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Small Group Mathematical Modeling (SGMM)

Integrating more engineering contexts, introducing advanced engineering topics, addressing multiple ABET Criteria, and serving under-represented student populations in foundation engineering courses are some of the opportunities realized by the use of this framework for developing real-world client-driven problems.

Name Description Documents History
Aluminum Crystal Size

Aluminum Crystal Size provides students with an opportunity to work with images and utilize actual procedures used in industry. This task requires students to develop a procedure to measure the average crystal size of aluminum crystal images of three different samples. The motivation for developing the procedure is established by using a realistic context in which the quality of aluminum being produced is trying to be improved and can be assessed based on the size of the aluminum crystals in a sample. Student teams of four are required to establish a procedure for measuring the average crystal size. The students then apply their procedure to three different samples.

Concepts

  • Algebra
  • Dimensions and Units
  • Statistics

MEA Documents
Extension Documents
Tested in ENGR106 - Spring 2005
CD Compilation

The CD Compilation MEA requires teams of students to develop a generalizable procedure to select songs for custom CD compilations for a company called Brand New Sound Co. The motivation for developing this procedure is established using a realistic context in which the company spends a significant portion of their time trying to select songs to meet the client's needs from a large database. The Engineering Project Manger wishes to be able to improve efficiency in establishing compilations based on the client's requested CD properties. The teams must take into account the various properties of songs, such as genre, length, and royalty cost. The student teams are required to (1) develop a reusable general procedure for selecting and organizing songs on a playlist (2) use the procedure to provide a sample playlist based on a subset of the song database and the client's requested properties.

Concepts

  • Logic

MEA Documents
Tested in ENGR106 - Spring 2005 and Spring 2006
Campus Lighting Design

The Campus Lighting Design MEA requires teams of students to develop a generalizable procedure for placing lights around campus buildings and walkways for a university Board of Trustees. The motivation for developing this procedure is established using a realistic context in which the Board of Trustees plans to redevelop the campus lighting system and standardize around a single installation design plan. The board wishes to improve the current lighting system and provide a consistant look and feel to the overall campus lighting scheme. The teams must take into account the size and strength of lights and the effects of having too much or too little light in a given area. The student teams are required to (1) develop a reusable general procedure for lighting layout such that the minimum lighting requirements are met but not exceeded to the point of causing light pollution and (2) use the procedure to provide a sample layout on a provided map of a sample building and the surrounding walkways. While designed around the same context as the Campus Lighting Economics MEA, the two problems can be given independently.

Concepts

  • Geometry
  • Units and Unit Conversions
  • Additive Properties

MEA Documents
Tested in ENGR106 - Fall 2003
Campus Lighting Economics

The Campus Lighting Economics MEA requires teams of students to develop a generalizable procedure for evaluating the economic viability of lighting proposals for the lights around campus buildings and walkways for a university Board of Trustees. The motivation for developing this procedure is established using a realistic context in which the Board of Trustees plans to redevelop the campus lighting system and standardize around a single installation design plan, but must do so in a financially efficient manner. The board wishes to evaluate which of the proposed lighting schemes are the most financially viable. The teams must take into account the number, type, cost, and lifespan of lights and the various replacement schemes to minimize the cost while maintaining proper lighting conditions. The student teams are required to (1) develop a reusable spreadsheet for calculating the cost of the various proposals and replacement schemes, (2) select the most economically viable proposal and replacement scheme, and (3) explain why that proposal and replacement scheme were selected. While designed around the same context as the Campus Lighting Design MEA, the two problems can be given independently.

