I know this isn't an original idea, but it seemed like a good fit for the end of Precal (for juniors: my classes had both juniors/seniors, and seniors needed some time to review for their final, which was two weeks earlier than the juniors'). Here's how my version of a Desmos Art project went this year.

This semester, we studied polynomial, rational, and trigonometric functions. Use these functions (plus any other functions or relations you want) to create an original piece of art using Desmos.
This is an Awesomeness project, which means there are 5 points available. To earn them, make sure your creation:
1. Uses domain and/or range restrictions
2. Uses inequalities for shading
3. Uses all three function types studied this semester.
4. Uses three or more functions or relations not studied this semester and/or not studied in this class.
5. Is awesome! Convince me on the last slide by discussing any struggles you had, anything new you learned, what your creation means to you, etc.
Pretty good results: some kids got into it, and I'm trying to stay positive about things at the end of the year so I won't get into those who didn't (you can probably tell), or those who borrowed a little too heavily from stuff you can find online (or right on the staff picks page, ffs- if you see anything down there that bothers you, please let me know). Some of these are great! The sword and the mosques, the war/peace, the mountain scene: pretty sure all of these were original, and noticed these students putting in some effort.

Ok,
I read a lot of science fiction
+
I struggle sometimes to come up with good contexts for problems
= Alien Math

My first escapade into alien math was a problem about alien units, the point of which was to understand conversions without getting hung up on feet/meters/etc. I wrote it a few years ago, and it works pretty well. I use it when the opportunity presents itself.
This year, I wanted to do something with my Geometry classes for the final modeling unit after we talk about volume, density, etc. There are lots of problems about surface area and volume and density, making comparisons, maximizing, etc. But I wanted to have a little fun with it, so I came up with ​





The Flerkus Miners of Gleep!

Introduced it to the ss after our last assessment. There was some satisfying (for me) confusion, then people got to work!
Step 1: Make sense of the problem
and
Step 2: Plan and calculate

Turned out to take a couple of class periods for most kids to get a handle on this, which was a very interesting process to watch. And I did my best to JUST watch, not giving clues or hints or judgement, just observing their thinking and how they got into it.

• Lots of pencil/paper, write down important info, figure out what to do first.
• Surprising number of ss went straight to digital. Tinkercad was popular (they must be using it in another class), as was google drawings. Some of these I suggested go back to paper, as they were getting hung up on the technical details of the program they were using.

They needed a little more information about the weight of flerkus (some were looking up how much a grain of rice wieghs and going from there: resourceful, but I wanted them to be a little more accurate and use the actual rice I had), and they needed a visual for the size, so I hung these up in the room as a couple of guides when I went to a conference for a few days.
​
​Step 3: Build it!

Things were messy and chaotic, but it was pretty fun. Couple of days on this, running out of class time, then we were ready to start
Step 4: Product Testing
A. I made a submission form for students to check off requirements and write down measurements. Mostly, this gave some students a bit of time to frantically add last-minute touches.

B. Blamium distribution ended up taking entirely too much time, and was kind of hard to judge, so I scrapped it after these first few gave it a try.

C. The Flerkus Weigh Station was tons of fun! Rice everywhere, students fighting to be the one who got to pour the flerkus, be the scale expert, make predictions, etc.

Step 5: Awesomeness!
(Yes, I'm focusing on the positive here)
The kids came up with some great stuff for their "Awesomeness" point. 
Drawings!

COMICS!

Advertisements!

Even Prose!

Reflection:
This was fun, and a great way to end the year. The whole points thing needs some work, and the logistics of the testing, too. I think it was worth the time we spent, got more out of the students than anything else would've the last few weeks of school, and left them with a good "taste in their mouth" as they leave my class for the year.

So, when I made up my grading scale in August, I left 5 points for "awesomeness", which I didn't define very well. Here's my description from my assessment document:
Awesomeness:

• It’s not extra credit - I expect all of my students to show some evidence of awesomeness.
• It’s intentionally vague - I don’t know exactly how students are going to be awesome, so they will have to come up with what this looks like, and convince me, on their own.
• It’s probably different for everyone - Are you a great artist? Love writing poetry? Like tinkering or building? Spend all of your free time on the computer? OK, do something awesome for math class with that.

The idea was, I think, that students would have to figure this out for themselves and come up with something on their own. That didn't end up happening, so I didn't count the points first semester. But for some reason, things just clicked together for me at the end of second semester, and I was able to come up with 3 "Awesomeness" projects, one for each of my classes, to make the last thing the ss do in my class this year something AWESOME! This will be a series of 3 posts sort of chronicling each.

