Calculus Students Use Tartan Field for Experiential Optimization Activity

Tartan Field recently had a three-foot-tall gnome at the center circle, with Upper School calculus students walking heel-to-toe across the field in an activity that experientially dives into optimization problems.   

The task was simple: Get from the corner of the field to the gnome in the center of the field in the most efficient way. The variant was that walking inside the out-of-bounds line required a slower heel-to-toe walk, while outside out-of-bounds lines could be walked normally.

Students timed how long it took to get from the corner of Tartan Field to the gnome, doing a variety of routes. They started with a straight diagonal heel-to-toe walk to the gnome, then continued by walking a swift 10 yards out of bounds before cutting diagonally to the gnome, walking 20 yards before cutting diagonally, all the way up to 50 yards along the sideline and a heel-to-toe walk along the 50-yard line to the gnome.

Students recorded the times of all their routes to the gnome, and plotted the information to Desmos to compare the data.

“We will continue this unit, doing calculus with other real-life applications,” Mr. Spellmire said. “For example, a lifeguard running along the sand versus swimming in the water, or construction crews laying cable underground versus under a river.”

Calculus is an Upper School math elective which studies limits, continuity, differentiation and integration, and the applications of these concepts.