Concepts

  • Pricing Models
  • Comparing Alternatives
  • Economics

MEA Documents
Tested in ENGR106 - Fall 2003
Campus Sprinkler Design

The Campus Sprinkler Design MEA requires teams of students to develop a generalizable procedure for placing sprinkler heads around campus open spaces for a university. The motivation for developing this procedure is established using a realistic context in which the university would like to redesign the existing system to better distribute water for grass and plants and to reduce overwatering of these items. The client wishes to improve the current sprinkler system and provide a more efficient campus sprinkler system. The teams must take into account the size and strength of sprinklers and the effects of having too much or too little water in a given area. The student teams are required to (1) develop a reusable general procedure for sprinkler placement such that the minimum watering requirements are met but not exceeded to the point of causing overwatering and (2) use the procedure to provide a sample layout on a provided map of a sample building and the surrounding walkways and grassy areas.

Concepts

  • Geometry
  • Units and Unit Conversions
  • Additive Properties

MEA Documents
Tested in ENGR106 - Fall 2004
Condominium Pricing

The Condominium Pricing MEA requires teams of students to develop a generalizable procedure to create a pricing model for condominiums in a the newly developed Morgan Place Complex. The motivation for developing this procedure is established using a realistic context in which the company needs to demonstrate that the model is competitive with similar units in the area to obtain financial backing. The Real Estate Division Director wishes to be able to quickly establish the price of any unit in the complex using the model. The teams must take into account the size of the unit and the features associated with a given unit such as the presence or absence of a balcony or lake view.

Concepts

  • Pricing Models
  • Cost per Area

MEA Documents
Tested in ENGR106 - Spring 2005
Factory Layout

The Factory Layout MEA requires teams of students to develop a generalizable procedure to layout the floor plan of aluminum tubing production plants for a company called Tube Alloy. The motivation for developing this procedure is established using a realistic context in which the company plans to open several new plants in the next few years. The General Manager of Industrial Planning wishes to be able to improve efficiency in establishing layouts for future plants that have different department sizes and overall plant sizes. The teams must take into account the size of the plant, the size and limiting aspect ratios of the departments, and the processing steps for the products that the plant will manufacture. The student teams are required to (1) develop a reusable general procedure for plant layout such that the travel distance of each product is minimized and (2) use the procedure to provide a sample layout for a particular plant with provided specifications.

Concepts

  • Area
  • Ratios

MEA Documents
Tested in ENGR106 - Fall 2005
Image Tiling

The Soccer Ball MEA requires teams of students develop a generalizable procedure to cut out as many of a single shape as possible from an 8 ½ by 11 sheet of paper. The motivation for the problem is established through a news article relating child labor in India and Pakistan to the manufacture of professional soccer balls. One sport equipment manufacture wishes to automate more of the manufacturing process. Here students are asked by the company to use the idea of “nesting” shapes to reduce waste when cutting out pieces. The students start with hexagons and move on to pentagons. Other sports related shapes are used to extend the problem.

Concepts

  • Image Tiling
  • Tessellations
  • Geometry

MEA Documents
Tested in ENGR106 - Spring 2006
NASA Life Support

This activity requires students to create a procedure for analyzing life support systems in order to determine which system is best for use in space. The teams are given a set of data for five systems that experts from NASA have already ranked from best to worst. Team must use this data to develop a mathematical procedure that uses the data given to rank these five systems. When the teams’ procedures are applied to the NASA ranked data, the systems should be ranked in the same order. The students are then asked to apply their procedure to a new set of specifications for life support systems in order to rank them from best to worst.

Concepts

  • Weighting Systems
  • Factors

MEA Documents
Tested in ENGR106 - Fall 2005
Nanoscale Roughness

Nano Roughness provides students with a hands-on experience with relevant scientific and mathematical concepts used in nanoscale technologies and research. This task requires students to develop a procedure to measure roughness given atomic force microscope (AFM) images of three different samples of gold. The motivation for developing the procedure is established by using a realistic context in which a company specializing in biomedical applications of nanotechnology wishes to start producing synthetic diamond coatings for joint replacements. The company intends to extend its experience with gold coatings for artery stents to this new application. Student teams of four are required to establish a procedure for measuring the roughness of gold samples that could be applied to diamond samples. The students then apply the procedure to three different samples of gold and develop a list of additional information they need to improve their procedure.

