Fractals

My geometry classes have been doing quite a bit of coloring (they're so quiet and focused when they color! Plus, learning is happening while they make things look pretty). First we color coded midsegments to highlight their properties and now they are working on fractals. I introduced the topic when students noticed that drawing 3 midsegments creates a similar triangle (even though we haven't studied similarity yet- love when that happens!).  So I shared that fractals are a repeated pattern; when you 'zoom in and out you see essentially the same picture' (not a precise definition but it will have to suffice for the type we're currently studying). I passed around some pages from the fractal calendar my mom gave me while exuberantly explaining how cool it is the word fractal wasn't even invented until 1975, an especially exciting fact since everything else we study is from the age of Euclid. The students all oohed and ahhed and then we watched a Vi Hart video that just happened to end with the Koch Snowflake. Everyone was given the choice of which fractal to make, among the Sierpinski Triangle, Koch Snowflake and Anti-Snowflake. Then they set to work drawing equilateral triangles on the isometric dot paper and cutting/adding from there. I assigned this as homework last year which wasn't terribly successful, so this year we started in class and finished for homework.  Everyone did well once they figured out how the dot paper worked. Hopefully I'll get some awesome results to re-decorate the hallway (I'm tired of the triangle quilt) and some mind-boggled students trying to wrap their brains around infinite perimeter on a finite area.

I adapted my worksheets from this website: http://math.rice.edu/~lanius/frac/

My handouts: Sierpinski, Snowflake, Anti-Snowflake, Dot Paper