Tessellations were created in Ancient Rome and in Islamic art in various palaces. The real mathematician is M.C. Escher which made tessellations a creation for artistic effects.

When looking at various images in class, I realized that there can be either complex and simplistic patterns. Thus, I wanted to see what it took to create both kinds of tessellation. My tilling’s are shown below. I created a simplistic one and a more complex design.

In the figure to the right, I started with the three pink triangles connected together at the tips. Then realized that I could create three smaller purple triangles which can look like a hexagon behind the pink triangles. Then I colored in the yellow to make a bigger triangle. I began to think about how to make sure this pattern will repeat. Thus, I colored around the shape created to form a hexagon. Then connected the hexagons together.

Once I finished creating the repeated pattern I realized that by connecting them together I created an orange smaller hexagon. Therefore, I realized that if you were to do this as a profession, such as the Islamic art in palaces, it would take a lot of planning and thinking even though you are connecting shapes together.

Next, I decided to try a simpler concept of tessellation but still incorporating repetition. (This figure is shown below. Thus, with this new tessellation I started with filling in a 5x5 square and then repeating the pattern. I then created a smaller square inside the 5x5 square and realized I could create four trapezoids and a square to fill that inner square. Then, as I thought about what to put around the inner square, I wanted to create a cross type shape (pink) and filled in the remaining space with the color blue.

I again sat back and noticed that once I connected the access blue it created another wider cross. As I stated before, I didn’t think by doing a simpler tessellation that I would be able to form another shape when connected. This is a neat concept to see that you wouldn’t notice by looking at someone else tessellation work.

This concept is really intriguing to me because as try and relate it to my future classroom. I feel that in order to get children used to shapes and their relation to other shapes this type of interaction would be a great activity. This activity would also focus on a couple Standard for Mathematical Practice. Them being able to reason and also to think abstractly.

As I think about my own tessellation creations I begin to realize before started I pictured the whole idea in my mind before actually creating it. Thus, displaying the thinking abstractly mathematical practice. Then, having to discuss why and how I created would be the best for my future students on being able to communicate their mathematical ideas to others.