The Sumerians used tessellations with building wall decorations around 4000 BC. These decorations were formed by patterns of clay tiles. In 1619, Johannes Kepler studied tessellations. In his book Harmonicies Mundi, he was the first to explain the hexagonal structures of honeycomb and snowflakes. In 1891 Yevgraf Fyodorov proved that every periodic tilling contains one of seventeen different groups of isometries. With Fyodorov proving this, it unofficially began the mathematical study of tessellations. The start of the tessellation era led us to tiling on walls with clay but now we have realized we can do them anytime anywhere and how beautiful they look. They have been around for thousands of years and are here to stay forever which is great for me considering I cannot wait to teach my students about tessellations.
In class I started out using pattern blocks. Giving students the option to use all different sorts of manipulates allows their mind to run free with what they are wanting to create. When pulling out the pattern blocks there were a few things I had to remember and look for. I needed to look for shapes that went together without overlapping and leaving no gaps. This really let me explore my options. Another thing I needed to keep in mind was that I needed a pattern. So I can’t just put all these random shapes together. I needed to create something cool out of the shapes then remake it over and over again creating a tessellation. Below is the tessellation I created in class.
I went home and for our daily homework I really wanted to create another tessellation so I did just that. I got out isometric cubed paper and started creating. What I came up with is pictured below.
This is a great activity for students. They get to integrate art within math. There are a couple of big things students get to see within doing this activity, those things being reflection, rotation, and translation. Just like with my second tessellation we found it had rotation and kids will be able to see these things after they are done without even realizing they have done so. This activity also allows students to explore different geometric shapes along with the shapes that can be made using other shapes just like in my first tessellation I had trapezoids, triangles and squares making a hexagon. This is not only a fun activity for the classroom but a very beneficial one as well. I am looking forward to working on tessellations with my students when I get a classroom of my own.