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Real-World Application, Reconnection in Outdoor Eighth-Grade Geometry

Eighth graders from Karen Seder’s geometry classes have spent this week eyeing, measuring, and estimating the height of campus landmarks using only string, protractors, simple measurements . . . and their eyes.

“It is great to see more real-world applications of what students are studying,” Seder said. “This unit allows them to see how trigonometry can help them in a more day-to-day way. I also love seeing students work together towards a common goal.”

The goal was to use a handmade clinometer made with a protractor, a straw, and a weighted string, to measure the angle of elevation of the campus flagpole, the Belltower, or the top corner of the Upper School. Then, using the angles and the measurements of their distance from the base of the objects, they used the tangent ratio to determine their height.

“To me, it is the cooperation and communication that create my favorite moments,” Seder said. “Students help each other with tape measures, make sure their clinometer is level, and read angle measures. The ‘aha’ moments about the accuracy—and inaccuracy—of their measurements and why that may have occurred are wonderful to see.”

The activity is part of the study of the basic trigonometric ratios of sine, cosine, tangent, and their inverses. Using their learning and measurements, the next day students compared all of the groups’ measurements, voted on which measurement they believed was most exact, then calculated the mean and median measurements to make a final decision on the heights.

“In this time of Covid when students have not been able to do so many of the things they love, being outside and working together is a way to connect with each other again,” Seder said. “It lets them be a true team, as opposed to a virtual team, where they can interact and then react in real-time. This activity, coupled with their original trig-based illustrated word problems, helps them see how math connects to the world around them.”