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Introducing Tessellations



  • Mathematics


  • 6-8
  • 9-12

Brief Description

Students use the drawings of M.C. Escher, as well as online research, to deduce what tessellations are. Then each student creates tessellations from both regular and irregular polygons.


Students will:
  • understand the concept of tessellations.
  • express that understanding by creating two tessellations.


tessellations, symmetry, geometry, Excel

Materials Needed[shopmaterials]

  • Student access to the Internet
  • Student access to Microsoft Excel (and possibly a word processing program, such as Microsoft Word)

Lesson Plan

Introduce tessellations to your middle or high school class with this fun and hands-on computer lesson. The lesson can be taught during a discussion of symmetry (reflection, rotation, translation) and is best used as an introduction to tessellations.

Introduce the lesson by showing a picture of one of M.C. Escher's works. Click the Gallery link, choose a picture of a tessellation, and ask, "What does this piece of art have to do with math?" If students are stumped, ask them to look at what makes up the picture. Help them see that the picture contains many representations of the same image, or shape, fit together with no space between them. Explain that that is called a tessellation.

Depending on computer resources, time constraints, and personal preference, you might want to provide an overview of what tessellations are and how they fit in math class, or you might ask students to research the topic and share their findings with one another. The following Web sites will help with that research.

After students have shared 3-5 tessellation facts they've learned (or after you've discussed the basics with them), it's time for students to create their own tessellations.

  • Begin by showing students examples of other Student Tessellations from MathForum.
  • Help students complete steps one and two in the Education World techtorial, Create Tessellations with Excel. Make sure each student was able to create a tessellation with the chevron (regular polygon).
  • Encourage students to try to make more tessellations using other basic shapes, such as circles, squares, hexagons, octagons, and so on.
  • Have students record the results of their attempts -- what shapes worked in tessellations and what shapes did not -- and share the results with their classmates. Brainstorm with students why some shapes worked and others did not.
  • If time permits, have students complete step three in the in Create Tessellations with Excel techtorial. Give students time to create uniquely shaped and colored polygons, and then explore why some of the irregular polygons might not have worked.
  • Conclude the lesson by printing black and white copies of students irregular polygon tessellations and displaying them in class.


Students will be assessed on their:
  • understanding of what a tessellation is; and
  • understanding of why some regular and irregular polygons can be used in tessellations and others cannot.

Lesson Plan Source

Education World

Submitted By

Lorrie Jackson

National Standards

GRADES 6 - 8
NM-GEO.6-8.3 Apply Transformations and Use Symmetry to Analyze Mathematical Situations
NM-GEO.6-8.4 Use Visualization, Spatial Reasoning, and Geometric Modeling to Solve Problems
GRADES 9 - 12
NM-GEO.9-12.3 Apply Transformations and Use Symmetry to Analyze Mathematical Situations
NM-GEO.9-12.4 Use Visualization, Spatial Reasoning, and Geometric Modeling to Solve Problems