You re probably familiar with the riddle, "When is a door
not a door? When it s ajar." How about this riddle? "When is a
cylinder a rectangle?" Give up?
From this lesson your students will find the answer to this riddle and
discover
the relationship between three-dimensional objects and their
two-dimensional
building blocks. Students will also view a video segment of an imaginary
world where the Flatys feel inferior to the Roundys, leading students to
construct familiar three-dimensional objects from their two- dimensional
shapes. A final activity will highlight students discoveries of the two-
and three- dimensional objects found within the physical and natural
world
of their school.
Math Works, #5: Exploring Geometric Shapes
Students will be able to:
identify the difference between a two-dimensional shape and a three
dimensional object
construct a simple model of a cone, cube, cylinder, rectangular
prism
and triangular pyramid
diagram and identify the two-dimensional shapes which make up a
cone,
cube, cylinder, rectangular prism and triangular pyramid
describe in writing how each of these three-dimensional objects is
created
locate two- and three-dimensional objects within the classroom and
the school building
For Teacher--REQUIRED:
paper towel/toilet paper tube
paper coffee filter (Mr. Coffee style)
stick of butter/margarine-chilled, wrapped
an orange
Container Chart--Appendix A
scissors
SUGGESTED LIST: Select three containers from this list: oatmeal box,
butter/margarine
box, raisin box, milk carton (any size), brown lunch bag, cereal box,
empty
bag of potato chips or pretzels
For each student pair:
Shape Up sheet (Appendix B--Worksheets 1a, 1b, 2) one piece of
construction
paper--12 x 15 inches
scissors
glue or tape
Whole class access to: crayons, markers, colored pencils, glue, scissors,
single hole punch, colored yarn, construction paper
In preparation for the video segment of this lesson, it will
be important for you to assess your students understanding of two- and
three-dimensional
shapes and objects. It will also be important for your students to have
a basic understanding that three-dimensional objects are comprised of
simple
two-dimensional shapes. By taking apart familiar objects such as a paper
towel tube, students will begin to see this relationship and relate it to
other examples in and out of the classroom.
In order to assess what your students know about two- and
three-dimensional
shapes and objects and their construction relationship, gather three
simple
containers from the Suggested Materials list along with the paper
towel/toilet
paper tube, stick of butter/margarine, paper coffee filter and an
orange.
Review with the students the simple geometric shapes of a square,
triangle,
rectangle and circle by drawing them on the chalkboard and by locating
examples
of these shapes within your classroom. Explain to your students that
these
are two-dimensional shapes have only length and height. Identify and
label
the length and height of each shape.
Next, hold up the paper towel/toilet paper tube and ask: Is this a
two-dimensional
shape? Students shouldn t recognize it as such, because it is not flat
like
the simple shapes previously discussed.
Ask: What makes this tube different from a two-dimensional shape like a
circle or a square? Students should suggest ideas leading to a
description
of a three-dimensional object which has length, height, and width
(depth).
Identify the length, height and width of the tube and also identify the
tube as a cylinder.
Ask: What two-dimensional shape will we have if we cut the tube
vertically?
Listen to the predictions of students, cut the tube vertically and
flatten
it out. Hold it up and again ask students what two-dimensional shape
forms
a cylinder. They should respond by saying a rectangle.
On a Container Chart (Appendix A) poster, record your findings. Plan to
display the disassembled objects for students to refer to during the
lesson.
Then hold up the paper coffee filter. Ask: What two-dimensional shape is
used to make this filter? Then hand the filter to a student volunteer and
ask her/him to flatten it out on top of a desk. Ask: What did you find
out?
The student should recognize the flattened filter as a circle.
Repeat this with the stick of wrapped butter/margarine. Ask students to
identify and count the two-dimensional shapes that make up the stick (2
squares, 4 rectangles=6 shapes). Next, ask students to predict the
two-dimensional
shape of the wrapper. Ask for a student volunteer to unwrap the
butter/margarine
and discuss your findings. Record them on the chart.
