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Tessellations

Rotation Translation

Reflection

Teacher’s PageAssessment

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!Go Back

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 semi-regular 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 semi-regular tessellation because it does not have any gaps or overlaps and all of the vertices are the same!

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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

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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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Click here for more 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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Click here for more Practice!

Quiz

Why are the following NOT regular tessellations?

Directions: Write one to two sentences for each of the following questions.

1. 2.

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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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Teacher’s Page

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• 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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• 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

References

• 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

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