Spatial and Logical Connections: Tessellations!

  Since our blog on origami, I have been thinking about tessellations and why they make origami patterns so interesting. Tessellations are any number of patterns such as square (also known as tiling), triangular, and hexagonal patterns. Nature sometimes mimics tessellation patterns. For example, the honeycomb in a beehive is a hexagonal tessellation. You may look at your floors or walls and notice that they are square or triangular tessellations.

 What makes these patterns so cool may be the fact that every inside angle of a polygon adds up to 360 degrees. Don’t believe me? Crack out the protractor and start measuring! For example, a square has 4, 90 degree angles: 90 + 90 +90 + 90 or 4 x 90 = 360. Try it!

  Another great thing we can do with these patterns is very artistic in nature. Quilting is one of my favorite past times (when I have time!). Quilting is completely based on geometry and tessellation patterns. One of my favorite things to do is introduce tessellations, areas, and perimeters using a Math Quilt. It is a classroom quilt made out of paper or cloth. Kids can choose their favorite polygon, or combination of polygons, and fit their pattern into an 8″, 10″, or 12″ square. Below is an example of several square patterns, somewhat complex, in a quilt design:

  You can ask students how to calculate the total perimeter of all the pieces in their block, or each separate piece, or the area of each piece, or the total square area. For example, the perimeter of a square is all four sides added together. P = S + S + S + S. The area of a square is the length multiplied by the width. A = L x W.

  As you can see, you can use really basic polygons and move into more complex polygons like hexagons and octagons. You can make these activities simple, moderate, or difficult; which makes it easier to use differentiation in your lessons.

  Happy Tessellating!