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POLY WANT A HEDRON?
MASTER TEACHER Lori Fleet
MATH AND SCIENCE
GRADES 4-6
OVERVIEW
This lesson provides students with an opportunity to use their
knowledge of two-dimensional shapes as they view the three-dimensional world.
Through interaction, students make associations between polygons and
polyhedrons. Characteristics of both polygonal shapes and polyhedrons are
presented by architects, engineers, inventors, and scientists. Students
will use Euler's mathematical plan to discover geometric patterning in
polyhedrons. Plateau's scientific theory of surface tension is
conceptualized as students relate geometry to real world applications.
ITV SERIES
The Eddie Files:#3 Invasion of the Polygons
Math Vantage:#5Networks, Path and Knots
LEARNING OBJECTIVES
Students will be able to:
*define, locate, and identify polygons and polyhedrons
*discover what a polyhedron is and make comparisons/contrasts to
polygons
*make polyhedrons with prior knowledge of polygons
*experiment with Euler's Theorem by making bubble patterns
inside of polyhedrons
*analyze and predict the benefits of knowing about geometric
structures (2-D and 3-D) and Joseph Plateau's principle of surface tension
*identify and list various occupations that use geometry as a
basis for problem solving, creativity, and exploration
MATERIALS
(per student)
1 Poly-puzzle (see File Folder Flips - attached )
1 Polyhedron formula chart
1 Polyhedron prediction chart
1 pencil
1 student journal or notebook paper
1 bottle of glue
1 pair of scissors
(per group of four)
1 newspaper
1 large plastic container
1/2 cup of liquid dish soap
water to fill plastic container
6 plastic sandwich bags each containing one of the following
sets:
(1)70 raisins (inexpensive raisins that have
hardened work best)
(2)50-60 toothpicks
(3)1 small spool of thread
(per class)
posters of regular polygons
Vis-´å-Vis markers
Polyhedrons made with toothpicks and raisins
VOCABULARY
polygon
regular polygons
polyhedron
(polyhedrons included within the lesson:
octahedron, tetrahedron, triangular prism, pentagonal prism, hexagonal prism,
octagonal prism, and a cube.)
vertices (vertexes)
edge
face
pyramid
surface tension
morph (slang term for metamorphosis)-
A complete change in form or appearance.
PREVIEWING ACTIVITIES
(Prior to lesson, have students arranged in groups of four.
Also, throughout the entire lesson, keep a running list of the various
occupations that use geometry as a basis for problem solving, creativity, and
exploration.) Hold up pictures of regular polygons in view of the students.
Ask for volunteers to point out specific traits of various polygons.
Elicit discussion leading to the conclusion that the word polygon comes
from the Greek language. Tell students that "polys" means many,
and "gonia" means angle. Thus, a polygon is a shape with many
angles. Tell students that polygons are two-dimensional shapes.
Elicit discussion with students leading to the conclusion that 2-D shapes are
flat, having length and width.
Say, "Now, students, I am going to show you some more
shapes." (Show students polyhedrons made with raisins and toothpicks.)
Have students discuss in their groups the various characteristics of the
presented shapes. Have each group briefly share what they discovered about
the three-dimensional shapes. List all appropriate traits of the 3-D
figures while students are sharing them with the large group. Say,
"Mathematicians have a name for these three dimensional shapes and they are
called polyhedrons. We know that "poly" means many, and our new
word "hedron" means sides. Thus, polyhedron means what,
class?" (A shape with many sides.)
Distribute poly-puzzles (file folder flips) and ask each
student to try and match the appropriate polygon or polyhedron with their name
and definition.
Ask, "Did you identify the polygons and polyhedrons
correctly?"
Provide an opportunity for students to share the similarities
between polygons and polyhedrons. Also, have students point out the
differences between the 2-D and 3-D shapes.
FOCUS FOR VIEWING
To give students a specific responsibility for viewing say,
"You are going to see a video that shows a teacher holding and discussing a
geometric shape. I am going to turn off the sound to see if we can come up
with a description similar to that stated in the video."
