Musical and Exponential Models

Gilberto Franco, Math, Collinswood Language Academy

Final Unit(pdf)   Implementing Teaching Standards(pdf)


This curriculum unit has been made to introduce the concept of exponential models, but also to relate mathematics with real world, to connect math concepts with contexts we don’t usually explore. We don’t need to be a music expert to use this unit. We just need to enjoy music, and be prepared to learn a little bit more about basic music concepts which will help us to understand the idea of exponential growing or decreasing. We don’t notice, but exponential forms are around us, different cases of animal reproduction, spreading news, and some companies have a pyramidal structure with one headmaster and two or three people working directly with him or her, then every one of them is in charge of other two or three people, etc.  The students will learn about how to identify an exponential model, how it works and apply this concept in real world situations. The students will also use tables and graphs to represent mathematically this situation and any other, in order to create an equation to solve the specific situation and others related. This unit includes activities with guitars, but it’d be possible with different strings instruments (violin, banjo, and ukulele). There is also an activity using graphic calculator TI 83Plus, but it’s optional for the purpose of the unit.