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Instruction
Display the overhead “Tiles from the Alhambra.”
Explain that these images are based on sketches made by M.C.
Escher during his visits to the Alhambra Palace (Escher on
Escher, 26). Demonstrate each type of transformation to the
class using geometric shapes and the overhead, “Transformations.”
Ask students how each type of transformation earns its name.
(In rotation, the triangle rotates around a center point.)
Allow students to re-examine “Tiles from the Alhambra”
and explain which images are examples of rotation, translation,
or reflection. Show examples of tessellations from the Internet.
Ask students to explain which images demonstrate translation,
rotation, and reflection.
These sites can provide a starting place for the activity:
Hop’s Escher Tiles: http://www.tabletoptelephone.com/~hopspage/HopsTiles.html
M.C. Escher’s Symmetry Drawings:
http://www.mcescher.com/Gallery/gallery-symmetry.html
Grotesque Geometry: Andrew Crompton:Z
http://www.cromp.com/tess/home.html
Demonstrate to the class how the shapes in each example glide,
rotate, and flip over to create each type of transformation.
Have students find their own examples of tessellations. Images
can be art found on the Internet, artworks from presentations
in Lesson One, or objects in the environment (floor tiles,
wallpaper, etc.). Students should be able to explain why the
image or design is a tessellation, and describe what type
of transformation is exemplified.
Go over vocabulary using the overhead to illustrate various triangles, quadrilaterals, and the concept of congruence.
Assist students in creating cutouts of triangle and quadrilateral
shapes using the student handouts, “Triangles”
and “Quadrilaterals.” Use the transparency, “Transformations”
as an example when explaining the different types of transformations
used in a tessellation.
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THE ORIGIN OF
PATTERNS BEFORE TIME
The concepts for the unit featured in this issue
were adapted from a lesson developed by Nancy Walkup,
entitled, Order in the Universe: Geometry, Symmetry,
and Congruency in Art, Math, and Science.Adaptation and added
material by Lisa Galaviz and Dr. Jaqueline Chanda.
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After students have cut their shapes from the tag board,
they should experiment with each shape to see if it will fit
together with no gaps or overlaps: select a shape, trace it
once, then slide the guide into the new position to trace
it again. If the figure must be flipped over to fit, the transformation
is a reflection (flip). The pattern will be an example of
reflectional symmetry. If the figure will fit without flipping
it over, the transformation is a translation (slide). The
pattern will be an example of translational symmetry. Students
can record their results using the “Tessellation Chart”
located at the end of this unit.
Next, the class will use the shapes already cut from previous
exercises to explore rotational symmetry. Students can practice
rotational symmetry by drawing a dot for the center of rotation
with a sharp pencil. After choosing one corner of each shape
to align with the center of rotation, the student will then
trace the shape while rotating it around the dot. If the shape
meets itself with no gaps or overlaps, the shape will demonstrate
rotational symmetry. Students should use one shape at a time
and record their results using the “Tessellation Chart.”
(continued on page 9)
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