Topic:
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l. Creating designs using the geometric shapes.
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2. Combining these designs with tessellations.
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3. Use repetitive patterns to create designs.
Objectives:
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(a) Students will use geometric figures to create designs.
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(b) Student will define and use the properties of tessellation to create their own designs.
Materials:
Paper, pencil, straight edge.
Background Information:
Students will have been studying the properties and names of the regular polygons. They will also have read some information on the use of geometric shapes in geometric designs. Students will also have discussed the concepts of tessellation and translation.
This lesson will be able to provide enrichment to a lesson after students have studied translations example tessellation reflection, and transformation. The purpose would be to provide students with a project using those concepts.
Procedure:
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l. Discuss African patterns that contain geometric designs. Students could discuss the various shapes and the formations used to achieve the designs.
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2. Discuss the use of tessellation and repetition in the design.
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3. Have students select different shapes that would be suitable to produce similar designs.
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4. Introduce students to other designs used for tessellations, notable the work of Escher and Voderberg.
Activities:
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l. Students will complete their own designs, using tessellation with regular and non-regular polygons.
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2. Students will research the artist M.C. Escher’s work in creating designs by tessellation with nontraditional objects.
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3. Students can explore designs using translation, rotation, demi-regular, pure tessellation, semi-pure tessellation, and reflection, to create designs.
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4. Students can explore the use of the animals used for African ornaments and a combination of the different types of tessellations with regular polygons to create their own designs.
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5. Students will be introduced to spiral tilings using non traditional polygons. These monohedral spirals developed by voderberg will be discussed (examples in the appendix). Students can experiment with using different polygons ( ex 8—gons) to generate new ideas.
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6. Discuss the ideas behind the development of patterns . Students can develop their own patterns from the motifs they designed, and using the coordinate systems introduced and the combination of transformations.
Curriculum coordinates.
Art.
Students can use these ideas for spiral in developing patterns for fabric.
Research : The life and work , their contribution to mathematics of M.C Escher and Voderberg.
