A tessellation is “the filling of a plane with repetitions of figures in such a way that no figures overlap and that there are no gaps” (Billstein, Libeskind, & Lott, 2010) . Tessellations can be created with a variety of figures, including triangles, squares, trapezoids, parallelograms, or hexagons. Tessellations use forms of transformations to show the repetitions of the figures. The transformations can includes translations, rotations, reflections or glided reflections. Any student would be able to create their own original tessellation by piecing together a variety of geometric shapes in a repetitive pattern by a transformation, either by hand or on a computer. The tessellation that I have created includes hexagons, squares, and triangles. I placed the squares and triangles around the hexagon to fill in the open spaces; this is to ensure that it is a complete tessellation. I did that because I found it to be very eye catching and adding the colors makes it a visually stimulating piece.
This tessellation has the transformation of translation. Each shape is moved from one point to another in a straight line. The line can either be up or down, left to right, or even diagonally, but the shape itself is a copy of the original. The different colors of the hexagons allow you to see where the repetition occurs. Tessellations have been found in real-life. Soccer balls, plaid clothing, honey combs, and brick lying are examples of tessellations. One of my favorite things as a child was a kaleidoscope. This was a toy the when you held it the light showed a tessellation and if you rotated the scope, the tessellation would change. It was a fascinating toy for a child and it introduced them to the idea of a tessellation without knowing about them. Tessellations are a visual stimulate and cause many of happy days in my childhood and hopefully will be that way for my children as well.
Billstein, R., Libeskind, S., & Lott, J. (2010). A problem solving approach to mathematics for elementary school teachers (10th ed.). Boston, MA: Pearson Addison Wesley..