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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)
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)
W1: Math, Science and Engineering Relationship Worksheet
The Engineering Design Process
How are math and science involved in:
- Step 1:
- Step 2:
- Step 3:
- Step 4:
- Step 5:
- Step 6:
W1: Math and Engineering Relationship Worksheet (teacher’s copy)
The Engineering Design Process
How is math involved in:
- Identifying the problem: -Can help quantify problem
- Brainstorming Ideas: -Setting a budget
- Developing Design: -Evaluate mathematical soundness of designs using geometry, algebra, probability and statistics -Minimize/maximize design features such as cost, material used or
- Test Design: -Numerically quantify performance on tests -Calculating probability of failure
- Revising Design: -Evaluate mathematical soundness of designs using geometry, algebra, probability and statistics -Minimize/maximize design features such as cost, material used or
- Final Report: -Statistics to show effectiveness of design
Identify Problem
Brainstorm Ideas
Develop Design
Test Design
Develop Final Report
Revise Design
W2: Engineering Example: Designing A Building (teacher’s copy)
- What is the problem? How do we fit many people in a limited space? How do we provide shelter?
- Possible Solutions -Building -Underground shelter
- 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…
- Testing Design
- Test under various loads (tension, compression, shear, etc…) -Test under various weather conditions -Test for natural disasters (hurricane, earthquake, lightning storm, etc…)
- Revising Design -Using test data, evaluate how we can change design to improve quality
- Final Report -Detailed drawings and specifications to begin construction
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 measurement b) 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 intersecting lines, 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: Standard 7: The Influence of Technology on History:
Problem number three: Let b = 5 and c = 13, find the other leg of the triangle using the Pythagorean Theorem.
a^2 + b^2 = c^2 a^2 + 5^2 = 132 a^2 + 25 = 169 a^2 = 144 a = 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.
a^2 + b^2 = c^2 32 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 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.
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.
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.
W3: Different Types of Bridge Designs
Suspension Under-Arch
Over- Arch Beam Bridge
Cantilever Bridge Truss Bridge
Materials: Project Guidelines Worksheet Popsicle sticks, glue fishing line string Clippers Clothesline pins Monopoly Money Tape
Description of Class:
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 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,
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.
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. 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!
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?
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
