## Introduction

The main focus of this module will be on using the kinematic equation h(t)=1/2at^{2}+v_{0}t+h_{0} to introduce students to graphing quadratic equations and how each parameter affects the graph. Using kinematics to introduce the topic gives students a concrete example so that they can better visualize how a, b, and c affect a quadratic graph. Instead of simply discussing the general parameters or features of the graph, students can use their intuition about something like a ball flying through the air to visualize how changing parameters would change a graph. So, instead of thinking how b would affect the graph of a quadratic equation, students could think, "what would happen if I threw two baseballs into the air, but threw one harder than the other?" the students would think in terms of the context of the problem, "would the ball go higher or lower? Spend more or less time in the air?" and use their intuition about the world around them to understand the idea first with the kinematics example and later in a more general and abstract case.

## About the HHMI-FT Internship

This module was created as part of my experience in the HHMI-FT Internship Summer 2012. Through this internship, I was able to work on research projects in the UNC Applied Math Fluids Lab. I worked on the Trachea Project, headed by Jeff Olander and Reed Ogrosky, which was focused on gaining an understanding of air flow in the trachea. I also worked some on the Pipe Flow Project, headed by Tom Nelson. Under the guidance of Jeff Olander, Reed Ogrosky, and Tom Nelson, I was able to observe (and be a part of) their scientific process. The layout and ordering of this module is designed to be similar to their process. The students begin the module using the knowledge they already have and their intution to hypothesize and come up with answers to the questions posed in the first section. From there, students are pushed to abstract that knowledge to understand the problem in a general sense. And finally, the students apply their knowledge to a real-world (or in this case Mario world) situation to see the application in action. This layout is also helpful for teachers becasue the module generally follows a lesson plan format and I have included a lesson plan document at the end of this section. If you are interested in learning more about the UNC Applied Math Fluids Lab click here.