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LESSON THREE:
TESSELLATION GAME

Overview

In this lesson, students will apply their knowledge of Islamic design by creating a design based on a shape that will tessellate. They will create a symmetrical pattern from this original design using translation, rotation, or reflection.

Objectives

• Apply the concepts of translation and tessellation by creating an original design based on a geometric shape that will tessellate.
• Explore mathematical concepts behind Islamic tile work by developing an original shape that will tessellate, then creating a pattern from that design.

Materials and Resources

• Copies for each student of the “Circle Template”
• Transparency of “Circle Template”
• White drawing paper thin enough to see through, photo copy paper will work
• Pencils, markers, and colored pencils
• Transparencies: Geometric Design: "Triangle” and "Star"
• Color images of Islamic Tile Work and M.C. Escher’s Symmetrical Work (Recommended Websites, page 2)

Preparation and Background Information

Review the three kinds of transformation and symmetry discussed in the unit. Review the activities from Lesson One, discussing which geometric shapes will tessellate and why. Pass out the “Circle Template." Review the significance of the circle in Islamic Art, and examples of geometric shapes found within overlapping circles. Students can demonstrate to the class by outlining the shapes using the template on the overhead.

Questions to consider when outlining geometric shapes:
Which of these shapes will tessellate?
What types of transformations can be applied to each shape?

Instruction

After reviewing tessellation concepts from Lesson One, students should be able to select a geometric shape for the basis of their design. Show how the design concepts the students will be learning are directly related to Islamic design using the following transparencies found at the end of the unit:
“Geometry in Islamic Design” This transparency demonstrates how a circle becomes a hexagon, then the hexagon is used as the base for a star, a popular image in Islamic tile work.
“Shapes within a Circle” These examples, demonstrate the basis behind the circle templates the students will be using to create their original designs.
Geometric Design Examples: "Triangle” and “Star” These transparencies demonstrate how to use the “Circle Templates“ to create a design based on a geometric shape.

In “Geometry in Islamic Design,” the final design is created from first finding a shape within the circle, drawing a design within the shape, then using that design to create a pattern. Students will follow this process in their own work by using the “Circle Template” to draw an original design within a geometric shape. After completing the design, students will trace the same shape several times to create a pattern. Using one of the transformations discussed in Lesson One, reflection, translation, or rotation, the students will create a tessellation from their original geometric design.

After filling the plane (the sheet of paper) completely with the pattern created from the repeated shape, students will complete the designs with marker or colored pencil. Display color images of M.C. Escher’s symmetrical drawings and tile designs from the Alhambra Palace to inspire students in selecting colors for their work.

Summary

Upon completion, display student work. Have students identify which geometric shape is the basis of each design. Compare the final designs with the work of M.C. Escher and images from the Alhambra Palace. Discuss the concept of tessellation and how it applies to both Islamic design and the symmetrical works by M.C. Escher. Review the similarities between Islamic tile work and M.C. Escher’s fascination with the regular division of the plane.

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