Math Focus 8
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# Creating a Tessellating Design

## INTRODUCTION

Tessellations (or tilings, as they are sometimes called) are very visually appealing. There are probably many tessellations in your everyday surroundings—in nature, in your home, in your school, and outside. Can you think of some tessellations that you see every day?

## THE TASK

Since you and your class have just learned all about tessellations, you want to create a visually appealing tessellation design that you could use to decorate your bedroom. You will create a tile, trace your tile to create a tessellation design, and then write a detailed description that someone else could follow to recreate your tessellation design.

## THE PROCESS

1. Read Symmetry in Tessellations to find out about different types of symmetry and to see examples of tessellations that use different types of symmetry.

2. Choose at least one type of symmetry to use in your tessellation.

3. Choose a regular polygon that you know will tessellate. Then, alter the opposite sides the same way, using appropriate transformations, to create a different shape. This shape will be the tile you use to create your tessellation. How do you know your new shape will still tessellate? Will it tessellate according to the type of symmetry you chose in Step 2?

4. Create your tile out of cardboard, stiff paper, or Bristol board. Then trace your tile on large poster paper to create your tessellation. Colour your tessellation.

5. Write a paragraph describing your tessellation and giving detailed instructions for how someone else could recreate you tessellation design.

## RESOURCES

Websites:

Symmetry in Tessellations

Materials:

cardboard, stiff paper, or Bristol board

poster paper

markers

pen, pencil, paper

## ASSESSMENT

 Criteria Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Connections: Demonstrate an understanding of tessellations Makes insightful connections between at least two mathematical concepts (tessellation and symmetry) Makes meaningful connections between at least two mathematical concepts (tessellation and symmetry) Makes simple connections between at least two mathematical concepts (tessellation and symmetry) Makes minimal or weak connections between at least two mathematical concepts (tessellation and symmetry) Visualization Uses visual representations insightfully to demonstrate a thorough understanding Uses visual representations meaningfully to demonstrate a reasonable understanding Uses visual representations simply to demonstrate a basic understanding Uses visual representations poorly to demonstrate an incomplete understanding Communication Provides a precise and insightful explanation of mathematical concepts and/or procedures Provides a clear and logical explanation of mathematical concepts and/or procedures Provides a partially clear explanation of mathematical concepts and/or procedures Provides a vague and/or inaccurate explanation of mathematical concepts and/or procedures