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Can You Stand on Me?

Printable ResourcesCan You Stand on Me?

Appendix A: Forces Pre-Test and ANSWER KEYAppendix B: Transcript of "Africa Colors A Destiny" Presentation/Background

Reading – Service LearningAppendix C: Journal TemplateAppendix D: Forces Review and ANSWER KEYAppendix E: Engineering Design ChallengeAppendix F: Engineering Design Challenge RubricAppendix F: Team Career RolesAppendix H: Engineering Design Challenge Introduction: Exit SlipAppendix I: “What is it About Bees and Hexagons?” ArticleAppendix J: Transformation Mini-Lesson: Guided Notes (Student & Teacher copies)Appendix K: Pack It Up! Challenge: DirectionsAppendix L: Pack It Up! Challenge: Shape TemplateAppendix M: Pack It Up! Challenge: Justify It!Appendix N: Pack It Up! Challenge: 3-Sentence Essay Exit/Entrance SlipAppendix O: Decision Analysis Matrix InstructionsAppendix P: Table Testing: Quantitative and Qualitative DataAppendix Q: 3–2–1 Entrance/Exit SlipAppendix R: Reflection InterviewAppendix S: Presentation RubricAppendix T: Google SketchUP Reference CardsAppendix U: Engineering Technical Brief–Additional Technical Information for Students/Teacher

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Appendix A: Pre/Post-TestName _____________________________ Date ____________ Period _____1. There are no horizontal forces acting on the boat below because it is not moving.

Draw a force diagram around the image to represent two forces acting on the boat. (2 points)

2. Are the forces you drew on the boat above balanced or unbalanced? Using domain-specific words, provide reasoning for your answer. (2 points)

3. Explain which of the two diagrams demonstrates balanced forces. Refer to the diagram(s) in order to provide evidence for your explanation.Draw upon your prior knowledge, and use domain-specific, science vocabulary to explain what is happening to the speed of both the rocket and the boat. (4 points)

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4. Compare and contrast what happens to your weight and to your mass when you get a haircut. (2 points)

5. The amount of matter in an object is called its:A. massB. balanceC. forceD. weight

6. The forces of gravity acting on a person or object at the surface of a planet is known as:A. massB. air resistanceC. inertiaD. weight

7. The greater the mass of an objectA. the less force it can exert.B. the more space it takes up.C. the more balance it has.D. the greater its inertia.

8. An example of a balanced force is…A. a car sliding on ice.B. a tug-of-war game in which no one wins.C. a car hitting a telephone pole.D. a roller coaster going down the first loop.

9. An example of an unbalanced force (net force) isA. a car parked in the garageB. a tug-of-war game in which no one winsC. a bridgeD. a roller coaster going down the first drop

10. In physical science, a push or pull is called a(n)A. gravityB. forceC. universal lawD. inertia

11. When two equal forces act on the same object in opposite directions, the net force isA. a push force.B. greater than either force.C. zero.D. smaller than either force.

12. You are an engineer given the task of designing a table able to withstand the greatest amount of weight. What would your first step be in the engineering design process? Justify your response with scientific reasoning. (2 points)

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13. Provide an example of something that could take place to make the forces acting on the table and book below become unbalanced. Justify your response using scientific reasoning and domain-specific words. (2 points)

In the diagram below, a transformation of parallelogram 1 resulted in parallelogram 2.

14. Which transformation or transformations were used? Describe the movement with regard to direction and the X-axis and/or Y-axis. (4 points)

15. Robert designed an aluminum chest used to transport desk parts overseas for a medical office. The length is 2 meters, the width is 0.5 meters, and the height is 0.5 meters. How many cardboard cylinders will he be able to fit if their height is 0.5 meters and their diameter is 10 centimeters? Provide your answer and an explanation as to how you arrived at your answer: (2 points)

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16. The diagram to the right shows a transformation of trapezoid 1 resulting in trapezoid 2. What type of transformation was used? What was the magnitude of the transformation? (2 points)

17. The right triangle shown is translated 6 units to the right and 3 units down and reflected across the y-axis.Graph the resulting transformations. What property of the triangle that will remain the same? _____________________(2 points)

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Appendix A: Pre/Post-Test – ANSWER KEYName _____________________________ Date ____________ Period _____1. There are no horizontal forces acting on the boat below because it is not moving.

Draw a force diagram around the image to represent two forces acting on the boat. (2 points)

2. Are the forces you drew on the boat above balanced or unbalanced? Using domain-specific words, provide reasoning for your answer. (2 points)

1 point: labeled upward force 1 point: labeled downward force 2 points: The forces on the boat are balanced because there is no movement indicated on the

surface of the water.

3. Explain which of the two diagrams demonstrates balanced forces. Refer to the diagram(s) in order to provide evidence for your explanation.Draw upon your prior knowledge, and use domain-specific, science vocabulary to explain what is happening to the speed of both the rocket and the boat. (4 points)

1 point: The forces on the boat are balanced because the force arrows are equal and opposite 1 point: The speed of the rocket will accelerate upward; I know because the force arrow of the thrust

from the rocket is longer than the force area of the weight. 1 point: The boat is not moving and I know that because the force arrows are equal and opposite in

length. I can also observe that the water does not appear to be moving indicating no motion is taking place.

1 point: for providing evidence and using domain-specific, science vocabulary in their explanations.

