[Post Updated June, 2018]
This semester I gave my Grade 12s a term project to practice function transformations. I began by sourcing the #MTBoS to see who had ventured down this road before. Luckily, several had and they had great advice regarding how to structure the task.
I use Desmos regularly in class, so it was not a huge stretch for them to pick up the tool. I did show them how to restrict domain and range (although most of them stuck exclusively to domain).
I gave them the project as we began to talk about function transformations, and they had 3.5 months to complete it. They complained, but the results were fantastic. (…bunch of drama queens).
Couple of important points, and then I’ll let you peruse/steal the handouts and view the samples of student work (of which I am extremely proud).
Pointer #1: It was important that students copied a piece of art (this was typically a cartoon of sorts). Making them copy a pre-existing piece meant they must think about how the parameters shift to match. No lines are arbitrarily chosen.
Pointer #2: Illustrate how a variety of functions could model the same segment of line. When I do it again, I may even have weekly challenges as they are introduced to more and more function variety. Something small. I may project a simple image and ask, “What functions would you use to draw this?”
With all that out of the way, here are the materials I used:
- Here is the handout I gave them. (It stresses the pre-drawing as well as the replication of a piece of art)
- Here is a tutorial sheet that Mary Bourassa gave me to show a simple example from quadratics. Her blog post can be found here.
- Here is a .pdf that contains several samples of student work.
I was skeptical throughout the process because they resisted giving me updates on their progress. On the whole, they were fantastically done. I can also say that they did very well with function transformations on exams.
Now that I (and you) have samples of work, it will go all the smoother the next time.
Since the initial class, I have made a few refinements to the process. Most notably, I no longer require them to pre-draw the piece of art. I found that this encouraged them to choose very simplistic images, and their drawing did not connect well to the understanding of function transformations. In particular, I found that students used the language of function transformations when working with the technology, and hardly at all when they drew by hand.
Like anything, it is still a work in progress; I’m sure it will change before I give it to students again. Several more examples have also been added to the “samples of student work” (see the link above).