Geometry Assignment: Tessellations

In this assignment you will apply transformations: translation, reflection, rotation and dilation.

Introduction:

A tessellation is created when a shape is repeated over and over until it covers a plane without any gaps or overlaps. Think of your bathroom tile or the tile in your kitchen. What does the colorful tessellation remind you of?

The most famous mathematician was M. C. Escher. In black and white is an example of his artwork. It is titled Escher's Reptiles (1943).

Part 1: Create the original template

Your first step is to create an "original" template to tessellate. Follow the steps below.

Step 1: Use a ruler and index card to make a 3 inch by 3 inch square.
Use the image below as an example. It is not drawn to size.

Step 2: Cut a "piece" (wavy line, zigzag line, etc) from the top right corner to the top left corner.
Use the image below as an example. It is not drawn to size.

Step 3: Cut a "piece" (wavy line, zigzag line, etc) from the bottom left corner to the top left corner.
Use the image below as an example. It is not drawn to size.

Step 4: Slide the bottom piece to the top edge of the square and tape.
Use the image below as an example. It is not drawn to size.

Step 5: Slide the left piece to the right edge of the square and tape.
Use the image below as an example. It is not drawn to size.

Step 6: Create an image using your template
Use your creativity and decide what your "original" template resembles. The image I am using as an example can be a fish or a turtle standing in water.

You may need to try part 1 several times unitl you create a template you are satisfird with.

Part 2: Tessellate your template

On an 8 1/2 by 11 sheet of paper (either construction paper or computer paper. do not use lined notebook paper), tessellate your template. It must cover the entire sheet with no gaps or overlapping. It is easier if you begin in the center by tracing your template and then continue the pattern over the entire sheet. After you have filled the entire sheet, add the details of your image. The more creative you are the better your tessellation will look. Use the image below as an example. It is not drawn to size.

Part 3: A letter to your friend

Your friend, Miya, was absent and missed the lesson(s) on transformations and tessellations. She is really contagious so you drop off the homework and the tessellation project to her dad. She emails you later that night and is really confused. Her questions are in bold below. You have to reply to her email answering her questions. (Even though you are talking to a friend, you need to use proper spelling, grammar, complete sentences, etc. Do not list her question and then write the answer. You need to write your response in paragraph format. Your explanations should be in your own words. Knowing the "math definition" is not enough evidence that you (and Miya) understand.)

a. What is a transformation? Be sure to explain it in your own words. Knowing the "math definition" is not enough evidence that you (and Miya) understand what a transformation is.

b. What are the different types of transformations? (Be sure to explain what they are in your own words and one real-world example of each so that Miya really understands them.)

c. What is a tessellation? (Be sure to give at least one real-world example so Miya understands what a tessellation is. It cannot be given in the directions or on this sheet. You might have to use the Internet)

d. Why did we have to make a tessellation? What does ot have to do with transformations? Be sure to explain what type of transformation(s) is/are use in your tessellation.