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Force of the water upward

Weight of the boat downward


4. Compare and contrast what happens to your weight and to your mass when you get a haircut. (2 points)

Mass is the amount of matter that something has, so when I cut my hair my mass changes very slightly because some of the matter that was a part of my person has been removed. Student may create a before and after sketch or use a t-chart to show a before and after comparison.

Weight is dependent on the force of gravity on a person or object, so when I cut my hair my weight varies slightly just as it does when I eat or put on a heavy coat.

5. The amount of matter in an object is called its:A. massB. balanceC. forceD. weight

6. The forces of gravity acting on a person or object at the surface of a planet is known as:A. massB. air resistanceC. inertiaD. weight

7. The greater the mass of an objectA. the less force it can exert.B. the more space it takes up.C. the more balance it has.D. the greater its inertia.

8. An example of a balanced force isA. a car sliding on ice.B. a tug-of-war game in which no one wins.C. a car hitting a telephone pole.D. a roller coaster going down the first loop.

9. An example of an unbalanced force (net force) isA. a car parked in the garage.B. a tug-of-war game in which no one wins.C. a bridge.D. a roller coaster going down the first drop.

10. In physical science, a push or pull is called a(n)A. gravityB. forceC. universal lawD. inertia

11. When two equal forces act on the same object in opposite directions, the net force isA. a push force.B. greater than either force.C. zero.D. smaller than either force.

12. You are an engineer given the task of designing a table able to withstand the greatest amount of weight. What would your first step be in the engineering design process? Justify your response with scientific reasoning. (2 points)

Accept all reasonable responses that reflect at least 2 steps in the process for 2 points and 1 point if they can identify at least 1 step.

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13. Provide an example of something that could take place to make the forces acting on the table and book below become unbalanced. Justify your response using scientific reasoning and domain-specific words. (2 points)

In the example of the table with the book, the forces could become unbalanced if you added enough books to the surface that the table structure could no longer support them. The force diagram would change then with the weight of the books causing more force downward due to weight than the table could withstand.

In the diagram below, a transformation of parallelogram 1 resulted in parallelogram 2.

14. Which transformation or transformations were used? Describe the movement with regard to direction and the X-axis and/or Y-axis. (2 points)

The parallelogram has been translated to the right across the Y-axis. It was also rotated in a direction, which can described as clockwise.

15. Robert designed an aluminum chest used to transport desk parts overseas for a medical office. The length is 2 meters, the width is 0.5 meters, and the height is 0.5 meters. How many cardboard cylinders will he be able to fit if their height is 0.5 meters and their diameter is 10 centimeters? Provide your answer and an explanation as to how you arrived at your answer: (2 points)

100 cylinders will fill the box. The cylinders diameter is converted from 10 centimeters to .1 meters. Since they have to fill square compartments the diameter is squared to get the area dimension of a similarly sized square shape. You will reach the answer multiplying .5 meter by 2 meter to get the area of the box and divide by the similar “square” area of the cylinder.

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16. The diagram to the right shows a transformation of trapezoid 1 resulting in trapezoid 2. What type of transformation(s) was/were used? What was the magnitude of the transformation? (2 points)

There has been a reflection and a slide that moved the trapezoid across the Y-axis, and 3 units. down.

17. The right triangle shown is translated 6 units to the right and 3 units down and then reflected across the y-axis.Graph the resulting transformation. What properties of the triangle will remain the same? size and shape (they are congruent)(2 points)

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Appendix B: Transcript of "Africa Colors A Destiny" Presentation/Background Reading – Service Learning

By Michael Varga; Country of Chad; Dates of Service: 1977-1979Related Publication: Watch slide show | Africa Colors A Destiny

