Tessellations
Rotation
Translation
Reflection
Assessment
Teacher’s Page
Click on one of the pictures to learn more!!
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 60+60+60+60+60+60= 360
degrees
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Squares
• The interior angle of a square is 90
degrees
• The vertex angels are 90+90+90+90= 360
degrees
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Hexagons
• The interior angle of each hexagon is 120
degrees
• The vertex angles are 120+120+120= 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 semiregular tessellation
because it does
not have any gaps
or overlaps and all
of the vertices are
the same!
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Yes! You are right!
This is a semiregular tessellation
because it does
not have any gaps
or overlaps and all
of the vertices are
the same!
Go Back
Sorry! Wrong answer
This is not a semiregular 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
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Click here for more
Practice!
Rotation
(Turn)
• Rotate is another name for turn
• Every rotation has a center and an angle
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Practice!
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
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Practice!
Quiz
Directions: Write one to two sentences for each of the following questions.
Why are the following NOT regular tessellations?
1.
2.
Next
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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Teacher’s 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:
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•recognize, name, build, draw, compare, and sort two and threedimensional shapes
•describe attributes and parts of two and three-dimensional shapes
•identify, compare, and analyze attributes of two and threedimensional shapes and develop vocabulary to describe the attributes
Teacher’s Page
• CT Standards:
• Grade 5 #1- The students are able to draw and classify 2dimensional 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
References
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http://www.coolmath.com/tesspag1.htm
http://mathforum.org/sum95/suzanne/tess.intro.html
http://standards.nctm.org/document/appendix/geom.htm
http://www.mathsisfun.com/geometry/rotation.html
http://www.mathisfun.com/geometry/reflection.html
http://www.mathsisfun.com/geometry/translation.html
http://library.thinkquest.org/16661/Escher.html
Virtual Manipulative websites
Google images
CT standards