a set of regular triangles, squares, pentagons, hexagons, and octagons that they can slide around and fit together.
These shapes can be bought from a mathematics education supply company or made with paper. Exploring the
relationships in this way gives the students a fuller understanding of the concepts.
Use On-Line Resources –A quick search on tessellations will produce many beautiful, artistic examples like the
work of M. C. Escher and cultural examples like Moorish tiling. This bit of research will inspire students and show
them how applicable this knowledge is to many areas.
Tessellation Project –A good long-term project is to have the students create their own tessellations. This is an
artistic endeavor that will appeal to students that typically struggle with mathematics, and the tessellations make nice
decorations for the classroom. Here are some guidelines for the assignment.
a. Fill an 8^12 by 11 inch piece of solid colored paper with a tessellation of your own creation.
b. Make a stencil from cardboard and trace it to make the figures congruent.
c. Be creative. Make your tessellation look like something.
d. Color your design to enhance the tessellation.
e. Your tessellation will be graded on complexity, creativity, and presentation.
f. Write a paragraph explaining how you made your tessellation, and why your design is a tessellation. Use
vocabulary from this section.This project could also be done on a piece of legal sized paper. The tessellation can fill the top portion and the
paragraph written on the lower part.
Symmetry
360 DegreesDoesn’t Count –When looking for rotational symmetries students will often list 360 degree rotational
symmetry. When a figure is rotated 360 degrees the result is not congruent to the original figure, it is the original
figure itself. This does not fit the definition of rotational symmetry. This misconception can cause error when
counting the numbers of symmetries a figure has or deciding if a figure has symmetry or not.
Review Quadrilateral Classifications –Earlier in the course students learned to classify quadrilaterals. Now would
be a good time to break out that Venn diagram. Students will have trouble understanding that some parallelograms
have line symmetry if they do not remember that squares and rectangles are types of parallelograms. As the course
draws to an end, reviewing helps students retain what they have learned past the final. It is possible to redefine
the classes of quadrilaterals based on symmetry. This pursuit will make the student use and combine knowledge in
different ways making what they have learned more flexible and useful.
Applications –Symmetry has numerous applications both in and outside of mathematics. Knowing some of the
uses for symmetry will motivate student, especially those who are not inspired by pure mathematics, to spend their
time and energy learning this material.
Biology – Most higher level animals have bilateral symmetry, starfish and flowers often have 72 degree rotational
symmetry. Naturally formed nonliving structures like honeycomb and crystals have 60 degree rotational symmetry.
These patterns are fascinating and can be used for classification and study.
Trigonometry – Many identities of trigonometry are based on the symmetry of a circle. In the next few years of
mathematics the students will see how to simplify extremely complex expressions using these identities.
Advertising – Many company logos make use of symmetry. Ask the students to bring in examples of logos
with particular types of symmetry and create a class collection. Analyze the trends. Are certain products more
appropriately represented by logos that contain a specific type of symmetry? Does the symmetry make the logo
more pleasing to the eye or more easily remembered?
Functions – A function can be classified as even or odd based on the symmetry of its graph. Even functions have
2.12. Transformations