Marcia Wallin Teaching Portfolio                                                    

Lesson: Geometric Shapes and Tessellation      

                                                               
Subject: Math                                                                                                                              
Grade Level: 2 (Can be adapted for elementary-middle school students)                      
Time: 2 class periods – 50 minutes each
Brief Description: Students will work with visual models to develop an understanding of tessellations. They will review the names of polygons. They will learn to recognize shapes that tessellate and explore tessellation shape composition. Tessellations can be found in nature and in art and architecture examples throughout world cultures.
 

Objectives:                                                                                                                                        
At the conclusion of the lesson, students will be able to:
Identify regular polygons (equilateral triangle, square, hexagon)  
Describe a tessellating pattern                                                                                                    
Use math vocabulary words: polygon, angle, adjacent, tessellation                            
Recognize tessellations in the environment.                                                                          
Create original works of art using tessellations patterns
 

Standards:                                                                                                                          
Common Core State Standards for Mathematics Grade 2                                
Geometry 2.G Reason with shapes and their attributes. CCSS.Math.Content.2.G.A.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Ann Arbor Public Schools Art Curriculum                                                                          
The arts platform will allow teachers to make learning more relevant by integrating science and social studies outcomes through the fine arts.      http://www.a2schools.org/aaps/academics/elementary_humanities
 

Materials and Resources                                                                                                
Geometric pattern blocks (or paper geometric shapes)                                              
Computers with Internet connection                                                                                        
Online Tessellation programs    

http://www.shodor.org/interactivate/activities/Tessellate/ or http://gwydir.demon.co.uk/jo/tess/tri.htm                                                                            Images of natural tessellations    http://www.tessellations.org/tessellations-all-around-us.shtml
 

Introduction                                                                                                                              
Review the identification of regular polygons. Note that “regular” polygons have all sides equal and all angles equal.
 

Lesson
    1.    Distribute square, triangle and hexagon shapes
    2.    Introduce the concept of a tessellation.  A tessellation, or a tiling, is a collection of shapes that fit together without gaps or overlaps

           to tile a surface. With pattern blocks show how squares can fit together without gaps or overlaps to tile a surface.

           Emphasize that the tessellation could extend forever.
    3.    Ask students to make patterns with triangles or squares or hexagons
    4.    Introduce computer tessellation program

           Tessellate   http://www.shodor.org/interactivate/activities/Tessellate/

            or  http://gwydir.demon.co.uk/jo/tess/tri.htm. and encourage students to make tessellations.
    5.    Ask students if they think that circles or ovals could tessellate a surface. Encourage discussion about why not.

           Remind students that  shapes need corners or straight edges to tessellate.

           Remind students of the definition of a polygon, and refine the definition of a tessellation to be a collection of polygons

           with no gaps or overlaps.
    6.    Ask students if they have seen any tessellations anywhere before. Show photographic examples of honeycomb, pineapple

           and orange  sections and other natural tessellations.

           If possible, provide actual pieces of items from nature.

           Examples are available at: http://www.tessellations.org/tessellations-all-around-us.shtml

Assessment                                                                                                                                    
Note students identification of polygons                                                                            

Observe students construction of tessellations                                                                        

Note students’ observations of tessellations in nature                                                          

Quiz students on vocabulary

 

Post-lesson Comments and Reflection                                                                            
Discuss with students their experiences making tessellations. Did they find it easier to work with geometric manipulatives or on the computer? What differences do they notice between natural tessellations and computer generated patterns? Why do they think tessellations have been used among so many cultures in art and architecture? How have artists added something extra to the tessellations of  geometric tessellating patterns?

 Extension Activities
    •    Collaborate with the art teacher to create tessellation patterns for an art project
    •    Collaborate with an IT teacher to use Logo to create tessellations https://www.youtube.com/watch?v=zis99LQ5_Lk
    •    Discuss use of tessellations among the cultures of the world throughout history. 

          Examples of Art and Architecture tesselations available at: http://library.thinkquest.org/16661/history.html                                                     
    •    Examples of Tessellations in Math and Art are available at: http://www.incredibleart.org/lessons/middle/tessell.htm
    •    Introduce the work of M. C. Escher and other artists using tessellations  

          http://www.pbs.org/parents/education/math/games/first-second-grade/tessellation/    http://www.tessellation.info/en/info/artists
    •    Look at the online galleries of other students tessellations http://mathforum.org/alejandre/frisbie/tess/sea.tess.html

Additional Teacher Resources:
Dynamic Paper                   
TessellationWorkbooks                    
Math Information for Tessellations                                                          
Tessellation How-To Information and Examples                                                                                                   
Escher like interactive Tessellation Game