Strut Your Stuff
Targeted grades: 4 - 5
Developed by Linda Cantrell and Bryan Street
OVERVIEW
Students will identify the relationship between the number of sides in a regular polygon and the number of struts (diagonals) needed to make each polygon rigid. Students are challenged to determine the least number of struts/supports they would need to add to the rectangles, pentagons, and hexagons to make them rigid. They use these patterns to see the relationship between the number of sides in a polygon and the number of struts needed to make various shapes rigid.
Students will see that a structural system must fit together with the right materials and design to carry its own weight. Finally, they will design and build a structure with newspaper rolls that will stand and support its weight.
Time: three to five 45-minute periods.
ITV SERIES
Magic School Bus #304: "Under Construction"
Additional Video
"Skyscraper: Higher and Higher" (#5 in the series)
by Films for the Humanities & Sciences, Inc.
PBS MATHLINE Videos: Elementary School Math Project
1. Struts 'n Stuff Lesson
2. Math Grows Up (Patterns/Relationships)
LEARNING OBJECTIVES
Students will be able to understand: (1) that all shapes are not rigid; and (2) that a structure can be made to fit together, stand on its own and bear its own weight with a good design and the right materials.
Materials
For the teacher
--Large summary chart
--Polygon models made from paper strips and fasteners
--Activity Sheet: "Template Page - Strips"
(TIP: precut the short and long strips from the Template Page--all the students have to do is hole-punch the ends.)
Each Student
25 strips of paper, 1 cm X 7 cm, with one hole punched close to each end
(TIP: using a heavier weight paper--"recycled" manila folders, for instance--will be easier for students to use.)
10 strips of paper, 1 cm X 30 cm, with holes punched on one end of each strip (See Activity Sheet: "Template Page - Struts")
--25 paper fasteners (1/2 inch)
--Plastic ziplock bag for paper strips
--Scissors
--2 sheets of graph paper (Activity Sheet: "Graph Grids")
--Several hole punches (students can share)
--Student journal
PRE-VIEWING ACTIVITIES
Prerequisite Knowledge: Concept of angles, polygons and design. The effect of structural systems design and variables has been introduced via experiments with physical structures. (Paper airplane designs or race car designs).
Day One
Ask: What is a system? Define a system.
Continue: What things can be changed in a system, what happens when things in a system are changed? Show a paper airplane and discuss how to change your design of the system to make it fly higher/farther. Brainstorm with the class about two-dimensional geometric shapes they have learned about. (triangle, square, rectangle, pentagon, hexagon, and others)
Continue: In your journals/learning logs draw and label the shapes we discussed. Discuss number of angles and sides of each shape.
Continue: Today I am going to give you some paper strips and paper fasteners. I want you to make a triangle, square, rectangle, pentagon and hexagon by punching holes into the ends of the strips and connecting the pieces with paper fasteners.
Demonstrate hole punching and connecting of the two strips.
Students are given plastic bags containing strips of tag paper and paper fasteners. Ask the students to make a triangle, rectangle, pentagon, and hexagon as demonstrated.
See attached sheet for specific directions on materials, copy masters and preparation of lesson.
Continue: Let's look at your structures. What have you noticed about the shapes? Allow the students to explain/demonstrate how the shapes are flexible--except for the triangle.
Continue: Why is the triangle rigid? Could we make the other shapes rigid? Discuss.
Continue: I want you to use the other strips of paper to make the other shapes rigid, we'll call them struts, I also want you to keep a record of how many struts each shape needs to make it rigid. You must follow these rules when making your shapes.
(Tip: Have these rules on a large chart in the front of the room.)
RULES:
1. The struts must go from vertex to vertex.
2. The struts may not cross each other.
3. The polygon must keep its original number of sides.
4. Use the fewest number of struts as possible to make the shape rigid.
Students use the chart below to keep a record in their journals of struts needed for each shape:
Shape Name or Picture Struts Needed
Students determine the least number of struts or supports to make their shapes rigid. They then record their findings on a chart in their journals and look for patterns. Say: Did anyone notice a pattern in your struts chart? Could you predict how many struts would be needed for any polygon? Can we state a rule for the number of sides in a polygon and the number of struts needed to make it rigid?
