TANTALIZING TESSELLATIONS – Irregular Polygons, Colour

Students will be able to:

• use translation to create an irregular shape that will tessellate;
• create a design filled with blended colour;
• ddd details to the shape to make it interesting;
• explain why the tessellation works; 
• demonstrate technical accomplishment and creativity.

1. 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 of shape made up of TWO OR MORE different regular polygons
   - triangles or quadrilaterals
   - irregular shapes created by transformation and rotation
2. Have students select an art image by M. C. Escher and explain how it works.
3. Have students use the work of M. C. Escher as inspiration for their own tessellating artwork.

1. Prior to this lesson have students explore tessellations involving repeated use of one polygon and shapes made up of 2 or more different polygons.
2. Download and display the Colour and Value posters available on this website.
3. Download tessellations in nature images from the Internet.
   Pineapple
   Honeycomb
   Fish Scales
   Snake
4. Download M. C. Escher images from the Internet.
   Den Haag
   Princessehof
   VoorHout
   Alhambra
5. 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, by Pam Stephens; and Introduction to Tessellations, by Dale Seymour and Jill Britton
6. Create a sample irregular shape that will tessellate.

1. View the images of tessellations in nature and discuss them. Review and/or introduce the term tessellation and have students describe the characteristics of a tessellation, e.g.,
   - patterns of repeated shapes that cover a flat surface with no gaps and no overlaps
2. Discuss what kinds of regular shapes can tessellate and why
   - regular polygons (triangles, squares or hexagons)
   - because the sum of their interior angles is 360°
3. Discuss how to use translation to create an irregular shape that will tessellate.
   - a translation is when the shape is slid across the paper and drawn again in another place 
4. View and discuss the images of Escher's art.
5. Introduce the challenge. 

1. Once all the designs are complete display them for a group discussion. 
2. Ask students to:
   - Look closely at the tessellations.
   - Choose one that interests you for some reason.
   - Share thoughts about the work.
3. During the discussion include references to:
   - blended colours - How does the use of blended colours contribute to the effectiveness of the overall design?
   - design - How does the use of detail contribute to the effectiveness of the overall design?
   - 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 tessellation designs – 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 - TESSELLATION_tracking.pdf)
5. Have students use the self-assessment form to evaluate their work. (Downloads - Tessellation_self-assessment.pdf)