MASTER TEACHER  Cerise Weeks

GRADES  3 - 5

OVERVIEW
The world is filled with tessellations.  In this lesson students will learn what tessellations are and where they are found.  The students will be provided with examples of tessellations, discover other examples of tessellations,  and be able to create their own tessellation.  This lesson will review areas of geometry,  pre-algebra,  investigate concepts for visualizing, representing and interpreting patterns and use the scientific method to form and test hypotheses.

ETV SERIES
Math Vantage: #104 Tessellations/Transformation 

LEARNING OBJECTIVES
Students will be able to:
*  Recognize and define a tessellation
*  Illustrate examples of rotational, translation, and    mirror symmetry
*  Create a tessellation using manipulative
*  Identify and provide examples of where tessellations can be found in the world around us.
*  Explain which geometric figures (polygons) can form tessellations 
*  Use the scientific method to form and test their hypothesis 

MATERIALS
2 - 4 containers of wooden pattern blocks       (enough    for each student to have access to 10 pieces of the    identical     shape)
Tantalizing Tessellations Worksheet
2 sheets of chart paper
1 sheet of notebook paper for every     student
1 index card for every student
1 sheet of card stock for every student
   markers, crayons, map colors

VOCABULARY
tessellation - a collection of shapes which fit together to cover a surface without 
overlapping or leaving gaps.
congruent - having the same size and same shape.
symmetry - a regular, balanced arrangement on opposite sides of a line or plane.
polygon - a closed plane figure with three or more sides and angles.
translation - when a figure slides in any direction.
rotation - when a figure is turned around a point or vertex.
reflection - when a figure is flipped across a line.

PRE-VIEWING ACTIVITIES
Show the class some examples of tessellations (quilt, bee's honeycomb, mosaic tiles).  Ask the students what they notice about these items.  List observations on the board.  Ask the students what they think these items have to do with math.  List observations on the board.  Discuss the observations.  If  students have not mentioned patterns, point out the patterns to them.  Explain that these types of repeating patterns are called tessellations.  Discuss the history of tessellations:  Many years ago the Romans laid down pavements and covered the floors of their houses with mosaics.  Many of the mosaics were in the form of pictures but most of them were made of repeating patterns.  To make these patterns the Romans used small cubes of stone that were set in cement.  One of these cubes was called a tessella.  It is from this word that we have the name of a tiling pattern.  Tessellation once meant tiling by using equal squares.  It now means using any shapes which can be repeated in a way that leaves no gaps. 

FOCUS FOR VIEWING
To give the students a specific responsibility while viewing, hand out the worksheet  Tessellation Vocabulary.   Review the vocabulary words on the worksheet and say, "We are going to view a video that explains the definitions of these words and shows examples of each.  It is your responsibility to record the definitions on your worksheet as we view and discuss this video.  In the first section of the video, I want you to look for the highlighted patterns  and write down what you notice about each of them."

VIEWING ACTIVITIES
Start the video at the beginning of the segment titled, "Tessellations/Transformations."  Pause the video when the screen shows Ellen  holding a tie and saying, "It's a tessellation."  Discuss patterns with students and have them record the definition of  tessellation (the shapes repeat, they don't overlap, and there aren't any gaps).  Resume video.  Pause video when you hear Ellen say, "Congruent shapes are the same size and shape" and the screen shows the word congruent.  Have students record definition of congruent (same size, same shape). Resume video.  Pause video when you hear Ellen say, "Would I kid you?" and the screen shows three types of tessellations.  Provide wooden pattern blocks to students.  Have students choose one pattern example (triangle) and use their wooden pattern blocks at their desk to build it.  Discuss the results. Resume video.  Pause the video when the screen shows Ellen in repeating boxes and she says, "Another name for a slide is translation."  Have students record definition of translation (slide).  Resume video.  Pause the video when the screen shows Ellen in rotating triangles and she says, "Another name for this turn is rotation."  Have students record definition of translation (turn).  Resume video.  Stop the video when the screen shows Ellen in mirror images and you hear her say, "This is called a reflection."  Have students record the definition of reflection (one shape is the mirror image of another).  Have students complete illustrations of geometric concepts of rotation, translation, and mirror symmetry on the bottom of their Tantalizing Tessellations  handout

POST-VIEWING ACTIVITY
Before staring the post-viewing activities review vocabulary definitions, illustrations of geometric concepts (provide examples of each using reviewing video) and discuss what students learned in the video using the Tantalizing Tessellations worksheet.

