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LESSON TWO:
GEOMETRY AND GRAPHIC DESIGN

Overview of Lesson

As we have seen Islamic art and M.C. Escher prints have several things in common, they both make use of geometric shapes to create patterns called tessellations that are symmetrical in nature. Creation of these patterns involves transformation: changing the position of an object on the plane while perserving all of the angles. A transformation occurs when a shape is moved or changed using reflection, rotation, or translation--three concepts essential to the creation of tessellating shapes and repeated patterns.

Objectives

· Students will define mathematical vocabulary and concepts involved in creating tessellations.
· Students will pick out examples of the concepts of transformational geometry, reflection, rotation, and
translation, by analyzing several examples in works of art (Art Criticism).
· Students will demonstrate an understanding of
reflection, rotation, translation, and congruency by
correctly using shapes to make symmetrical patterns (Art Criticism, Art Production).

Materials and Resources

· Copies of the student handouts, “Triangles” and
“Quadrilaterals”
· Copies of the student handout, “Tessellation Chart”
· Overhead transparency, “Translations”
· Strips of tag board
· White drawing paper
· pencils and rulers


Background Information

Translation: (also called slide) in this method of transformation, a shape moves the same distance and the same direction to its new position. Translating an object means moving it without rotating or reflecting it. You can describe a translation by stating how the shape slides, and in what direction.

Reflection: (also called a flip) In this method of transformation, the figure is moved to a new location on a plane by flipping it over. The image is then a mirror image or reflection of the original.

Line of Reflection: the line over which a figure is flipped in reflectional symmetry.

Rotation: In this method of transformation, a figure is moved to a new location on a plane by rotating it around a fixed point.

Center of rotation: the point in the plane around which the shape rotates.

Teacher Preparation

Become familiar with the Background Information and Instruction from the previous lessons. Make an overhead transparency of “Transformations” located at the end of the unit. Use this transparency to explain or review the concepts of translation, rotation, and reflection to the students. The student handouts, “Triangles” and “Quadrilaterals” can be applied to this lesson in two ways. Students can use the examples as a guide to trace shapes to tag board and more advanced students can use the instructions on the page to draw their own shapes to the tag board.

Repeat the instructions included in the lesson for each set of shapes. When working with the handout, “Triangles,” students will apply transformations to equilateral, isosceles, and scalene triangles. Using the handout, “Quadrilaterals,” students will repeat the process with a rhombus, parallelogram, rectangle, and square.

 

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