VIEWING ACTIVITIES
The Eddie Files #3 Invasion of the Polygons
Begin tape immediately following Eddie's
introduction to Mrs. Toliver's geometry lesson. Video is Mrs. Toliver
holding a polyhedron; audio is Mrs. Toliver saying, "What are some of the
characteristics and things you would talk about in writing a description of this
structure?" Eliminate Audio. Pause tape with visual of a
female student pointing to polyhedron while Mrs. Toliver is holding it.
Allow an opportunity for students to approach the television and mark off
various polygons on the polyhedron using a Vis-´å-Vis. Also, elicit
discussion about the differences between polygons and polyhedrons. Say,
"How do you know that the structure Mrs. Toliver is holding is a
polyhedron?" (It takes up space and has length, width, and depth.)
Wipe off television screen. Resume sound.
Rewind tape to where you formerly eliminated the
audio. Say, "I want you to listen to Mrs. Toliver ‘s class as they
describe the same shape that you just did. Listen for similarities and
differences in their description. Resume tape. Pause video with
visual of Mrs. Toliver smiling and holding the polyhedron saying, "See, I
am loaded with magic this morning. You didn't know that." Ask,
"Did we come up with the same description as Mrs. Toliver's class?"
Discuss. Say, "Many times, polygons and polyhedrons are found in
structures. I want you to locate and identify polygons and polyhedrons
that you see in this video of Eddie in New York City."
Fast forward and begin tape with visual of
Hispanic construction worker; audio is, "You, what are you doing
here?" Pause tape when construction worker says, "But
there." Visual is large beams of partially completed building.
Using a Vis-´å-Vis on the television screen have students locate polyhedrons
and polygons within the construction site. Elicit discussion of the
variety and quantity of shapes. Wipe off screen after discussion. Resume
tape and ask students to listen to see if their answers compared to those of
the construction workers.
Pause tape with visual of building rooftops; audio is
music. Ask a student to highlight the building that has a green roof with
a Vis-´å-Vis while the class determines what type of shape it is. (Triangular
prism.) Say, "Why do you think that this roof is shaped this
way?" Discuss various appropriate responses. Wipe off the
television screen. Say, "Francis Halsband is an architect who
uses shapes. Listen to Mrs. Halsband as she describes how she designed
Penn Station. I want you to tell me in your own words how an architect
uses shapes when designing a building. Also, what type of
information is needed when a person designs a building?" Resume tape.
Pause tape with visual of New York City at night;
audio is Frances Halsband saying, "Seeing a drawing come to life and become
a real piece of a city. That's pretty exciting!" Ask students
to elaborate how Ms. Halsband used shapes to design Penn Station. (She
used shapes to draw various buildings. She used shapes of other buildings
to compare with the building she was making.) Ask students what
information Ms. Halsband needed prior to designing Penn Station. (Who, what,
when, where, and why.) Say, "Now, I want you to listen to a
structural engineer. Listen carefully so that you can tell me what a
structural engineer does and how he uses shapes." Resume tape.
Pause tape with visual of Ysrael Seinuk, structural
engineer, talking to Eddie; audio is Seinuk saying, "But there are many
other structures that have nothing to do with a tall building."
Elicit discussion about how shapes can become stronger. (Folds on flat shapes,
2-D made into 3-D.) Show students a square and a cube made with toothpicks
and raisins so that they can conceptualize structure strength. Ask
students to define what a structural engineer does. (Makes sure buildings are
engineered correctly, structures stand correctly.) Say, "Now, let's
listen and watch an inventor, Chuck Hoberman, who uses polygons and polyhedrons
in his work. After this video segment, I want you to tell me what it means
to morph a shape." Resume tape.
Pause tape with large Hoberman structure; audio is
Hoberman saying, "Just imagine what can be that isn't there yet.
That's the first step of inventing." Ask students to share without
words what it means to morph a shape. (Charade.) Discuss orally metamorphosis of
shapes. (Shape changing into another, relate to the study of topology.)
POSTVIEWING ACTIVITIES
Divide class into groups of four students each. Say,
"Today we are going to be an inventor like Chuck Hoberman."
