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LESSON TWO:
GEOMETRY AND GRAPHIC DESIGN
Overview of Lesson
As we have seen Islamic art and M.C. Escher prints have
several things in common, they both make use of geometric
shapes to create patterns called tessellations that are symmetrical
in nature. Creation of these patterns involves transformation:
changing the position of an object on the plane while perserving
all of the angles. A transformation occurs when a shape is
moved or changed using reflection, rotation, or translation--three
concepts essential to the creation of tessellating shapes
and repeated patterns.
Objectives
· Students will define mathematical vocabulary and
concepts involved in creating tessellations.
· Students will pick out examples of the concepts of
transformational geometry, reflection, rotation, and
translation, by analyzing several examples in works of art
(Art Criticism).
· Students will demonstrate an understanding of
reflection, rotation, translation, and congruency by
correctly using shapes to make symmetrical patterns (Art Criticism, Art Production).
Materials and Resources
· Copies of the student handouts, “Triangles”
and
“Quadrilaterals”
· Copies of the student handout, “Tessellation
Chart”
· Overhead transparency, “Translations”
· Strips of tag board
· White drawing paper
· pencils and rulers
Background Information
Translation: (also called slide) in this method of transformation,
a shape moves the same distance and the same direction to
its new position. Translating an object means moving it without
rotating or reflecting it. You can describe a translation
by stating how the shape slides, and in what direction.
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Reflection: (also called a flip)
In this method of transformation, the figure is moved to a new
location on a plane by flipping it over. The image is then a
mirror image or reflection of the original.
Line of Reflection: the line over which a figure is flipped
in reflectional symmetry.
Rotation: In this method of transformation, a figure is
moved to a new location on a plane by rotating it around a
fixed point.
Center of rotation: the point in the plane around which the
shape rotates.
Teacher Preparation
Become familiar with the Background Information and Instruction
from the previous lessons. Make an overhead transparency of
“Transformations” located at the end of the unit.
Use this transparency to explain or review the concepts of
translation, rotation, and reflection to the students. The
student handouts, “Triangles” and “Quadrilaterals”
can be applied to this lesson in two ways. Students can use
the examples as a guide to trace shapes to tag board and more
advanced students can use the instructions on the page to
draw their own shapes to the tag board.
Repeat the instructions included in the lesson for each set
of shapes. When working with the handout, “Triangles,”
students will apply transformations to equilateral, isosceles,
and scalene triangles. Using the handout, “Quadrilaterals,”
students will repeat the process with a rhombus, parallelogram,
rectangle, and square.
(continued on page 8)
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