Senior "Foundations" class ended up on 3D graphing at the end of the year, and ss had a really hard time visualizing and conceptualizing 3D spaces. We did tons of activities, made 3D coordinate planes, even installed semi-permanent x/y/z axes in my classroom. When we were getting ready for our last summative assessment, one of the students, being a senior, asked, "can we just, like, do a project or something instead of a test for this?" So I, after a little bit of mwahaha, said, "OF COURSE WE CAN!!!" Then I came up with this:

​​Final Awesomeness Project- Graph My Room!
Using isometric graphing paper, make an accurate scale drawing of my classroom. Use your drawing to find the following.
A. The distances PQ and RT (These points will be posted around the classroom).
B. The equations of all of the planes that make up the walls, floor, ceiling.
Prepare all of this in a poster.
Scoring: 
There are 5 awesome points available. 
1-2. Distances are within 50 cm of the actual distance
3. Plane equations are accurate
4. Working for the above is clear
5. The poster is awesome!

About 4-5 class periods to get this done, with varying levels of success. A few notes on the process:

• most ss had trouble just figuring out what to measure just to get started. ie: many started by measuring lengths of walls rather than distance from axes. The x/y lines up with my floor tiles, so I clued them in to this pretty early on just to save us all a lot of trouble.
• weirdly prevalent trouble with units! STILL TROUBLE WITH UNITS!! Lots of "3 meters 24 inches" or "8.7 feet"... Scale on the graphs was also tricky...
• Z axis was nearly insurmountable as an obstacle; they just couldn't visualize it. 
• Coordinates proved to be a real challenge. Spent significant time walking from the origin to the corners of the room to find coordinates for the corners
• graphed floor in two dimensions, figured out z coordinate, sketched on isometric paper, then just went "up" the height of the ceiling.
• One group got right to work, asked about units, and (with a little point in the right direction) decided on cm based on the requirements.
• Second group had some trouble getting into it. Before I knew it they were measuring in inches and then dividing by 20 to come up with their own scale (based on ?). I thought this approach was strange, but it made sense to them, sort of.

Reflection:
I've spent this year really focusing on summative assessment. For the last few months, I've been thinking a great deal about formative assessment, and changing the way I introduce students to concepts, figure out what they know and what they need some help with, and move towards a goal. 
In hindsight, this project feels to me like it could have been THE UNIT rather than something we did at the end. I have dreams of one day having a good, meaty problem to START. Create the headache, etc.
I'm really starting to think this is going to be my focus for next year, and I'm pretty excited about it.
​

Back in January, I was wracking my brain about how to make assessments go better in my classes; there was too much stress, too much concentration on the wrong things: it felt too much like a big bad test that everyone should be stressed out about. So I thought to myself, what if they could take a break, take a walk, talk about the test, get rid of misconceptions and jitters, etc. 
And that's what we did. 

Evolution:
Phase 1
I didn't really have a good idea about how to do this the first time, so I was kind of loose with everything.
"Work on the test for 10 minutes, then we'll take a walk. Come back, work for another 30, we'll do it again. then 20 minutes to finish."
The idea here was to have some time to get into it, then ask questions that might have come up, then some more work, then final questions.
I didn't talk or answer any questions. I let students take notebooks and pencils with them, and bring them back into the room.

Student Feedback
After each class's first test walk, I asked for some feedback about the process:

Ok, nothing really shocking there. I used the "cheating" results to have some conversations about why I write assessment questions the way I do, why I ask for so much from one question, why my assessments are only 1-2 questions.

The next few questions on the survey gave me some more interesting feedback (summarizing and cherry-picking some results here).

Did anything bother you about taking a break during the test?

1. lots of "no"s, "it was too cold", "it was too noisy", "more time"  --meh
2. Sometimes it got even more confusing because you would mix what the other person was saying to you with what you already thought.​ / The break lead me to panic and question myself about whether I got the concept.​ --I get this and was surprised that there weren't more like these. I'm hoping that they get more confident as they go on, or learn to ignore others or have productive discussions if they're pretty sure of themselves.
3. if we would have been allowed to take our test around or have been able to view it during our break, it would have been even more helpful. But I understand why you won't do that, it is a test after all. --Glad they understand :)
4. Not really, except people screaming. --Hmm, discussions too heated? I must have missed this :)
5. everyone either crowded around one person and I couldn't help but feel bad for the person in the middle. / I think we should have groups while walking outside. Otherwise everyone gets on one person. --This was something I should have worked harder to address. It was a big problem in one class (which I'll discuss later), but not so much in the others.
6. Stopping in the middle of a problem. --a couple of different variations of this one. I think Phase 3 takes care of it.

 Is there anything you really liked about taking a break during the test? 

