Unit Content
This curriculum unit is an introductory overview to geometry, with enrichment lessons that can be used with the curriculum or scattered throughout the school year for a boost of creativity. I plan to cover shapes and angles, symmetry, tessellations, patterns, and sequences with this unit, and I approximate it will last 10-15 days, with enrichment lessons covering 5-6 more days. Students will explore art and nature up close; hold it in their hands and feel it. They’ll find patterns in the biology of our world, and all the while learning the math vocabulary and concepts that go right into all of those ideas. They’ll create as they learn, learn as they create, and use both math tools and art tools to master the basics of geometry.
Students will begin with jumping right into art and close observation of abstract paintings by Dutch modernist Piet Mondrian. Something not typical in the mathematics classroom, is likely to catch student attention in this introduction to geometry unit. This is meant to review basic polygons with students, with a focus on quadrilaterals. Polygons and polyhedra are covered in middle school math, but 3 years is a long time for students and a review is much needed. Lessons will also use the art of Russian abstract painter Wassily Kandinsky to show polygons of all sorts for students to work with. Students will spend about 4 class periods breaking down art into shapes, and analyzing and classifying those shapes using math tools both independently and in groups. They will create shapes on the coordinate plane, reviewing the coordinate plane and practicing with graph paper while also getting into the nitty gritty of polygons. Students will practice measurement with rulers and protractors, and compare shapes, classifying them as specifically as possible.
Two lessons on symmetry should be sufficient for students to review what they’ve learned in previous years while catching up those who may have some gaps in their knowledge when it comes to symmetry. This can, however, be extended to take longer as needed for students to get to a point where they can identify symmetry. Students will explore the art of American Artist Georgia O’Keeffe and British designer William Morris, as well as nature images like starfish, butterflies, and other photographs of the natural world that show both bilateral and radial symmetry. Students will be encouraged to find and photograph examples of symmetry in their own experience.
Another two lessons on pattern will reinforce concepts of similarity when it comes to different shapes, primarily that all circles are similar. Most students have covered patterns in middle school, but the concept of similarity may be new to many students. Studying the art of contemporary conceptual and installation artist Yayoi Kusama immerses the students into the world of circles, and students will slowly begin to generalize similarity through patterns in nature like leaves and flowers.
Finally, several lessons on tessellations will close out the unit and bring it all together. Students may or may not have studied tessellations in middle school, and regardless of their prior knowledge should be just fine jumping into the tessellations of twentieth-century Dutch draftsman and printmaker M.C. Escher and analyzing why shapes do and do not tessellate. Lessons explore tessellations in the real world, including honeycomb, turtle shells, pineapple skin, fish scales, and many more. Students will look at Islamic mosaic tile designs that use tessellations, and wrap up the unit with hands-on activities creating tessellations using ceramic and glass tiles. (Glass and ceramic tiles can be ordered online and shipped.)
By the end of this unit, students will be able to: identify and classify shapes, identify and roughly recreate symmetry, determine if a shape will or will not tessellate and why, and differentiate between patterns and sequences in nature and beyond. Students will have the vocabulary to talk about all of those topics, and they will have used problem solving, critical thinking, and investigative skills to come to those conclusions for which they can accurately explain using appropriate vocabulary.
Enrichment activities and lessons for this unit could go in many different ways. Exploring modern textiles and fashion in terms of pattern and tessellation seems like an obvious choice for an extension. Working with shapes on a graph, which comes up later in the geometry curriculum, also seems like a good way to take symmetry for an extension and preview of later materials. Most of the extension activities, and even some of the artists of focus, are directly influenced by Tim Barringer’s YNI seminar on Art, Design, and Biology. Extension and enrichment activities may also extend into other subjects, like diagrams in the sciences, visual arts, and flags and other art symbols in social studies.
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