Below is a geometric tessellation I created:
In order to create my tessellation, I started by drawing the squares that are colored yellow and green. Once those were drawn I thought about what I could add next and I noticed there were little squares which are colored orange and purple in between the yellow and green squares. I felt like the squares themselves were not enough and decided to draw diagonal lines through the squares in order to create triangles within the squares, keeping in mind that all shapes had to be polygons. I then drew horizontal and vertical lines splitting the paper into 20 squares. From doing this I created a pink and blue square outline around my original yellow and green squares. Once the outline was drawn I decided to color the tessellation in a pattern as well because when you look at a geometric tessellation not only the shape pattern continues but also the color pattern.
I could see myself introducing tessellation in my classroom once I become a teacher in order to have my students explore how different geometric shapes can connect and create a different polygon. For example how four triangle can create a square which can be seen in my tessellation below or how six triangles can create a hexagon. Another observation they could make it that hexagons can connect to one another and not have any gaps. I think creating a tessellation could help students understand shape properties as well as having them work on problem solving and puzzle skills, if they are given certain shapes and asked to make as many different combination as possible where there are no gaps. I think in elementary or middle schools I would prefer to have students work with manipulatives of the different shapes, so they are not limited to the shapes they can easily draw by hand. Overall I think using tessellations can help further students learning in several different content areas.