Slide show Can also be found at: https://www.youtube.com/watch?v=5p9haTyq5mYHi, my name is Michael Varga. I was a Peace Corps Volunteer in Chad, Central Africa. That's me standing next to a camel. I was 21 years old at an animal market outside of N'djamena, the capital of Chad. People were selling camels and goats and sheep and cattle. I wasn't used to being around animals since I had grown up in Philadelphia.My Peace Corps service taught me to be comfortable with foreigners, and to have confidence in my linguistic abilities. I learned how much I enjoyed functioning in another language. It also made me much more aware of cultural sensitivities in dealing with people who have grown up in a different environment with different values. I learned that "different" did not mean inferior, and this helped me to succeed later in life as a diplomat in the U.S. Department of State. I had learned how to show understanding and compassion when negotiating with representatives of other countries. In Africa, I was a "minority" for the first time in my life, and I learned how important it is for everyone to feel that he or she gets a fair shake. Chad allowed me to re-define myself as a citizen of the world, and not just a boy from Philadelphia.We were about twenty Peace Corps Volunteers who arrived that summer. As we wandered through the animal market, Chadians were calling out, "Narsara! Narsara!" This is the word commonly used in Chad for a white-skinned person. Some Chadians speak Arabic or French, as well as an African language, depending on which tribe they belong to. But this word "Narsara" was used by most Chadians to refer to white people. The Peace Corps sent me to Baibokoum, a village of about four thousand people in southern Chad. I was to teach English at the high school. Baibokoum is very isolated—far from other villages and the muddy roads, so it is impassable much of the year when during the rainy season those roads become soupy rivers. Most Chadians didn't have cars. Some had bicycles or donkeys to get around. But most Chadians get from village to village by hopping into the back of pick-up trucks and paying the drivers for the ride. Since the roads are not paved, the rains sometimes cause all travel to stop.The living conditions in Baibokoum were tough. No running water, no electricity. I had to walk three miles to the Logone River to wash. Many days I didn't have time to walk there and had to buy a bucket of river water at the market. I used a coffee mug to pour some water over me, pushed a bar of soap over my body, and then rinsed off. It's amazing to learn how you can stretch one bucket of water so far. Because water was a scarce commodity, whenever we would have rain Chadians used to run and position containers—plastic tubs, buckets, earthen jars—in the open fields to collect water. The same water we would use to wash our hands before a meal—we didn't have forks and knives but used our hands to eat—was used after the meal to wash the dishes and cooking pot.I was the only Narsara living in Baibokoum, although there were some itinerant Italian priests who came through sometimes to run a little Catholic mission.Since my house had been vacant for months, the sous-prefet, a kind of mayor, told me I could stay in his guest house until all of the snakes were cleared out. But just when I arrived, the prefet, his boss, decided to visit, so I had to go to my derelict house that first night. I didn't get much sleep and kept a kerosene lamp burning to try to keep the snakes away from me. Fortunately, they stayed away.My house was made of concrete with a tin roof. This was much more than most Chadians had. They lived in huts made from dried mud with a thatched straw roof. This photo shows how dry things became during the dry season. After that first night, I set up my mosquito net over my bed and had a short wave radio to get news from the BBC or the Voice of America. Otherwise, I wouldn't know what was happening in the rest of the world. Mosquito nets were very important since mosquitoes carry a lot of diseases, and they would swarm during the rainy season. Even though I took my

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medications, I got malaria a couple of times. I would be feverish, shaking with chills, yet perspiring in the African heat. The symptoms sometimes lasted for days. But I was lucky. The Peace Corps had provided me with a first aid kit with medications to rely on. Chadians often had no medical care. Pills were sold at the village market, and Chadians often asked me to translate the instructions. But many times the pills were sold loosely—not even in any container—and so no one had any idea what the pills were for or how harmful they might be.The market was very close to my house. It was divided up into two sections. One section had rows of women lined up to sell peanuts and peanut butter, bananas, tomatoes, lettuce, spices, and plant roots. The women chattered through the morning, and in the afternoon when the sun got too hot, they would go home and prepare a meal for their families.Men controlled the other part of the market—little shops that sold woven mats, rice, soap, and canned goods imported from Europe. They also slaughtered a cow or goat to sell the pieces, but sometimes—especially during the dry season—there would be no meat to eat. The dry season generally lasted from October until April. Chadians who had stored grain to eat often ran out during the dry season, and it was not uncommon for my students sometimes to go days without food. Some of the bolder students used to ask me for food, but some were too ashamed, and I had to try to make sure no one starved. The school was just a simple concrete structure with a tin roof and no glass in the windows. Supplies were scarce. We distributed just one notebook to each student for the whole school year, so students had to be very careful about what they would write down. Some months we ran out of chalk, so it was hard to teach English without being able to write anything on the blackboard. There weren't enough teachers, so sometimes I had to teach French and mathematics, too. Each class I taught had about eighty students in it, although they were almost all boys since girls rarely got an education at that time and were often married young and began having children in their teens. Classes were held from 7:00 a.m. until 12:30 p.m. It was too hot in the afternoons, so that's when I used to work at the village medical dispensary or work at the library at the Catholic mission. Friends in the U.S. sent me magazines and books to stock the library.Although Chad is a very poor country, Chadians used to save up some money to visit a photo studio and have their photos taken. Here are some friends in a typical Chadian pose. That's me wearing a specially embroidered Chadian shirt. Here are some Chadians wearing traditional clothes in the bush. They wore western-style clothes to school, but liked to wear their African traditional garb at home in the bush. The Peace Corps Coverdell World Wise Schools program used an essay I wrote, "A Straw Fence The Height Of A Man," in its book Uncommon Journeys. In this photo, you can see what straw fences were like in Chad. The people took a lot of pride in weaving together the stalks to create something very durable and strong. These fences were used to separate groups of huts from each other.Chad produces a lot of cotton and peanuts, and those were the predominant crops that people used to farm to make money. This is a cotton collection station. People would bring their cotton harvests and load it onto the big trucks. The government hired people to stomp it down. You can see them on the top of the truck.Chadians use fermented millet to make their own alcoholic drink, called bili-bili. This is a bili-bili stand that, especially on Sundays, would be filled—mostly with men—passing around a calabash of bili-bili and sharing stories. During my second year, civil war broke out, and all Americans were evacuated. We rode in an overland convoy to Cameroon, the country to the west of Chad. But the war worsened, and we couldn't return to Chad.After the Peace Corps, I devoted myself to my diplomatic career and to writing. I have drawn many times on stories from my experiences abroad, beginning with those years in Chad. Much of the resiliency, creativity, and perseverance I learned derives from my time in Chad, where I was so challenged. The Peace Corps opened so many doors for me. Thank you for sharing this little bit of my journey with me.

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Appendix C: Journal Template

Name _____________________________ Date ____________ Period ______

What are some of the challenges individuals in third world countries must face on a daily basis?