Next, hand out the three containers to student volunteers and ask them to
take the objects apart in order to reveal their two-dimensional building
shapes. Once completed, have the students trace their disassembled
container
on the chalkboard revealing its actual two-dimensional shapes and then
record.
To give students a specific responsibility while viewing, ask
them to give a thumbs up sign whenever they recognize a three-dimensional
object from the Previewing Activity during the video segment. In
addition,
ask them to be listening for any new classifying or descriptive
information
about an object which needs to be added to the Comments column on the
Container
Chart.
Note to Teacher: Prior to viewing, cover the television
screen
with acetate, plastic wrap or other clear, markable material and have a
water soluble or overhead pen ready for use during the video segment. You
will also need a spray bottle containing water and paper toweling for
cleaning
the screen in between pauses.
START video after the opening credits at the Math Works
graphic.
PAUSE video on the close up of Jason ( younger boy) lying on the
floor with his building blocks after Nancy says . . .so please chill out.
Ask: Are these building blocks two or three dimensional? Once students
respond
three dimensional, RESUME video.
PAUSE video on the close-up of Nancy s blender diagram, after she
says, I want to make sure I know how these pieces go back together. Ask:
Is a diagram two or three dimensional? Students should respond two
dimensional.
Ask a student who responds correctly to explain why. Her answer should
include
the ideas that it s flat and has no depth. RESUME video.
PAUSE video: After Roy (older boy) says to Nancy, Can you hear
yourself?
A lot of shaping words coming out of your mouth. Ask: What are some of
the
shaping words Nancy just used? Replay a short segment prior to pausing if
the students have a difficult time remembering. The shaping words used by
Nancy include square, circular and cylindrical. Ask: What two-dimensional
shape does the word circular refer to? Answer: circle. Ask: What
two-dimensional
shape does cylindrical refer to? Answer: cylinder. RESUME
video.
PAUSE video after Nancy says, It s funny, one moment you re seeing
something in three dimensions all together and the next. . . Ask: What
three-dimensional
object is Nancy now seeing in two dimensions? Answer: the blender she s
taken apart. RESUME video.
PAUSE video: On the photograph of a fire station ask: What
two-dimensional
shapes do you see? Trace out each shape with the marking pen as the
students
identify them. Wipe screen clean. RESUME video.
PAUSE video when Roy says, There s a circular shape on the
close-up
photo of a child s face. Ask: "What circular shape is Roy referring
to? Have the student who correctly identifies the shape come up and trace
it with the marking pen. Wipe screen clean. RESUME video.
PAUSE video: After Nancy says, There s a triangular one. . . on a
photo of a door. Ask: What two-dimensional object does triangular refer
to? Students should respond triangle. RESUME video.
PAUSE video after Nancy says, There s a pyramid on the photo of a
building with a pyramidal top. Ask: Where is the pyramid? Have a student
volunteer trace out the pyramid on the video screen. Ask the student:
What
two-dimensional side can we see? Student should answer a triangle. To
utilize
prediction skills, say: Although we can t see all of the sides, how many
triangles do you think make up this pyramid? If the students doesn t
guess
four ask the class to help out. Even if the students still don t guess
four
ask: What two-dimensional shape makes up the base of this pyramid? Once
students guess a square ask: Now how many triangles make up this pyramid?
Students should respond easily now with four. Wipe screen clean.
RESUME
video.
PAUSE video on the photo of the three smokestacks. As a review of
the Previewing Activity, ask: Is this a cylinder? Students should respond
yes. Ask: If we cut this cylinder vertically and flattened it out what
two-dimensional
shape would we have? Students should recognize the comparison with the
paper
towel/toilet paper tube and respond rectangle. RESUME video.
PAUSE video after host says, Here s a cube. Ask: How many sides
does
a cube have? Students should respond six. Ask: What two-dimensional shape
makes up those six sides? Students should respond squares. RESUME
video.
PAUSE video after narrator of cartoon says, . . .where they all
loved
a flat existence indeed on a close-up of the Flatys yawning. Ask: Are the
Flatys two or three dimensional? Students should answer two dimensional
and be able to explain why. RESUME video.
