Math Mondays: Taking time for Tessellations

Tessellations are a beautiful, engaging, and interesting activity for math class.  Perhaps the most famous tessellations were created by M.C. Escher.  Escher showed how beautifully mathematical concepts could be conveyed in original art pieces. He also cleverly demonstrated that there are different perspective for looking at things. 
 For example, in drawing hands, which hand is drawing which?  Escher's work sparks fascinating discussions.

When students create their own tessellations, there is even more learning to be done.  Benefits of tessellations include:

  • Problem solving skill development.  Tessellations involve patterns and spatial reasoning.  
  • Measurement.  Students can use different tiles to measure or identify the perimeter of a design.  How many tiles must be used to make a shape that is at least X cm by Y cm?
  • Area.  For younger students, tessellations demonstrate the concept of area.  There are no holes between tiles, so the area increases with each tile placement.
  • Symmetry.  Tessellations patterns have many lines of symmetry.  Students can identify the lines of symmetry in their own designs and those of others.  
  • Creativity.  Creating an abstract geometric shape 

I did this tessellation project with a mixed age group of students.  One cool thing about tessellations is that elementary students through high school students can work with them.  Tessellations do not depend on numerical skills and are great for spatial thinking.  The more advanced the student, the more complicated their designs might get.  Some of my students chose to trace their patterns while others constructed their tessellations out of cut paper.  The results are varied, fascinating and fun.  This is a great activity for centers as part of a geometry unit.

The steps are pretty simple:

  1. Give each student a small square or rectangle of paper.  We used 3" x 3" pieces of paper from the recycle bin.  It helps if there is writing or color one side of the paper so that students can always identify the top of the paper.
  2. Have students cut out shapes from one side and slide it over to the other side of the square without turning the cutout or square.  Tape the piece onto the other end.  Do this step multiple times to create a shape to tessellate.

  3. Then trace and make a pattern with the tessellation tile.
For a full lesson plan to create your own tessellations with all the details and M.C. Escher designs for inspiration click here.

Math Mondays 
is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.



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