T ESSELLATIONS Stacie D. Wight EDIM 508 Instructional Purpose: This PowerPoint will be used as an independent learning center for 6 th grade math students. Students will be expected to navigate through the PowerPoint by using the table of contents and completing all of the included activities. While completing this learning center students will explore the biographies of well known artists that have contributed tessellations to the art and computer world. In addition, students will be able to create their own tessellations using the computer as well as follow directions to make one using paper and pencil.

P ENNSYLVANIA S TATE S TANDARDS PA State Standard A Invent, select, use and justify the appropriate methods, materials and strategies to solve problems. PA State Standard C Classify familiar polygons as regular or irregular up to a decagon. PA State Standard H Use simple geometric figures (e.g., triangles, squares) to create, through rotation, transformational figures in three dimensions. PA State Standard I Generate transformations using computer software. PA State Standard J Analyze geometric patterns (e.g., tessellations, sequences of shapes) and develop descriptions of the patterns. PA State Standard K Analyze objects to determine whether they illustrate tessellations, symmetry, congruence, similarity and scale.

L ET ’ S G ET S TARTED ! 1. M.C. Escher2. Hans Kuiper 4. Tessellation Creation 5. Back to Basics with Tessellations 3. Tessellations Around Us FINISHED

M.C. E SCHER HOME Let’s read about one of the most famous irregular tessellation artists. Please follow the following links to watch video about M.C. Escher and how his artistic career began. Brief Biography Watch the video clip entitled “Studying Graphic Arts.” Examples of Escher’s Work Watch the video clip entitled “Geometric Shapes of Form and Counterform.” Picture Gallery Visit the “Picture Gallery” found at the link above. Try to spend just a few minutes viewing the different works Escher created over his entire artistic career.

H ANS K UIPER HOME Hans Kuiper created tessellation software for computers. Through his software creation he has been able to create many different types of tessellations. Below are a variety of tessellations Kuiper created using his computer software.

T ESSELLATIONS A ROUND U S HOME If you look around your home and classroom, you will be able to find tessellations everywhere. Watch the video clips below and look at the following images of tessellations in our environment and try to think of additional everyday tessellations. Video: Tessellation Overview Make sure you understand what makes a tessellation regular and irregular. Importance and Uses of Tessellations Images: Tessellation Review and Images Read through the descriptions of tessellations at the beginning and then view the three pictures of tessellations in nature. In your math journal, make a list of five tessellations you see almost everyday and where you see them. Tell me if they are regular or irregular.

T ESSELLATION C REATION HOME Now it is time for you to create your own unique tessellation. Follow the directions to create your own tessellation using the computer. Freeform or Irregular Tessellation Directions Make sure you follow each direction carefully. If you get stuck use the help links on the website. Take pride in your work and create a tessellation you will be proud to display for our Tessellation Gallery opening.

B ACK TO B ASICS WITH T ESSELLATIONS HOME Before you watch the video clip below, make sure you have your learning center supply packet. We have seen that tessellations have been created by artists using woodcuts, on the computer, and can be found naturally in nature. Now that you have had the opportunity to create a tessellation on the computer, you will create one using paper and pencil. Take your time and finish your tessellation for homework. Follow the link below to watch the step-by-step creation of a stencil that can be used to make an irregular tessellation. Pause the movie when instructed in order to follow the directions. Feel free to re- watch the video if you get stuck. Tessellation Stencil Creator

W RAP I T U P Before we finish, make sure you have completed all of the assignments. - Math Journal Entry - Computer-created Tessellation - Paper/Pencil Tessellation Listen to the following learning center summary for directions on your final activity. Make sure you direct any questions immediately to Miss Wight. Click the Speaker!

C ITATIONS (2009). Discovery Education. In M.C. Escher: Master of Graphic Arts. Retrieved November 4, 2009, from (2009). Discovery Education. In Math All Around Us: Tessellation Time. Retrieved November 4, 2009, from (2009). Discovery Education. In Importance and Uses of Tessellations. Retrieved November 4, 2009, from (2009). Fractals & Tessellations. In Tessellations. Retrieved November 4, 2009, from (2009). Discovery Education. In How to Create a Tessellating Template. Retrieved November 4, 2009, from (1994). Pineapple. In Shodor. Retrieved November 4, 2009, from Tessellations. Retrieved Nov from dhydorn. (October 14, 2009). EscherMath Fall In EscherMath Fall Retrieved November 4, 2009, from Kuiper, Hans. Computer Art by Hans Kuiper 17 Wall Paper Symmetry Groups to Create a Regular Division of the Plane. In Computer Art by Hans Kuiper. Retrieved November 4, 2009, from Roberts, Carolyn. Tessellation-Art. In Tessellation Lesson. Retrieved November 4, 2009, from Creating A Freeform Tessellation. In Creating a Freeform Tessellation Using Microsoft Paint. Retrieved November 4, 2009, from The Official M.C. Escher Website. In Picture Gallery. Retrieved November 4, 2009, from