(Rule: sides of a polygon--minus 3--will be the number of struts needed.)
Use the graph to predict the number of struts needed to make different polygons rigid. Discuss the relationship between the number of sides of a polygon and the number of triangles formed by the struts. Students look for a pattern in order to make a generalization. Write the generalization on a chart or the chalkboard. Have the students write this in their science/math journals.
Say: Tomorrow we will be looking at triangle shapes around the school. Try to bring pictures of buildings, bridges or other structures that show how triangles are used in the construction.
Day Two
Students may bring to school samples they've seen or cut from magazines or you may use class time to tour the school, or look in magazines or books for examples of triangles used in construction for support at home and school. They can refer to books and magazines that show architecture and engineering, particularly in bridge building.
VIEWING ACTIVITIES
Tell students they will be watching a part of the video: "The Magic School Bus: Under Construction" and they will be hearing Ms. Frizzle talking about structures. She will help her students discover a way to build a structure to escape danger. Ask students to predict what designs the students might come up with.
Focus for Viewing--Ms. Frizzle's class has been shrunk and now they have to get out of a locked bathroom...they try several escape structures and get to the top of the toilet using a pyramid of blocks and hair rollers. They then decide to build a bridge across the toilet. Listen for their plan to build a successful bridge.
NOTE: VCR time codes vary from machine to machine. Times noted are approximate.
START video when the boys rip the tape, you'll hear, "Let her rip, Tim." (11:48)
PAUSE when Wanda starts across the toilet.(12:16)
Focus for Viewing--What were their strategies for building a successful bridge? (Strong joints, light enough to put into place, long enough.) Will it work?
START tape (11:58-12:24). PAUSE when the bridge breaks.
Focus for viewing--Did their strategy work? Why? Let's listen to see what will be their new strategy? Look for materials they plan to use and why they might work.
START tape (12:24-13:47}and PAUSE when Wanda says, "Isn't there some way we can stick two beams together?"
Focus for Viewing--What materials did they choose, why? (Hairpins were flexible, easy to carry and gumdrops made flexible joints). Ask class: How do you think they will join the two beams together? (Students should say they will try to make triangles with the hairpins and gumdrops.) Let's watch to see if you are right.
START video (13:47 -14:17) PAUSE when Tim does a chin up and says, "And STRONG !"
Say: Were you right? What was the quality the triangular shapes had when Tim tried to do a chin up? (They were strong and rigid.)
Continue: Watch now to see how they finish the bridge. Listen to the reasons the bridge worked this time. (Triangle power.)
Say: What POWER did Mrs. Frizzle say made the bridge work this time? (Triangle power.) What are the words the students used to describe the bridge? (Strong triangle shapes.)
More VIEWING ACTIVITIES
Say: We will be viewing another video, this time of real buildings in New York City and Chicago. You will see buildings using shapes that are strong and rigid, made of triangles. Introduce the video saying that this video will give some 'real world' reference by showing the Empire State Building, the Hancock Building, the Sears Tower and a model of a mile high building.
START "Skyscraper: Higher and Higher" video: PAUSE after the word "...skyscraper".
Focus for Viewing--I will be stopping the video to ask you if you see any "Triangle Power" being used in any of the buildings.
START video: PAUSE after David Child's says, "Halfway up is the Sears Tower"
Focus for viewing--Even though Mr. Childs was referring to a model, not a real skyscraper, what did they use on the model to make it strong and rigid? (Struts, triangles.) He will use the word DIAGONALS to tell how such a tall building could stand rigid without "racking" (twisting).... Listen.
START video: PAUSE after "...make a very, very efficient structure"
Ask: What qualities did this building have to make it an "efficient structure"? (i.e. strong, rigid...diagonal beams, concrete corners)
START video: PAUSE when announcer says, "distribute the load evenly among the vertical columns."
