Group Members:Antonio Perez

John Burns

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Day 1: Introduction to Engineering and Relationship between Math and Engineering

Overview: The students will learn the basic principles of engineering. They will also learn about the engineering design process and how it uses mathematical analysis. Students will look at how engineers design bridges as an example of this process and the type of math that is involved.

Teacher Prep Time: 10 min Make copies of Math and Engineering Relationship Worksheet (W1) and

Engineering Example: Designing A Building worksheet (W2) for all students Bring packets for designing a building activity to class

Objectives: Students will be able to understand the engineering design process Students will see how engineers apply math to real-world problems Introduce students to process of bridge design and spark their interest in bridges

Teaching Standards:Virginia SOLs: Grades 6-8: Students will also identify real- life applications of the mathematical

principles they are learning that can be applied to science and other disciplines they are studying.

Massachusetts Science and Technology / Engineering Curriculum Framework: 2.1: Identify and explain the steps of the engineering design process, i.e., identify

the need or problem, research the problem, develop possible solutions, select the best possible solution(s), construct a prototype, test and evaluate, communicate the solution(s), and redesign.

ITEA’s Standards for Technological Literacy: Standard 9: Engineering Design

o F: Design involves a set of steps, which can be performed in different sequences and repeated as needed.

o H: Modeling, testing, evaluating, and modifying are used to transform ideas into practical

Materials: Math and Engineering Relationship Worksheet (W1) Engineering Example: Designing A Building worksheet (W2)

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Description of Class:Relationship Between Math and Engineering (20 min) T. distributes worksheets 1 and 2 to students. Students will fill in answers as the class

progresses T. asks students what they know about mathematical study and investigation.

T. writes students responses on board. T. Discusses responses with class

T. discusses how mathematics studies quantities and space to explore and seek out patterns

T. asks students how math can be applied to real-world situations and problems T. writes responses on board T. discusses responses with class

T. discusses how one of biggest applications of math is through engineering Engineers apply math throughout engineering design process Engineers use math to build structures, consumer products, improve systems and

further technology T. goes through engineering design process.

T. goes through steps in engineering design process with students Students fill out worksheet as they go along (W1)

T. asks students what steps in engineering design process they think math is involved in? T. writes student ideas on board

T. explains how math involved in every step of engineering design process. Students fill out worksheets as they go along (W1)

T. sums up major relationship between math and engineering (reference Teacher Manual)

Building Example (30 min)

T. gives students material for students to build building Students will try to build the tallest building that can hold up Students will fill out W2 for this activity as they go along T. will test every building for structural soundness T. leads discussion of steps in engineering design process and how students addressed

them (W2) T. gives overview of what bridge ETK will cover in future classes and introduce the

bridge design challenge at end

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W1: Math, Science and Engineering Relationship Worksheet

The Engineering Design Process

How are math and science involved in:

1. Step 1:

2. Step 2:

3. Step 3:

4. Step 4:

5. Step 5:

6. Step 6:

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W1: Math and Engineering Relationship Worksheet (teacher’s copy)

The Engineering Design Process

How is math involved in:

1. Identifying the problem:-Can help quantify problem

2. Brainstorming Ideas:-Setting a budget

3. Developing Design:-Evaluate mathematical soundness of designs using geometry, algebra, probability and statistics-Minimize/maximize design features such as cost, material used or

4. Test Design:-Numerically quantify performance on tests-Calculating probability of failure

5. Revising Design:-Evaluate mathematical soundness of designs using geometry, algebra, probability and statistics-Minimize/maximize design features such as cost, material used or

6. Final Report:-Statistics to show effectiveness of design

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IdentifyProblem

BrainstormIdeas

Develop Design

TestDesign

DevelopFinal Report

ReviseDesign

W2: Engineering Example: Designing A Building

1. What is the problem?

2. Possible Solutions

3. Design Options

4. Testing Design

5. Revising Design

6. Final Report

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W2: Engineering Example: Designing A Building (teacher’s copy)

1. What is the problem?How do we fit many people in a limited space?How do we provide shelter?

2. Possible Solutions-Building-Underground shelter

3. Design Options Once we Decide on Building-Material Options-Dimensions of building (will affect stability of building)-How many floors?-Windows/doors/ventilation system, etc…

