Right here’s what I hung up final week:
Right here’s a closeup of a few of them…
These are polar graphs that college students designed utilizing Desmos. Then I printed them out on photopaper and hung them up.
This was one thing I wished to do after introducing polar graphing. Why? As a result of sooner or later throughout the polar unit, I began taking part in round with desmos and unintentionally created:
… from one thing so easy …
(Now to be truthful, desmos isn’t nice with creating nice difficult polar graphs… and it’s higher to jot down them parametrically to get a bit extra accuracy… so this can be a little bit of a lie of a graph in that it isn’t completely correct… however it’s oh so fairly.) 
So after our unit on polar graphing, I took 10 minutes firstly of sophistication to introduce this concept of a Polar. Graph. Contest. First I threw this picture up:
I then pulled up desmos and requested my youngsters to shout out some polar operate. I graphed it. Then I put in a slider or two. So for instance, in the event that they mentioned , I may need added the slider . After which I began altering the sliders. Then I may need altered the operate a bit extra, like and we noticed what occurred. Then I gave everybody 7 minutes to simply provide you with one thing fairly.
It was magical.
Youngsters simply began taking part in. They dug into previous features that they had realized about. They acquired excited by what they had been seeing. They gasped and turned their screens to point out their mates. Some who had been getting boring graphs noticed the cool graphs their classmates had been getting and had been impressed to combine issues up since they knew they may make neat issues. #mathjoy in the home.
My coronary heart was singing.
Then I confirmed youngsters a google doc which had all the data for the competition — and the hyperlink to the google type to submit their entries. There have been initially two contests. College students wanted to create the best polar graph with one equation. And college students wanted to create the best polar artwork utilizing a number of equations. Nevertheless, some college students had been animating the sliders and developing with enjoyable animations (like this or this… watch each for some time). So I added an elective third animated polar graph class.
I haven’t but advised my youngsters who the winners are. I need to simply allow them to admire the work of their classmates for now.
After creating the bulletin board, I’ve seen youngsters have a look at the paintings. Youngsters from my class, but in addition youngsters from different grades. And what I’ve discovered fascinating is that to this point, only a few youngsters decide the identical polar artwork items as their favorites. I anticipated everybody to like the identical ones I do. But it surely simply isn’t the case. I feel once I announce the winners, I’ll have the category go to the board, have everybody level out just a few that they like, after which I’ll make my grand pronouncement.
I requested my youngsters, when submitting their paintings, “This is something new I came up with this year. I want to know if you enjoyed doing it or not. No judgments if you didn’t. Y’all tend to be honest when I ask for feedback, and I appreciate it! I genuinely want to know. I also am a bit curious if you had any mathematical thought as you were playing on Desmos? You don’t have to say what thoughts you had (if any) — just if you had any.”
Each scholar responded positively. Some responses included:
- I feel this was so superior! I like artwork and this felt like artwork to me. It’s so enjoyable when artwork and math intersect, I cherished it!!!!!
- Messing round with the graphs was really extra entertaining than I assumed it could be. I spent much more time on this than I assumed I’d, and I really feel like I’ll in all probability spend extra time on this looking for a extremely cool design I like (and presumably gaining a greater understanding why the graphs look the way in which they do…).
- I had a lot extra enjoyable doing this than I assumed I’d, actually. As soon as I completed my multi-equation graph, I appeared on the clock on my laptop and realized I had been engaged on it for almost 20 minutes; it had appeared like perhaps 5.
- I actually loved doing this task. I felt that I realized rather a lot about polar by means of it. I didn’t suppose an excessive amount of about math whereas making my graphs, nevertheless I considered math rather a lot with the intention to observe and take into consideration patterns I discovered in my graphs.
Now I need to be frank: there isn’t a lot “learning” that occurs when youngsters are doing this task. This isn’t a technique to train polar. However it’s a technique to get youngsters to understand the ability of polar when they’re finished working with polar, and what types of various sorts of graphs in comparison with the boring ol’ rectangular coordinate system. I simply wished youngsters to play, like I performed, and get excited, like I acquired excited. It’s a barely completely different technique to admire the ability of math, and I’m good for that. Particularly because it solely took 10 minutes of classtime!
As an apart, I like that once I tweeted this out, a tweep mentioned he was going to be doing this in his class after his youngsters find out about circles. Um, hell yeah!
 So there are two methods to graph polar in desmos. First is the straight up polar means, and the second is the parametric means. It seems that the polar means is strong for many issues, however it loses refinement at occasions. Let me present an instance. If we graphed , we should always get a flower with 57 petals.
And fortunately, if we graphed it in each polar and parametric, we get the identical wanting graph:
Nevertheless if we zoom in a bunch, we will see that the crimson graph (the polar equation) is attention-grabbing and gorgeous, however simply isn’t appropriate. Whereas the zoomed in blue graph (the parametric equation) is extra boring, however is technically appropriate.
It seems desmos samples extra factors utilizing parametrics than polar.
In consequence, just a few of the polar artworks my youngsters made aren’t “true.” Their items are a desmos quirk, just like the crimson graph is above. However what a stunning desmos quirk.