I had wanted to do a unit about fractals for a long time, and this year I finally got the opportunity! I had originally envisioned my Math Four class as a traditional fourth course through more of a visual lens. Fractals involve some complicated mathematics, mainly exponentials and infinite sums, but also some complicated intricate designs.
We started with an exploration task. I would have assigned this in groups but I definitely burned them out of group work earlier in the year – live and learn. It started with Sierpinski’s Carpet, an increasingly-dense set of squares with an easily-recognized exponential growth pattern.
They then explored the Koch curve, finding the proportion of the area of triangles added in successive iterations.
As a group, students created a big giant Sierpinski’s Pyramid! Credit where credit’s due, I got the idea from this school in Winston Salem. Excellent idea!
I kept tripping on it because my room is not exactly large enough to accommodate a large pyramid, so I moved it into the administrative building. There, it encountered this guy and met an untimely demise.
To wrap up content for the entire year (?!!), students used grids to draw their own fractals. First we used triangle grids to draw the Sierpinski arrowhead curve, then regular square grids for the Dragon Curve. Vihart has an excellent video about that – a few students finished early and I had them watch it.
Next week is review week and then it’s exams – I’m starting to reflect on what I’ll be changing about this open-ended course next year, but mainly to avoid thinking about writing and grading exams! Although I will admit I secretly do enjoy exams in some ways.