### Summary

Student groups are provided with a generic car base on which to design a device/enclosure to protect an egg as it rolls down a ramp at increasing slopes. During this in-depth physics-science-technology-math activity, student teams design, build and test their prototype creations to meet the design challenge, and then perform basic mathematical calculations using collected data, including a summative cost-benefit ratio. The activity has great potential to build on with additional physics and math explorations. Many student handouts are provided.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Automotive manufacturers hire engineers to redesign cars in order to make them safer. This process always involves a trade-off between cost of manufacturing a new design and level of safety. After this activity, students will be able to recognize this trade-off and understand the concept of cost to benefit ratio.

### Pre-Req Knowledge

Students should have a basic understanding of ratios, proportions, Newton's laws, linear motion calculations, data collection and graphing.

### Learning Objectives

After this activity, students should be able to:

- Explain the engineering design process.
- Explain the relationship between distance, time and speed.
- Describe how one can use math to solve a problem.

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###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Apply Newton's Third Law to design a solution to a problem involving the motion of two colliding objects. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Solve unit rate problems including those involving unit pricing and constant speed. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- The development of technology is a human activity and is the result of individual and collective needs and the ability to be creative. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Requirements are the parameters placed on the development of a product or system. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Design is a creative planning process that leads to useful products and systems. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- There is no perfect design. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Requirements for design are made up of criteria and constraints. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Brainstorming is a group problem-solving design process in which each person in the group presents his or her ideas in an open forum. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Modeling, testing, evaluating, and modifying are used to transform ideas into practical solutions. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Specify criteria and constraints for the design. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Make two-dimensional and three-dimensional representations of the designed solution. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Test and evaluate the design in relation to pre-established requirements, such as criteria and constraints, and refine as needed. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Make a product or system and document the solution. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Transportation vehicles are made up of subsystems, such as structural propulsion, suspension, guidance, control, and support, that must function together for a system to work effectively. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Massachusetts - Math

- Perform operations with multi-digit whole numbers and with decimals to hundredths. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
- Apply and extend previous understandings of multiplication and division to divide fractions by fractions. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Apply and extend previous understandings of arithmetic to algebraic expressions. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Recognize and represent proportional relationships between quantities. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Analyze proportional relationships and use them to solve real-world and mathematical problems. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Investigate patterns of association in bivariate data. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Summarize, represent, and interpret data on a single count or measurement variable (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. Identify significant figures in recorded measures and computed values based on the context given and the precision of the tools used to measure. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Massachusetts - Science

- Given a design task, identify appropriate materials (e.g., wood, paper, plastic, aggregates, ceramics, metals, solvents, adhesives) based on specific properties and characteristics (e.g., strength, hardness, and flexibility). (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- 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. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Demonstrate methods of representing solutions to a design problem, e.g., sketches, orthographic projections, multiview drawings. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Describe and explain the purpose of a given prototype. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Explain how such design features as size, shape, weight, function, and cost limitations would affect the construction of a given prototype. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Given a transportation problem, explain a possible solution using the universal systems model. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

One-time costs:

- a wooden ramp with adjustable incline; 6-ft long, 7-8 inch wide track, elevation 0º to 90º; 1 per class; see the Ramp Construction Method for details on how to build
- 5 x 8-inch wooden base, 1 per group
- screw eyes, 4 per group
- threaded rod to fit through screw eyes or wooden dowel, 2 per group
- wheels, 4 per group; use hobby wheels or cut them from a wooden dowel
- e-clips or washers, 4 per group
- stopwatches
- meter stick
- protractor
- balance
- string
- stapler
- scissors
- razor blade

Suggested materials:

- eggs, at least 1 per group
- (optional) wooden eggs for practice
- an assortment of construction materials and supplies, such as: cardboard squares, pipe cleaners, twist ties, small and large rubber bands, cotton balls, soda straws, craft sticks, masking and scotch tape, string, soda bottles, super glue, packaging peanuts, paper and plastic cups, bubble wrap, binder clips, staples

### Introduction/Motivation

You and your team are members in the research and development department of a major car manufacturing company. You are in charge of testing a prototype safety harness on the latest line of cars. Your research team has provided you with instructions to create the device. Now it's your job to construct and test this prototype and determine how effective it is.

In a real lab situation, the car would be accelerated into a wall. Since you do not have the facilities to perform this test, you will use a ramp to simulate acceleration of a model car. To do your test, run your prototype car down the ramp starting at the lowest angle and see how well it performs. If it passes one angle, increase the slope and run the experiment again. If it fails, record the angle and stop testing. Compare your results with those of the other tests in the class to determine the average angle at which the prototype's safety mechanism failed. Based upon your results, make a recommendation as to whether or not the safety mechanism is effective. The company standards require that the safety mechanism be able to withstand an impact at a 50º incline run.

