I begin class with a function like f(x)=x^2-4 on board and ask my students for summary of any key features they see and different ways to represent the function to show other key features. (MP7) I expect them to be able to comment on the zeros, x and y-intercepts, max/min points, end behavior, and symmetry, as well as suggesting that we could factor the equation, could graph it, and could write it in table form because these are what we've been studying in this unit. If they are really on top of it today, someone will suggest that we need a verbal description of a real-world problem this function might represent to give more meaning to the key features. I then ask my students to pair-share which representations give the best information about which key features and why. After a few moments I randomly select students to share what they discussed then tell them that today they will be comparing a variety of functions represented in different ways, so they can test their opinions about what works best and why.
For this activity I tell my students that they will be working with their back partner to compare two different functions given different representations. I explain that they will be looking for things like which has steeper rate of change, how their end behavior is similar/different, or which has higher maximum or lower minimum point. I distribute the Compare and Contrast handout, ask if there are any questions, then tell my students they have about 20 minutes to complete this assignment. (MP1, MP2) Some students will struggle with two different representations and for them I suggest that they try looking at one function at a time, listing the key features for that function before moving to the second function. I also recommend that they choose the representation that makes the most sense to them and convert the other function into that same form. When everyone is done or after about 25 minutes I ask for volunteers to share their work with the class. I state my expectation that each team will share at least one problem and have a meaningful critique of the others. (MP3)
I close this lesson by having my students write summary of the lesson for an "absent" classmate, a strategy I explain further in my video. These summaries help my students pull together what they've learned today and give me some insight into which students might need additional support.