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. 
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.

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.
Complete the tessellation table
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.
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.

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:
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

6. 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

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
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

9. Resources Links to Escher's work:
Links to guidelines on making your own original tessellation:
Links to examples:
Geometer Sketchpad