A Tribute to M.C. Escher: Tapestry Tessellations MacKinnon Middle School Seventh Grade Math Teachers

Introduction Tessellations are geometrical shapes that completely cover a plane without gaps or overlaps.  Tessellations are found in many natural forms, examples include: honeycombs and the scales on a snake.  Tessellations are also found throughout the world in different cultures.  From art work to the tiling on the floor, tessellations can be found in any place at anytime. Reflections are mirror images.  You see your reflection everyday when you look in a mirror.  Like tessellations, reflections are found in many natural forms, examples include: reflections off of water in a pond, or seeing a mirror image of yourself in a window.  Many artists use tessellations and reflections in their artwork.  In this activity you will researching the art of MC Escher. You will describe what technique (tessellations, rotations, reflections, etc.) he has used in his artwork.  In addition, you will be creating your own tessellation.  In order to evaluate your work, please see the rubric below.

Task In order to research Escher, you will be given links to sites that may help you complete your project.  Feel free to look around in other places to do your research.  You will be expected to complete: Identify who Escher is, how his work relates to math, and find one piece of art. Complete the tessellation table An original tessellation

Process Step 1: Become familiar with Escher and his work. Compare and contrast at least two pieces of art from Escher's collection. Step2: Choose a regular polygon tile provided by your teacher and carefully trace it on a sheet of blank paper. Step 3: Extend the sides of the polygon so you can measure all the interior angles with a protractor. Step 4: Calculate the sum of the interior angles. Step 5: Complete the table indicating the following for each: Name of polygon Number of sides Number of internal triangles Sum of angles Compute formula Identify whether the regular polygon will tessellate.

Process continued… Step 6: Plan and design your tapestry of tessellating regular polygons with your partner. You can make your design using a range of materials: pick out what geometrical shapes you want to make your tessellation with including:  triangles, squares, rectangles, and any other polygon that has angle sum measure divisible by 180.  draw the design, by hand or on the computer, and color it create your design using pieces of colored paper, fabric, cardboard, etc. create your own method of presenting your design

Process continued… Step 7: Write a detailed description of your tapestry design. Include the following: Name of polygon(s) used Sum of the interior angles for each polygon used Sum of angles at each vertex

Evaluation Novice = 7 Apprentice = 8 Practitioner = 9 Expert = 10 Compare and Contrast _____x 2 = ____ Students identify who Escher is. All Novice plus: Identify how Escher’s work relates to math All Apprentice plus: locate at least one piece of Escher’s art All Practitioner plus: Compare and contrast at least two pieces of Escher’s art Completing a table _____x 4 = ____ Table indicates name of polygon and number of sides identified the number of internal triangles Apprentice plus: Calculated sum of the angles correctly Practitioner plus: Completed table on-line Tessellation tapestry _____x 3 = ____ Some attempt to create a tessellated tapestry pattern is evident, but gaps were present. Student successfully used one regular polygon to create a tessellating tapestry pattern Successful use of more than one regular polygon to create a tessellating pattern Used Geometer Sketchpad or Paint to enhance their tessellation. Written description (Step 7) _____x 1 = ____ Includes the names of the polygons used in step 7 Sum of the interior angles for each polygon Includes sum of the interior angles Practitioner plus : Includes formula for finding the sum of the angles of a polygon

Resources Links to Escher's work: http://WorldOfEscher.com/misc/penrose.html http://www.geocities.com/williamwchow/escher/escher.htm Links to guidelines on making your own original tessellation: http://www.wsd1.org/bitsbytes/9798/bboct97/default.htm#STORY4 Links to examples: http://www.kenston.k12.oh.us/khs/math/top4.html http://www.geocities.com/wenjin92014/crompton/sampler.htm http://mathforum.org/sum95/suzanne/hawaii.html Geometer Sketchpad