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:
- Define tessellations and explain how they relate to geometry
- Participate in several activities where many discoveries about tessellations
will be made
- Locate tessellations in the real world
- Create tessellating patterns using translations, rotations and transformations
Teacher:
- overhead projector
- transparencies
- markers
- transparencies of pattern sheets (squares, triangles, and hexagons)
- overhead pattern pieces
- Butcher paper
Class (at least one per four students):
- baggies of polygons, ( triangles, hexagons, pentagons, squares, octagons,
- decagons)
- two 3"x3" squares of index paper per student
- scotch tape
- two 8 1/2" x 11" sheets of white paper
- patterns
- tessellations
- tessellate
- simple pattern
- complex pattern
- congruent
- fundamental region
- polygons
- translations
- rotations
- transformations
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
Lesson Plan Database
NTTI
Thirteen Ed Online
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