Motion in Baseball

Background/Introduction

 

This project is designed for an Algebra II class with a strong foundation in Algebra I and basic pre-algebra and arithmetical skills.   Neither the students nor the teacher need to know very much about baseball for the unit. 

 

            The first part of the unit is a project designed around the use of calculators and motion detectors.  Students will have to formulate relationships between various math functions and the motions they represent.  Students will make use of the coordinate plane system and graph their results in the calculators.

 

            Students will also cover topics in algebra including linear and non-linear relationships.  Students will also make use of graphs in this section.  Since students will be investigating linear relationships, variable changes, and solving equations, they will deal with variable manipulation, slope, and point slope equations.  Students will then cover the idea of linear functions and interpret how they relate to the idea of motion and its mathematical principles.

 

            One of the major topics covered in our project will be the idea of quadratic relationships and functions.  The idea of linear relationships is a good introduction to the world of quadratic functions for they fit well in representing motion mathematically.  The project will cover this area by first comparing and contrasting quadratic and linear relationships and then going into the definitions and parts of quadratic functions.  Students will have to make use of graphs, variable manipulation and equation solving to work with quadratic functions.  The quadratic transformations section will make use of graphing calculators and will show the students what different values in the quadratic equations do to the functions.

 

     The next major topic in the unit is parametric equations.  Parametrics can be used to model many different types of motion.  First, students learn to graph parametric equations and then to convert between parametric and rectangular equations.   Students also explore graphing parametric equations on a graphing calculator, including modifying the t-step and window dimensions.  Finally, students apply what they have learned about parametrics to modeling the path of a baseball through the air, which will directly aid them in the final project.

 

     At the end of the unit, students will present a project in which they have modeled aspects of motion in baseball using linear, quadratic, and parametric functions.  Students will work in groups of 3 and will need to create a visual aid such as a Powerpoint presentation or poster board.