Integrating Art and Math: Tessellations and Symmetry - Lauren Grover

Ed 3601 Art Unit Plan

Integrating Art and Math: Tessellations and Symmetry

A Lesson Plan for Grades 5 and 6

Melissa Martin

"For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art."

? M.C. Escher

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Introduction and Rationale

This unit plan is focused on integrating grades 5 and 6 art with mathematics. It is important to try and integrate subjects together to help make students' learning more meaningful. They will understand how these different subjects apply to each other in the real world. Art also makes learning math much more interesting and fun for a class. It is a creative way to show students different mathematical theories and principles. It is beneficial for visual and hands-on learners who are not able to understand elements of mathematics written down on paper. Once they are able to create artistic examples of mathematical properties, then they will achieve a better understanding of what they are expected to know in their math class.

This unit is focused on tessellations and symmetry. It is related to the Shape and Space strand of mathematics. It is also categorized under Component 4 of the art curriculum that concentrates on Main Forms and Proportions. Tessellations can easily be used in lower grades as well as junior and senior high classes. Tessellations are excellent examples of how to illustrate mathematical properties of symmetry and geometric shapes. In grades 5 and 6, students are beginning to look at symmetrical objects and trying to understand their properties. This topic in math requires a lot of hands-on activities to show the students how symmetry is applied to objects. Tessellations allow the students to study the symmetry of these objects and create beautiful designs and patterns.

In order to integrate art history into this unit, the students will observe works by M.C. Escher. His drawings show how he was able to visualize different theories of mathematics by using his creativity to produce magnificent works of art. His drawings of tessellations will show students that the possibilities of applying symmetry and pattern to objects are endless. This can inspire students to try creating their own tessellations and experiment with different methods of symmetry. By giving students visual demonstrations and examples of a theme in art, this will help them to better understand what that theme is and how they can go about creating it.

This unit plan also integrates math and art with computer technology. The computer program TesselMania allows students to manipulate a geometric shape and then copy it into a tessellation pattern on the computer screen. This is an excellent method of teaching students how to use computers to create works of art. It also reinforces the students' memory of what they learned about symmetry and geometric shapes.

Once the students have created a graphic design of a tessellation on the computer, they will have a chance to extend this project by using a 3D medium. Clay tiles allow the students to imprint designs using a variety of tools. They can take the design they created on the computer and imprint it onto their clay tile. The students can also glaze their tile in different colours to enhance the effect of the tessellation pattern in the clay. Once the clay tiles are fired, the students can look at the tessellations they created on paper, using the computer, and on a 3D medium. This will show students how art projects can be studied through the use of different methods and materials. They can study the

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similarities and differences between the projects and determine which ones are better or worse for this type of activity.

My goal with this unit plan is to show how math can be creative and artistic. I also want this unit to encourage students to be more optimistic about learning math by incorporating hands-on art activities. This unit plan is meant to show students how symmetry is incorporated into artwork. It will also teach them how to create symmetrical shapes and develop them into a tessellating pattern that can be carried on into different types of media.

Scope and Sequence: Program of Studies

The following are the strands and learner outcomes that this unit applies to for art and math in grades 5 and 6. It was obtained from the program of studies for elementary art and math.

Mathematics ? Grade 5

Strand: Shape and Space (Transformations)

General Outcome: Describe motion in terms of a slide, a turn or a flip.

Specific Outcomes: 21. Recognize tessellations created with regular and irregular shapes in the environment. 22. Cover a surface, using one or more tessellating shapes. 23. Create tessellations, using regular polygons. 24. Identify planes of symmetry by cutting solids.

Art ? Grade 5

Component 4: MAIN FORMS AND PROPORTIONS: Students will modify forms by abstraction, distortion and other transformations.

Mathematics ? Grade 6

Strand: Shape and Space (Transformations)

General Outcome: Create patterns and designs that incorporate symmetry, tessellations, translations, and reflections.

Specific Outcome: 19. Create, analyze and describe designs, using translations (slides) and reflections (flips).

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Art ? Grade 6 Component 4: MAIN FORMS AND PROPORTIONS: Students will modify forms by abstraction, distortion and other transformations Unit Overview

Lesson 1: Exploring Symmetrical Shapes

In this lesson the students will use the Mira Math Kit to look at symmetrical shapes in their symmetry booklets from math class. They will see how the Mira reflects a mirror image of different objects. This lesson is meant to introduce the students to the concept of symmetry and allow them to experiment with it by using Miras to draw the reflected images and shapes. With these tools they can begin to create geometric patterns (i.e. mosaics) and understand how symmetry is used to create artistic patterns.

Lesson 2: Tessellation Techniques

This lesson introduces the topic of tessellations. Students will learn the definition and different characteristics of tessellations by observing different examples. They will learn the four techniques for tessellating shapes: translating (sliding), nibbling (cutting), rotating (turning), and reflecting (flipping). The students will be able to associate the technique of reflecting with what they learned about symmetry. The class will experiment with these four techniques and illustrate them in their symmetry booklets to be used as a reference for subsequent lessons.

Lesson 3: Tessellations of Polygons

This lesson reviews the introduction of tessellations. Students will observe examples of tessellations of geometric shapes (polygons). Using geometric grid handouts, the students will learn how these shapes can be manipulated to create tessellating patterns. They will achieve this by incorporating the four techniques of tessellations that they learned in the previous lesson. Once the students have enough practice using the grids, they can draw geometric tessellations by freehand.

Lesson 4: Tessellations of Curved Shapes (Escher Style Tessellations)

This lesson will apply the art history component by looking at tessellation works by M.C. Escher. Escher's works began with basic geometric shapes. Then he transformed these shapes by using the four tessellation techniques to create curved shapes and objects. These objects would then be tessellated into different orientations (positions) to create interlocking shapes with no spaces or overlapping objects. The students will recognize these patterns as works of art as well as illustrations of mathematical principles (i.e. symmetry). The students will follow these same steps to create their own tessellating objects on a piece of paper.

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Lesson 5: Creating Tessellation Shapes on Computer

This lesson will consist of a tutorial of the computer program TesselMania. The class will incorporate what they learned about tessellations and symmetry onto the computer. Students will learn the basic steps of the four tessellation techniques in the program. The students will follow the TesselMania tutorial that is included in the program to help guide them in creating their own tessellation shape.

Lesson 6: Creating Tessellation Patterns on Computer

The class will review what they learned about TesselMania in the previous lesson by briefly going over the program's tutorial again. They will be able to look at other students' examples of tessellations online to help them visualize what they will be creating. The students can make more objects and learn how to create a tessellation of these shapes. They will also learn how to apply colour to their design. Once the students have finished their tessellations they can print out their designs.

Lesson 7: Creating a Tessellation Pattern with Clay

This lesson will transfer the design of tessellations onto a 3 Dimensional medium. The students will make a clay tile and imprint the tessellation pattern they printed off the computer onto the clay. This lesson will allow students to become more creative with their tessellations as well as introduce them to the techniques of clay.

Lesson 8: Glazing and Firing Clay Tessellation Patterns

This lesson extends the use of clay by allowing students to glaze and fire their tiles. The students will learn the technique of glazing. This will allow the students to incorporate the use of colour in their tessellation pattern to create interesting and original works of art. Once the clay tiles have been fired, the students can look at their tessellations created on paper, computer, and clay. This will show the students the different effects each medium has on the patterns of tessellations.

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