Recently, I was given an invitation to put together some learning projects for a couple of middle school girls. How fun! They want princess projects, so I suggested doing these stain glass castle windows, done in fractal patterns. I was so excited when I received these pictures of the work they did! I thought you would like to see them too.
To make a fractal pattern, choose a shape and repeat it systematically. In the example above, she chose squares and put a smaller square on each corner. Then, she put more squares on the corners of those squares.
Doing fractals inspires mathematical thinking on many levels. In this case, I was hoping to reinforce the students ' sense of multiplication as they think through how many shapes are needed for the next level. "If I have four squares with four corners, I will need 4x4 more squares." Count the shapes above to find the answer to "4x4=?"
Since this is practice in repeatedly multiplying by the same number, it also gives a nice introduction to exponential powers. Exponential powers are expressed with a "^" . In the example below, we see a three cornered object repeated four times. In math terms 3^4, or three to the fourth power. Count the triangles to find the answer to 3^4=? My son says this one looks like castles.
My inspiration for the "stain glass" came from Jean Van't Hul at The Artful Parent.
I got excited about fractals while taking an on-line class at Moebius Noodles, Math Adventures. The class is over, but I found the class so useful I also downloaded Moebius Noodles: Adventurous Math for the Playground Crowd to our Kindle. You may want to check it out.
What projects have made you excited recently?