1. If you had any confusions they could be cleared out / seeing different methods / noticing mistakes  --alot of this
2. Stress relief / helped me cool down / feeling of comfort that you could still get help / fresh air --and this
3. I couldn't understand what to do in the test and my classmates explained the question for me. --and this
4. I think this was the first test I actually took happily and didn't panic or anything and just overall it was very different but I believe this would overall as a class improve and help everyone understand better
5. It acted as a type of kickstart to get me started on completing the test on my own
6. Yes, it felt a lot less stressful and it felt like the teacher understood where students were coming from.
7. It was good to see that a lot of people didn't understand what was happening just like you didn't. --umm, ok? I think? Maybe not ok?

Describe any suggestions you have for how we can make tests less stressful.

1. more time / more breaks --Eh, I put a lot of thought into time limits, and I think there are always going to be people who ask for more. Part of "Proficient" for me means efficient, confident, and prepared enough to show some solid understanding on a single problem in 20 minutes or so.
2. extra credit / MCQs / more questions but easier questions  / traditional math tests / grading scale gripes (summative assessments are worth at least 85% in my class) / only one topic at a time / fewer tests  -- Meh! spent all first semester discussing these things. Not gonna happen.
3. We can practice the types of questions on the test so it's not a surprise and much harder on the test. / More time and review the topics in the the class before the test. / Maybe more practice questions similar to the ones on the test. Like with the same type of wording and format.-- I did start doing this more, maybe to a further degree than I'm really comfortable with as I reflect here. Part of "Proficient" for me also means being able to apply math you know in unfamiliar situations.
4. We can take tests in pairs? --Couple of these. I'm interested in this idea, but not with these students, at least not yet. Academic dishonesty has been too much of an issue this year.
5. We could not call them tests but rather anything else.  --I'm trying, man! "Summative Assessment" is just so many damn syllables, it's never gonna catch on!
6. The rubric is quite confusing and vague, it would be nice to have examples of what a 1:4, and so on look like specifically for the topic we are doing -- Yup, that would be nice. Working on it.

Phase 2:
Teachers with more foresight than me probably know exactly what went wrong with this: some students used the breaks, especially the last one, to just copy each others work. Of course they did!

The process with the rest of the classes in this first round of tests allowed us to have some great discussions about how to show your understanding (and how to show that it's YOUR understanding).

​I pretty quickly stopped letting students take notes or any paper with them, instead sending a basket of whiteboards and markers with them that got erased before they came back into class. I also got rid of the second break: work 10 minutes, 10 minutes to discuss, 40 minutes for the rest of the test.

Results?
I don't have really good data on this. Visual modeling increased, but also paragraphs of writing where some good algebra steps would do just fine. "Less tell, more show!" became my most often used comment on assessments.
I think it "felt" better, at least to me. At least most of the time. It also gave me some more freedom (along with some more directed test-prep on my part) to ask more open-ended questions: "Make up your own triangle and solve it to show me you understand trigonometry". 

Then there was
The oblique asymptote incident:
So, one of my precal sections, my "difficult" class, last period of the day, test over rational expressions and functions, Illustrative Math question about fuel efficiency...

In this class, I have one student who's way ahead of everyone, a transfer this year from another school where his algebra 2 class covered most of what I have to cover to meet the needs of the students here. He's the "go to guy" during test walks, the one the other students crowd around. He and I had had a discussion about a similar problem, and and how to tie the idea of an oblique asymptote to the context and the solution. It wasn't something that most of the students were ready for, but he was. Here's some of the nonsense I got back on this test:

I threw these and a few others into a presentation (yes, along with some positive things, too) and used it to have a very pointed discussion about cheating. I also found ways to remove this student from the conversation during walks (by having my own conversation with him) so that the others wouldn't get distracted by things they're not ready for.

Phase 3:
I settled on a 3 minute reading period (look over the test and strategize: no talking, no writing, no calculators) followed by a 10 minute walk before each test, with whiteboards if students want to use them. Some students still try to memorize the entire problem and get classmates to give them the "answer" (whatever that means), but this is where I think I can feel comfortable. This is what I did for the rest of the year.

Reflection: Why do this?
Test walks are a pain in my ass, mostly because they cause me to spend so much time thinking about and watching for academic dishonesty. I'm not sure if they really help with assessment results because I'm too lazy to do a real look into the scores, and my records aren't good enough to call this useful data yet. I still have assessments where the majority of students miss the mark completely and/or give nonsense answers to questions. 

I do this, and I'm going to continue to do this, because of the mathematical discourse it produces. The "pressure" of these discussions produces the best mathematical discussions I ever get to witness, even from the students who are the most disengaged in the classroom. Students argue their case, critique the reasoning of their classmates, ask questions, and don't stop asking until they get it. On one of the last walks this year I tried to capture this in a video. It's kind of hard to hear what they're saying, but you could probably get the idea with the sound off.

So, the question I'm working on now is: How do I get this kind of engagement as a normal part of my classroom... without having to give a test every day!