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Symmetry, Tessellations, and transformations!

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.

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Symmetry, Tessellations, and transformations!

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  1. Symmetry, Tessellations, and transformations! K. Snyder April, 2010

  2. Symmetry • Symmetry is hard to define in words. • Look at this example of LINE SYMMETRY.

  3. Symmetry, continued Practice identifying line symmetry. Draw a line of symmetry. Identify 5 ways each side is the same.

  4. Radial or Rotational Symmetry Do you see the radial symmetry? Here is another example of rotational symmetry.

  5. 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 tessellation.

  6. 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.

  7. Transformation: Motion geometry The pictures below demonstrate flips or reflection transformations. • Transformation • Slide or Translation • Flip or Reflection • Turn or Rotation • Helpful reference • This movie demonstrates translation • Solids of translation

  8. More translations Rigid translation Each point is moved in the same way.

  9. Rotations, another type of translation “A rotation is performed by “spinning” the object around a fixed point known as the center of rotation.”

  10. Similar Figures • Same shape, not the same size. • Definition: Look here.

  11. Review your angles • Match the letters K, L, V, and X to the types of angles they demonstrate. • Obtuse • Right • Acute • Vertical

  12. 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. • 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.

  13. Projects: Highest possible grade: A+ • Visit this site and create a Math basketball game (rules, problems, the way shots are earned, teams, keeping score, etc.) • 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. • 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.

  14. Projects: Highest possible grade: B+ • 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. • 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.

  15. Projects: Highest possible grade: B- • 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

  16. References for images • Title slide background: http://cmsdigiarts.wordpress.com/ • Symmetry: http://www.flickr.com/photos/webmink/183008/in/pool-stock/ • Frog tessellations • 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

  17. 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

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