Tessellation Simulation Project

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Tessellation Simulation Project
By Leonora Spyros Math409
Click To Begin!
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Main Menu
Tessellations
Rotation
Translation
Reflection
Assessment
Teachers Page
Click on one of the pictures to learn more!!
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Tessellations

• A tessellation is another name for a tiling
• Tessellations are made up of regular polygons
  that are repeated over and over again to cover an
  entire plane
• They cannot have any gaps or overlaps
• Every vertex of a tessellation must be the same,
  and the angles of the vertices must add up to 360
  degrees

Regular Tessellations
Semi-Regular Tessellations
Click on one of the two types of tessellations to
learn more!
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Regular Tessellations

• The tessellation must tile a floor completely
  with no gaps and no overlaps
• The tiles must all be the same regular polygon
• All the vertex angles must look the same
• There are 3 examples of regular tessellations

Triangles
Squares
Hexagons
Click on one of the three shapes to learn more!
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Equilateral Triangles

• The interior angle of each equilateral triangle
  is 60 degrees
• The vertex angles are 606060606060 360
  degrees

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Squares

• The interior angle of a square is 90 degrees
• The vertex angels are 90909090 360 degrees

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Hexagons

• The interior angle of each hexagon is 120 degrees
• The vertex angles are 120120120 360 degrees

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Semi-Regular Tessellations

• A semi-regular tessellation is made up by using
  two or more different regular polygons
• The arrangement of polygons at each vertex must
  still be the same and the vertices must add up to
  360 degrees

Which of the following are examples of
semi-regular tessellations? Click on the ones
that you think are the answer to find out!
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Yes! You are right!
This is a semi-regular tessellation because it
does not have any gaps or overlaps and all of the
vertices are the same!
Go Back
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Yes! You are right!
This is a semi-regular tessellation because it
does not have any gaps or overlaps and all of the
vertices are the same!
Go Back
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Sorry! Wrong answer
This is not a semi-regular tessellation because
it does not follow the rule that all the vertices
must have the same configuration
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Translation(Slide)

• A translation is another name for a slide
• If you move an object from one area to another on
  a plane without rotating or reflecting it, it is
  a translation
• Every point of the object must move the same
  distance in the same direction

Click here for more Practice!
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Rotation(Turn)

• Rotate is another name for turn
• Every rotation has a center and an angle

Click here for more Practice!
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Reflection(Flip)

• Another name for reflection is a flip
• The reflected figure is always the same size, it
  just faces in the other direction
• To reflect an object means to produce its mirror
  image
• Every reflection has a mirror line

Click here for more Practice!
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Quiz
Directions Write one to two sentences for each
of the following questions.
Why are the following NOT regular tessellations?
2.
1.
Next
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Create Your Own Tessellation!!
Directions Create your own unique tessellation
that includes reflections, rotations, and
translations by clicking on the button below.
Mark a few places where these things occur in
your tessellation. Once you have completed it,
print it out and hand it in.
Click here to create your own tessellation!
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Teachers Page

• Lesson Objective This lesson is geared towards
  students in the 5th grade. It is designed to
  help student understand the concept and the
  process of creating tessellations. The students
  will learn what a tessellation is, and what the
  rules for creating a tessellation are. They will
  also learn what a reflection, rotation, and
  translation is. They will then use all of the
  skills that they learned to be assessed by
  creating their own unique tessellation. Also
  included in the assessment is a quiz. The rubric
  for these assessments will be based on how well
  they answer the quiz questions, and how well they
  do on creating their own tessellation and
  identifying where it reflects, rotates, and
  translates.
• NCTM standards
• recognize, name, build, draw, compare, and sort
  two and three-dimensional shapes
• describe attributes and parts of two and
  three-dimensional shapes
• identify, compare, and analyze attributes of two
  and three-dimensional shapes and develop
  vocabulary to describe the attributes

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Teachers Page

• CT Standards
• Grade 5 1- The students are able to draw and
  classify 2-dimensional shapes and geometric
  vocabulary
• Grade 5 6- The students will be able to relate
  geometric shapes to nature and the real world
• Lesson Plan click to see the lesson plan

References on next page
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References

• http//www.coolmath.com/tesspag1.htm
• http//mathforum.org/sum95/suzanne/tess.intro.html
  
• http//standards.nctm.org/document/appendix/geom.h
  tm
• http//www.mathsisfun.com/geometry/rotation.html
• http//www.mathisfun.com/geometry/reflection.html
• http//www.mathsisfun.com/geometry/translation.htm
  l
• http//library.thinkquest.org/16661/Escher.html
• Virtual Manipulative websites
• Google images
• CT standards

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