Fa-La-La: Pre-Winter Break Math

The week leading up to winter break for a middle school teacher is a unique mix of giddy, feisty, whining, forgetful, happy, flirtatious and most of all exhausted teens.  Oh yeah, and lots of absent ones who left early for holiday travels or trips back home to see family in other countries.  Every year I seem to make different choices about how much to embrace this perfect storm of challenging teaching and how much to ignore the reality and just carry on.  This year I decided I wanted our last two days of school to feel as joyful as possible so that everyone would leave simply loving the beauty of math.

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But how to achieve that elusive goal?  I tried my luck at a Twitter post.

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I owe a huge thank you to everyone who responded.  If you are looking for art projects suitable for both 8th Grade Math and Math 1, click here to see the incredible ideas gathered from my post.  And most certainly click if you are looking for art projects for yourself or your family for winter break.  Since posting my request, I have done nearly every one of the recommended projects at home with my kids and have a few more we’ll try over winter break.

I chose to do Susan Russo’s (@Dsrussosusan) Kaleidoscope Project because it was the one which literally made me squeal in delight when she shared it with me.

Since I wasn’t sure all my students would know what a Kaleidoscope was, I started with this video from inside the world’s largest, located on a resort in upstate NY.  I showed 10-15 seconds, then paused it and asked students what they noticed and wondered.  They talked about repeating shapes, wondered how it was made, or if mirrors are involved, and how the video was taken from inside it.  We played and paused a few times, to see it through various iterations.  After the video I mentioned a few fun facts from this travel web site.

Building a model in GeoGebra requires both a general understanding of reflection and also what y=x and y=-x looks like.  We haven’t yet studied linear equations, so wanted to do a brief introduction.  Using this graph in Desmos,  I asked table groups to come up with as many points as they could which would be graphed by each equation.  After graphing their coordinate pairs, I had them predict what the graph would look like.  I then turned each graph on.

We were then ready for GeoGebra. My students had used GeoGebra a few times during our transformation unit, so they were already comfortable with how to create rigid motions.  Creating a Kaleidoscope is surprisingly simple.  Using both axis plus y=x and y=-x, you add a single point, then reflect it 7 times over both ends of each lines.  Once you have 8 points, they all move in unison since they were created as reflections from point A.  To create the drawing effect, you highlight all 8 points and turn on the trace tool (through settings)

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Some students were satisfied with a single color (which is easy to change by highlighting  points and changing their color).  However helping them understanding dynamic colors became quite thrilling.

The idea of dynamic colors is that the color changes depending on how far the points are from (0,0).  To do this, you add (0,0) to your graph, then add a segment between point A and (0,0).  Once again, select all the points, then right click and open settings.  Choose the advanced tab and play around with values for red, green and blue using multiples of your segment length (called h in my graph).

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Students played around for a LONG TIME with both colors and drawing and redrawing designs in their kaleidoscopes.  I simply let them explore and run around the room checking out each other’s designs.  Eventually, I asked that they choose a design they wanted to use for a permanent display.  I had them take a series of screenshots of their design as it morphed and grew.  They used gify.com to create gifs with their screenshots.  ***I learned that having students make their own accounts in gify is a nightmare so I eventually just signed everyone into my account which was far easier as now I have all their work in 1 place.  I also (thankfully) learned that lots of people can be logged into a single gify account at once, all creating and saving gifs. ***


They’re each so proud of their gifs and I cycled them together into a slide show which will play on the monitor in our school’s hallway when we return from break.  And with that, I’m good and ready for vacation!

2 thoughts on “Fa-La-La: Pre-Winter Break Math

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