Image Tiling
Concepts
 Image Tiling
 Tessellations
 Geometry
MEA Description: 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.
Implementation Strategy:
 Individual Activity ï¿½ Individually, students read the interoffice memo and news article from the client which establishes the need to create a pricing model to quickly establish the price of prosthetic hands based on the properties of the device. Students individually begin to explore what features of a prosthetic hand would affect the unit price. They also calculate the cost of a piece of aluminum used the construction of a prosthetic hand. The focus is on establishing what factors may need to be considered for pricing of a prosthetic hand.
 Team Activity ï¿½ In teams of 4, students develop a memo to the client detailing which features of the prosthetic hands have an impact on the price, how to calculate a price given those factors, and the pricing model was developed. The goal is to have students develop a complete pricing model and provide an explanation of both the development of the model as well as how to use the model.
 Homework  Continuing in teams of four, students revise their procedure based on TA feedback of the original procedure. Students are asked to estimate the accuracy of their existing model by comparing the price provided by their model to the current price of some of the units the client currently sells. Once the accuracy has been determined, teams are to revise their model in an attempt to improve the accuracy.
Six Principles:
Principle  Description  How the principle is addressed in the MEA? 

Model Construction 
Ensures the activity requires the construction of an explicit description, explanation, or procedure for a mathematically significant situation Describe the mathematical model the students will be developing when solving this MEA:

Elements Type and volume of materials used in construction, price per kilogram of materials, number of joints, and number of pressure settings Operators The weights applied to each factor to form the final price Relationships How the elements are weighted to form the final price 
Reality 
Requires the activity to be posed in a realistic engineering context and be designed so that the students can interpret the activity meaningfully from their different levels of mathematical ability and general knowledge Describe the context. What is the story? What knowledge will students need to bring to this problem? What background information must be provided? Describe how the problem is openended. 
Pricing models are a common problem throughout throughout industry. 
SelfAssessment 
Ensures that the activity contains criteria the students can identify and use to test and revise their current ways of thinking
What is provided in this MEA that students can use to test their ways of thinking? 
Students are given data for existing prosthetic hands priced without using the model to help develop a standardized pricing model. It can also be used to assess the quality of their own solutions. 
ModelDocumentation 
Ensures that the students are required to create some form of documentation that will reveal explicitly how they are thinking about the problem situation
What documentation are the students being asked to produce in this MEA? 
Memo to the client describing the procedure for processing the prosthetic hand properties 
Construct ShareAbility and ReUsability 
Requires students produce solutions that are shareable with others and modifiable for other engineering situations
What will indicate to the students that a sharable, reusable, or generalizable solution is desired? 
Sharable produce a model that the company can use to determine the price of any configuration of prosthetic hand.
Generalizable the model should be general enough so that it can be applied to existing units and result in similar prices to those of the established unit prices. 
Effective Prototype 
Ensures that the solution generated must provide a useful prototype, a metaphor, for interpreting other situations
What are other examples of structurally or conceptually similar problems that would required a similar solution? 
Pricing models are common across every aspect of industry. 
Author Information:
 Original Author(s):
 Carla Liguore
 Ben Eick
Files:
 MEA Documents
History:
Tested in ENGR106  Spring 2005