisions, results and analysis.