A friend at work reminded me of this activity today. Charles teaches the Advanced Algebra/Algebra 2 course I taught a few years ago and mentioned how much he liked this. I remembered the impact it had on the kids so I thought I would share it.
Quick edit: my former colleague Jenny reminded me of the original source of this. I truly couldn’t remember if this was original or not. Thanks for sharing the source material in the comments.
Piecewise functions always seems to trip up students. It’s a tad abstract but still pretty obtainable so I was always frustrated when my students struggled. One night before I taught it, I had this idea for a hands-on activity. (PDF version; Word version)
First, I had the students graph two functions (I chose two linear functions for sake of ease for the first time I did this), each on its own set of axis:
From there, students graphed x = 1 on both graphs.
Then the scissors came out and cut the graphs out and then split the graphs on the x = 1 line. See where I’m going with this?
From there, I have the students take the left side of Graph 1 and the right side of Graph 2 and glue/tape them onto a new set of axes.
From there, I introduce the piecewise function notation in addition to dealing with the “which-graph-do-I-use-at-x=1” question. We finalize it here:
There are then two three-part piecewise functions to work on.
It turned out to be one of those relatively simple activities that pays off in big ways. Students immediately got the start-stop idea. Some students graphed the parts separately and cut and paste the homework questions. And most importantly, the understanding of the concept was better as were the scores.
Here again are the links to the files (PDF version; Word version). If you have any issues with downloading the files, e-mail me or reply to the tweet. And please let me know how it goes if you use this or some variation of it.