[*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.

*2018 Update:*

*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. *

*Because I no longer require this step, I now give this updated project handout (as a .docx file to allow you to edit to fit your context). 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). *

NatBanting

Great work, students!

Thanks for sharing.

I do a similar desmos art project. I like the idea of preapproval. Are you looking for level of difficulty? Do they email the picture for preapproval to you or just show you in class?

I do this project with my grade 10s & have them submit their drawing for approval, but I really like the replicate a piece of art aspect. Thanks!

@JFairbanks @mslwheeler The students just show me the tentative design in class. I don't structure this, and most just took a couple minutes after class. I look to see that they will be able to use multiple function types (i.e. I don't want the whole thing to be straight lines). We have a quick discussion about what they might use for certain shapes, and then I send them on their way. Short and sweet.

Thanks for reading!

This is amazing! I have done the Desmos function transformations project, but nothing like this. Awesome awesome awesome!

Excellent work. The hand with the feathers is especially impressive! I agree that it is key to ask kids to create something deliberate. Without this requirement, they do meander and while the results are sometimes interesting, they are not always stretching their math skills. When I have done this, I have allowed them to make an original piece, but I require that they draw this piece first before graphing. I think that this demands the same purposeful graph creation.

I think that your grading criteria are maybe a little vague. There is a lot of room for judgement calls, and some concrete thinking students might struggle with this. It might be better with a bit more specific math guidelines, and we might be able to use an art rubric to help with some specific language. Always a fine line – we want to be precise and specific, but we want to leave room for creativity and voice.

Thanks for sharing.

I took a shot at refining the project criteria. http://bit.ly/1QGreFx What do you think?

Thanks to you both for this. Ever since I saw some teachers do this with their classes I've been trying to work out the details so this comes at a perfect time!

That's really good. We tried our luck drawing our own Redditbots using 219 equations/inequalities, and writing a guide about it alongside. Lots of work, accompanying by lots of fun!

What do you think is the best way to phrase more specific guidelines without intimidating the students away from creativity? It seems that including a lot of mathematical vocabulary may be discouraging for some of the students.

These students were familiar with the language because they had been studying the various types of functions. If you are working with younger students, Fawn Nguyen has a great Puppy House project. http://fawnnguyen.com/desmos-puppy-house/