


Prep for Teachers
Download the Shockwave plugin, available at http://www.macromedia.com
to computers that will be used during the lesson. CUE
the videotape to the appropriate starting point, which is when
the opera singer with the horned helmet is standing on platform
singing. Prepare the handouts for the lesson by providing a copy
for each student. Also, give each student (or small group of students)
two plastic bags: Materials Set #1 and Materials Set #2 as described
below.

Materials Set #1
 25 strips (1/2 inch by 3 inches) cut from manila folders, with
one hole punched close to each end of the strip
 10 strips (1/2 inch by 6 inches) cut from manila folders, with
one hole punched close to one end of each strip
 25 paper fasteners
Materials Set # 2
 "Building
a Bridge" Activity Worksheet
 30 wooden stirrers
 Several rolls of pennies
 Centimeter ruler
 Paper towels
Have the glue available when beginning the Culminating Activity,
but do not include the glue in the bag of Materials Set #2. This
will encourage the students to complete the Activity Sheet and make
their sketches before beginning assembly of their model. Once they
have shown their completed handout and sketch to the teacher, then
the teacher may issue the glue.
When using media, provide the students with a FOCUS FOR
MEDIA INTERACTION, a specific task to complete and/or information
to identify during or after viewing video segments, Web sites, or
other multimedia elements.

The world of mathematics is one that works in
tandem with science. This lesson is designed to show students how
valuable it is to use models to solve problems. Students will build
a model of a bridge, and then test it for strength. The activity
begins with a discussion about what a model is and how models are
used in the real world.
Step 1:
Ask students: "Have you ever seen a model of something? What
kind of model was it?"(Accept all answers.) Ask your students
what are some other examples of models? (Students answers will vary;
they may answer with examples of model airplanes, model cars, architectural
models, etc.) Ask students what the difference is between a model
and the thing it represents? (A model is simpler, cheaper, and smaller.
It is a simplified version of something complicated that allows
you to easily and safely understand how it works.) Why do people
sometimes build models before building the real thing? (Cost, size,
effort. It's easier to make a change to a model than to make
a change to a real thing. A model can help you see how something
will work. Also, a model is portable. You can easily show it to
others.)
Step 2:
Tell the class that later on in the lesson, they will be building
a model of a bridge. But before they get started, it is important
to discover shapes that make a structure strong. Ask the students
to make simple shapes using the materials in the bag (Set #1). The
shapes they construct out of the paper strips and fasteners should
include, but should not be limited to, a square, parallelogram,
pentagon, and triangle. Tell the students to try to create as many
flat shapes as possible given the materials in front of them. Allow
students to punch additional holes in the paper strips to create
their shapes. Ask them to show the shape to the class by raising
it up in the air when finished. As students share their shapes,
have them also describe what shape they have made.
Ask them to investigate which shape is the strongest  which holds
its shape when you try to make it collapse? (One way to test a shape
is to hold it upright and push down on it.) Ask your students to
determine which shape is the most rigid? Is a square rigid? Why
or why not? (A square is not rigid. It collapses.) You might want
to point out that as the square collapses, it forms a shape (a rhombus)
that still has four equal sides, but the angles are not right angles.
Ask your students if a rectangle is rigid? (It also collapses easily.)
How about a triangle? (Triangles seem to be the strongest  the
most rigid  of the paper shapes, and can't be collapsed as readily.)
Might a triangle be a useful shape to use when building a model
of a structure? (Yes.) If students made a pentagon or hexagon, discuss
them at this point. Note that they both collapse and are not rigid.
Ask: How could you make the square or rectangle more rigid? (Add
internal supports.)
Step 3:
Explain to students that they have just used models to explore which
shapes are strong and which are not. Their models helped them discover
some of the geometric characteristics of the shapes. Before the
class begins building their own models of a bridge, they will examine
how the Cyberchase kids use models to solve their problems. At this
point in the lesson, have the students place their shapes and extra
strips back in the bag to lessen distraction during the video.
The Cyberchase episode "Modeling Behavior," will help
emphasize some of the concepts introduced in the Introductory Activity.
