A simple paper cutout helped students understand complex concepts in calculus at Bob Jones High School.

Bob Jones students 'fly' their helicopters in calculus class. (Photo by Kennedy Booker)

Students in Calculus ‘A’ classes participated in a helicopter optimization project. Before testing, students cut out paper helicopters and attached wings of different sizes.

“Students were given a formula to calculate which optimal wing length would be used next for testing,” Teresa Tarter said. “This project created a relaxed environment where students could work on math and have fun doing it.” Tarter and Kyna Schutzbach teach these classes, along with advanced calculus.

Tarter modified Dr. Madhuri Mulekar’s presentation, “Paper Helicopters to Teach Exploratory Data Analysis and Inference,” from the Alabama Council of Teachers of Mathematics conference in 2011.

Mulekar’s presentation emphasized gathering statistics. “I changed the experiment … for application of differentiation, specifically optimization (finding absolute minimum and maximum values),” Tarter said.

The Bob Jones students received two sheets of neon paper to make nine different paper helicopters with varying blade lengths. They divided into teams with each member designated for certain responsibilities, including ‘dropper,’ timer and data transcriber.

“Their goal was to determine wing length that maximizes flight time. They collected data on various wings by flying (dropping) all nine helicopters four times each,” Tarter said. “The paper helicopters spin when dropped, so they appear to be flying.”

The student mathematicians applied the scientific method in collecting their data and analyzing corresponding results.

After collecting data, the students used “regression capabilities of their graphing calculators to fit a curve to their data,” Tarter said. “The resulting graph is called a mathematical model. They can use the function to determine the blade length that maximizes their paper helicopter’s flight time.”

With the helicopter experiment, the students used calculus to solve a real-world optimization problem. “They also used a prediction equation, randomization to more accurately collect data and discussed the effect of other variables, besides wing length, involved in the experiment,” Tarter said.

What was the experiment’s conclusion? Helicopters with shorter blade lengths tended to work better, Tarter said.