TWO, FOUR, SIX, EIGHT…HOW COOL IS IT TO TESSELLATE?

AN M.C. ESCHER-TESSELLATIONS WEBQUEST FOR 5-301

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TESSELLATIONS AND M.C. ESCHER INTRODUCTION:

Introduction

Imagine you are an applicant for a position at Martha Stewart Home Collections. However, securing a position with Martha Stewart is no easy task. What you have worked so hard for over the last four years, at The Flushing College of Textiles and Design, is just within your reach. You are familiar with the company's quality products and have noticed the unique detailing and design of their bed and bath collection. You are fascinated by their geometrical and mathematical use of tessellations. How would you design a comparable tessellation? Where do you see repeating patterns in your surroundings? How do the patterns repeat? What are some other sources of tessellations?

TASK:

 As part of the application process, you are required to submit a portfolio of your work. In this portfolio, you must include samples of patterns using basic geometric shapes, examples of designs you find inspirational, samples of designs developed on a software program, and a final product -- a sample quilt. While developing ideas for your tessellation, you will explore various patterns and designs. You will hand-draw three tessellations using triangles, rectangles, and hexagons. You will collect four samples of tessellations from other designers and identify the repeating elements of each pattern. You can use the Kid Pix drawing software (if you have it) to build thumbnail sketches of your tessellation, any other computer software or you may use only NEAT hand drawings. The steps taken will progress into the final product, which is a four foot-squared sample quilt, consisting of four identical one foot-squared tessellations.

CONTINUED TASK FOR ALL:

   No matter which “ artistic ” endeavor you choose to pursue, you must all include the following: A short report explaining the geometry of your tessellation -- include a description of its transformations as well as the reasons why the shapes you chose to tessellate "work." A cardboard-oaktag template of your polygon and its modifications.

AND THERE

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S MORE:

          Research paper (2-3 paragraphs) about Escher and his work and a one-two paragraph specific response paragraph to his work.

Key vocabulary words will be defined on a separate sheet with a diagram or picture

Key Vocabulary:

Acute angle Adjacent angles Regular tessellation Tessellation Tessellate Regular polygon Tessellation vertex

PROCESS:

   In order to successfully develop your portfolio, you will:

Use the manipulatives to create various tessellations with basic geometric shapes and sketch the designs.

   Create a tessellation with triangles.

Create a tessellation with rectangles.

Create a tessellation with hexagons.

This activity will give you an opportunity to practice creating repeating patterns without spaces or overlapping shapes. This may be done in groups of four.

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Collect four examples of tessellations and identify the elements or shapes within the pattern.

 Sources may include:    websites, magazines, and/or newspapers.

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PROCESS:

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Design two original tessellations with dimensions of one foot by one foot.

  The first must be drawn using the Kid Pix or computer software.

The second can be drawn using the Kid Pix software or created by hand.

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Create a four foot-squared sample quilt (four identical, one foot-squared tessellations).

 The final product may be:    hand-drawn, computer-generated, or machine or hand-sewn.

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ALTERNATE TASK:

     OR YOU MAY CHOOSE TO GO ABOUT IT THIS WAY: You are to create a tessellation and find where tessellations are used in the "real world." Your final project will include: At least three different real world applications of tessellations mounted on paper to be included with your project. Find pictures in books, magazines, newspapers, etc.

A worksheet with two practice tessellations.

The actual, full size tessellation on the construction paper that was provided in class.

An attached piece of tissue paper on which you will draw a diagram of the transformations that your tessellation used. Use arrows to show how the shapes reflect or flip, translate or slide, and/or rotate or spin.

ALL-REFLECTIONS:

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Reflection

As you showcase your final product, share your thoughts on the process of creating the portfolio with the class. Was this task difficult/easy? Do you think you will use tessellations in areas other than math?

What discoveries have you made by completing this assignment (self, abilities/talent, math, etc.)?

 You have first-hand experience in developing and using tessellations: How might you apply this knowledge and experience to other situations? Science? Art? Interior design? Landscaping? Architecture?

RUBRIC:

         SCORE DESCRIPTION: 4 Completes all parts of the process to the best of ability: Creates and hand-sketches three tessellations using triangles, rectangles, and hexagons. Collects four examples of tessellations and identifies the elements or shapes within the pattern.

 The sources of the example tessellations are cited (website address, magazine/journal name with the date of the issue, etc.).

Designs two original tessellations (one foot by one foot dimension).

  The first tessellation should be drawn using the KidPix-computer software. The second tessellation can be drawn using KidPix or can be created by hand.

Creates a sample quilt (four identical, one foot by one foot square tessellations). 3 Includes research, vocabulary and reflection.

3 Successfully completes all parts of the process (one section could be more thorough).

2

Completes only half of the required sections to the best of ability.

1

Completes one or two parts of the process to the best of ability.

RUBRIC:

RESOURCES:

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Resources:

The following links contain information and examples that may be useful in the development of your portfolio. Please review the websites and brainstorm ideas for your own tessellation. http://www.mathacademy.com/pr/minitext/escher/ Official: http://www.mcescher.com/ Mathematically speaking: http://www.ams.org/notices/200304/fea-escher.pdf

Tessellations investigations: http://home.comcast.net/~tessellations/tessellations.htm

http://www.coolmath4kids.com/tesspag1.html

MORE RESOURCES:

    What is a tessellation?: http://mathforum.org/sum95/suzanne/whattess.

html ESCHER GALLERY: http://www.tessellations.org/eschergallery1thum bs.shtml

Advanced Artistic approach to creating tessellations—try, if you like: http://juliannakunstler.com/art1_tessellations.ht

ml#.UZlvFKLVDhI