Activity 1 - Which Shapes Can Tessellate?
The purpose of this activity is to allow students to use the scientific method to form a prediction about which of the shapes given will and will not form tessellations.  The students will then be able to test their hypotheses using a hands-on approach and develop a conclusion from their data.

Activity 2 - Creative Tessellations
This activity will allow students to design and create their own tessellations following a step-by-step approach.  Students will be able to be as creative as they can.

ACTION PLAN
Have an architect come to your class and discuss the uses of tessellationlocate, record and describe tessellations in construction.
Have students go out into the community and they find. Have students go out into the community and bring National Geographic and Architectural Magazines to class.  Students can then look through magazines and locate, cut out, and mount tessellations they find onto a Tessellation Collage. 
Take a field trip to the park, aquarium, or nature museum and have students discover tessellations in nature.

EXTENSIONS
Art
Research the Dutch artist M.C. Escher and his fascinating tessellation designs of optical illusion.  Gather examples of his work and report back to class.
Language Arts
Have students write a "How-To" composition about their tessellation.  How did they create it.  Step by step.
Create a story to go along with or explain one of M.C. Escher's designs.
Math
After completing activity 2 have students measure and find the perimeter and area of their tessellations.
Social Studies
Have students research how ancient civilizations used tessellations in their everyday life.  Gather examples and report back to the class.
Technology
Have students use a computer (see Enrichment Activity 1) to create their own computer generated tessellations.

Internet
http://www.tessellations.com/
http://forum.swarthmore.edu/sum95/suzanne/cwtips.html
 
 

Tantalizing Tessellations 
Focus for Viewing Handout

While viewing MathVantage: Tessellations/Transformations fill in the following
vocabulary terms.

Description of patterns:_______________________

__________________________________________________

Tessellation:________________________________

__________________________________________

Congruent:__________________________________

___________________________________________

Polygon:____________________________________

___________________________________________

Translation:__________________________________

___________________________________________

Rotation:____________________________________

___________________________________________

Reflection:___________________________________

___________________________________________

Symmetry:___________________________________

___________________________________________
 

Illustrate an example of the following geometric concepts using the triangle below: 
Rotation             Translation          Mirror Symmetry
 
 

Activity 1 - Which Shapes Can Tessellate?

Materials

Wooden Pattern blocks divided into 10 specific shapes (diamonds, ovals, triangles, parallelogram, pentagon, circle, semi-circle, hexagon, rectangle, square)
2 sheets of  chart paper
1 sheet of notebook paper for each student

Review

Teacher and students will review definition of a polygon (a closed plan figure with three or more sides and angles). 
Introduction
Teacher shows examples of each shape.  Students will be asked to predict and record on their paper which of these shapes will form tessellations.  Discuss with students the concept of predicting and the fact that your prediction does not have to be correct, it is just a guess.  Students will vote as a whole class as to which shapes will form tessellations and which will not.  Teacher writes predictions on chart paper.

Activity

Stations of each shape will be set up in centers around the room.  Students will work in groups of 2 - 3.  Each group of students will have time to explore whether each shape tessellates or does not tessellate by manipulating shapes in each center.  Students will record results on paper.  After the students have explored each center the class will regroup, revisit, and revise the prediction chart.  Students will then write a math journal explaining what they discover with this activity (conclusion).
 
 

Activity 2 - Creative Tessellations

Materials

1 index card for every student
1 sheet of card stock for every student
markers, crayons, map colors

Introduction

Have students design and create their own tessellation using manipulatives (wooden pattern blocks or draw various geometric shapes on construction paper, laminate, and cut out for students to use). 

Activity

Students can create their own tessellation patterns.  Give each student an index card and follow these steps:

1.  Draw any design on one side of a square piece of index card.  The design should start and end on the same side, and should not touch any other side.

2.  Cut out the design in one piece.  Slide the piece directly to the opposite side, and tape the pieces together along the two straight sides.

3.  Repeat steps 1 and 2 with the top and bottom of the square.  The shape is ready to tessellate. 

4.  Begin tracing and repeat your tessellation onto card stock until you form a pattern.