As you can see with the picture to the left and the pictures at the bottom of this post, there are some excellent ways of creating tessellations online (for free). We used to have to buy "Tessellmania," a computer game that students would use once per year, create a tessellation, print it out, and hang it in the hallway. Now, we can spend a few minutes in class making dozens of these, taking a screen shot of each, and posting them on our blogs for all to see! It's definitely better on the environment, and more people can see these tessellations than before!
All of the computer-generated images in this post were from the same student - they obviously got into it and had some fun! I was thrilled to see my students so engaged and enjoying their time in math class. I was able to walk around and clarify misconceptions because everyone was self-directed, which freed me up to do what I needed to do!
Some of the students who were working with the pattern blocks didn't realize that a pretty pattern is not necessarily a tessellation. I made them show me how their pattern tessellates up, down, left, and right using the same pieces. I had them separate their original shape from the repeating shapes so that they could see which pieces made up the actual original. Some students had trouble with this and others saw it right away.
Take a look at the pictures below. The pattern block patterns shown are not actually tessellations until they repeat left, right, up, and down. The one on the left is nearly perfect, but is missing a couple green triangles to make it complete. The one on the right is the original shape that would need to be repeated up, down, left, and right in order to call it a tessellation. (So it is not a tessellation as is.) But it's pretty, huh?! :)
I highly recommend doing this with your students if you teach tessellations because the computer-generated images are beautiful and encourage creativity, and the pattern blocks encourage critical thinking and pattern-creation. While students are working online, they are tinkering with the design, the shapes, the colors, and the overall appearance of the tessellation. They are comparing their final products with each other and analyzing what makes their tessellations attractive. While working with pattern blocks, students are scrutinizing over the shapes to determine which ones should be used, which ones can tessellate, and how many of each they need to have in order to prove that their pattern tessellates. This critical thinking is important to synthesize what they've learned from our in-class lesson and their experience online.
I also will usually have my students create a slide tessellation and a rotation tessellation on a piece of construction paper by cutting out a shape according to specific directions. We have not done that yet, but will if we discover that we have a little extra time before our test. :)
Here is a link to the directions page we used in class - feel free to use it with your kiddos! There are four links. The third one is the one to use to create tessellations like we did.