Ask: What makes the John Hancock building a strong and rigid structure? (Steel diagonal beams.)
Focus for Viewing--Now you will see another strategy of keeping a building strong and rigid in the Sears Tower. They talk about the bundled tube design to help the building be strong. Listen for what other design feature gives a building strength.
PAUSE after: "...skyscraper one mile high..." Ask: What is the design to build a strong structure? (Diagonal braces, bundled tubes.)
Focus for Viewing--Finally you will see a prototype (model) of a mile high, 500 story building where they again use the bundled tubes design. Listen to what other building design they combine with the building tubes to make it strong enough to be built a mile high.
START video: STOP after the architect tips over the building model to show the triangular shaped tubes and says, "...because the triangle is the most stable shape, it cannot be distorted. It gives it a rigidity that no other structure can give it."
Ask: What shapes made the structure strong and rigid? (triangular tubes)
REWIND to where he is pointing to the tubes with his pen and is saying, "...the system we have used." PAUSE.
Focus for Viewing--I am going to show this part again. This time listen to what he says about triangle shapes.
PLAY to when he tips over the model and says "It gives it a rigidity that no other structure can give it." STOP. Ask: What did he say about triangle shapes? (They are the most efficient structures, they have a rigidity that no other structure has.) What did you notice about the bundled triangles when the architect showed you the ends of the bundles? (They formed a large triangle.)
Ask: What did you learn about how to build super structures like sky scrapers? (They need to use triangle shapes for rigidity and strength.) How do they stay standing? (The design and plan uses triangular shapes.) What would you advise builders like Ms. Frizzle's kids when they want to build a tall escape structure?
Day Three:
(TIP: have the students roll the newspaper rolls before this part of the lesson. Also, more tape will not make the roll hold better, but the WAY they put on the tape will make a difference.)
Show students how to roll the newspaper and tape the ends so it stays rolled. Also show them techniques on how to join the joints of the rolled papers to keep them together. Tell them that if they use the tape in a figure 8 fashion it will hold the joints well.
Say: Now that you are experts on building structures, you will build a structure big enough to walk into and strong enough to stay standing.
These are the building materials we will be using. As a team you will build a wall to be joined with the other team walls until we have a space large enough to walk inside. We won't be building a ceiling. Somehow we will figure out where the door should be!
Remember to use your knowledge of how to build strong structures like the ones you saw on the Skyscraper and Magic School Bus videos.
Your team should combine the rolls of newspaper to create a wall about 10 feet by 6 feet using as few rolls as possible. When all walls are finished we will combine them to make a small room.
Your team needs to draw a possible design of your wall. Think about strategies to use as few rolls as possible. I will be watching your team to see how you use your design and I will be listening for your newly learned vocabulary words: struts, rigidity, triangle, structures, systems.
After the structure is built, debrief. Ask: What were some of your problems, how did you solve them?
Assessment: In their science journals students write to Mrs. Frizzle's class and advise them on how to successfully build a tall, rigid, and strong building. Have them include a finished design of their building. Label parts of their design showing scientific principles that give it the ability to stand.
(TIP: before beginning the structure the class might develop it's own rubric for a successful design and wall. What would this wall look like if the students used principles of science and mathematical knowledge?)
ACTION PLAN
Tour the school and grounds looking for structures using triangles for support, "triangle power".
Walking tour of local business area looking for structures supported by triangles.
Visit a construction site of a house or city skyscraper, have the builder explain strategies for support for the building.
Invite an architect or engineer to visit the classroom to discuss design and building support systems.
Collect pictures of buildings, structures using triangular support systems to highlight on a bulletin board.
Take photographs of "triangle power" structures for the bulletin board.
EXTENSIONS
Build the tallest tower possible with toothpicks and gumdrops.
Build a toothpick and gumdrop bridge between two equal stacks of books high enough to hang a cup from the bridge. Test the strength of the bridge by hanging a small cup from the bridge, adding pennies to the cup until the bridge collapses.
Draw world-wide structures showing "triangle power", see the x-ray books of Big Buildings of the Ancient World and Buildings of the Modern World.
