![]() In this exploration, students will use the polygons on Polypad to create regular and semi-regular tessellations. They also create their own tessellating design. Therefore, there are only three regular tessellations (composed of the Hexagon, Square, and Triangle). Students will also also create their tessellating design by transforming the regular polygons using Escher-like techniques. Tessellations can be specified using a Schlfli Symbol. This activity can be extended using reptiles, spidrons, sphinx, Penrose tilings, and kite-square activities to design a longer unit. This explorations contains a variety of activities around tessellations. Each activity below could be a separate lesson plan. 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. Warm-UpĪsk students to draw a bee-hive on blank Polypad canvas and talk about the properties of the bee-hive. Then, ask them to share about the design of kitchen or bathroom tiles at their home or school. Perhaps even the floor of your classroom at school is a good example. Example 6: What combination of regular shapes tessellates a plane A regular octagon by itself will not tessellate a plane however, combine it with a square. These examples can be used to emphasize the importance of having no gaps and overlaps in a tiling pattern. Share some student work and add some examples if necessary. 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. Activity #1Īfter students explored that all types of triangles tessellate, let them explain their reasoning. Clarify with the students that any two congruent triangles will make a parallelogram which will always tessellate.Īgain, all quadrilaterals tessellate. Let them use the free-polygon tool to create concave quadrilaterals to investigate the answer. Then, invite some students to share their designs. The history of tessellations dates way back to ancient times. These designs were used by the Sumerians (about 4000 BCE) as clay tiles to decorate walls. 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. Since almost every civilization used tessellations throughout history, there are practically endless different examples of tessellation. An overview of some of the well-known type of tessellations might be interesting to students. There are different types of tessellations. The first ones are called Regular Tessellations. In a regular tessellation, all the shapes are the same regular polygon and all the vertices are the same. Invite them to create regular tessellations Let students use regular polygons to create tessellations. ![]() Remind them that they can only use one kind of regular polygon for each of their designs. They probably will come up with designs made up of equilateral triangles, squares, and regular hexagons quickly. Discuss the reasons why a pentagon, heptagon, octagon, or any other won't tessellate. Polygons need to meet at a vertex in a way to create 36 0 o 360^o 36 0 o angle.
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