I had a project idea kicking around related to polar equaitons of conics. It was going to be something all my Pre-Cal groups got to do, but with May approaching and the need to get Calculus materials underway, that didn't happen. However, during testing week, I did have an opportunity to see one class for their normal block period. Rather than continue on with Calculus and get all the groups out of alignment, I let them try out the project.
Step 1: Instructions
The goal was to create a model of the solar system using polar equations. Some research work would be required. I gave them this set of instructions (ignore the fact that I can't spell "Halley's Comet"):
Step 2: To the Internet!
iPads in hand, they set about looking up the required information for each planet. It's readily accessible on the respective Wikipedia entries, or in lots of other places. In my preparation for the project I found a nicely compiled planetary table that gives you almost everything you need. Responsibilities were up to them. Some groups divided up the objects, some groups had one person doing the research while others started finding planet images for the fact cards. Usually someone was compiling all the information into a table for later use.
Step 3: Output
To continue to support the idea that desmos is fantastic for this sort of thing, I had them create their models on the iPad. Using some printer magic, they were able to get hardcopies of the inner and outer planet diagrams for use on the poster. I suggested in the directions that they could print pictures of planets as well, but everyone chose to recreate them in marker anyway. Orbit maps were labeled and the equations for each object were to appear on the fact sheet. The assembled work looked pretty neat and the kids took to the task incredibly well. It was fun uncovering a lot of the information they dumb down in elementary school.
Step 4: Debrief
The day after I had the full model up on the board for us to look at. We went over the definition of eccentricity, commented how crazy far Eris is from everything else, and poked a lot of holes into elementary school assumptions. We even verified that thing about Pluto and Neptune switching places. For added effect, I included the orbit of the moon which is practically invisible.
Supporting Player: AirPrint
iPads, iPhones, and iPod Touches have the ability to print directly to supported printers. There are tons of them on the market. I have a laser printer in my room and while properly supported by AirPrint, I have it directly connected to my computer, not a wireless network. Through a hack similar to AirServer, the app handyPrint (among others) will run on your computer and trick an iPad into thinking your locally attached printer is available for use. After creating their graphs in desmos, the students took a screenshot, went to the local Camera Roll and found the printer in the room. It was flawless, we got the result we wanted without having to fight a thing. The app kindly asks for a donation, it was worth the $10 I threw at it.
The kids got to research planets. It drew a "this is pretty cool" from a student who is not BFFs with math. We got to see an application of polar equations. We learned some science. We got to practice modern graphing skills. We output those graphs with zero issues. It complemented marker and pencil beautifully. In times gone by I would've booked a computer lab for this, fought with interpretations of pixelated TI-84 graphs, spent way too much class time building up the technical knowledge needed to create the graphs, or (in all honesty) never done this project in the first place. Given the flexibility of desmos, you could pull this off in a computer lab, but I appreciated the flexibility of not having to worry about that.
Added bonus was that since they've had a lot of exposure to the iPads all year, and desmos in the last six weeks, I spent zero time teaching them about the device. Every question I answered during this had something to do with material and had NOTHING to do with a technical hurdle.
Instructions to result took 90 minutes and everyone finished. It needs some more depth, but I liked it.