Provide the students with a FOCUS FOR MEDIA INTERACTION,
asking them to log on to the "Meet the Characters" page of the Cyberchase
Web site at http://pbskids.org/cyberchase/meet.html
and look at the page and list the main characters. This will allow
the students to become more familiar with the characters. If the
students are familiar with the characters, this step may be skipped.
After students have viewed the site, their list of characters should
include:
Inez, Matt, and Jackie – The Cyberchase kids
Digit their sidekick, a talking cyberbird
Motherboard and Dr. Marbles guardians of Cyberspace
Hacker – the villain, out to destroy the Motherboard and gain
control over Cyberspace
Buzz and Delete – Hacker's evil sidekicks
Step 1:
CUE Cyberchase #122: "Modeling Behavior"
to the point of the video where an opera singer with a horned helmet
is standing on a platform singing. Provide the students with a FOCUS
FOR MEDIA INTERACTION, asking them to describe the problem
the Cyberchase kids have encountered with the table. PLAY
the tape.
Step 2:
PAUSE the tape when the platform topples over the
first time and the town crier says, "Hear ye, hear ye. The
platform has collapsed and the wicked witch is not happy."
Ask students why the platform did not support the wicked witch?
Ask students to state what would be a logical plan of action in
solving the problem (Students should brainstorm for possible solutions
and choose the most logical.) What would you suggest to the Cyberchase
kids to help them solve the problem with the broken platform? (Listen
to student suggestions but do not correct them as of yet.) Let's
see if the Cyberchase kids will follow the class' suggested
solution of fixing the table.
Step 3:
Provide your students with a FOCUS FOR MEDIA INTERACTION,
asking students to determine why the Cyberchase kids' solution
doesn't work. PLAY the video. PAUSE the video when the platform
falls for the second time. Check for student comprehension, and
have students state what was wrong with the Cyberchase kids'
solution (Allow students time to fully describe the solution, this
is as important as completing the problem). Ask students what shape
is formed by the legs of the platform, the platform and the floor?
(A rectangle.) And what do we know about rectangles? (They collapse.)
Have students pull out the geometric shapes they formed in the Introductory
Activity and review that the triangle was the only shape that makes
a figure rigid. How can they make the other shapes rigid? (Add internal
supports or braces on a diagonal, thus making the shape supported
by rigid triangles.) Have students make the square rigid. For example:
Have the participants use the longer strip to make a brace for the
square. Fasten one end and then cut the strip so it "fits."
Punch a hole in this end and attach. Note that this creates a diagonal
that forms two triangles. Point out that the square is now rigid!
Discuss how the use of a physical model helped test the mathematical
idea that solved the problem. Discuss the different ways the braces
could be placed and the importance of a model. It can be changed
or modified easily, cheaply, quickly, and safely.
Students may also choose to could also make their other shapes rigid
by adding internal braces at this point in the lesson.
Step 4:
Provide your students with a FOCUS FOR MEDIA INTERACTION,
asking your students to determine if Jackie's solution is
similar to their solution for strengthening the paper shapes. PLAY
the video until the Cyberchase kids reinforce the platform with
the additional boards. STOP the video when the
three pigs are holding hands, spinning around, and singing, "Ashes,
ashes, we all fall down." Ask the students if any of their
models were close to or just like Jackie's model. How was
Jackie's experience with the model different from Matt and
Inez's experience with trying their ideas on the real thing?
(Jackie didn't use a physical model. She used a computer model,
the Sqwak pad, and was able to change certain things to solve the
problem. This was a computer model, which functions like a physical
model. The kids used the real pieces of the platform, which took
considerably more time, and wasn't very safe.) Whose job is
easier? Who gets to the solution faster? (Student answers will vary.)
Step 1:
Explain to students that it is time to use the skills learned in
problem solving using models. Tell the students to imagine that
the President of the United States is holding a contest and would
like for the class to engineer the creation of a new bridge over
the Potomac River in Washington, DC. The bridge must be very sturdy.
He is seeking the most outstanding engineer, who can create the
strongest bridge. The only problem is that the bridge must not cost
a lot of money. Keeping cost in mind, it would be in the best interest
of the President and his budget to make a model of the bridge rather
than make many mistakes while building the real bridge. The winner
of the best bridge (strongest yet costing the least) will receive
the Presidential Award of Engineering. The winner will be determined
by how many rolls of pennies the bridge can hold before breaking.
