My students and colleagues all know how much I love Desmos, and how much I rely on it in my classroom. I've been playing around with doing an art project using Desmos for awhile, trying to find the right time, the right content connection, the right group of students, etc. I've thrown the idea out to different groups of students as an alternative or enrichment in a couple of cases, but never really prepared for it or made it an intentional goal. The way I presented and assessed it over the last couple of weeks with my 9th grade Integrated 2 class is the closest I feel like I've come (yet) to doing it right. I also feel like a lot of other teachers must do something like this, but I couldn't find anything that really fit what I wanted to do (although Jon Orr's Beautiful Functions was kind of an inspiration).
The content
I've got a growing love affair with "functions" as a specific area of focus in my instruction, and a growing understanding of how they fit into all the other areas, and how they fit into the grades 8-10 currriculum I've been working on for the past 4 years. Grade 9 is the first time we really dig into function transformations, and we're also at a point where we've had some experience dealing with functions that are a little more "interesting" than linear and exponential (mainly quadratics, but we also dabble in radicals and cubics). 
Tech and Prep
Working up to this assignment included the following desmos activities.
​1. Transformations Review by Suzanne Von Oy
This worked as a nice intro, with answers students could check. Also, the "library" of functions used matched up nicely with where we were.

2. Match My Function by Jon Orr
​This was nice because it asked for the functions in function notation, something I was shooting for in the project. It also let students play around with unfamiliar function types, and drove home the idea that transformations are universal, and apply to all functions, even ones we don't know yet.

3. Make a Face! by Me!
I'm still in the process of finding the right balance between spending my time making my own materials and spending my time searching for existing materials. This was fun to make, and focused in on some of the main aims of the project. I think it got the kids ready pretty well. Building it also gave me a better idea of the time and effort it would take for the students.

The assignment
Part of the "success" of this project, I think, was that I put some thought into the requirements, and into how I would assess it. Not perfect (I'd like to find a way to make it a little more "mathy"), but at least it's clear. Here's the Google Doc of the assignment and rubric.

Providing a model
I remembered to do this this time! It always helps, especially with the language I was looking for at the end.
"Link: https://www.desmos.com/calculator/8y5nzp27wy 
This is a recreation of the mask of one of my favorite comic book characters, Grendel. I used an image from this link for a guide: https://www.redbubble.com/people/bighairmonkey/works/3126293-grendel. For the nose, I used two transformations of the quadratic parent function, one of which was a vertical reflection so that the parabola opened down. I shaded between them using the top function as a restriction for the shading on the bottom function. For the eyes, I used exponential, quadratic, and absolute value functions, which I dilated, reflected, and translated, then used inequalities to shade. I found some of the shapes in the mask difficult to reproduce using functions, because they curve back in on themselves. This would make them fail the vertical line test, so they couldn’t be functions. In order to reproduce these shapes correctly using functions, I would have had to write many different small functions. Instead, I decided to simplify the shapes to make them easier to draw with fewer functions."

The Results
I gave the students two 90-minute class periods to work on this so that I could make sure they got off to a good start, and then two weeks outside of class to put in whatever amount of effort they wanted. I'm really happy with what they came up with. (The one on the top left's supposed to be me, BTW :)

The Follow-Up
To take care of a 40-minute Friday class, students showed off their work to the class, practicing their academic language. Fun way to finish off the week.

​I had a really rough class last week with my 8th graders. They'd been using a Chinese word pretty regularly in class that I suspected was a swear word. So I decided to call them out on it. When I heard a student using the word, I'd ask them what they said. And what did they do? As you can probably imagine, they totally lied to me. Then their classmates backed them up. 
I left that class pretty furious and went directly to the Mandarin teacher to confirm my suspicions (it's like the worst word you can say in Mandarin). Then I started stewing... Losing sleep... Plotting my revenge...
Because of the schedule, it turned out that I didn't see this class again for a week, which was probably a good thing. I asked a colleague for five minutes with them at the end of her class the next day, and I let them know that I knew what they were saying, and I was really disappointed with them. I tried to make sure they understood that it wasn't the profanity that really bugged me (I use profanity, although I don't throw it around in public), it was the dishonesty. Also, that this was an indicator of a bigger problem with this class: the lack of academic language in our daily discourse. 
Silence... Blank stares... Some guilty looks... Some grins...
So then we all had a week to think about it. I spent a lot of mental energy on it, although I doubt they did. I got an email from one of the students involved apologizing for the profanity, but didn't hear anything else.
The next time I had them in class, I started out by making sure they understood the problems:

1. Dishonesty- I can't teach this class the way I want to if I can't trust you.
2. Academic Language- The language we use in class directly affects our ability to respond to directions and show our understanding using the language of the classroom, regardless of our home language.
3. Responsibility- All of us need to take responsibility for the language we use in this class. It's not always enough for YOU to do the right thing; sometimes you need to take the time to encourage those around you to do the right thing. It's your learning, so take charge!

And then I went on strike. "I can't teach you until we figure this out. I've tried everything I know how to do, and it's not working. You fix it. I'll be at my desk when you've got a solution."
I sat at my desk in the corner and left them to have a conversation. Slow start... leaders emerge... They ended up having a pretty decent conversation for 8th grade students. 

• Punishment! - But punishment doesn't work.
• Only English in class! - But sometimes you need things translated that you don't understand
• Why should I care? - I care!

They ended up passing around a whiteboard and each writing some personal agreements on it about how they would contribute to a solution​. Also came up with some norms/rules addressing when/why mother tongue is needed (I was actually impressed with this: it's pretty close to what I would have had them do if this was teacher-led). 

After about 45 minutes, I stepped in and gave a little direction to solidify and wrap things up, and then led them through some roleplaying scenarios (1 plays teacher and 2 play students).

• Teacher is teaching and you have no idea what he's talking about. What do you do?
  • Raise my hand, ask to have it translated, partner translates.
• Partner is speaking about math in non-academic language
  • Ask partner to repeat in AL, help her if she needs it.
• Partner is speaking in English, about math, but using incorrect terminology
  • Correct partner by paraphrasing using AL
• ​Partner is speaking in any language about something not related to math class
  • "We're in math class. Let's stick to the material."

Then I actually got to finish up class by teaching a little math!

The school trip is coming up, so again, we have a long period of time until our next class. I feel like they did some good work today, and I hope it sticks. At least it got them talking and thinking about this.
Take-aways, Lessons Learned:

• I need to be more intentional about classroom management
• I need to remember to involve students in formulating classroom norms
• I need to do more of this in the beginning of the year (while responding to a problem can be a powerful way to learn and grow, it might be better not to have the problem in the first place)
• I need to remember to give myself and my students space to reflect when things go poorly