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Lesson Plans
Modeling Mania
OverviewProcedure for teachersStudent Resources and Materials
Prep for Teachers

Download the Shockwave plug-in, 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.

Introductory Activities: Setting the Stage

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.


Learning Activities

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 cyber-bird
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.)


Cross-Curricilar Extensions

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:
  1. Length of the bridge: 30 cm long
  2. Width of the bridge or roadbed: 5 cm wide
  3. Height of the bridge or clearance: 10 cm tall
  4. 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).
  5. 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.
  6. 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 bridge-building, 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.


Cross-Curricilar Extensions

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:
  1. The significance of building temporary pontoon bridges in the Civil War.
    http://www.kenmore.org/farmcivilwar.html
  2. The soldiers built bridges across swamps to deceive the enemy.
    http://americancivilwar.com/tl/tl1865.html
  3. The allies attempted to capture bridges to open the way into Germany.
    http://history.searchbeat.com/worldwar.htm
  4. 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

Community Connections
  • 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.