Step 2:
Give each student or group Materials Set #2, and distribute the
"Building
A Bridge" Activity worksheet to each student.
Step 3:
The handout lists the exact dimensions the bridge should be built
using only the materials in the bag. The criteria is as follows:
 Length of the bridge: 30 cm long
 Width of the bridge or roadbed: 5 cm wide
 Height of the bridge or clearance: 10 cm tall
 Cost of the bridge: $10 per wooden stirrer (students may opt
to use additional stirrers but the cost of the bridge will increase
with each stirrer).
 The bridge must be constructed at school using only the materials
in the bag or the glue issued. No other reinforcing materials
may be used.
 Wooden stirrers can be broken to construct the bridge. Remind
students that they will need to keep track of the total number
of stirrers in their bridge.
Step 4:
To prevent students from moving ahead with the building process,
retain all the bottles of glue until they have filled out the questions
on the handout. This will reinforce problem solving and encourage
them to create a sketch before building. Review with students the
concepts the Cyberchase kids used in building reinforcements on
the platform. (Determining the problem, brainstorming a solution,
making a sketch showing how all the parts fit together, and building
the model and testing it.) Students may wish to visit the bridge
Web sites listed at the beginning of this lesson for inspiration
and ideas.
Step 5:
Have students sketch out their ideas for their bridge. Students
may manipulate the wooden stirrers around to help give them ideas
for their sketch. Once the students have shown the teacher their
handouts and a sensible sketch, issue them the glue.
Step 6:
The building process may take more than one class period. Some of
the wood pieces will need to dry before completing the construction.
One of the questions on the handout asks the students to describe
what parts of the bridge will be constructed on day 1, and what
parts will be built on day 2. This helps the student to know that
the bridge will need drying time before proceeding to the next part.
Step 7:
Set up for the bridge test by pushing two desks close together (not
touching). Place a bridge on the two desks so the ends of the bridge
rest on each edge of the desks, spanning the gap between. Make sure
each bridge tested has the same amount of bridge surface touching
each desk. Begin placing rolls of pennies on the bridge. When the
bridge breaks, have the students record how many rolls of pennies
their bridge was able to hold. Be sure to thoroughly tape up the
rolls of pennies so they don't fall all over your classroom
floor.
Step 8:
Have students complete their Activity Sheets and write on the board
the cost of their bridges and the number of rolls of pennies the
bridges held. Ask students if their sketches were helpful in the
construction process. (Students will offer a variety of answers.)
Ask your students how they would you modify their model or bridge?
(Listen to student responses.) Award the student with the most outstanding
bridge based on the criteria listed above (most cost efficient,
held the most weight). Ask students to describe what they discovered
about bridgebuilding, how they would change their approach if they
could do it again, and how making a model made it easier to test
the strength of the structure rather than building the real thing.
Art
Students can research different shapes and designs of bridges. Such
designs could include all types of materials. Have student draw
versions of their model incorporating unusual yet useful materials
into the overall design of the bridge.
Social Studies
Students may want to research how the existence or destruction of
bridges have been instrumental in numerous wars (i.e. Civil War,
World War I or II etc.) The following Internet sites might be useful
in composing a report on such a topic:
 The significance of building temporary pontoon bridges in
the Civil War.
http://www.kenmore.org/farmcivilwar.html
 The soldiers built bridges across swamps to deceive the enemy.
http://americancivilwar.com/tl/tl1865.html
 The allies attempted to capture bridges to open the way into
Germany.
http://history.searchbeat.com/worldwar.htm
 Throughout World War II in the Pacific, North Africa, and
Europe high performance medium bombers were employed successfully
against bridges destroying them and the enemy's access to American
troops.
http://www.nasm.si.edu/galleries/gal205/gal205.html
 Research other occupations that create models before actually
building structures or objects.
 Create a list of places in your community where architectural
models are showcased.
 Invite an architect or engineer into your classroom to discuss
how they use models in their professional life.

