Jacob Nazeck ; Algebra II Teacher

Ridgeview Classical Charter School ; Fort Collins, Colorado

When I started thinking about my Cell Phone Problem lessons, I was looking for a fairly simple but relevant context for rational functions. I wanted something that the students could grab onto easily, that made sense to them, and would naturally lead to a fairly straightforward rational function. These two “cell phone problems” do that.

The first lesson ( The Cell Phone Problem, Day 1) focuses on signal strength. It was a little less accessible because it’s a physics equation. Some students felt a little uncomfortable for that reason, but they got the idea: they look at their phones, they see those little bars that show signal strength, they already know the idea. So, that context got them in. As they constructed this graph they could see what a rational function would look like. That one was a very straightforward, very simple version of a rational function.

Cell Phone Problem, Day 2 ups the ante just a little bit. Again, it is a fairly simple but relevant context for these kinds of functions. We’re taking very gradual, incremental steps from a really simple, rational equation that has all of the fundamentals and bringing it to a slightly more complex system of rational functions.

The cost equations in this problem are fairly easy to generate. They come from a natural, everyday situation so the students can get into them easily. Best of all, this problem brings up all of the major elements that I want to hit on throughout the rest of the unit. First, the equations: What do they look like, and why do we call them rational equations? Next, it brings up the graphs. What’s the graph of a rational function look like? What’s an asymptote? Lastly, we start solving systems of rational equations to find the intersections of the graphs.  It’s not a complex situation, but it brings up all of these things naturally and meaningfully.

In one or two days, we’ve basically surfaced all of the big ideas. We’ve got equations, we’ve got tables, we’ve got graphs, we’ve got all of the features of graphs and we’ve got systems of equations to solve. It all comes out in this really natural way, which is great. I just taught these lessons over the last couple of days, and it took me three class periods. It really brought up a lot of misconceptions that we were able to clear away. So hopefully, as we move forward they’ve got this concept to hang onto. They have seen all of this once before in this setting – so let’s relate it all back to that.

So that was the idea – to kick this unit off with these problems to see all of the major features in one fairly simple, relevant, real world context. There’s no more applicable, real world concept to students than cell phones.