Concepts

  • Nanoscale Devices
  • Algebra
  • Dimensions and Units
  • Statistics

MEA Documents
Extension Documents
Tested in ENGR106 - Fall 2003
Office Space Pricing

The Office Space Pricing MEA requires teams of students to develop a generalizable procedure to create a pricing model for office space in a the newly developed Foster Tower Complex. The motivation for developing this procedure is established using a realistic context in which the company needs to demonstrate that the model is competitive with similar units in the area to obtain financial backing. The Real Estate Division Director wishes to be able to quickly establish the price of any unit in the complex using the model. The teams must take into account the size of the unit (both in terms of both number of offices as well as total square footage) and the features associated with a given unit such as the presence or absence of a lake view.

Concepts

  • Pricing Models
  • Cost per Area

MEA Documents
Tested in ENGR106 - Fall 2004
Prosthetic Hand Pricing

The Prosthetic Hand Pricing MEA requires teams of students to develop a generalizable procedure to create a pricing model for prosthetic hands for the Helping Hands Prosthetics Company. The motivation for developing this procedure is established using a realistic context in which the company needs to develop a faster mechanism for pricing its units than the current method. The teams must take into account the volume, material costs, and asthetic look of each hand when developing their model for the client.

Concepts

  • Pricing Models
  • Units and Unit Conversions
  • Volume and Density

MEA Documents
Tested in ENGR106 - Spring 2005
Shredded Documents

Shredded Documents provides students with a hands-on experience developing an algorithm to solve a tangible problem. This task requires students to develop a procedure to develop a quantitative method for analyzing if the scans of two shreds should be rejoined, as well as developing a brute force algorithm in MATLAB to perform the reassembly. The motivation for developing the procedure is established by using a realistic context in which a company specializing in security software development wishes to design software to aid in the reassembly of shredded legal documents. The company intends to use their software to assist government lawyers in their case against a fraudulent tire company. Student teams of four are required to establish a procedure for performing the reassembly using quantitative methods. The students then apply the procedure to an actual shredded document to analyze the correctness of their algorithm.

The MAA extends the MEA by having students implement a given de-shredding algorithm using MATLAB. Focusing on the use of looping structures, user defined functions, and image processing, the algorithm makes use of linear regression to rank how well two strips align.

Concepts

  • Logic
  • Regression (in MAA)

MEA Documents
Extension Documents
Tested in ENGR106 - Fall 2005 and Spring 2006
Tire Reliability

The Tire Reliability MEA requires the teams of students to develop a generalized procedure to determine whether a set of data regarding tire performance is demonstrating acceptable reliability. The Peterson Tire Company is aware of a few accidents caused by tire failure in one of its tire product lines. The company wishes to know if there is a reliability issue with this set of tires so that the company can fix the problem if one exists. They also intend to use the procedure for tire data on future tire product lines. The teams (1) use the data from three types of tires to develop the procedure for determining if a set of data regarding tire performance is demonstrating acceptable reliability, and (2) use the procedure to classify the reliability of the tires as well as determine if the products are correctly rated based on when failure is expected.

Concepts

  • Distributions
  • Histograms
  • Quality vs. Reliability

MEA Documents
Tested in ENGR106 - Fall 2005
Travel Mode

The Travel Mode Choices MEA requires the teams of students to develop a generalized procedure to rank a student's preferred travel mode based on a set of parameters. The University of Central Florida is developing a master development plan and is trying to determine which modes of travel will be utilized most as the university grows. Based on survey results from students, the university would like a mechanism for determining which mode of transportation a student is most likely to take to get to campus. Among other things, the survey results contain such diverse information as how far a given student is from bus stops in numbers of blocks, bus frequency in minutes, how much parking would cost if the student were to drive, and whether that student owns a car. Students must develop a mechanism for taking information with a wide variety of units and assimilating that information into a ranking system.

Concepts

  • Pricing
  • Combining Dissimilar Factors

MEA Documents
Tested in ENGR106 - Spring 2006