Let the students know what it is they will be doing and learning today. The lesson can begin by introducing the Tessellation applet to introduce students to the. In pairs, let the children explore the tessellations on the Tessellation Town to create tessellations, using the Shodor Educational Foundation Tessellate!. Alternating Tessellations by Quipitory on deviantART Tessellation Patterns, Clay Stamps, Science Art, .. Let’s Draw ESCHER-STYLE Coloring Pages.

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This lesson allows students to examine tessellations and their geometric properties. This 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 our culture. Upon completion of this shidor, students will: Geometry The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. The student demonstrates a conceptual understanding of geometric drawings or constructions. Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. Operations and Algebraic Thinking Analyze patterns and relationships. Congruence Experiment with transformations in the plane Understand congruence in terms of rigid motions.

Geometry Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems. Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial shodog, and geometric modeling to solve problems.

Data Analysis and Probability Competency Goal 3: The learner will transform geometric figures in the coordinate plane algebraically. Geometry and Measurement Competency Goal 2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

## Tessellations: Geometry and Symmetry

The learner will use properties of geometric figures to solve problems. The learner will measure and apply geometric concepts to solve problems. Geometry and Measurement Competency Goal 1: Geometry The student will demonstrate through the mathematical processes an understanding of the connection between the identification of basic attributes and the classification of two-dimensional shapes.

Geometry The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among shodpr properties of quadrilaterals. Geometry The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

Sjodor The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. Examples of noncongruent lest congruent figures will be included.

Has anyone ever heard of M. Escher was a famous artist who enjoyed twisting perceptions of reality. He was responsible for works such as Reptiles, Horseman and many more that incorporated the use of tessellations. Let the students know what it is they will be doing and learning today.

Say something like this: Today, class, we are going to learn about tellellations. We are going tesselatw use the computers to learn about tessellations, but please do not turn your computers on until I ask you to.

I want to show you a little about this activity first. Have the students explore which regular polygons tessellate and why. Start them by examining tessellations of regular polygons including number of sides tessflate interior angle measurements by using a data table.

Encourage students to determine a pattern among tesselats polygons that they tessellate. Ask the students to predict which regular polygons will and will not tessellate and why. Follow-up by having the students write a concise definition for a regular polygon tessellation. Have them expand tesselxte definition to describe a tessellation made from non-regular polygons.

After the students have determined which shoor polygons tessellate, discuss the types of symmetry present in tessellations. Have the students build tessellations and identify the types of symmetry present.

### Symmetry in Tessellations Discussion

Give them a table to record the basic shape used to tile and the types of symmetry present in the basic unit and in the tessellated pattern.

Discuss how angle measure, area, and perimeter apply to tessellations. Allow students time to practice their knowledge about tessellations. Have teams of students work together. Instruct one student on the team to create a tessellation. Have that student describe the tessellation to other students and see if the other students can recreate the tessellation without looking.

The students should formalize their terminology and describe the tessellation in terms of angle measure, polygon shape, symmetry, area and perimeter. Lead a discussion about tessellations in the world. Ask students to tessselate tessellations that they see in their daily lives and in nature. Discuss the ways that we perceive patterns.

Lead a discussion about optical illusions tezselate demonstrate how we perceive patterns. Also discuss the use of color in tessellations. Suggest that the students change the colors in their tessellations to see what effect that has on how they perceive the pattern.

They may want to record their observations in a journal. Ask the students to use the Tessellation Activity to build tessellations of patterns they see in art and nature.

You may also ask students to stretch the regular polygons into the letters of the alphabet or the letters of their name and tessellate the pattern. Have them record which polygon is best used to shape each letter. Also have them record what type of symmetries are present in each tessellation.

You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson. This lesson can be rearranged in several ways. Here is an example of a shorter version: The lesson can begin by introducing the Tessellation applet to introduce students to the idea of tessellations and how they developed. Discuss the types of symmetry present in tessellations. After these discussions and activity, the students should have practiced their ability to recognize symmetry in plane figures.

Students can gain a deeper understanding of other pr inciples of geometry by exploring tessellations in the Geometry Lesson. The tessellation activity could also be used to explore spatial visualization and pattern recogni tion with the Visual Pattern Lesson. Abstract This lesson allows students to examine tessellations and their geometric properties.

Objectives Upon completion of this lesson, students will: Grade 3 Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. Grade 4 Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. Grade 5 Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. Grade 6 Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 7 Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. Grade 8 Geometry The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes. Grade 9 Geometry The student demonstrates an understanding of geometric relationships. Geometry Congruence Experiment with transformations in the plane Understand congruence in terms of rigid motions Third Grade Geometry Reason with shapes and their attributes.

Grades Geometry Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems Grades Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems.

Students must be able to: Recognize regular polygons, such as triangles, rectangles and hexagons Understand the difference between an edge and a corner Technological: Key Terms polygon A closed plane figure formed by three or more line segments that do not cross over each other tessellation A tessellation is a repeated geometric design that covers a plane without gaps or overlaps.

Alternate Outline This lesson can be rearranged in several ways. Suggested Follow-Up After these discussions and activity, the students should have practiced their ability to recognize symmetry in plane figures. Grades Geometry Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems Grades Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems Geometry Data Analysis and Probability Competency Goal 3: