Topics
8. Transformations & Congruence
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United States of America
Grade 8

Investigation: Tessellations

Lesson
Practice
Overview
Activity
Reflection

Investigate tessellations and how to create your own.

Objectives
  • To understand what a tessellation is.
  • To create a tessellation.
  • To relate symmetry and translations to tessellations.
Materials
  • Multiple sheets of paper
  • Pen or pencil
  • Straight edge (optional)

Tessellations

You may have heard that numbers go on for infinity. In other words, numbers never end- pretty crazy right? Well, a really cool designer and artist named M. C. Escher played with how to represent the concept of infinity by using tessellations, or patterns that go on forever.
A tessellation is a repeating pattern of polygons (shapes) that covers a plane (flat surface) with no gaps or overlaps. The tessellation below is modeled after a famous work called Bird Fish.
A repeating images of bird and fish.
The easiest way to think of it is someone tiling a floor. All the pieces fit together perfectly, without any gaps. There are some beautiful examples of tessellations in nature, such as the cute little hexagon array that makes up honeycomb, as well as in architecture around the world.
Research
Research some different examples of tessellations around the world. You can look at works by M. C. Escher or one of the examples mentioned. Or you can find some cool ones of your own. Share the different tessellations you find with your class.

You'll now build a tessellation of your own.

Start with a known tessellating shape like a square or rectangle (let's pick an easy one to begin with).

A rectangle.

Draw any shape/line you like along one of the long edges of the rectangle. It's important you don't touch any other sides.

A rectangle with curve line at the top.

Now do the same along the short edge.

A rectangle with curve line at the top and at the right.

Cut out the two pieces you have just drawn and slide them into position on the opposite side.

This is your tessellating piece.

An abstract image. Speak to your teacher for more information.

Grab a piece of paper and start tracing, add some color and you will create a beautiful tessellating masterpiece in minutes.

A tessalation. Speak to your teacher for more information.,
Investigate
Consider the following questions once you have completed the above procedure.
1.
What types of symmetry do you observe in your tessellation?
2.
Describe the types of transformations that occur when creating a tessellation.
3.
What types of symmetry exist in tessellations that you researched?

Answer the questions below after you have completed the activity.

Discussion
1.
How might we use mathematics to communicate how to create a tessellation?
2.
Can we use any type of transformation to create a tessellation? Describe why or why not.
3.
Explain how we can recognize a tessellation.

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