Developed by Linda Cantrell and Bryan Street
OVERVIEW
Students will identify the relationship between the number of sides in a regular polygon and the number of struts (diagonals) needed to make each polygon rigid. Students are challenged to determine the least number of struts/supports they would need to add to the rectangles, pentagons, and hexagons to make them rigid. They use these patterns to see the relationship between the number of sides in a polygon and the number of struts needed to make various shapes rigid.
Students will see that a structural system must fit together with the right materials and design to carry its own weight. Finally, they will design and build a structure with newspaper rolls that will stand and support its weight.
Time: three to five 45-minute periods.
ITV SERIES
Magic School Bus #304: "Under Construction"
Additional Video
"Skyscraper: Higher and Higher" (#5 in the series)
by Films for the Humanities & Sciences, Inc.
PBS MATHLINE Videos: Elementary School Math Project
1. Struts 'n Stuff Lesson
2. Math Grows Up (Patterns/Relationships)
LEARNING OBJECTIVES
Students will be able to understand: (1) that all shapes are not rigid; and (2) that a structure can be made to fit together, stand on its own and bear its own weight with a good design and the right materials.
Materials
For the teacher
--Large summary chart
--Polygon models made from paper strips and fasteners
--Activity Sheet: "Template Page - Strips"
(TIP: precut the short and long strips from the Template Page--all the students have to do is hole-punch the ends.)
Each Student
25 strips of paper, 1 cm X 7 cm, with one hole punched close to each end
(TIP: using a heavier weight paper--"recycled" manila folders, for instance--will be easier for students to use.)
10 strips of paper, 1 cm X 30 cm, with holes punched on one end of each strip (See Activity Sheet: "Template Page - Struts")
--25 paper fasteners (1/2 inch)
--Plastic ziplock bag for paper strips
--Scissors
--2 sheets of graph paper (Activity Sheet: "Graph Grids")
--Several hole punches (students can share)
--Student journal
PRE-VIEWING ACTIVITIES
Prerequisite Knowledge: Concept of angles, polygons and design. The effect of structural systems design and variables has been introduced via experiments with physical structures. (Paper airplane designs or race car designs).
Day One
Ask: What is a system? Define a system.
Continue: What things can be changed in a system, what happens when things in a system are changed? Show a paper airplane and discuss how to change your design of the system to make it fly higher/farther. Brainstorm with the class about two-dimensional geometric shapes they have learned about. (triangle, square, rectangle, pentagon, hexagon, and others)
Continue: In your journals/learning logs draw and label the shapes we discussed. Discuss number of angles and sides of each shape.
Continue: Today I am going to give you some paper strips and paper fasteners. I want you to make a triangle, square, rectangle, pentagon and hexagon by punching holes into the ends of the strips and connecting the pieces with paper fasteners.
Demonstrate hole punching and connecting of the two strips.
Students are given plastic bags containing strips of tag paper and paper fasteners. Ask the students to make a triangle, rectangle, pentagon, and hexagon as demonstrated.
See attached sheet for specific directions on materials, copy masters and preparation of lesson.
Continue: Let's look at your structures. What have you noticed about the shapes? Allow the students to explain/demonstrate how the shapes are flexible--except for the triangle.
Continue: Why is the triangle rigid? Could we make the other shapes rigid? Discuss.
Continue: I want you to use the other strips of paper to make the other shapes rigid, we'll call them struts, I also want you to keep a record of how many struts each shape needs to make it rigid. You must follow these rules when making your shapes.
(Tip: Have these rules on a large chart in the front of the room.)
RULES:
1. The struts must go from vertex to vertex.
2. The struts may not cross each other.
3. The polygon must keep its original number of sides.
4. Use the fewest number of struts as possible to make the shape rigid.
Students use the chart below to keep a record in their journals of struts needed for each shape:
Shape Name or Picture Struts Needed
Students determine the least number of struts or supports to make their shapes rigid. They then record their findings on a chart in their journals and look for patterns. Say: Did anyone notice a pattern in your struts chart? Could you predict how many struts would be needed for any polygon? Can we state a rule for the number of sides in a polygon and the number of struts needed to make it rigid?