4. Testing Design-Test under various loads (tension, compression, shear, etc…)-Test under various weather conditions-Test for natural disasters (hurricane, earthquake, lightning storm, etc…)

5. Revising Design-Using test data, evaluate how we can change design to improve quality

6. Final Report-Detailed drawings and specifications to begin construction

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Day 2: Geometry-Pythagorean Theorem-Characteristics of Different Structures/Bridges

Overview: The students will learn the basic principles of geometry and the Pythagorean Theorem. Students will be able to apply the Pythagorean Theorem to right triangles in order to find the unknown lengths. By experiment, students will discover that side measurement is important in determining the angle classification of a triangle. By squaring sides, they will predict whether triangles will be right, obtuse, or acute. 

Teacher Prep Time: (10 min) Hand out cut outs of different right angle triangles, and have them calculate the

length of the unknown side given the length of two of the sides. Supply a ruler in order to verify if their calculations are correct.

Objectives: The students will be able to describe and define the Pythagorean

Theorem-Pythagorean theorem: For any right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.

Given two sides of the right triangle, the students will be able to solve the Pythagorean Theorem for the missing variable.

The students will be able to define and differentiate between when they are and are not supposed to use the Pythagorean Theorem.

We will go over where the square root key is on the calculator and how the students should use this key.

Teaching Standards:

Virginia SOLs: Grade 8:

a) Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurementb) Apply the Pythagorean Theorem to find the missing length of a side of a right triangle when given the lengths of the other two sides.

Massachusetts Science and Technology / Engineering Curriculum Framework: 8.G.3 Demonstrate an understanding of the relationships of angles formed by

intersectinglines, including parallel lines cut by a transversal.

8.G.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.

ITEA’s Standards for Technological Literacy:

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Standard 7: The Influence of Technology on History:E: The design and construction of structures for service or convenience have evolved from the development of techniques for measurement, controlling systems, and the understanding of spatial relationships.

Materials: Cut out triangles of different sizes K’Nex Beam made from Popsicle sticks Rulers Calculators

Description of Class:

We will go through examples on the board of how to write numbers in radical form, which is necessary in order to prepare the Pythagorean Theorem. (2-4 min)

We will go over where the square root key is on the calculator and how the students should use this key. (1-3 min)

Onto the handout, explain to the students that you are going to do number one and number two with them, but they should also do it at their seats on their handout. (1 min)

Write the Pythagorean Theorem on the board,a2 + b2 = c2.

Read the first problem out loud to the students.Let a = 24 and c = 25, find the other leg of the triangle, b. (2-3 min)

a2 + b2 = c2

242 + b2= 252

576 + b2 = 625b2 = 49b = 7

Read the second problem out loud.Let a = 4 and b = 5, find the hypotenuse, c, of the triangle. (2-3 min)

a2 + b2 = c2

42 + 52 = c2

16 + 25 = c2

41 = c2

Ask students if there are any questions. (1 min) Make sure to let the students know that their answers aren't always going to come out to

an exact number; they may find a side of the triangle to be a square root. Read the third problem out loud and have them do it at their seats with other students. I

will walk around and monitor to make sure that they all understand the concept. Have one student come up to the board and demonstrate how to do the problem. (2-3 min)

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Problem number three:Let b = 5 and c = 13, find the other leg of the triangle using the Pythagorean Theorem.

a2 + b2 = c2

a2 + 52 = 132a2 + 25 = 169a2 = 144a = 12

Ask the students if there are any questions. (1 min)

Announce to students that they should try to complete the fourth problem on their own. I will walk around the room and monitor to make sure that everyone understands the concept. Have a student volunteer to come up to the board and complete the problem for everyone to see. (2-3 min)

Problem number four:Let a = 3 and b = 4, find the hypotenuse of the triangle using the Pythagorean Theorem.

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

5 = c

Ask for a student to volunteer to tell you what the parts of the right triangle are called. (Answer: a = leg, b = leg, c = hypotenuse)

K’Nex demonstration on which shapes are the strongest.

Hand out the K’nex to the students, and have them construct each of the shapes shown below. Then have them push with their hands on each shape to see which breaks the easiest. Then ask them how they can reinforce the shapes with more K’nex to make them stronger.

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Explain why an I beam is great for bridge building.