PAUSE video after narrator says, They were all real hunks on a
close-up
of the Roundys. Ask: Are the Roundys two or three dimensional? Why?
Students
should respond three dimensional with additional information on
identifying
the object. RESUME video.
PAUSE video after narrator says, If only they could be good, solid
citizens instead of being skinny and wimpy. In order to make a
prediction,
ask: What suggestions would you make to the Flatys about their feelings?
Allow students to share their ideas and RESUME video.
PAUSE video after the two circular Flatys say, We could make
ourselves
into a cylinder. Ask: Do the predictions of these Flatys match any of our
observations from the Container Chart? Depending upon the containers you
chose, students should be able to recognize the correlation between your
class data and the Flatys predictions. RESUME video.
STOP video after the narrator says, Who were really nothing but a
lot of flat shapes stuck together when you came to think of
it.
At the conclusion of the video segment ask: What did the Flat
Earthers learn about themselves that made them realize their similarities
to the Round Earthers? Students should answer with ideas about how the
Flat
Earthers two-dimensional shapes were responsible for the formation of the
Round Earthers three-dimensional design.
Refer back to the Previewing Activities and ask: How could we make a
diagram
of the containers we examined before the video like Nancy did? Students
should respond by suggesting to trace around the various sides of the
disassembled
containers. In order to reinforce lesson objectives ask: Is a diagram two
dimensional or three dimensional? Why? Students' answers will lead
towards
defining the term diagram. Record students ideas about this definition
brainstorm
style next to the term written on the chalkboard. Repeat this process for
the other terms on the chalkboard mentioned as a Focus for Viewing before
the video. Ask for two student volunteers to write up a completed version
of the definitions as an extra credit assignment. The completed
definitions
may be written on poster board and then displayed in the classroom.
Next, divide your class into pairs and hand out Shape Up sheets (Appendix
B--Worksheets 1a, 1b, 2) to each pair. Depending on your own style, hand
out or refer to the additional materials needed to complete this activity
(see Materials section--Part One). Explain to the whole class that this
activity will give them practice constructing their own Round Earthers
from
two- dimensional diagrams. Each students pair needs to cut out and
construct
the three-dimensional objects from Worksheet 1a and 1b and complete the
data chart on Worksheet 2 as they work. Students may color and/or
decorate
the three-dimensional objects as they choose.
Once all of the objects are constructed, have student pairs arrange the
objects into a freestanding sculpture on the piece of construction paper.
Students will not need to secure the sculpture onto the paper until they
complete the next activity. Tell student pairs they are responsible for
writing a descriptive paragraph about their sculpture. Encourage students
to observe their sculpture from various positions, i.e., rotating it; and
points of view, i.e., while standing over it, at eye level, and decide as
a pair what perspective they most enjoy. Their paragraph needs to include
a name for the sculpture and must describe the sculpture from their
favorite
perspective. The writing will provide insight into the pairs
understanding
of the lesson objectives, as well as serve as an excellent opportunity to
explore and write from different points of view.
After the sculptures and descriptions are finished, spend some class time
allowing pairs to share their projects. Ask: How did you decide on the
design
of the sculpture? Did you make many changes while designing it? Does your
sculpture have a base or did you rely on all of the objects working
together?
Now, as one student holds up the sculpture, have her/his partner read
their
description aloud. Ask: How did you name your sculpture? What various
arrangements
did you try before deciding on one?
As a concluding activity, hold up an orange and say, Nature also provides
us with two- and three-dimensional examples. What three-dimensional shape
is this? Students need to identify this as a sphere.
Have students make predictions by asking: What two-dimensional shape can
make up a sphere? Allow students to respond with their ideas, but do not
tell them the correct answer.
Slice the orange in half horizontally and show students the exposed
triangular
shaped sections. Again ask: Now what two-dimensional shape to you think
makes up a sphere? Students should respond triangles. To reinforce this
concept, make a slice of orange 1/4 -1/2 thick. Carefully slice through
one side of one orange section (Figure 1). Gently pull the slice apart
which
should separate it into several triangles (Figure 2). Ask: How many
triangles
do you see? If we continue to cut this orange into slices and separate
them
like this, can you predict how many triangles would make up this orange?