Brainstorm ideas for ways in which these individuals may overcome these challenges.

Choose three of your ideas and explain how individuals may profit from each.

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Appendix D: Forces Review

Name _____________________________ Team Name: ________________________

A FORCE is defined as a PUSH or PULL. When forces are BALANCED, the forces pushing (or pulling) on an object in one direction

are the same size as the forces acting in the opposite direction. When forces are UNBALANCED, the forces pushing an object in one direction are greater

than the forces pushing the object in the other direction. (Also known as the resultant or NET FORCE)o When an object is at rest or moving at a constant speed, it has a net force of zero.

Directions: Use arrows to identify the forces acting on each of the 3 objects shown below.

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What does Gravity have to do with it?The natural force of attraction between objects = GRAVITY.

As an object’s height above ground level increases, the energy gained is known as the objects GRAVITATIONAL POTENTIAL.WEIGHT, or Force due to gravity acting on an object (measured in Newtons)


Appendix D: Forces Review ANSWER KEY

Use arrows to identify the forces acting on the objects shown below.

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Other forces on the bike and car may include wind resistance and rolling Friction- be open to other ideas that students generate!

Gravity

Gravity

Gravity

GravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravity

GravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravityGravity


Appendix E: Engineering Design ChallengeName _____________________________ Date ____________ Period ______

Starting Date: __________ Completion Date: __________

Engineering Design Challenge:

Visitors to many schools in underdeveloped countries have found that students suffer from a lack of technology. In some areas, students do not even have access to a flat surface on which to write. Service

groups and industries in the United States have shown interest in providing learning materials for students of such schools. When groups ship materials overseas, packages must be as compact as possible in order

to save space as well as shipping fees.Therefore, your team's challenge is to create a desk that will serve the basic needs of a primary student in

underprivileged areas. In order to efficiently pack and ship desks stacked together, your team’s design must be easy to unassembled and reassemble as necessary. For cost savings and ease of shipping, the total, unassembled and packed up desks must be lightweight and able to ship in flat, stackable packaging.

Established Prototype Design Criteria: No smaller than 30 cm x 30 cm x 30 cm No larger than 60 cm x 60 cm x 60 cm Hold at least 100 kg (200 lbs.) of weight (text books) Include a flat surface for writing Made from cardboard, packing tape and/or glue

Engineering Design ProcessUsing an analytical and experimental process to design complex systems that meet stated objectives and take into account specific scientific and societal constraints.

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Ask:What is the need or problem?What have others done?What are the constraints and criteria?

Think:What are some possible solutions?Brainstorm ideas and choose the best ones.

Plan:Write your plan for solving the problem.Draw a diagram of your solution.Make a list of materials you will need.

Test:Follow your plan for solving the problem.Test your solution.

Improve:Think about design modifications.Make a plan for implementing modifications.Follow your plan and test again.


Appendix F: Engineering Design Challenge RubricName _____________________________ Date ____________ Period _____

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4 3 2 1

Engineering

Design Process/

FinalPrototype

Prototype is built on time according to height, width, and material constraints.

Prototype tested successfully and able to hold at least 15 ponds.

Final design can be replicated.

Prototype is built on time, and tested, but follows only 2 out of 3 constraints.

Final design can be replicated.

Prototype is built and tested, but follows only 1 out of 3, constraints, OR is not completed on time.

Final design needs further clarification to be replicated.

Prototype is built and tested, but loosely follows 1 out of 3 constraints, OR is not completed on time.

Final design cannot be replicated.

Decision Analysis

Matrix

Team fully utilizes the Decision Analysis Matrix by identifying at least 5 goals and rankings for use in design selection.

Team scores and calculates each proposal in order to come to a consensus about the best design choice.

Team fully utilizes the Decision Analysis Matrix by identifying 4 goals and rankings for use in prototype design selection.


Team utilizes the Decision Analysis Matrix by identifying 2 or 3 goals and rankings for use in design selection.


Team utilizes the Decision Analysis Matrix, but does not identify objectives and/or rankings for use in design selection.OR, team does not properly score and calculate each proposal in order to come to a consensus about the best design choice.

Reflection

All artifacts display in-depth understanding of content.Student reflection includes all of the following: Journal Exit Slip Think, Pair,

Share 3,2,1 3 Sentence

Essay

All artifacts display understanding of content.Student reflection includes 4 out of 5 of the following: Journal Exit Slip Think, Pair,


Essay

All artifacts display partial understanding of content.Student reflection includes 3 out of 5 of the following: Journal Exit Slip Think, Pair,


Essay

All artifacts display partial understanding of content.Student reflection includes 1 or 2 out of 5 of the following: Journal Exit Slip Think, Pair,


Essay

Interview

Student interviews 3 or more individuals and records detailed responses to all assigned questions.

Student interviews 2 individuals, and records detailed responses to all assigned questions.

Student interviews 2 individuals, but records limited responses to all assigned questions.

Student interviews 1 individual, or records limited responses to all assigned questions.

Design Critique

Articulates specific areas for both the prototype’s design improvement(s) and design success.

Articulates multiple considerations for implementing full-scale design.

Represents ideas for improvement and full-scale design considerations graphically.

Articulates specific areas for both prototype’s design improvement(s) and design successes.


Articulates specific areas for prototype design improvement(s).


