My tessellation that I had worked on in class was simple but that is most likely what everyone thinks because a tessellation is just one shape transformed throughout a plane. The shape can be reflected over lines (reflection), rotated about a point (rotation) or moved without losing its position (translation). Who would have thought that by applying different transformations to a shape could result in such awesome designs?

I personally chose to translate my shape, which consisted of the two short bases of the trapezoid coming together with the two rhombi fitting into each end. By repeating this pattern of translating my shape we can see other shapes besides just the rhombus and trapezoid such as a regular hexagon and a parallelogram, along with different looking hexagons.

My next tessellation that I created included two hexagons and two rhombi as the transformation piece. The familiar shapes that I see are stretched down hexagons that are skinnier in relation to a regular hexagon if you look at it as in the picture from top to bottom. These two tessellations are similar because they both use rhombi and since two trapezoids make up a hexagon we can see them as such. But the tessellation itself is different because of the pattern we see. In the red and blue tessellation we see two rows of rhombi lined up but in the yellow and blue tessellation we only see one two of rhombi lined up. That has to do with what we are calling our base piece or the piece that you are transforming.

Keeping my future students in mind I can see myself using this activity to integrate math and art as we did in class. I like the idea of letting the students be creative with the types of patterns they make while also allowing them to make mathematical connections unknowingly. When math is being done without it being too obvious students seem to benefit. They benefit because they aren’t as intimidated because it’s not “really” math. But when they can draw connections on their own about their tessellations that is when learning is being done.

In my MTH 322 geometry class we engaged in an activity that used pattern blocks to explore fractions. I thought that this activity was awesome to really show what fractions are all about, a part of a whole. By asking questions like, “how many green triangles can fit into this hexagon?” we allow students to explore the relationship between the triangle and the hexagon. The triangle is now some portion of the hexagon. I would love to explore an activity using a tessellation out of pattern blocks to teach fractions to students. I could have them come up with the different proportions that are seen in the tessellation and question them about the ratios they see.

In my MTH 322 geometry class we engaged in an activity that used pattern blocks to explore fractions. I thought that this activity was awesome to really show what fractions are all about, a part of a whole. By asking questions like, “how many green triangles can fit into this hexagon?” we allow students to explore the relationship between the triangle and the hexagon. The triangle is now some portion of the hexagon. I would love to explore an activity using a tessellation out of pattern blocks to teach fractions to students. I could have them come up with the different proportions that are seen in the tessellation and question them about the ratios they see.