Tessellations

 

By:

Mavis Robbins and Janelle Tang

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Introduction | Task | Process | Resources | Evaluation | Conclusions | Reflection | Extensions | Notes to Teacher

 

 

Introduction

 

Imagine you are an applicant for a position at Ralph Lauren Home Collections.  However, securing a position with Ralph Lauren is no easy task.  What you have worked so hard for over the last four years, at The Phoenix 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?

 

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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 will use the Kid Pix drawing software to build thumbnail sketches of your tessellation.  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.

 

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Process

 

In order to successfully develop your portfolio, you will:

  1. 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.

     

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

    • Sources may include:

      • websites,

      • magazines, and/or

      • newspapers.

       

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

    • The first must be drawn using the Kid Pix software.

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

     

  4. 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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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.

 

For an overview of tessellations, click below:

        http://www.gwydir.demon.co.uk/jo/tess/

        http://mathforum.org/sum95/suzanne/whattess.html

        http://mathworld.wolfram.com/Tessellation.html

 

For sample tessellations produced by students, see:

        http://www.worldofescher.com/contest/HallOfFame/index.html

 

Here are some suggestions on how to create your own tessellation:

        http://www.arttech.about.com/cs/mathematicalart/ht/tessellations.htm

 

EXTRA – To view animated tessellations, visit:

        http://www18.big.or.jp/~mnaka/home.index.html

 

Disclaimer:  At the time this WebQuest was created, the above websites were active and age-/content- appropriate.  After exiting this page, we are not responsible for external links.

 

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Evaluation

 

This project is worth 100 points.  Click on RUBRIC to see how you will earn your points.

 

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Conclusions

 

You've finally completed your portfolio.  You now have an appreciation for the time and effort that is required in designing a tessellation.  What will you do next?  Do you complete your quilt sample?  Will you apply what you have learned to other mediums (e.g., tile, wallpaper, rugs, etc.)?  The skills that you have developed in completing your portfolio should be expressed beyond this project.

 

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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.)?

 

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Extensions

 

So now you're back in your 8th grade math class and your teacher is continuing the discussion on tessellations.  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?  Share your ideas with your parents, after you showcase your portfolio.

 

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