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).
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.
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.
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."
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 :)
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.
Every once in awhile (sometimes in a LONG while), a lesson just clicks. It's some combination of the right planning, the right group of students, the right materials, etc. that just works. For myself, I'd like to start keeping track of those lessons so that I can build on them and refine, polish, or just re-use them in the future. For others, I hope I can provide some materials and ideas to help build a great lesson in other classrooms. I'm going to try to keep posting these as the "Lessons I Like" (LIL) series on this blog.
A few weeks ago, I had the opportunity to take over a colleague's classroom for a day to introduce his students to GeoGebra. This was my first time fully teaching another teacher's class, and there are some parts of that dynamic that I would do differently next time, but the lesson went well.
Setting the scene
Introducing a new piece of technology can be super frustrating. I've learned from experience that it's best, at least for the instructor, if -at least for the preliminaries like account creating, passwords, etc.- I can keep all of the students on the same page. Otherwise, they can sort of get all over the place and the room becomes really difficult to manage.
To curb this frustration and keep everyone together, I use Red/Green Cards (RGC) (two sheets of construction paper, one red, one green, sandwiched together and laminated, then cut in quarters).
I've been playing around with these for awhile, but this is the first lesson where I was really intentional about using them as a management tool, and they worked pretty well. Here's the idea:
Why this works
I decided to have the teacher set up a GeoGebra group to keep track of student progress. If you use GeoGebra in class, but haven't tried their groups, I strongly suggest you check it out.
Here are my slides for the introduction:
Some things to note
I was lucky enough to stumble across this bundle of transformations exercises on tes.com by Mark Horley. It includes a paper worksheet and a bunch of GeoGebra files, which I've uploaded to GeoGebra (they can be found here).
I really like this blend of paper and tech, and the directions are very clear. These students would have benefited from a little more of an introduction, but they seemed to get into the activity pretty quickly. For a 40 minute lesson, this was a great introduction to one of my favorite math tools. Special thanks to Elizabeth (@eab69), Lilian, and Marty for supporting.