Here is a table to prove why there are only three regular polygons that create regular tessellations: As a class, you may create a table that shows the total measure of angles when different numbers of polygons come together at a vertex. You may want to avoid mentioning being a divisor of 360 so as not to cause any possible misconceptions for the other type of tessellations. Polygons need to meet at a vertex in a way to create 36 0 o 360^o 36 0 o angle. Discuss the reasons why a pentagon, heptagon, octagon, or any other won't tessellate. They probably will come up with designs made up of equilateral triangles, squares, and regular hexagons quickly. Remind them that they can only use one kind of regular polygon for each of their designs. Let students use regular polygons to create tessellations. Invite them to create regular tessellations In a regular tessellation, all the shapes are the same regular polygon and all the vertices are the same. The first ones are called Regular Tessellations. There are different types of tessellations. An overview of some of the well-known type of tessellations might be interesting to students. Since almost every civilization used tessellations throughout history, there are practically endless different examples of tessellation. The art of tiling a plane might have been around for the last 6000 years, but there are still many things to discover about it. 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.
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