Symmetry, Tessellations, and
transformations!
K. Snyder
April, 2010
Symmetry
• Symmetry is hard to define in words.
• Look at this example of LINE SYMMETRY.
Symmetry, continued
Practice identifying line
symmetry.
Draw a line of symmetry. Identify 5
ways each side is the same.
Radial or Rotational Symmetry
Do you see the radial symmetry?
Here is another example of
rotational symmetry.
Tessellations
• Here is the definition of “tessellations” from a
math dictionary*.
– A repeating pattern of closed figures that covers a
surface with no gaps and no overlaps.
– Here is an animation.
– What is a closed figure?
• A figure that begins and ends at the same point.*
• Here is an animation.
Visit this link to
locate a
template/handout to
create your own
Create a tessellation
• M. Escher is famous for his tessellations.
• Visit this link to see examples.
• What shapes tessellate? Try one of the options by
clicking on the links.
• Find the relationship between the number of sides
on the tessellated shape and the minimum number
of different colors you can use to color it.
Transformation: Motion geometry
• Transformation
– Slide or
Translation
– Flip or Reflection
– Turn or Rotation
• Helpful reference
• This movie
demonstrates
translation
– Solids of
translation
More translations
Rigid translation
Each point is moved in the same
way.
Rotations, another
type of translation
“A rotation is performed by “spinning”
the object around a fixed point known
as the center of rotation.”
Similar Figures
• Same shape, not the same size.
• Definition: Look here.
Review your angles
• Match the letters K, L, V, and X to the types of
angles they demonstrate.
– Obtuse
– Right
– Acute
– Vertical
Project Selection
• Projects must be selected and started on April 21.
• Students may not work together.
• Projects must be student created. Class time will be utilized.
– Students ineffectively using their time in school will lose 2 points per
Incident.
– If 3 incidents occur, their project will be changed to the “B-” option.
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Some portions may be assigned for homework.
Benchmark deadlines must be met.
Projects are due by April 28.
If the project is late, 10 points will be lost for each day the project
is late.
• Spelling, grammar, punctuation, and capitalization must be correct.
• Resources must be documented correctly.
• Rubrics will be utilized for A+ and B+ levels.
Projects:
1. Visit this site and create a Math basketball game (rules,
problems, the way shots are earned, teams, keeping
score, etc.)
2. Geometry Bingo: Create sets of blank bingo boards, and
lists of terms (or a power point to use in displaying them),
and cards showing the terms. for the following topics:
Basic geometry, angles, 2-D figures, 3-D figures,
transformations, and tessellations.
3. Create a model, game, or activity that helps students
choose color patterns for tessellations dependent upon
the shape they select. Process , decision making
methodology, checking methods , and examples must be
provided.
Projects:
4. Create a set of game cards and pictures for “I
have Who has.” Instead of only speaking the
geometric terms, students will raise a picture
(drawn or printed on a 5” by 8” piece of oak
tag.) List of terms will be provided by Mrs. S.
5. Create a geometry board game. The game
board must be the inside base of a large pizza
box. Game pieces, cards, and game rules must
be included. Game pieces must be in the form
of 3-D geometric solids. All terms reviewed in
class must find their way onto the game board.
Projects:
6. Correctly complete practice workbook
pages:19.1, 19.2, 19.4, 19.5 Complete all
problems on these pages in your math text:
– page 407 2, 3, & 4.
– Page 408 5 through 9, only the odd numbered
problems.
– Page 410: activity
– Page 411 #1 through 4, and 8 through 10
– Page 415 #1 through 20
References for images
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Title slide background: http://cmsdigiarts.wordpress.com/
Symmetry: http://www.flickr.com/photos/webmink/183008/in/pool-stock/
Frog tessellations
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http://teach.sdstate.edu/users/vestals/images/2008%20tessellations/frogs%20tessellation.JPG
Tessellation instructions: http://mathsyear7.wikispaces.com/Tessellations
Animated froggy images: http://www.frogsonice.com/froggy/animated.shtml
Butterfly: http://www.harcourtschool.com/glossary/math2/index4.html
Similar figures: http://www.icoachmath.com/Sitemap/SimilarFigures.html
References for terms and information
• Harcourt School Math Glossary:
http://www.harcourtschool.com/glossary/math2/index4.html
• Tessellations on line:
– http://gwydir.demon.co.uk/jo/tess/escher.htm
– http://gwydir.demon.co.uk/jo/tess/grids.htm
• Symmetry:
– http://www.misterteacher.com/symmetry.html#line
– http://www.misterteacher.com/radialsymmetry.htm
• Transformation:
– http://www.misterteacher.com/abc.html