Articulates areas for prototype design improvement(s).


Omissions in details are evident.


Appendix G: Team Career Roles

Name _____________________________ Date ____________ Period _____

DrafterAssigned to: __________________________

Leads team in designing of the project and translating the idea onto paper. Ensures that the design is complete and thorough, containing all necessary measurements and structural details.

Industrial EngineerAssigned to: __________________________

Evaluates materials available and leads the team in using those materials in the most efficient possible way. Oversees safety, cost, quality control and control of environmental concerns.

Packaging EngineerAssigned to: __________________________

Leads the team in the research necessary to begin construction of a cardboard table. Determines in what ways to use the cardboard and what type of/how much cardboard is needed for the project to be successful.

Structural EngineerAssigned to: __________________________

Leads in the analysis of the strength of the final product so it will be successful. Helps with the design process by determining the best shape, or combination of shapes, that will be strong, yet lightweight.

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Appendix H: Engineering Design Challenge Introduction: Exit SlipName _____________________________ Date ____________ Period _____

1. Compare some of the challenges faced in underdeveloped countries to those in the United States.

2. What career were you assigned within your team? How will you fulfill your role?

3. In regards to the challenge given, begin the brainstorming process by briefly explaining two ideas for best completing the challenge.


Appendix H: Engineering Design Challenge Introduction: Exit SlipName _____________________________ Date ____________ Period _____

1. Compare some of the challenges faced in underdeveloped countries to those in the United States.

2. What career were you assigned within your team? How will you fulfill your role?

3. In regards to the challenge given, begin the brainstorming process by briefly explaining two ideas for best completing the challenge.

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Appendix I: “What is it About Bees and Hexagons?” ArticleWhat Is It About Bees And Hexagons?

By ROBERT KRULWICH May 14, 2013 9:50 AMhttp://www.npr.org/blogs/krulwich/2013/05/13/183704091/what-is-it-about-bees-and-hexagons

Solved! A bee-buzzing, honey-licking 2,000-year-old mystery that begins here, with this beehive. Look at the honeycomb in the photo and ask yourself: (I know you've been wondering this all your life, but have been too shy to ask out loud ... ) Why is every cell in this honeycomb a hexagon?

Bees, after all, could build honeycombs from rectangles or squares or triangles...

Robert Krulwich/NPRBut for some reason, bees choose hexagons. Always hexagons.

And not just your basic six-sided hexagon. They like "perfect" hexagons, meaning all six sides are of equal length. They go for the jewelers' version — precise, just so. Why?

Well, this is a very old question. More than 2,000 years ago, in 36 B.C., a Roman soldier/scholar/writer, Marcus Terentius Varro, proposed an answer, which ever since has been called "The Honeybee Conjecture." Varro thought there might be a deep reason for this bee behavior. Maybe a honeycomb built of hexagons can hold more honey. Maybe hexagons require less building wax. Maybe there's a hidden logic here.

I like this idea — that below the flux, the chaos of everyday life there might be elegant reasons for what we see. "The Honeybee Conjecture" is an example of mathematics unlocking a mystery of nature, so here, with help from physicist/writer Alan Lightman is Varro's hunch.

The Essential HoneycombHoneycombs, we all know, store honey. Honey is obviously valuable to bees. It feeds their young. It sustains the hive. It makes the wax that holds the honeycomb together. It takes thousands and thousands of bee hours, tens of thousands of flights across the meadow, to gather nectar from flower after flower after flower, so it's reasonable to suppose that back at the hive, bees want a tight, secure storage structure that is as simple to build as possible. So how to build it? Well, suppose you start your honeycomb with a cell like this ... a totally random shape, no equal sides, just a squiggle...

If you start this way, what will your next cell look like? Well, you don't want big gaps between cells. You want the structure tight. So the next cell will have to be customized to cling to the first, like this...

And the third cell, once again, will have to be designed to fit the first two. Each cell would be a little different, and that means, says Alan Lightman. This method of constructing a honeycomb would require that the worker bees work sequentially, one at a time, first making once cell, then fitting the next cell to that, and so on.

But that's not the bee way. Look at any YouTube version of bees building a honeycomb, says Alan, and you won't see a lot of bees lounging about, waiting for their turn to build a cell. Instead, everybody's working. They do this collectively, simultaneously and constantly.So a "squiggle cell plan" creates idle bees. It wastes time. For bees to assemble a honeycomb the way bees actually do it, it's simpler for each cell to be exactly the same. If the sides are all equal — "perfectly" hexagonal — every cell fits tight with every other cell. Everybody can pitch in. That way, a honeycomb is basically an easy jigsaw puzzle. All the parts fit.

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http://www.npr.org/blogs/krulwich/2013/05/13/183704091/what-is-it-about-bees-and-hexagons


OK, that explains why honeycomb cells are same-sized. But back to our first question: Why the preference for hexagons? Is there something special about a six-sided shape?Some shapes you know right away aren't good. A honeycomb built from spheres would have little spaces between each unit, creating gaps that would need extra wax for patching. So you can see why a honeycomb built from spheres wouldn't be ideal. Pentagons, octagons also produce gaps. What's better?

"It is a mathematical truth," Lightman writes, "that there are only three geometrical figures with equal sides that can fit together on a flat surface without leaving gaps: equilateral triangles, squares and hexagons."

