Persistent Parabolas

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persistent-parabolas-1The Roberto Clemente Community Academy College Algebra students finished their unit on quadratics by seeking out and modeling parabolas found in the real world.  Throughout the unit, students engaged in lessons where they often discovered rules that govern quadratics’ behaviors.  For example, one lesson tasked the class with finding the formula of both of the arches in the McDonald’s arch. Students used Desmos graphing software to manipulate a parabola to match the two arches.  A few lessons were learned including identifying what part of a quadratic equation changes, how wide or narrow the parabola is, and in which direction the parabola will open.  The final project required students to recall rules like these as well as the skills they honed throughout the unit to successfully complete the project.

Our budding IB mathematicians went to the internet to find objects that could be in some way represented by a parabola.  Students chose objects as small as bananas to as large as the Golden Gate Bridge that could be modeled by parabolas.  They then, either by using the graphing software Desmos or, for our more artistically inclined students, by hand, drew a parabola that simulated the path of the object.  Using the skills developed throughout the unit, they were able to create descriptions of their modeled parabolas and provided insights about the modeled objects.  Further investigation allowed the students to discover the formula of the parabola by hand. Subsequent manipulations of the equation resulted in further information the students used to increase their understanding of quadratics.  

Beyond the computation, students were asked to justify why parabolas were appropriate to model the objects they chose.  They were asked why they chose the object that they did and what the significance of the parabolic shape was.  The push to think beyond the math was meant to give Clemente students a meaningful connection to how math is involved in everything around us not only numerically, but in how any object can be viewed through the lens of mathematics.