Building an Effective Interactive Math Activity

Throughout the semester we have used technology like Desmos and Geogebra to facilitate learning of different topics. Though different methods are used, it usually involves some correlation between equations and graphs, which I have found helpful in developing understanding. Specifically, sliders are something new to me; I have found them to be very helpful as I can manipulate different terms in an equation and immediately see how it affects the graphical representation. From there I can evaluate trends and build understating based on multiple sources, equation and graph.

I decided that it would fun and practical to learn how to make an activity; so, with students in mind, I built one in Desmos. One of my favorite activities up to this point has been the Marbleslide activities that we have done using a couple different types of equations, so I decided to make one for exponentials and logarithmics. I wanted to include both types with the idea that it would help students make connections between the two related forms. 

When developing this activity I realized that a lot more planning has to go into it than I would have originally thought. The first thing I had to think about was, "what do I want students to get out of this?" I decide that I wanted to design an activity that would make students think about how the different terms in exponential and logarithmic equations relate to a graph, and how those graphs relate to each other. As such, I started with two activities that allowed the use of sliders to change the graph. The first challenge was uses an exponential equation and the second uses a logarithmic, though the ball drop and stars were in the same location. I wanted them to see that, even though the functions are inverses you can still make the graphs look very close to, or identical to each other. Moving forward I wanted to make sure that the game offered an opportunity to use a variety of different graphical shapes, and in a few cases I actually stipulated that the student must use one of each graph type (exponential and logarithmic) in collecting all of the stars. I also tried vary the difficulty of the tasks, creating some that were more simple, and one that I considered quite challenging.

This was a fun learning experience for me and something that I will definitely use in the future with my students.

Here is my finished product:

https://student.desmos.com/?prepopulateCode=cw6gs