December 18, 2014
“Frozen Fractals All Around”| 3D Printing in the Classroom
We are in the last week of school before winter break and my students are ready for it. Let’s be honest, so am I. The week before any break is always an interesting time. This week we have taken a trip to the ballet to watch a couple of our students perform in The Nutcracker, we have had a chorus performance, and tomorrow we have a class party. Curriculum can seemingly take a back seat, but the break down of our normal routine can also yield opportunities for learning that can otherwise be difficult to find. I think many teachers feel that there are many projects that they wish they could teach, but standards and routines make it hard to find the time.
With this week being so out of the normal routine I decided to take advantage and teach some mathematics that did not come from our textbook. However, I assure you that it met the rigorous standard of the Common Core.
This morning we did an art project (adapted from this lesson at artprojectsforkids.org) that involved snowflakes. I introduced it by saying that we were going to be making frozen fractals. They immediately recognized the reference to Disney’s Frozen and were interested in the connection. After a quick definition of fractals and some images from fractals found in nature we were off making our own snowflake fractals.
When math started I reviewed the definition of fractals and gave them an example by creating Sierpinski’s Triangle. My students who play video games immediately liked this because it looks like a “triforce” from The Legend of Zelda. I liked it because it really illustrated that a fractal is a geometric shape that is slightly modified then repeated. I know it is much more complicated than that, but I wanted to keep it somewhat simple for my students. Even with that simple definition I was worried my students would I have a challenging time demonstrating their understanding. Once again they proved to me that I had nothing to worry about.
My students were given 2 options to show their understanding of fractals. Option one was to use the pattern blocks that we already had in class to make a stop-motion video of a fractal being created. Option 2 was to create their own pattern blocks on the computer so they could 3d print their own blocks and use them to make different fractals.
I was immediately impressed with the diversity and accuracy of the fractals being created. The students who were making the videos came up with some really interesting designs. I will be sure to post them in as soon as they are complete.
The group that started designing their own pattern blocks for the 3D printer challenged my thinking right away. They wanted to create 3D fractals. I hadn’t even thought of that, and didn’t know the answer. So I did what any good educator does and messaged a mathematician.
My friend Jacob, who just had an article written about him, is a math teacher at Mojave High School. I know this is the kind of question that he would love. His first reaction was to say that a 3 dimensional shape can be fractal but he had to confer with a colleague to be sure. They could not find a compelling reason for the shape to not be a fractal, and that is good enough for me. Tomorrow, my fourth graders will be 3D printing 3D shapes and trying to make them into 3D fractals. Once again the 3D printer has stimulated some deep thinking and deep learning in my class. Stay tuned to see how they come out.