Demonstration of an I-beam versus a regular beam with popsicle sticks to see which structure holds more weight.

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Day 3: West Point Bridge Builder: Design, Modeling, Trusses, Connection Points

Overview: The students will learn the basic principles of real world design through modern technology. They will use West Point bridge builder to construct a computational model, and then simulate the model in order to see where the highest stresses on the bridge are. Then, when they construct their actual bridge with popsicle sticks, they will understand where they need to place their support beams in order to support the most weight.

Teacher Prep Time: (10 min) Cds with west point bridge builder will be handed out to load onto the

laptops/computers. We will load the program, and explain how to design the bridge using the program.

Objectives:The students will learn how computational models are important within design

We will go over how to support the bridge the most without using excessive amounts of trusses.

The students will be able to use the software by themselves in order to see where the highest stress concentrations are on their bridge.

They will be able to incorporate what they learned from the software into their actual design.

Teaching Standards:

Virginia SOLs: Grade 8: 8.9: The student will construct a three-dimensional model, given the

top, side, and/or bottom views.

Massachusetts Science and Technology / Engineering Curriculum Framework: 8.M.5: Use models, graphs, and formulas to solve simple

problems

ITEA’s Standards for Technological Literacy: Standard 10: The Role of Troubleshooting, Research and Development,

Invention and Innovation, and Experimentation in Problem Solving:o Troubleshooting is a problem-solving method used to identify the cause of

a malfunction in a technological system.o Invention is a process of turning ideas and imagination into devices and

systems. o Some technological problems are best solved through experimentation.o Innovation is the process of modifying an existing product or system to

improve it. Standard 11: Apply the Design Process:

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o Apply a design process to solve problems in and beyond the laboratory-classroom.

o Specify criteria and constraints for the design.o Make two-dimensional and three-dimensional representations of the

designed solution.o Test and evaluate the design in relation to pre-established requirements,

such as criteria and constraints, and refine as needed.o Make a product or system and document the solution.

Materials:

West Point Bridge Builder Program 5 Laptops/Computers

Description of Class:

First we will load all of the software onto the computer before the class starts so the students will be ready to go.

We will open West point bridge builder, and show them how to place points of intersection, and trusses onto the screen. Show them how they can vary the material type, and length of the trusses.

Once they have a working design (every point is connected with a truss) then show them how to simulate the design. Simulation runs a truck over the bridge to see if it would make it to the other side.

When the truck drives over the bridge, you must explain to the students that the red means the stress is

high, and the blue means the stress is low. Therefore the red must be reinforced, and you can take away trusses from the blue.

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W3: Different Types of Bridge Designs

Suspension Under-Arch

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Over- Arch Beam Bridge

Cantilever Bridge Truss Bridge

Day 4: Introduction to Bridge Building Competition

Overview: The students will be introduced to the bridge building competition. They will be given all the needed materials, rules and constraints and they will begin building their bridge. 

Teacher Prep Time: 10 min Print out Project Guidelines Worksheet Bring design project supplied to class

Objectives: Students will exercise the engineering design process Students will learn to manage a budget and make design choices Students will learn to work collaboratively and creatively

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Teaching Standards:

Massachusetts Science and Technology / Engineering Curriculum Framework: 2.4 Identify appropriate materials, tools, and machines needed to 2.5 Explain how such design features as size, shape, weight, function, and cost

limitations would affect the construction of a given prototype.

ITEA’s Standards for Technological Literacy: Standard 8: The Attributes of Design

o G: Requirements for design are made up of criteria and constraints Standard 9: Engineering Design

o F: Design involves a set of steps, which can be performed in different sequences and repeated as needed.

o G: Brainstorming is a groups problem-solving design process in which each person in the group presents his or her ideas in an open forum

o H: Modeling, testing, evaluating, and modifying are used to transform ideas into practical

Standard 11: Apply the Design Processo H: Apply a design process to solve problems in and beyond the

laboratory-classroomo I: Specify criteria and constraints for the designo J: Make two-dimensional and three-dimensional representations of the

designed solution

Materials: Project Guidelines Worksheet Popsicle sticks, glue fishing line string Clippers Clothesline pins Monopoly Money Tape

Description of Class:

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Teacher divides students into groups of three students and gives each group a copy of project guidelines handout with the allotted amount of monopoly money and the starting materials.

