These designs were used by the Sumerians (about 4000 BCE) as clay tiles to decorate walls. The history of tessellations dates way back to ancient times. ![]() Then, invite some students to share their designs. Let them use the free-polygon tool to create concave quadrilaterals to investigate the answer. Clarify with the students that any two congruent triangles will make a parallelogram which will always tessellate.Īgain, all quadrilaterals tessellate. Activity #1Īfter students explored that all types of triangles tessellate, let them explain their reasoning. Then, you may identify these designs as tessellations and define a tessellation as a pattern of shapes covering an entire surface with no gaps and no overlaps. Share some student work and add some examples if necessary. These examples can be used to emphasize the importance of having no gaps and overlaps in a tiling pattern. Perhaps even the floor of your classroom at school is a good example. Then, ask them to share about the design of kitchen or bathroom tiles at their home or school. Warm-UpĪsk students to draw a bee-hive on blank Polypad canvas and talk about the properties of the bee-hive. This exploration could be used a mini-unit on tessellations that is either used as one sequential unit or as multiple explorations that are spread out over a period of time and interspersed with other topics of study. Each activity below could be a separate lesson plan. This explorations contains a variety of activities around tessellations. This activity can be extended using reptiles, spidrons, sphinx, Penrose tilings, and kite-square activities to design a longer unit. Students will also also create their tessellating design by transforming the regular polygons using Escher-like techniques. They also create their own tessellating design. In this exploration, students will use the polygons on Polypad to create regular and semi-regular tessellations. All Lesson Plans Tessellations Overview and Objective Here's a nice article that may give some ideas that students could look into to understand the purpose of tessellations in our natural world. As for the honey bees an interesting thing to look into is why do honey bees use regular hexagons rather than other regular polygon that tessellates- it has to do with optimizing the amount of honey a regular hexagon stores. I'm still thinking about how to move forward on this though. I am thinking about how I could create certain parameters in which the students will have to fill a finite plane of some shape and they will have to make some sort of prediction. I feel something is missing in my project that requires them to take it further than just designing their own. ![]() ![]() Although it is true that tessellations can be found both in the natural world as well as in more synthetic (man-made) products/ art/architecture. I am stuck in how to make this project more authentic to the students though. This entails an understanding in transformations, interior angles of a polygon and I differentiated by creating different roles: some students had to design a mutated figure that would tessellate with an equilateral triangle, square, regular hexagon, irregular triangle, and irregular quadrilateral. ![]() I am an 11th Grade math teacher and I have done a larger project with my students in which they have to design their own tessellation using Geometer's Sketchpad. I agree with John Golden, in that you could extend the idea to have student think about the "so what". I really like the idea of using pattern blocks to work with semi-regular tessellations.
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