So which to choose? The triangle? The square? Or the hexagon? Which one is best? Here's where our Roman, Marcus Terentius Varro made his great contribution. His "conjecture" — and that's what it was, a mathematical guess — proposed that a structure built from hexagons is probably a wee bit more compact than a structure built from squares or triangles. A hexagonal honeycomb, he thought, would have "the smallest total perimeter." He couldn't prove it mathematically, but that's what he thought.

Compactness matters. The more compact your structure, the less wax you need to construct the honeycomb. Wax is expensive. A bee must consume about eight ounces of honey to produce a single ounce of wax. So if you are watching your wax bill, you want the most compact building plan you can find.And guess what?

Two thousand thirty-five years after Marcus Terentius Varro proposed his conjecture, a mathematician at the University of Michigan, Thomas Hales, solved the riddle. It turns out, Varro was right. A hexagonal structure is indeed more compact. In 1999, Hales produced a mathematical proof that said so.

As the ancient Greeks suspected, as Varro claimed, as bee lovers have always thought, as Charles Darwin himself once wrote, the honeycomb is a masterpiece of engineering. It is "absolutely perfect in economizing labor and wax."

The bees, presumably, shrugged. As Alan Lightman says, "They knew it was true all along."

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Appendix J: Transformation Mini-Lesson: Guided Notes (2-Page Student Copy)

Name _____________________________ Date ____________ Period _____

Transformation Description/Names

Shape Coordinates

Draw It NewCoordinates

Translation

Dilation

Reflection

Rotation

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Trace the “cut out” shape in quadrant “A”

Reflect it across the Y-axis.

Explain why the transformed shape is congruent or similar.


Translate it across the X-axis.



Rotate it around the intersection of the X-axis and Y-axis.



Dilate two points so that the shape remains the same but is larger.


Appendix J: Transformation Mini-Lesson: Guided Notes (2-Page TEACHER Copy)

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Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:CongruentDefinition:

SimilarDefinition:


Transformation Description/Names

Shape Coordinates

Draw It NewCoordinates

Translation Slide

A(−9 ,10)B(−8 ,3)C (−4 ,3)D(−2 ,10)

A(1 ,10)B(2 ,3)C (6 ,3)D(8 ,10)

Dilation Stretch

A(−8 ,8)B(−10 ,3)C (−5 ,3)D(−3 ,8)

A(−10 ,9)B(−12 ,4)C (−5 ,3)D(−3 ,8)

Reflection Flip

A(−6 ,8)B(−9 ,5)C (−8 ,1)D(−4 ,1)E(−2,5)

A(6 ,8)B(9 ,5)C (8 ,1)D(−4 ,1)E(−2,5)

Rotation Turn

A(−9 ,10)B(−9 ,3)C (−1 ,3)

A(−8 ,5)B(−1 ,5)C (−1 ,3)

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Reflect it across the Y-axis.


The shape is flipped over, but has the same angles and side lengths.


Translate it across the X-axis.


The shape slides over, but has the same angles and side lengths.


Rotate it around the intersection of the X-axis and Y-axis.


The shape turns, but has the same angles and side lengths.


Dilate two points so that the shape remains the same but is larger.


The figure has larger side lengths, but remains similar since angles do not change.

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Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Cut Out:Congruent

Definition:Two shapes are congruent if you can Turn, Flip and/or slide one so it fits exactly on the other.

SimilarDefinition:In Geometry, two shapes are Similar if the only difference is size


Appendix K: Pack It Up! Challenge: Directions

1. Each team has 4 copies of the “Pack It Up! Challenge: Shape Template” sheet. Use a glue stick to attach each whole sheet to a piece of corrugated cardboard.

2. Cut the cardboard along each shape’s dotted lines.

3. Now, your challenge is to make the smallest package possible by piecing all of the cardboard shapes together. Maximum Work Time = 5 minutes

4. Measure length, width, and height of your package (to the longest extending point).

5. Calculate volume of the package by multiplying the greatest measurements for length, width, and height.

6. Using the “Pack it Up Challenge: Justify It” sheet, diagram and explain six transformations your team used to complete the challenge.

7. Using a mini presentation format- present your package shapes to the class. Including:

A. one way each transformation was used (translation, reflection and rotation).

B. reasoning for specific packing methods

C. total calculated volume.

Can You Stand on Me?Appendix K: Pack It Up! Challenge: Directions

1. Each team has 4 copies of the “Pack It Up! Challenge: Shape Template” sheet. Use a glue stick to attach each whole sheet to a piece of corrugated cardboard.

2. Cut the cardboard along each shape’s dotted lines.

3. Now, your challenge is to make the smallest package possible by piecing all of the cardboard shapes together. Maximum Work Time = 5 minutes

4. Measure length, width, and height of your package (to the longest extending point).

5. Calculate volume of the package by multiplying the greatest measurements for length, width, and height.

6. Using the “Pack it Up Challenge: Justify It” sheet, diagram and explain six transformations your team used to complete the challenge.

7. Using a mini presentation format- present your package shapes to the class. Including:

A. one way each transformation was used (translation, reflection and rotation).

B. reasoning for specific packing methods

C. total calculated volume.

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Appendix L: Pack It Up! Challenge: Shape Template(4 Copies per team)

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Appendix M: Pack It Up! Challenge: Justify It!

