An Investigation into Reflections



This exercise will enable students to build through guided explorations a working definition of the geometric transformation known as a reflection.  They will take this knowledge and use it to make a written proposal accompanied by a class presentation targeted to a fictitious department store recommending the optimal angle settings for three-paneled mirrors.


The goal of this activity is to help students understand geometrically what is taking place when we see our reflection in a mirror and help them to realize mathematics can be used to simulate real world situations and ultimately help make the best recommendation for the situation being presented.  The report part of the exercise will provide experience in writing and presentations.  The primary focus is to provide students with opportunities to practice skills that are required to be a part of today’s workforce.  In addition, an exciting part of this practice is it will be done within a mathematical context!


This activity will be broken up into five parts.



Describing Reflections


Composition of Reflections-Reflection across Two Different Mirror Lines


Making Recommendations Based on Mathematical Investigation


On-site Measurements to Confirm Findings


Reports and Presentations