This is my absolute favorite lesson in Geometry (Right in front of my second favorite lesson Dance Dance Transversal)! We do a week long project where the students create a poster board sized work of art using the Tessellations they create. The best way to do this project is to collaborate with the art teacher to utilize both class times and standards effectively (plus they have all the good art supplies!)
Here is how I run the project...
First, lead the class through the tessellation creation process. Here are two videos that will teach you the process. There are 3 types of tessellations rotation, reflection, and translation (or slide). The videos cover the two easiest to create. This gives them a clear idea on how their cuts will affect their overall shape. (Hint for teachers: When creating the Slide Tessellation it is important that you preach to them making sure their cut goes from corner to corner. If the cuts do not go directly into the corner their shape will not tessellate when they tape it together and trace it. I always check their lines before they cut and then again before they tape. Just make it a requirement for them to show you their note card before they move on to the next step.)
I have them use a regular size poster board to trace onto and a 4x6 note card for the stencil. If you use too small of a note card it will take them for ever to cover the entire poster board when tracing. If you have them use a piece of paper for the drawing use a post it note or a smaller not card for the stencil. You want the stencil to be made of something with some substance to it. If it is too flimsy they will have trouble tracing it because it will bend, tear, and wear easier. Remember they will be tracing these stencils many times.
PART - TARP Method
Then I go through the project rubric and expectations. This is a 100 point project (test grade) in my class. There are three main things they need to know about the project.
1.) The project is a competition (make the reward whatever you want, possibly a homework pass or something of that nature. The first year I did this it as just for the glory and that worked just fine). The more glamorous, flashy, and amazing their project is the better! The projects are all hung up in the hallway and the students all get to vote on which project is the winner. I make the top 3 finishers prize winners.
2.) In order to be considered for the competition and in order to get an A on the project their project must actually tessellate (yes there will be students who mess this part up). If it does not tessellate the best grade they can get is a B for their efforts. The poster board must be completely filled even where it goes off the edges.
3.) The tessellation can not just be a shape or a blob of color. It has to be turned into something. I've seen everything from amazing flowers, animals, and people to Sponge Bob Square Pants and elaborate Super Heroes. Let them be creative! Here are some examples.
Here are some of the famous tessellations that your collaborating art teacher will be showing them.