Name _____________________________ Date ____________ Period _____

Cite 6 more examples of transformations in the table below. Explain the purpose of the transformation with the “Pack it Up!” challenge. An example has been provided for you.

Transformation Draw Shape Diagram Movement Explanation

Translation

The parallelograms can slide to the end of the bunch in order to place a trapezoid beside it.

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Appendix N: Pack It Up! Challenge: 3-Sentence Essay Exit/Entrance Slip

Name _____________________________ Date ____________ Period _____

1

State the big idea of the “Pack It Up! Challenge.”

2

Cite the math-learning standard/goal.

3

Connect the idea to your prior knowledge, and provide evidence of newly gained knowledge or understanding.

Final Essay: Combine the 3 sentences you wrote above into a final 3-sentence essay below.

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Appendix O: Decision Analysis Matrix Instructions

Decision Analysis Techniques in Engineering DesignMethod of Weighted Factors

Margaret Pinnell, PhD

This method of decision analysis can be used whenever a difficult choice must be made such as choosing a college or a certain product, etc. Step-by-step instructions for using

this method as a tool for assessing design plan ideas are provided below.

Identifying the objectives and constraints for a particular topic can assist in make a final decision. Safety should always be on the list, but some other items might include

aesthetics, cost, ease of maintenance, performance (ability to function as intended), recyclability, etc.

Instructions for Using the Matrix:

1. Determine the relative importance of each of these objectives and constraints, and rank them from 1 – 10 with 10 being the most important and 1 being of little importance (may be nice to have, but doesn’t really matter). All constraints will be rated a 10.

2. As a team, discuss each conceptual design, and rank the designs from 1-n in its ability to meet the identified objectives or constraints. For example, if you are analyzing three different designs, you will rank those designs from 1-3, with 3 being the best and 1 being the least. In some cases, the designs may have equal performance and they might get the same rating, an example of this is shown below.

3. For each design, multiply the attributed (objective or constraint) weighting factor by the rank, and add up a total score.

4. The design that has the highest score may be considered the “best.” Keep in mind though, that there is a significant amount of subjectivity to this approach, so if two designs have very close values, you may want to consider these designs a little more deeply.

An example is provided below for purchasing a car. This was done through the eyes of a college student who is looking for a new car to transport her from home to school. The ranking was done without any research, but certainly actual values could be obtained from reliable resources regarding relative safety, cost, gas mileage etc. If this information is available, this research should be done, but this is just a quick example. The college student, with input from her parents, identified the following factors that would help her decide which car to purchase. They decided that safety was, by far, the most important factor.

Since this was for a college student, cost-related issues including price of the car, cost of upkeep/maintenance and gas mileage were all very important as well. The student didn’t really have more than a suitcase that she would need to carry, so cargo room was not that important, but would be nice to have in case she did have some larger things to bring home. Also, since she only needed the car to last her through her 4 (or 5) years in college, the “life span” of the car was only marginally important. The college student protested regarding aesthetics, after all, she wanted a cool ride, so aesthetics were pretty important to the student. The student considered three cars available at a dealer close to her home.

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(Decision Analysis Matrix Instructions Continued)

Resultant Sheet:

Results of this decision analysis suggest that car 1 is the best choice for the student. However, had these factors been weighted differently, the results might have changed.

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Design 1

__________________Name

Design 2

__________________Name

Design 3

__________________Name

Design 4

__________________Name

Goals(Constraints and

Objectives)Weight Score Value

(weight x score) Score Value(weight x score) Score Value

(weight x score)Score Value

(weight x score)

TOTAL VALUESum of values:

_______

Sum of values:

_______

Sum of values:

_______

Sum of values:

_______

1. After all group members have presented their design ideas, use the numerical system below to score each design against the constraints and objectives.

3 = totally meets the goal 2 = somewhat meets the goal 1 = does not meet the goal2. Add the values for each design to determine a total score. The design with the highest score may be considered the “best.” Keep in mind

though, that some of the scoring is based on opinion, so if two designs have close values, you may want to consider these designs a little more deeply, or combine their best attributes.

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Appendix P: Table Testing: Quantitative and Qualitative DataName _____________________________ Date ____________ Period _____

Volume and Surface AreaBefore Adding Weight

Volume: Unassembled DeskPacked Flat and Ready to Ship

Surface Area: Assembled DeskSetup and Ready for Student Use

Calculated Volume (V): Calculated Surface Area (SA):

In what ways could your team minimize the volume of your packaged, ready-to-ship desk? Refer to specific details about your design to justify your answer.

Are the dimensions within the engineering design challenge’s given criteria? Refer to specific details about your design to justify your answer.

Durability Testing

Hypothesize

How much weight do you think your team’s structure will be able to hold?Refer to specific details about your design to justify your answer.

Quantitative and Qualitative DataHint: As weight is added, watch for deflection or failure and repeat until your desk reaches failure without being destroyed.

Weight Number:_____

Weight Number:_____

Weight Number:_____

Weight Number:_____

Weight Number:_____

Weight Number:_____

Weight Number:_____

TotalFinal weight supported

www.daytonregionalstemcenter.org

http://www.daytonregionalstemcenter.org/

Can You Stand On Me?

Appendix Q: 3–2–1 Entrance/Exit SlipName _____________________________ Date ____________ Period _____

3List three things that were completed in class today.

