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.
- Apply the concepts of translation and tessellation by
creating an original design based on a geometric shape that
- 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
- Transparency of “Circle
- White drawing paper thin enough to see through, photo
copy paper will work
- Pencils, markers, and colored pencils
- Transparencies: Geometric Design: "Triangle”
- Color images of Islamic Tile Work and M.C. Escher’s
Symmetrical Work (Recommended Websites, page
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
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?
Pattern: a design composed of shapes repeated in
a regular manner.
Tessellation: the tiling of a plane without any gaps
or overlaps by a pattern of one or more congruent
Transformation: Moving or changing a shape based on
a mathematical principle, such as rotation, translation,
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:
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.
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”
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.
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.
(continued on page 11)
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