### Procedure

Before the Activity

- Gather materials.
- Make copies of the student handouts in the Attachment section: Design Constraints Handout and Cost of Materials and Data Table Handout.
- Review the Notes by a Teacher for a background about pertinent math, physics and cost/benefit concepts for the activity.
- Make sure that when students are figuring the total cost calculations they include only the cost of the materials used in the final devices. They may have redesigned their devices while constructing and decided not to use some of the materials initially chosen. For purposes of this activity, do not charge them for materials that they did not end up using in the final product.

Overview

**Introduce the challenge:**To design a safety device that can hold an egg (passenger) on the model car and keep it from breaking as the car rolls down the ramp at increasing slopes. The target goal is to protect the egg during a roll down the ramp at a 50-degree angle without cracking. Give extra credit to groups that can achieve success at steeper angles.- Explain the constraints.
- Conduct the activity (see detailed steps below).
- After activity completion, discuss the importance of having the "cost-to-performance" ratio and review the physics principles that can be observed in each device prototype. (Refer to the Notes by a Teacher for details.)

With the Students

- Divide the class into groups of four students each and distribute the student handouts.
- Have teams brainstorm, discuss and draw possible solutions and then agree upon the best ideas. (Make a brainstorming/sketch a graded component of the project.) This is a possible breakpoint for a shortened activity; see the Activity Scaling section for an explanation.
- Verify that each group has a unified drawing or idea, and then permit each group to "purchase" materials.
- Give the engineering teams 30-60 minutes to construct their devices.
- Direct students to calculate their materials cost. This is another possible breakpoint.
- Have one group present to the class its design, describing the construction, explaining the logic behinid its design, and reporting the construction cost.
- Record the construction cost in the design database (such as a chart on the wall or a projected spreadsheet) for the class to see. Then the teacher revisits the design constraints and verifies that the device meets the requirements.
- Have each group measure the mass of its device and record in the data table.
- Then test the device at a low ramp slope.
- Record in the data table the time it takes to move down the ramp and the incline number of the ramp.
- Repeat the test for this device until the highest slope is reached or the egg is broken to any observable degree.
- If a device needs minor repairs between runs, give the design team a set amount of time (perhaps 1-2 minutes) to make minor repairs (remember to re-record the mass of newly designed devices).
- Repeat this process to check and test each device.
- (optional) Determine angle measurements for each incline number.
- Have teams calculate weight, speed and cost/performance ratio.* Use the Performance vs. Cost Projection Sheet/Handout (Excel file) to project the results on a classroom screen or wall.

* Note: Divide the fictional dollar cost from the "Cost Account" sheet by the highest ramp level survived to create the cost/performance ratio.

### Attachments

### Safety Issues

Watch students' use of the incline ramp to avoid pinched fingers and toes.

### Troubleshooting Tips

To save on broken eggs, use wooden eggs for the design and build phases.

An option if plenty of materials are available is to not charge for materials used in designs that were not tested. This encourages more experimentation. For purposes of this activity, the cost should be the finished cost (manufacture cost) not the development cost. It should be the cost of the materials needed to make the car they dropped.

### Assessment

*Rubric*: Refer to the Example Grading Rubric to guide grading.

*Hypothetical Bonus Exercise*: If cooperation and doing one's fair share of the work are issues, consider giving the engineering team a fictional "$10,000 bonus" to anonymously divide amongst its group members at project end, split as they deem fair; this is often very revealing! Or use the Team Member Peer Evaluation Form.

*Graphing/Analysi*s: Have students graph cost vs. speed from the data table and discuss their relationship (if any). Ask the students if the more money they spend, the better/faster their car will be. Is the relationship linear? Another option is to graph weight vs. speed. Are heavier cars faster?

### Activity Extensions

- If time and enthusiasm permit, have students re-design their solutions at home for presentation to the class at a later date.
- Have students evaluate their own devices: What is good/bad about the design solution and why? How could it be improved?
- Explore what formula might provide a fairer cost/performance ratio.
- Explore how to mass-produce the best design(s). All of the standards related to manufacturing could be addressed through the production process.
- Use weight of the device constructed as a design constraint.
- Refer to the Notes By a Teacher, created by Joshua Abrams of Meridian Academy, which explores possible activity extensions, scaling and concepts addressed by the activity from the physics and math perspective.

### Activity Scaling

Depending on the level of the class, make use of the "possible breakpoints" indications in the Procedure section. If materials are limited or unavailable, stop at the point at which students draw device sketches. Have them explain their designs and discuss how they might be successful or not. Another possibility is to have students bring in their own materials for the cars, although this makes the car bases uneven across the class, but the physics principles can still be observed in the devices they build.

### Additional Multimedia Support

Learn more about the steps of the engineering design process at https://www.teachengineering.org/engrdesignprocess.php.

### Contributors

Scott Beaurivage; Justin Riley; Ryan St. Gelais### Copyright

© 2013 by Regents of the University of Colorado; original © 2005 Worcester Polytechnic Institute### Supporting Program

K-12 Outreach Office, Worcester Polytechnic Institute### Acknowledgements

This project was developed as a WPI Interactive Qualifying Project by undergraduate engineering students at Worcester Polytechnic Institute, and funded in part by Pratt & Whitney.

Last modified: March 27, 2018

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