2Name two things that you would have done differently within your design.

1What is one question or comment that you have for the teacher?

Can You Stand on Me?Appendix Q: 3–2–1 Entrance/Exit SlipName _____________________________ Date ____________ Period _____

3List three things that were completed in class today.

2Name two things that you would have done differently within your design.

1What is one question or comment that you have for the teacher?

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Appendix R: Reflection InterviewInterviewee Name _____________________________ Date _________ Period ____

Interviewer Name _____________________________

Share and discuss the following questions with at least 3 people from other design teams. Your questioning should mimic a job interview.

1. How much weight was your table able to hold? Were you and your team satisfied with these results?

2. What was the volume of your team’s desk when unassembled, packed flat, and ready to ship? Are you satisfied with these results? Why or why not? Refer to specific details about your design to justify your answer.

3. What was the surface area of your team’s desk when assembled, setup, and ready for students to use? Are you satisfied with these results? Why or why not? Refer to specific details about your design to justify your answer.

4. Describe strategies your team used throughout the engineering design process while completing the challenge. Refer to specific details about ways in which your team followed the engineering design process design to support your answer.

5. After the first testing session, in what ways did your team modify the design in order to enhance table’s strength, volume, and surface area? Refer to specific details about your design to justify your answer.

6. Did your teams chosen design modifications produce successful results? How much weight was your table able to hold during the second testing session? Refer to specific details about your design to justify your answer.

7. Throughout the challenge, what are two successful accomplishments made by your team? Why?

8. Suppose your team was given the chance to start complete the challenge over. What are two things would you suggest be approached differently? Why

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Appendix S: Presentation RubricName _____________________________ Team Name: ________________________

Date ____________ Period _____

Presentation Rubric: Team Responsibilities 4 3 2 1

Content

The team provides a detailed explanation about all of the following:

The Design challenge’s objective (requirements)

Short description of each team member’s design proposal

Sketch of the final design

Explanation of the decision analysis matrix

Reflections shared by each team member

Suggestions for next steps team could take

The team provides an explanation of at least 5 out of 6 of the following with some detail:







The team provides an explanation of at least 4 out of 6 of the following with some or limited detail:







The team provides an explanation of at least 3 out of 6 of the following with some or limited detail:







MultimediaPresentation

Team integrates multimedia and visual displays into the presentation. All chosen multimedia help clarify and deepen understand of information, Team presentation includes: Pictures, video, sketch and hyperlink.

Team integrates multimedia and visual displays into the presentation. All chosen multimedia lead to clarifying information, Team presentation includes at least 3 out of 4 of the following: Pictures, video, sketch and hyperlink.

Team integrates multimedia and visual displays into the presentation. All chosen multimedia lead to clarifying or lacks some information, Team presentation includes at least 2 out of 4 of the following: Pictures, video, sketch and hyperlink.

Team integrates multimedia and visual displays into the presentation. All chosen multimedia lead to clarifying or lack some or most information, Team presentation includes at least 1 out of 4 of the following: Pictures, video, sketch and hyperlink.

Presentation Skills

All team members actively participate in presentation of shared material, while fully engaging the audience

All or most team members actively participate in presentation of shared material, while engaging the audience

All or most team members actively participate in presentation of shared material, but do not engage the audience.

Most team members participate in presentation of shared material, but audience is not engaged, and is confused due to flow of presentation.

Organization

Team presents information in a logical, interesting sequence, which the audience can easily follow and gain a deeper knowledge of the content.

Team presents information in a logical, interesting sequence, which the audience can easily follow.

Team presentation is difficult for the audience to follow because of lack of sequence the audience can easily follow.

Team presentation is confusing and/or lacks sequence that the audience can follow.

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Appendix T: Google SketchUP Reference Cards

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Appendix U: Engineering Technical Brief – Additional Technical Information for Students/Teacher

Name _____________________________ Date ____________ Period _____

Corrugated cardboard is made from a combination of two sheets of cardboard, called liners, which are glued to a corrugated inner medium called the fluting. The construction of this forms a series of connected arches, which are very capable of supporting strong weights as well as having considerable rigidity. In addition to this, the air circulating in the flutes also serves as an insulator, which provides protection against temperature variations.

Corrugated cardboard is engineered to withstand heavy weight and other damages. It is crush-resistant and passes burst-strength tests due to withstanding top and side pressure. Corrugated cardboard also offers tear and tensile strength as well as being resistant to impact, drop and vibration damage. The design of the corrugated cardboard makes it stackable and has an excellent weight distribution.

While corrugated cardboard is very strong, the strength also depends on several factors including: the strength and thickness of the two liner sheets and the inner corrugated sheet, the thickness of the corrugation (that is, the distance between the two liner sheets) and the number of corrugations per foot in the middle sheet.

There are three basic geometric shapes that are incorporated into all designs: squares, circles and triangles. Triangles are considered to be the second strongest two-dimensional shape because they have fixed points, are able to better balance tension and compression and distribute weight very evenly. For example, a geodesic dome is created out of a series of triangles or the base of a three-legged stool (which is the only type of stool that won’t wobble).

The circle is considered to be the strongest shape, however, a combination of the three basic shapes can prove to be an even stronger base than any individual shape. Adding arcs of a circle can add strength to the corners and incorporating triangles to straight, vertical lengths add side-to-side strength.

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