Distribute the polyhedron formula and prediction chart. Also, give
students the group materials to make geo-panes (bags with raisins, toothpicks
and thread). As a group, have students place the names of the polyhedrons
on their formula chart. Once students have completed the former task,
check for understanding, and have students glue the names of the polyhedrons
onto their chart. Have students make the first four shapes of the
polyhedron formula chart (A-D). Each student in the group makes a
different shape. Using raisins and toothpicks students build their
polyhedrons. Once the shapes are constructed, show students Euler's
Theorem on the chalkboard. (Vertices + Faces - Edges = 2) Tell students
that the relationship of vertices (raisins), edges (toothpicks), and faces was
first discovered by Leonard Euler in the 16th century. His theorem is true
for all convex or outward facing polyhedrons. Say, "Now students,
with the knowledge of Euler's Theorem we will calculate the relationship between
vertices, edges, and faces." (Tetrahedron [4+4]-6=2, Cube
[8+6]-12=2, Triangular Prism [6+5]-9=2, Pyramid [5+5]-8=2)
Say, "Inventors use mathematics and patterning in their
work to create. Now let's morph our shapes by dipping them into the soap
mixture. But first, try and predict what type of bubble shape or
"pane" will be formed in each structure." (You may have to dip
the square made of raisins and toothpicks to show the students what a geo-pane
is.) After the students have made their predictions, they may dip their
polyhedrons by threading a thin piece of string through the shape. Once
students have had the opportunity to dip their shapes a couple of times, elicit
discussion about the principle of surface tension. (Shapes will not follow the
edges as might be expected. Surprises in store.) Tell students that long ago a
physicist named Joseph Plateau found that the attraction of the molecules to one
another pulls the soap bubble to the smallest possible area. (Students write
results on their prediction worksheet and in their math journals after they
discuss molecular attraction with their teammates.)
Students will need to complete the remaining shapes (E-H)
during the next class period.
Prior to completing the second part of the geo-pane lesson, view
the ITV series called Math Vantage: Network, Paths & Knots. The former
will reinforce the first part of the lesson and is excellent for an oral
assessment. Reserve time for each group to report their geo-pane
discoveries to the class. Following the last group's presentation, conduct
a class discussion leading to the uses of polyhedrons and geo-panes in the real
world.
ACTION PLAN
Arrange a field trip to an urban area where there are many types
of buildings. Have students record findings of polygons and polyhedrons in
their math journals.
Arrange a walking field trip throughout a neighborhood
near your school. Walk with students around the school, on the playground,
and down a residential block. Have students locate polygons and
polyhedrons in their own
surroundings. Students record their findings in their math
journals.
Invite an architect, structural engineer, or an inventor to
visit your classroom. Ask her/him to discuss how structures are used in
their occupational planning.
EXTENSIONS
Language Arts
Have students build a town of many structures. Once
students have completed the task, ask them to name their structural city and
write a descriptive essay.
Have students write poems using shapes. Good examples
of shape poetry might be an inverted triangle poem or a concentric poem.
Math
In a group, have students build the tallest free-standing
structure with 30 gumdrops and 30 toothpicks. Make sure that students have
a planning session where they can draw their ideas before they build their
structures.
Art
Have students make poly-me-mobiles with paper polyhedron
patterns. Students can decorate the polyhedrons with pictures of
themselves.
Science and Medicine
Explore the area of DNA studies and how its pattern is a
geometric network. Ask the school nurse to share some information on DNA.
Have students make up a play with the DNA information that they receive.
Technology
Explore the internet finding on-line female and minority
mentors who use geometry in their jobs. Have students communicate with
their mentors and share their experience with the class. NASA Space Center
might be a good place to start!
NAME______________ FORMULA
CHART
"POLY WANT A HEDRON?"
A POLYHEDRON IS_______________________.
EULER'S THEOREM IS_____________________.
 
NAME________________
"POLY WANT A HEDRON?"
Cut apart polyhrdron names and use
them on the prediction chart.
___________MY GEO-PANE DISCOVERIES__________
NAME______________PREDICTION
CHART
"POLY WANT A HEDRON?"
Make a prediction! What geo-pane
pattern will appear with each shape? Record your thoughts. As a
group, take turns dipping each shape into the soapy water. Record your
results.
We Predict
Results 
Updated: April 01, 2008
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