Where in the World Do We Find Tessellations

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Where in the World Do We Find Tessellations?
Diana Houhanisin, LHS Mathematics, Huron Valley
Schools
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Welcome to The Escher Institute

• M. C. Escher is a famous artist. He is known for
  his work with tessellations. Today the Escher
  institute is looking for up and coming talent to
  take on as apprentices in the art of tessellation
  artwork. However, before you all get out your
  brushes there is a short interview process.
  During this process the institutes top artists
  will ask you 7 questions about tessellations and
  expects you to show him a sample of your work.
• Click below to check out tessellations from
  around the world!
  
• http//www2.spsu.edu/math/tile/grammar/index.htm

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The Interview

• Answer the following questions in Microsoft
  word.
  
• What is a tessellation?
• Where do we see tessellations in the world around
  us?
  
• What is symmetry?
• What transformations preserve symmetry?
• Explain the type of symmetry present in
  tessellations.
  
• What regular polygons may be used in tiling and
  why? (What must be true for tiling with regular
  polygons to occur)
  
• Explain how unit cells can be used to create
  tessellations? (Which unit cells can be used)
  
• You may find the answers at this totally
  tessellated sitehttp//library.thinkquest.org/166
  61/index2.html
  

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Show Us Your Portfolio

• Using paint, create your own tessellation. You
  may choose from any of the methods described in
  totally tessellated.
  
• During the process of creating your own
  tessellation document the process you are using
  by explaining the procedure step by step. Your
  direction should be explicit enough that anyone
  could recreate your tessellation. Use pictures
  if necessary to document your steps.
• If you need inspiration visit Escher's classroom
  http//britton.disted.camosun.bc.ca/jbescher.htm

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What Are We Looking For?

• Rubric Points Break Down
• Completion of Interview Questions (10)
• _____ Accuracy in answers (6)
• _____ Completeness (4)
• Tessellation (15 Points)
• _____ Creativity (5)
• _____ Style (5)
• _____ Accuracy (5)
• Written process for the creation of your
  tessellation(25)
  
• _____ Accurate Representation of Process (10)
• _____ Process can be duplicated (10)
• _____ Completeness (5)

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Going Deeper

• Find a drawing by Escher and explain how the
  tessellation could have been constructed.
  
• Give the explanation of your process to another
  student and see if they can recreated your
  tessellation.

Think about how you could make your tessellation
3-D. Go out into the world and find examples of
tessellations. Take digital photos of these
tessellations and share them with your class.
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Standards and Benchmarks
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• Mathematics
• G3.1 Distance-preserving Transformations
  Isometries
  
• G3.1.1 Define reflection, rotation, translation,
  and glide reflection and find the image of a
  figure under a given isometry.
  
• G3.1.2 Given two figures that are images of each
  other under an isometry, find the isometry and
  describe it completely.
  
• G3.1.3 Find the image of a figure under the
  composition of two or
  
• more isometries and determine whether the
  resulting figure
  
• is a reflection, rotation, translation, or glide
  reflection image
  
• of the original figure.
• G3.2 Shape-preserving Transformations Dilations
  and Isometries
  
• G3.2.1 Know the definition of dilation and find
  the image of a figure under a given dilation.
  
• G3.2.2 Given two figures that are images of each
  other under some dilation, identify the center
  and magnitude of the dilation.
  
• G3.2.3 Find the image of a figure under the
  composition of a dilation and an isometry.
  
• Art
• Standard 1 Performing
• All students will apply skills and knowledge to
  perform in the arts.
  
• Standard 2 Creating
• All students will apply skills and knowledge to
  create in the arts.
  
• Standard 3 Analyzing in Context

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Teacher Tips

• This lesson may take two days. Extra time may
  want to be arranged in advanced.
  
• Honors Geometry students could do both the
  activity and Going Deeper.
  
• If Microsoft paint is not available tessellations
  could be made in Claris works, Microsoft word, or
  geometers sketch pad.
  
• For a more guided tessellation students may
  follow these instructions to create a
  tessellation in Geometers sketchpad at
  
• http//mathforum.org/sum95/suzanne/tess.gsp.tutor
  ial.html
  
• As either an introduction or a follow up students
  could go out and find tessellations in the real
  world. Students could document their finds by
  using digital pictures. These pictures could then
  be shared with the class.
• For quick grading of the accuracy and making sure
  that their explanation allows for the duplication
  of the design. One could have the students Go
  Deeper by trading explanations then trying to
  recreate the design with the directions created.
  This in itself could also be an assessment.
• The following link assist in 3-D Tessellations
  http//www.origamitessellations.com/
  

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Bibliography

• Site Bibliography
• Escher in the classroom
• http//britton.disted.camosun.bc.ca/jbescher.htm
  
• Totally Tessellated
• http//library.thinkquest.org/16661/index2.html
• Tilings from history
• http//www2.spsu.edu/math/tile/grammar/index.htm
• Sketchpad lesson
• http//mathforum.org/sum95/suzanne/tess.gsp.tutor
  ial.html
  
• Technology and Art Standards
• http//mtn.merit.edu/
• Geometry Bench Marks and Standards
• http//www.michigan.gov/documents/Geometry_167749_
  7.pdf
  
• Image Bibliography
• Slide 1 Lego of Escher's Relativity
• www.andrewlipson.com/escher/relativity.html
• Slide 2 M. C. Escher Portrait
• http//illusionworks.com/mod/escher.htm

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