Name______Due Date: 9/9/16

St. Denis-St. Columba School Math 8/AlgebraMrs. Galletti

Tessellation Webquest (100 points)

You are about to embark on an adventure through the world of tessellations. People have always been interested in patterns, both planar patterns and spatial patterns. Classification of patterns started two and a half millennia ago with the Pythagorean discovery that there are five regular solids: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. Archimedes generalized these to some nearly regular solids, now called Archimedean solids, such as the solids made out of pentagons and hexagons that are used for soccer balls. Kepler found other nearly regular solids and noted the regular tessellations (tilings) of the plane. Tessellations (or tilings, as they are sometimes called) have a broad appeal, maybe because they exemplify how mathematics can unify the aesthetic, natural and rational worlds. From the art of M.C. Escher to crystal growth to the mathematics of Penrose tilings, tessellations fascinate everyone, from mathematician to artist to interior decorator to mathematics student.Check out the Tessellation Website links below. These websites may lead you to further websites. Just explore and have fun learning about how to create tessellation art. Begin thinking of one that you will design and make for your individual project.

How to make one, History of, and M.C. Escher

Create a tesselation

Explanations of types of tessellations

Definition of, Example, The math of a tessellation, different types of tessellations

Part 1- As you explore the websites (50 points)

Researching and Writing

As you research the concept of tessellation art, please answer the following questions in a (3-5) paragraph paper, typed in size 12 font. Add any other facts you found interesting in your research.

( Introduction: 5-7 sentences) Include a hook statement or question, background information and thesis statement. Do not use pronouns in your writing except when stating your opinion in conclusion

(Body 8-10 sentences,1-3 paragraphs) Include at least 3-5 examples or facts from your research, with commentary, to connect to your thesis.

(Conclusion: 5-7 sentences) Restate any significant points made in body paragraph, restate thesis, leave reader with one final thought. You may state your opinion about research or project here

1. Define what a tessellation is. What are its characteristics? Explain the history of tessellations

2. Describe the geometry and other math concepts (ie. Symmetry, angle of rotation) of a tessellation. How do math and art influence these designs?

3. Describe which polygons will tessellate and why?

4. Describe any places in nature or the real-world where you may find tessellations or gain inspiration for your design.

Part 2- After you explore and complete writing assignment. (50 points)

The design(the websites above have detailed instructions for the design)

1) Using a polygon that will tessellate, create a template by cutting a piece(s) from the polygon and move it and tape to another part of the figure, using translation, reflection or rotation. The original figure should be no larger than 1 ½ – 2 inches.

(No Larger-the design will seem larger after you transform it).

2) After template is drawn, trace it onto an index card so it will be easier to work with.

Use your template to trace a design over the entire paper (use light graph paper).

Your design should have no gaps or overlaps and should be straight and neat.

Save your template-this must be handed in with your tessellation.

3) Color your design to make it visually appealing-be creative! Think of an interesting title for your design and write it on the back. After the design is mounted on construction paper you will write the title on the front. Tape your template to top right corner of your design.Print Rubric below and hand it in with your design.

Name______Due Date: September 9

Tessellation Scoring Rubric

Geometric shape has undergone at least one transformation to create a template(included) / 5 / 4 / 3 / 2
Design covers the entire paper and contains no gaps or overlaps.
Design was created from original geometric figure no larger than a 1 1/2 -2 inches
Design is original, interesting and appealing.
Design is straight and neatly colored.
Total Points
25

*The rubric score will be doubled to achieve 50 points.