Anyone remember the $25,000 pyramid? That show where one person faces the board of words or phrases and has to describe them well enough for the other person (facing away) to say the word. This lesson is similar to that idea – only with graphs of functions! And yes, it was just as fun!!
This is a lesson that one of my PLC members, Hank Sohn, developed and shared with us. He doesn’t blog so I asked for permission to write about the lesson for him. He wanted to be sure I mentioned that he completely “borrowed” this idea from ones online. As we all know, sharing is caring! So this is not necessarily unique, just an adaptation of others excellent work and ideas.
Domain and Range – UGH! Somehow doesn’t seem that difficult to all of us but is super hard for Algebra 2 students to grasp. They just struggle really interpreting equations and graphs to make sense of it all. In my many years I’ve tried teaching it several different ways, all with varying levels of success. Basic notes telling students about domain and range, Sketchpad examples of “squishing” a graph to the x and to the y… you name it, I’ve tried it. Because of that limited success I’m always open to something new. At this point in Algebra 2, we’ve taught composition, inverses, and function families. We’ve mentioned/reviewed the vocabulary of domain and range but not specifically discussed them.
This lesson starts with students in pairs – back to back. One student has a blank graph and the other student has the graph of a function or relation. The student with the graph begins to describe the graph to the other student while that student draws the graph. They have a few minutes to try drawing the graph before they can check to see how they’ve done. They trade places – one drawing before describes now and visa versa – and try another. Originally we’d planned on giving some points and making it more of a competition but they didn’t really seem to need this. They had a great time trying to get it right and were super excited when their graphs turned out looking the same. We did this through three or four graphs before we moved on. The graphs we used are below.
Once we finished playing we debriefed by asking the students what words they used to describe their graphs. We got the ones we wanted – highest, lowest, point, furthest right, left, hill, valley, flat, root, intercept etc. We also got some unique ones – whip (perhaps from the whip-nana dance craze!), wave, swoop. The class had a discussion about which words seemed most useful. We used those to bring them around to domain and range. That discussion moved over to a more formalized set of notes covering the basic examples and a sort below.
These notes adapted from these.
Would love to hear how it goes for others. So far our kids seem to be doing better than I’ve experienced in the past – A WIN!
PS – One thing I’d change or add – some discontinuous graphs – rational functions with asymptotes – for them to draw. I’d also include those in the notes.