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

2. 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. 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. In addition, you will be creating your own tessellation. In order to evaluate your work, please see the rubric below.

3. 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. Identify who Escher is, how his work relates to math, and find one piece of art. Complete the tessellation table Complete the tessellation table An original tessellation An original tessellation

4. Process Step 1: Become familiar with Escher and his work. Compare and contrast at least two pieces of art from Escher's collection. 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. 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 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 4: Calculate the sum of the interior angles. Step 5: Complete the table indicating the following for each: Step 5: Complete the table indicating the following for each:Complete the table Complete the table Name of polygon Name of polygon Number of sides Number of sides Number of internal triangles Number of internal triangles Sum of angles Sum of angles Compute formula Compute formula Identify whether the regular polygon will tessellate. Identify whether the regular polygon will tessellate.

5. 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: 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. 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 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 design using pieces of colored paper, fabric, cardboard, etc. create your own method of presenting your design create your own method of presenting your design

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

8. 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 Identify how Escher’s work relates to math All Apprentice plus: locate at least one piece of Escher’s art locate at least one piece of Escher’s art All Practitioner plus: Compare and contrast at least two pieces of Escher’s art 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 All Novice plus: identified the number of internal triangles identified the number of internal triangles Apprentice plus: Calculated sum of the angles correctly Calculated sum of the angles correctly Practitioner plus: Completed table on-line 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 All Practitioner plus: Used Geometer Sketchpad or Paint to enhance their tessellation. 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 All Novice plus: Sum of the interior angles for each polygon Sum of the interior angles for each polygon All Apprentice plus: Includes sum of the interior angles Includes sum of the interior angles Practitioner plus : Includes formula for finding the sum of the angles of a polygon Includes formula for finding the sum of the angles of a polygon

9. Resources Links to Escher's work: 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: Links to guidelines on making your own original tessellation: http://www.wsd1.org/bitsbytes/9798/bboct97/default.htm#STO RY4 http://www.wsd1.org/bitsbytes/9798/bboct97/default.htm#STO RY4 Links to examples: 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 Geometer Sketchpad