Exponential Function Designs

To set up this section of the lesson, I tell students that I designed each page of the match-ups with a key idea in mind. I tell them, “While working on the match-ups, see if you can figure out what I think each page is supposed to be about.” In the end, I will ask them to write a 1-sentence summary of the big idea of each page of the packet, so as they work you can circulate and ask them to tell you what they think each page is about.

Some students simply use data points from each graph and plug them into each function until they get a match. This is totally fine, except that the purpose of this task is not to plug and chug but to learn about the behavior of the functions.  If I notice students using the plug-and-chug method, I tell them, “This is great but as you work, see if you can think of ways to do this without plugging and chugging.” Or I tell them, “That’s a great method. See if you can make a guess first and then check your answers by plugging in a point.”

Other students rush to shortcuts and don’t actually check their work using data points. They might be using theories that are not correct to make their match-ups, so it is important to encourage them to actually check points.

This is a great example of MPS2 in practice, because some students work only quantitatively and make no generalizations, so they need to be encouraged to make generalizations, while other students work only abstractly and don’t check any data points with numbers so they need to be encouraged to use some numbers. The most effective strategy for a student to use during this lesson is to make abstract theories and to test them quantitatively, or, alternatively, to find match-ups quantitatively and then develop more abstract theories.

One optional scaffold that you can use with the whole class is the page called Matching Exponential Function Graphs. This is just one page of match-ups that you can use to model the process of working both abstractly and quantitatively. This is the kind of resource I use when I notice most of my students struggling with something: you can project this and then show them your thought process in making the match-ups using both data points and some generalizations.