(Rule: sides of a polygon--minus 3--will be the number of struts needed.)
Use the graph to predict the number of struts needed to make different polygons rigid. Discuss the relationship between the number of sides of a polygon and the number of triangles formed by the struts. Students look for a pattern in order to make a generalization. Write the generalization on a chart or the chalkboard. Have the students write this in their science/math journals.
Say: Tomorrow we will be looking at triangle shapes around the school. Try to bring pictures of buildings, bridges or other structures that show how triangles are used in the construction.
Day Two
Students may bring to school samples they've seen or cut from magazines or you may use class time to tour the school, or look in magazines or books for examples of triangles used in construction for support at home and school. They can refer to books and magazines that show architecture and engineering, particularly in bridge building.
VIEWING ACTIVITIES
Tell students they will be watching a part of the video: "The Magic School Bus: Under Construction" and they will be hearing Ms. Frizzle talking about structures. She will help her students discover a way to build a structure to escape danger. Ask students to predict what designs the students might come up with.
Focus for Viewing--Ms. Frizzle's class has been shrunk and now they have to get out of a locked bathroom...they try several escape structures and get to the top of the toilet using a pyramid of blocks and hair rollers. They then decide to build a bridge across the toilet. Listen for their plan to build a successful bridge.
NOTE: VCR time codes vary from machine to machine. Times noted are approximate.
START video when the boys rip the tape, you'll hear, "Let her rip, Tim." (11:48)
PAUSE when Wanda starts across the toilet.(12:16)
Focus for Viewing--What were their strategies for building a successful bridge? (Strong joints, light enough to put into place, long enough.) Will it work?
START tape (11:58-12:24). PAUSE when the bridge breaks.
Focus for viewing--Did their strategy work? Why? Let's listen to see what will be their new strategy? Look for materials they plan to use and why they might work.
START tape (12:24-13:47}and PAUSE when Wanda says, "Isn't there some way we can stick two beams together?"
Focus for Viewing--What materials did they choose, why? (Hairpins were flexible, easy to carry and gumdrops made flexible joints). Ask class: How do you think they will join the two beams together? (Students should say they will try to make triangles with the hairpins and gumdrops.) Let's watch to see if you are right.
START video (13:47 -14:17) PAUSE when Tim does a chin up and says, "And STRONG !"
Say: Were you right? What was the quality the triangular shapes had when Tim tried to do a chin up? (They were strong and rigid.)
Continue: Watch now to see how they finish the bridge. Listen to the reasons the bridge worked this time. (Triangle power.)
Say: What POWER did Mrs. Frizzle say made the bridge work this time? (Triangle power.) What are the words the students used to describe the bridge? (Strong triangle shapes.)
More VIEWING ACTIVITIES
Say: We will be viewing another video, this time of real buildings in New York City and Chicago. You will see buildings using shapes that are strong and rigid, made of triangles. Introduce the video saying that this video will give some 'real world' reference by showing the Empire State Building, the Hancock Building, the Sears Tower and a model of a mile high building.
START "Skyscraper: Higher and Higher" video: PAUSE after the word "...skyscraper".
Focus for Viewing--I will be stopping the video to ask you if you see any "Triangle Power" being used in any of the buildings.
START video: PAUSE after David Child's says, "Halfway up is the Sears Tower"
Focus for viewing--Even though Mr. Childs was referring to a model, not a real skyscraper, what did they use on the model to make it strong and rigid? (Struts, triangles.) He will use the word DIAGONALS to tell how such a tall building could stand rigid without "racking" (twisting).... Listen.
START video: PAUSE after "...make a very, very efficient structure"
Ask: What qualities did this building have to make it an "efficient structure"? (i.e. strong, rigid...diagonal beams, concrete corners)
START video: PAUSE when announcer says, "distribute the load evenly among the vertical columns."
Ask: What makes the John Hancock building a strong and rigid structure? (Steel diagonal beams.)
