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TESSELLATING AROUND THE CLOCK
Grades 4 - 5

Geometry is motivating and children enjoy working with different shapes and figures. This lesson will familiarize students with tessellations. Through hands on exploration, students will discover the definition of the term tessellation and the shapes that tessellate.
"Math Vantage Tessellations/transformations #104"
Students will be able to:
Teacher:
Class (at least one per four students):
Show the students overheads #1,2, and 3 of sample tiling patterns. In groups of 3-4 students, have them identify the basic shapes in each pattern.

Ask the students to write down a definition of the word "tessellations". Provide each student with a list of vocabulary words and space to write their definitions and the definitions given in the lesson. Ask them to jot down the definitions of each word whenever they hear one given.
To give students a specific responsibility for viewing, SAY: "We are going to watch a video in which a young lady explains to us what tessellations are. As you watch this tape, listen for the three things that make the pattern a tessellation and write the definition on your vocabulary sheet."

BEGIN Tape after the Math Vantage Logo. To verify the three things that make the shape a tessellation, Pause Tape with the young lady holding the tie after she says, "It's a tessellation". Ask for a volunteer to repeat the definition.

To give students a chance to check their definitions, REWIND tape back to where she passes the white Mickey Mouse sweatshirt.

To give students a specific responsibility for viewing, SAY: "Listen and check your definition with her."

PAUSE Tape after she repeats the definition. Ask a student to repeat the definition while you write the definition on the butcher paper.

To give students a specific responsibility for viewing SAY: "Listen to how she describes the pattern on the jacket and the tie."

RESUME the tape and PAUSE the tape as soon as the young lady enters the dressing room. Allow students time to discuss the two descriptions.

To check students' understanding, REWIND tape back to where she begins to walk from the sweatshirt towards the jacket.

RESUME the tape to replay the descriptions.

PAUSE Tape as soon as she enters the dressing room.

To give students a specific responsibility for viewing, SAY: "Why do you think the jacket is a simple pattern? Why is the pattern of the tie complex?" To check for understanding, RESUME Tape after she enters the dressing room.

PAUSE Tape after she says, "...but I like them both."

To give the students a specific responsibility for viewing, SAY: "Listen to find out what the patterns have in common."

RESUME the tape after the young lady enters the dressing room.

PAUSE the tape to write on the butcher paper what the shapes have in common.

To check for understanding, RESUME Tape.

PAUSE after she gives the definition of a tessellation.

To give the students a specific responsibility for viewing, SAY: "What does congruent mean?"

RESUME Tape and play to the end of the definition of congruent.

To check for understanding, REWIND the tape back to the word "tessellation".


PAUSE tape. SAY, "Listen and check your definition".

PAUSE Tape after the definition to check students' understanding.



To give students a specific responsibility for viewing, SAY: "Listen for the definition of "fundamental region".

PLAY Tape through the definition of fundamental region.

To check for understanding, REWIND to where the second to last hexagon flips onto the last one to become one.

REPLAY Tape through the definition of fundamental region.

STOP Tape and allow students time to make corrections in their definition sheet.

TURN OFF tape player. Do Not Remove Tape!

Ask students to take out worksheet #1. SAY: "We are going to discover which shapes will tessellate a plane. Take one set of shapes (i.e., all squares) at a time, start in the center of your paper and cover the paper. Keep in mind the definition of tessellation. (Review the definition of a tessellation.) Keep track of which shapes do tessellate and which ones don't." Allow students time to explore the square, pentagon, octagon hexagon and an equilateral triangle.

TURN ON the Video. To give students a specific responsibility for viewing, SAY: "Watch the tape to compare your list of shapes that tessellate with hers."

PLAY the tape through her explanation of pentagons.

To allow students a chance to check their discoveries, PAUSE after she says, "Pentagons can't form tessellations".

SAY: "Did you find any that she didn't mention?"

To give students specific responsibility for viewing, SAY: "Let's think about the tessellation pattern on the tie. Was the shape any of the ones listed? Why do you think it is a tessellation? Listen to find out how the shape is able to tessellate."

RESUME the tape until the word translation is mentioned and the word appears on the screen.

To check for understanding, PAUSE Tape. SAY: "What is a translation?"

To allow students a chance to hear the definition again, REWIND the tape and PAUSE at the point where she is sitting in the square.

To give students a specific responsibility for viewing, SAY: "Listen to the tape to find out how we can change the shape so that it still tessellates."

STOP the Video after she demonstrates the computer program. Do not remove the tape!

SAY: "Take out your 3"x3" card and your scissors. I'm going to demonstrate how we can change one side of a square and the opposite side in the same way. (See figure 3 and figure 4 of the worksheets to demonstrate this.) Now I would like for you to try changing your card in a similar way." Allow time for students to cut their cards and trace a few of the shapes.

To give students a responsibility for viewing, SAY: "Now listen to find out how triangles are different and what the tessellation is called."

PLAY Tape and PAUSE after the triangles fall off the screen.

SAY: "What is the name for how we form tessellations with triangles?"

To give students a specific responsibility for viewing, SAY: "Let's listen for what happens to complex shapes and what it's called."

RESUME Tape to where the toes are patting.

To check for understanding, REWIND the tape back to where the triangles fall off the screen. Replay the definition of reflection.

REWIND tape and STOP where she says, "I think we've got the idea." Turn off the tape.

Activity SAY: "We are going on a tessellation scavenger hunt. We heard in the video that tessellations are found in the world around us. We will be working with our teammates to discover as many tessellations as we can in and around the school. You will have fifteen minutes to search. Each group should be prepared to present their discoveries to the rest of the group."

Give each group of four students a transparency for recording the tessellations, where they were seen and the polygons used.
SAY: Now we are going to design some shapes that use the transformation technique. Ask each student to take out the 3"x 3" index card. Demonstrate the cut and slide procedure to transform the card into a shape that will tessellate when slid to the opposite side of the same shape.

After cutting and taping the new shape, SAY: "How many of you remember lying on your backs in the grass and looking up at the clouds. Think about all of the different things you were able to imagine each cloud being. Look carefully at your shapes. What figure do you see? Draw the details onto the card so that anyone can see the same thing that you see."

Tell the students to place the shape in the middle of the page and begin tracing the shape on the paper so that there are no gaps, and no overlaps. Once they have created their tessellation, they should color it and make a cover for one of their books.
Invite a quilter to the class to show some of his/her quilts and to describe the patterns used. Students should identify any tessellations that are found in the quilts. Identification should include finding the fundamental region.

Provide students the opportunity to design and sew their own miniature quilt or to stitch patches for a class quilt. Donate the quilt to a homeless shelter, senior citizens home or community center.
Math: Have students explore the pairs of regular polygons that tessellate, (see worksheet #2).

Ask the students to measure all the angles around a point in their tessellation of regular polygons. What do they discover?

Look for symmetry in tessellations. What kinds of symmetry do they find (mirror, rotational, horizontal, vertical )?

Art: Introduce the students to Eschar and ask them to create some "Eschar style" tessellations.

Science: Research to find out why bees use hexagons to tessellate their hives.

Look for tessellations in science and nature. The segment which follows this one discusses math in science.

Resources: The School Mathematics Project, Teachers' Guide for Book B, Cambridge University Press

"How to Draw Tessellations of the Escher Type," The Mathematics Teacher, April, 1974

Introduction to Tessellations, Dale Seymour and Jill Britton ITV Series: Landscapes of Geometry #101

Master Teacher: Sharon Simpson





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