Let the students know what it is they will be doing and learning today. Finally, see what they already know about color and optical illusions and how they affect perception.See if the students are familiar with symmetry, and describe to them the different types present in tessellations.If needed, present the information in the introduction to tessellations discussion. Ask students what they know about tessellations.Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson: This lesson introduces students to the following terms through the included discussions: Visual Patterns in Tessellations Worksheet.Copies of supplemental materials for the activities:.use a browser, such as Netscape, for experimenting with the activities. perform basic mouse manipulations such as point, click and drag.Technological: Students must be able to:.be able to recognize types of symmetry after they are introduced.recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.use geometric models to represent and explain numerical and algebraic relationships.use visual tools such as networks to represent and solve problems.Use visualization, spatial reasoning, and geometric modeling to solve problems examine the congruence, similarity, and line or rotational symmetry of objects using transformations.describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationshipĪpply transformations and use symmetry to analyze mathematical situations.understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.The activities and discussions in this lesson address the followingĪnalyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships examined tessellating patterns in the world around them.learned about several types of polygons.Upon completion of this lesson, students will have: The activity and discussions may be used to develop students' understanding of polygons and symmetry as well as their ability to analyze patterns and explore the role of mathematics in nature and world culture. The most famous pair of such tiles are the dart and the kite.Ĭlick here for the lesson plan of non-periodic Tessellations.This lesson allows students to examine the mathematical nature of art, tilings and tessellations. The pattern of shapes still goes infinitely in all directions, but the design never looks exactly the same. In the 1970s, the British mathematician and physicist Roger Penrose discovered non-periodic tessellations. Whatever direction you go, they will look the same everywhere. They consist of one pattern that is repeated again and again. It may be better to show a counter-example here to explain the monohedral tessellations.Īll the tessellations mentioned up to this point are Periodic tessellations. All regular tessellations are also monohedral. If you use only congruent shapes to make a tessellation, then it is called Monohedral Tessellation no matter the shape is. You can use Polypad to have a closer look to these 15 irregular pentagons and create tessellations with them. Among the irregular pentagons, it is proven that only 15 of them can tesselate. We can use any polygon, any shape, or any figure like the famous artist and mathematician Escher to create Irregular tessellationsĪmong the irregular polygons, we know that all triangle and quadrilateral types can tessellate. The good news is, we do not need to use regular polygons all the time. If one is allowed to use more than one type of regular polygons to create a tiling, then it is called semi-regular tessellation.Ĭlick here for the lesson plan of Semi - Regular Tessellations. If you try regular polygons, you ll see that only equilateral triangles, squares, and regular hexagons can create regular tessellations.Ĭlick here for the lesson plan of Regular Tessellations. the most well-known ones are regular tessellations which made up of only one regular polygon. There are several types of tessellations.
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