Every person that studied Algebra made a big leap to the next mathematical level when they examined the properties of quadratic functions; the straight line they have been study for so long has magically bent. While working with quadratics, students typically labor to memorize the quadratic formula, factor expressions, complete the square, find a vertex, find x and y intercepts, graph functions, and solve "real world problems" in their textbooks. Practicing each of these skills is an essential first step for students to take in the process of learning mathematics. But they can't stop there.
Earlier this week, students took the next step by actually experiencing parabolic trajectories. Using their iPads, they videotaped themselves making parabolas by doing things like throwing a ball off the mezzanine level of the gym, flying off jumps on snowboards and sleds in the middle of quad, and jumping off stone walls. Using the app, Vernier Video Physics, students tracked their location during each frame of the video. They then used the data to create a quadratic equation that modeled their flight.
Students found meaning in the y-intercept, the vertex, and the x-intercept on their graphs. These points represented where they began flight, reached their peak height, and where they landed respectively. This project raised very interesting questions for students. For example, the app allows you to set the location of the origin on top of the video, which leads to the question, "Where should I set the origin so that my numbers can tell a clear story about the flight of the object?" Students also wrestled with data that wasn't perfect like all of the data given in "real world" problems in a book.
Once students finished, they critiqued the work of their classmates in an effort to figure how they could improve their work. It was fascinating to watch students cordially and professionally offer suggestions and debate fixes.