TESSELLATION WITH TWO MOTIFS – Translation, Rhythm, Contrast

Students will be able to:

• follow written instructions to create an irregular shape that will tessellate;
• tessellate a pattern with an alternating rhythm;
• identify and use contrasting colours;
• explain why the tessellation works; 
• demonstrate technical accomplishment and creativity.

Have students:

• create a Mathematics of Tessellation book that includes all or some of the following shapes used in tessellations with explanations of why the shapes tessellate: 
  - repeated use of one regular polygon
  - repeated use of a unit shape made up of two or more different regular polygons
  - triangles or quadrilaterals
  - irregular shapes created by transformation - flips, slides and turns
• select an art image by M. C. Escher and explain how it works;
• use the work of M. C. Escher as inspiration for their own tessellating artwork;
• share their work with the class.

1. Prior to this lesson have students explore tessellations involving repeated use of one polygon and unit shapes made up of 2 or more different polygons.
2. Download images of tessellations in nature from the Internet, e.g.,
   Pineapple
   Honeycomb
   Fish Scales
   Snake
3. Gather and make available books and pictures of tessellations, for example, Toads and Tessellations: A Math Adventure, by Sharon Morrisette; An Optical Artist: Exploring Patterns and Symmetry, by Greg Roza; Tessellations: The History and Making of Symmetrical Designs Pape, by Pam Stephens; Introduction to Tessellations, by Dale Seymour and Jill Britton.
4. Download and display the Repetition, Rhythm, and Contrast posters available on this website.
5. Create a sample irregular shape that will tessellate.
6. Download the tessellation worksheet - one per student. (Downloads - TessellationWorksheet.pdf)

1. View and discuss the images of tessellations in nature.
2. Review or introduce the term tessellation.
   - patterns of repeated shapes that cover a flat surface with no gaps and no overlaps
3. Discuss what kinds of regular shapes can tessellate and why.
   - regular polygons (triangles, squares or hexagons)
   - regular polygons can only tessellate if the sum of the interior angles is 360 degrees
4. Demonstrate how your irregular shape tessellates.
   - How did I make this shape?
5. Introduce the challenge. 

1. Once all the designs are complete display them for a group discussion. 
   - Look closely at the tessellations.
   - Choose one that interests you for some reason.
   - Share thoughts about the work.
2. During the discussion include references to:
   - Contrasting Colours - How does the use of contrasting colours contribute to the effectiveness of the alternating rhythm?
   - Motifs - What makes the motifs interesting and effective?
   - Technique – How and why does the tessellation work?

1. Observe students as they work – thoughtful focus, discriminating, seeking more information, elaborating, experimenting.
2. Observe students as they discuss their tessellations – speaks with a clear voice, looks at audience while speaking, points to areas in the designs, provides accurate information, answers questions from the audience effectively.
3. Observe students as they listen – looks at presenter, asks effective questions, supports ideas with evidence found in the artwork.
4. Use a checklist to track progress. (Downloads - Tessellation2_tracking.pdf)
5. Have students use the self-assessment form to evaluate their work. (Downloads - Tessellation2_self-assessment.pdf)