Students predictions will vary.
FIGURE 1 FIGURE 2 cutting line
Continue discussing examples of two and three dimensional objects in
nature
by asking students to share additional ideas they have. Stimulate
discussion
by asking: What two-dimensional shapes did the video mention? Can your
body
make two- or three-dimensional shapes or objects?
PART TWO As a whole class activity, plan to make a tour of your school
seeking
out the various two- and three-dimensional physical and natural features
it has. During the initial tour you take with your students, have them
record
their own observations of such features in a notebook or by using the
suggested
data chart from Appendix C. Because you re working towards a tour others
will share, emphasize to students the importance of writing their
discoveries
in the order they observe them.
After the first tour, divide students into groups of 4 or 5 and have each
group compile a list of the collected observations composed of their
group
s favorite six to eight choices. From this listing, make a class list
composed
of the top choices from all of the groups, probably numbering around 20
depending on your class size. Arrange these points of interest in a
logical
tour order, consulting your students in the process.
If possible, have a parent volunteer make photos of each point of
interest.
If not, assign your students to the various points and have them make
their
own drawings, and then compile a tour portfolio of the photos or
drawings.
If you are able to make a video, use your students as the tour guides
during
production.
As you put the portfolio together, hole punch each sheet, use string for
the binding and include extra sheets at the end. Then share your tour
with
another class. Following their tour, perhaps they can add additional
discoveries
which can be included on the extra sheets.
Once the class s Shapes Tour Portfolio is complete, present
it to another class and invite them to take your tour. Perhaps the other
class will make their own discoveries and add to the book. Include
several
blank pages to the end of the portfolio for additional ideas.
If a video tour is created, invite classroom parents in to view it and
take
the tour for themselves.
Have students create a Shapes Tour of their home (inside or out) or
neighborhood.
Have students bring in empty containers from home (perhaps from the
Suggested
Materials list), disassemble and camouflage them and create a riddle for
others to guess what the container was originally used for . Then place
their shape riddles and disassembled containers in a school display case
for a schoolwide contest. Perhaps a simple prize can be created for
correct
answers.
Language Arts: Write a follow up episode to the Flat
Earth Society cartoon.
Read the Dr. Seuss favorite, The Sneeches, and have students compare and
contrast it to the Flat Earth Society cartoon.
Create a class dictionary including definitions for the terms from the
video
segment and all of the two- and three- dimensional shapes and objects
discussed.
Encourage students to consider adding any original drawings or diagrams
that will enhance their definitions.
Social Studies: As a whole class, view the landscape architect
segment
of the selected Math Works video. As a class, brainstorm other
professions
that use geometric shapes and objects as part of their work.
Invite an architect into your class to share and discuss a portfolio of
her/his work.
Research into the life of Frank Lloyd Wright. (Access information through
CD-Rom programs such as Grolier s Encyclopedia.)
Science: Create Challenge Stations for further research into
models
and geometric shapes in nature. With a small portion of table salt and
sugar
and a magnifying glass, students can compare and contrast the two types
of crystals. Students should record their findings as well as draw a
simple
diagram representing the two samples.
Access to other mineral/crystal collections (even pictures from books)
for
students to examine will reveal naturally occurring geometric shapes.
Challenge
students to construct models of the crystals they examine using their new
knowledge about how three-dimensional objects are formed.
Create a challenge question posing the following predictions, How many
one-inch
triangles would it take to cover an orange? How many three-inch triangles
would it take to cover a basketball?
Music: Select several musical segments for students to listen to
which represent a variety of rhythms and textures such as a polka,
electronic/synthesized,
waltz, rap and classical symphony. Allow students to draw the geometric
shapes and objects they hear in the music. Students should share and
display
these perspectives.
Introduce the students to square-dancing. Point out the various shapes a
square dance forms, and ask students to explain how square-dancing
received
its name.
Encourage students to create a triangle or a circle dance.
Introduce the popular Country Western line dancing.
