Making Math Fun: Utilizing Technology to Teach

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In my Math Activities for Secondary Teachers course, we have had the pleasure of exploring Desmos, a math site that can function as a calculator, form graphs, and has many interactive activities students can use to learn.
We tried some of these activities in class. Notable mentions were Polygraph and Marbleslides. Polygraph can be thought of as a math Guess Who type of game: students are matched with a classmate, one classmate picks a graph, and the other must use yes or no questions to find the graph that their fellow student picked. This is especially useful in helping students become familiar in terminology such as intercepts, turns, degrees, and increasing/decreasing. Marbleslides is a game in which students must construct graphs in order to get the marble to roll into all the stars. This game can be done with all different types of functions (our class used rational functions) and is useful in helping students learn the behaviors of function graphs.
After using these activities from the perspectives of the student, I decided to take a look at Desmos activities from the perspective of a teacher. I asked myself: "What kind of unit would I want to teach? Where would I want to use a Desmos activity? What do I want to accomplish in using this activity?" I decided that I would look for an activity that can be used interchangeably: before, during, or at the end of a unit. Additionally, I wanted to use an activity that would take students all or most of a class period, since students would be learning a lot while doing the activity. I wasn't sure what kind of unit I wanted to teach, so I just began browsing.
The first activity that caught my eye was called "Function Carnival." (Here's the link). In this activity, students are whisked to a carnival that deals with various types of functions, which they must use to help the stars of the carnival.
First up is Cannon Man. Students must draw a graph representing his height over time, so that Cannon Man's act can be as spectacular as possible.  Since Cannon Man starts from the ground, goes to a specific height, and then goes back to the ground, students inevitably have to graph a parabola. So, this type of activity is useful in helping students understand a real-life situation that deals with quadratic functions.
The next act is bumper cars. Students draw a graph of a car's distance over time. Since the car is simply going from point A to point B at a constant speed, the function is linear. This activity helps students understand the importance of slope in relation to things such as speed and distance, and give students a perspective on when they will utilize linear functions.
Finally, students are taken to the Ferris wheel, where they draw a graph of a specific green car's height over time. Since this car's height goes from the ground, to a point at the top, to the bottom again, all at a different slope over time, the function ends up being a polynomial function. This one is perhaps the most difficult to master, but it helps students to understand the difference between quadratic and polynomial functions. That is, functions of a higher degree.
In addition to these three acts, students are asked questions about other work as well. For example, they will be given a scenario such as "John drew this graph in relation to Cannon Man. What did he do wrong?" These kinds of questions allow students to reflect on their own work, and allow them to demonstrate their own understanding.
I would use this activity in a variety of ways. I know I would use it in a unit about functions, probably with ninth or tenth graders. (Maybe even middle school students in a high-level algebra class). I could use it at the beginning of this unit, to introduce them to the various types of functions we will be dealing with. I could use it in the middle of the unit, as a type of formative assessment. Or I could use it at the end of the unit, as a fun type of preparation for the final test. This activity, no matter where I use it, is important because it allows students to apply different types of functions to different situations, which leads to more understanding about these functions.
I believe this type of activity is important because of its implications. In algebra, it is important that students understand polynomial functions, since it is the basis of so many concepts that will be introduced later. A polynomial graph has many of the same characteristics as sine and cosine graphs, quadratic functions are applied in higher-level math, and linear graphs are always relevant, even in three-dimensional math. Using an activity that helps students to solidify their understanding of these concepts is an important thing to do early on in math.
In conclusion, I think these types of activities are valuable in that they present a new, fun way for students to do math. We are in an age where we, as teachers, can use the technology given to us, and I think we would be foolish not to take advantage of that.