Focus for Viewing--Now you will see another strategy of keeping a building strong and rigid in the Sears Tower. They talk about the bundled tube design to help the building be strong. Listen for what other design feature gives a building strength.
PAUSE after: "...skyscraper one mile high..." Ask: What is the design to build a strong structure? (Diagonal braces, bundled tubes.)
Focus for Viewing--Finally you will see a prototype (model) of a mile high, 500 story building where they again use the bundled tubes design. Listen to what other building design they combine with the building tubes to make it strong enough to be built a mile high.
START video: STOP after the architect tips over the building model to show the triangular shaped tubes and says, "...because the triangle is the most stable shape, it cannot be distorted. It gives it a rigidity that no other structure can give it."
Ask: What shapes made the structure strong and rigid? (triangular tubes)
REWIND to where he is pointing to the tubes with his pen and is saying, "...the system we have used." PAUSE.
Focus for Viewing--I am going to show this part again. This time listen to what he says about triangle shapes.
PLAY to when he tips over the model and says "It gives it a rigidity that no other structure can give it." STOP. Ask: What did he say about triangle shapes? (They are the most efficient structures, they have a rigidity that no other structure has.) What did you notice about the bundled triangles when the architect showed you the ends of the bundles? (They formed a large triangle.)
Ask: What did you learn about how to build super structures like sky scrapers? (They need to use triangle shapes for rigidity and strength.) How do they stay standing? (The design and plan uses triangular shapes.) What would you advise builders like Ms. Frizzle's kids when they want to build a tall escape structure?
Day Three:
(TIP: have the students roll the newspaper rolls before this part of the lesson. Also, more tape will not make the roll hold better, but the WAY they put on the tape will make a difference.)
Show students how to roll the newspaper and tape the ends so it stays rolled. Also show them techniques on how to join the joints of the rolled papers to keep them together. Tell them that if they use the tape in a figure 8 fashion it will hold the joints well.
Say: Now that you are experts on building structures, you will build a structure big enough to walk into and strong enough to stay standing.
These are the building materials we will be using. As a team you will build a wall to be joined with the other team walls until we have a space large enough to walk inside. We won't be building a ceiling. Somehow we will figure out where the door should be!
Remember to use your knowledge of how to build strong structures like the ones you saw on the Skyscraper and Magic School Bus videos.
Your team should combine the rolls of newspaper to create a wall about 10 feet by 6 feet using as few rolls as possible. When all walls are finished we will combine them to make a small room.
Your team needs to draw a possible design of your wall. Think about strategies to use as few rolls as possible. I will be watching your team to see how you use your design and I will be listening for your newly learned vocabulary words: struts, rigidity, triangle, structures, systems.
After the structure is built, debrief. Ask: What were some of your problems, how did you solve them?
Assessment: In their science journals students write to Mrs. Frizzle's class and advise them on how to successfully build a tall, rigid, and strong building. Have them include a finished design of their building. Label parts of their design showing scientific principles that give it the ability to stand.
(TIP: before beginning the structure the class might develop it's own rubric for a successful design and wall. What would this wall look like if the students used principles of science and mathematical knowledge?)
ACTION PLAN
Tour the school and grounds looking for structures using triangles for support, "triangle power".
Walking tour of local business area looking for structures supported by triangles.
Visit a construction site of a house or city skyscraper, have the builder explain strategies for support for the building.
Invite an architect or engineer to visit the classroom to discuss design and building support systems.
Collect pictures of buildings, structures using triangular support systems to highlight on a bulletin board.
Take photographs of "triangle power" structures for the bulletin board.
EXTENSIONS
Build the tallest tower possible with toothpicks and gumdrops.
Build a toothpick and gumdrop bridge between two equal stacks of books high enough to hang a cup from the bridge. Test the strength of the bridge by hanging a small cup from the bridge, adding pennies to the cup until the bridge collapses.
Draw world-wide structures showing "triangle power", see the x-ray books of Big Buildings of the Ancient World and Buildings of the Modern World.
