![]() 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. Regular octagon are all congruent, each of these turns must be $\frac = 135^\circ.In this exploration, students will use the polygons on Polypad to create regular and semi-regular tessellations. $8$ of these turns you are heading in the same direction in which you startedĪnd have made one full revolution of $360^\circ$. Travelling counterclockwise along the octagon. This task could profitably used to foster growth with respect to the standards for mathematical practice: Like its companion ''Tile patterns II: hexagons'', it encourages students to engage in MP2 (reason abstractly and quantitatively) and MP3 (construct viable arguments). While aspects of this task might be used for assessment, the task is ideally suited for instruction purposes as the mathematical content is directly related to, but somewhat exceeds, the content of standard 8.G.5 on sums of angles in triangles. Their own patterns of polygons which can be used to tile the plane. ''Tiling patterns II: Hexagons.'' Students may be encouraged to develop Regular hexagons are also relatively common are considered in the task In a grid which can be extended as far as desired: Used for covering two dimensional surfaces is squares. Then the $4$Īngles must be right angles and this takes more care to show. That the regular octagons enclosing the square are congruent. First, the $4$ sides must be congruent: this comes from the fact There are two steps to the problem, corresponding to the two vital aspects ofĪ square. This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons. Tiles and tiling patterns are good sources for developing geometric intuition.
0 Comments
Leave a Reply. |