Teacher goes over handout with students to make sure they understand all the guidelines for the design project

Students will begin building their bridge, they can come purchase additional materials from the teacher at any time with the money

W4: Build your Bridge Design

Design Overview: The company SuperBridge is looking for a group of engineers to design a bridge to take cars across the James River. You are competing with your classmates for the right to design the bridge. They have asked everyone in the class to design a prototype out of the following materials. The team that can build the bridge that holds the most weight within the given budget will win and get paid a big salary for designing the bridge.

Materials:Every group is given a certain amount of starting materials:

50 Popsicle sticks 1 meters of String 1 meters of Fishing line Glue

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Clippers 5 Clothesline pins Tape

Groups can use their budget to purchase additional materials at the following prices: $250 for additional 10 popsicle sticks $100 for additional 1 meters of fishing line $50 for additional 1 meters of string $50 for extra clothesline pins

Total Budget: $1,000

Specifications:

Bridge need to be at least 12 in long. Bridge needs to be wide enough to fit at least two lanes of cars (Each lane is 1.5 in

wide), therefore must be 3 in wide.

You are free to build any type of bridge that you want. Use the knowledge that you have learned throughout the week to decide what sort of geometries and shapes you want to incorporate in your bridge. Use what you learned using the WestPoint Bridge Builder to efficiently distribute the weight on the bridge.

Day 5: Bridge Building Competition Continued….

Overview: The students will continue working on their bridge designs. Groups will need to work fast and effective in order to complete the bridge on time.  

Teacher Prep Time: 10 min Redistribute materials to make the bridge. Bring design project supplied to class

Objectives: Students will exercise the engineering design process Students will learn to manage a budget and make design choices Students will learn to work collaboratively creatively, and effectively

Teaching Standards:

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Massachusetts Science and Technology / Engineering Curriculum Framework: 2.4 Identify appropriate materials, tools, and machines needed 2.5 Explain how such design features as size, shape, weight, function, and cost

limitations would affect the construction of a given prototype.

ITEA’s Standards for Technological Literacy: Standard 11: Apply the Design Process

o K: Test and evaluate the design in relation to pre-established requirements, such as criteria and constraints, and refine as needed.

o L: Make a product or system and document the solution.

Materials: Project Guidelines Worksheet Popsicle sticks, Glue Fishing line String Clippers Clothesline pins Tape

Description of Class:

After bridges are complete, testing will begin.

Two desks will be set up 9 inches apart from each other. (That way at least 1.5 inches will be on each side of the desk)

Bridges will be measured to ensure that all size requirements have been met.

A bucket will then be attached in the middle of the bridge, and weights will be added in increments of 5lbs. The bucket itself will weigh about 5lbs to begin with. Figure 1 illustrates this mechanism.

The bridge that holds the most weight wins the competition. Good Luck!

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Figure 1: Illustration of system of hanging weights to test bridges.

W5: Lessons Learned from Design Competition

1) Did your team work effectively? Were there differing strategies/opinions? How did you deal with these? How did teamwork work to your advantage or disadvantage?

2) What was your design strategy? Did you plan out a design or start building immediately?

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3) What worked and didn’t work in your design and from the other designs you observed?

4) What would you do differently if you were starting over again?

5) What were your greatest challenges and how did you work to overcome them?

6) What did you learn about engineering from this example

W5: Lessons Learned from Design Competition (Teacher’s Copy)

1) Did your team work effectively? Were there differing strategies/opinions? How did you deal with these? How did teamwork work to your advantage or disadvantage?

-Working in teams important part of engineering-Effective teamwork crucial to successful design -Teams allow you to feed off of everyone’s strengths and come up with new ideas

2) What was your design strategy? Did you plan out a design or start building immediately?

-Important to plan in advance especially when on time and money budget-Consider big picture-how does everything fit together?

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3) What worked and didn’t work in your design and from the other designs you observed?

4) What would you do differently if you were starting over again?

5) What were your greatest challenges and how did you work to overcome them?-Time? -Budget-not enough popsicle sticks?-You often cannot make a perfect design because it has to be practical-You could make perfect bridge that would resists every situation imaginable but would it be feasible?

6) What did you learn about engineering from this example-Creativity-Teamwork-Resourcesful-Problem-solving

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