Back To School: Deriving Circles With Desmos

Being out of the classroom certainly has its disadvantages, most considerably the fact that I don't get to interact with students on a regular basis.  This means that when I was asked to go in and teach a lesson to show the incorporation of technology into a math classroom, I couldn't say yes fast (or enthusiastically) enough.  Woohoo!!! I get to go back into the classroom!  The only problem?  I've never taught the topic: deriving the equation of a circle.

Have no fear, because this is when the fun happened.  Immediately, I went out to my support group and asked for help:

#MTBoS, looking to help a geometry teacher introduce the derivation of the equation of a circle. Help? https://t.co/w81vMTl9zn @desmos

— John Stevens (@Jstevens009) April 2, 2014

And, of course, the response was nearly immediate and incredibly awesome:

@a_mcsquared @Jstevens009 @Desmos Yes, two of my suite of 16 conics applets. http://t.co/FQGQGGpXbr

— Jen Silverman (@jensilvermath) April 2, 2014

Some of the best feedback is often the toughest to swallow- pushback.  Bree (respectfully) questioned the flow and intent of the lesson and I appreciated it.  This really made me think about the connections that were trying to be made and how they could be better-formed to match the needs of the students and the topic.  Thank you Bree!!!

How about a graph like this @Jstevens009? https://t.co/3sjgZHztyb Ss try to create a border of 5 miles from epicenter. (cc @btwnthenumbers)

— Desmos.com (@Desmos) April 6, 2014

Aside from the Twitter love that I felt, and that was pretty strong, I also recruited a few people who I've leaned on quite a bit when trying to create an experience for students.  Matt "PD Aficianado" Vaudrey, Shauna "I Love Stats" Hedgepath, and Jed "Transformula Magician" Butler all lent a hand in making sure that the lesson went smoothly.  Without the community that I've got around me, none of this would really be happening.  What is this?  Let's dive in.

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Feel free to take all of these:

The Lesson Plan
The Slide Deck
The Handout

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I crack myself up

Photo Credit: _namtaf_ via Compfight cc

While this started off as a shaky (buahahaa) lesson, it quickly took shake and turned into something that was a pretty fun experience.  Here's the premise:


[side note: this can be changed to apply to cell phone towers, water distribution, or something else that would be more relevant in not-so-earthquaky regions]

• Start off with the hook of the La Habra Earthquake, a 5.1 that everyone in the classroom felt on that dreadful Friday evening in Southern California
  
• Plot a theoretical USGS and have the students find the epicenter in reference to the USGS
• Using the map that represents the zones of seismic activity, create circles to show each zone's radius and center
• Oh yeah, and Desmos all day, every day
• From this information, have students come to the conclusion of (h,k) being the center and r being the radius
• Also, have students come to the conclusion that manipulating h, k, and r is a whole lot like the Pythagorean Theorem and the Distance Formula
• Have them leave class feeling awesome

So now, the reality.  Coming into a brand new class when school is on the back slide of being done for the year is no easy feat.  Fortunately, I wasn't a sub, as the classroom teacher was there to introduce me and what I was hoping to do.  Also, I gave them a nice treat to chew on right away: 

"Alright class, how many of you have smart phones?"
-- whoosh of hands fly up --
"Get them out. They're going to get put to work"
-- shock, awe, astonishment

We went through the lesson and it really helped to have the regular teacher there as a supporter.  He was able to go around and assist students with the technology and, more importantly, help the students he knew would have a tough time with wrapping their heads around the math that was involved. Kids were using their cell phones to manipulate the sliders on their Desmos graphs and it. was. awesome. 

What I would change...

As with any lesson that a lot of time has been contributed to, I'm very critical of the outcome.  In reality, the lesson itself went pretty smooth.  There were a lot of good conversations, some pretty fun "oh yeahhhhhhh" moments, and a couple tangents that I enjoyed.  That being said, it could always be better.  In the future, this is what I would do differently:

• Less humor, more visuals.  These kids didn't know me, so they were playing school. They sat nicely and listened.  This is NOT the group that I'm used to.  With that in mind, I'll remember that I don't have the same easy-going relationship and get right into some visuals that would support the lesson directly
• Go through a basic overview of Desmos.  Most of the students had seen it before, but Desmos truly is a sight to behold.  There are so many things that it can do and I tend to take it for granted.  Next time, I'll start with a scaled down version and go over each component of the lesson
• Plan it for a two day lesson.  This would allow students to play around with the math a lot more and do more of the discovering on their own time.  I ended up staying for the next period and watching the regular classroom teacher rock the lesson and he didn't rush through anything to get it done.  He let the kids explore, even though it was taking time.  This is a great piece to remember

Overall, I'd chalk it up as a successful day back in the classroom (with some definite adjustments to make for next time).  If you'd like to steal any component of the lesson, please do.

I know you.  I know your style.  You have ideas to improve the lesson.  Feel free to comment below with what you would have done to make it better.  Seriously, thank you.

Happy "Not So Shaky" Fishing