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:

  1. Individual Activity � Individually, students read a page from the student handbook and an internal memo from the client which establishes the need to create a procedure to predict a student's preferred travel mode based on the results of a brief survey. Students individually begin to explore why an individual would select various travel options. The focus is on establishing what options are available and why an individual would choose one option over another.
  2. Team Activity � In teams of 4, students develop a procedure for converting survey results into a rank ordered list of preferred travel methods. This procedure is expressed in the form of a memo to the client describing the ranking process.

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:
  • What are the elements?
  • What are the relationships among elements?
  • What are the operations that describe how the elements interact?
 Elements – Factors (Own car?, Cost, Freq) and available modes of transportation
Operators – Add/subtract/weighting of factors
Relationships – Ranking of subsystems
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 open-ended. 		Transportation – mode choices
Public transit organization
University planning
Self-Assessment 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? 		Using their procedure on the sample cases to provide rankings for 3 test cases.
Model-Documentation 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
Construct Share-Ability and Re-Usability 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 board and LYNX can use for planning.
Generalizable – Should be able to use for other cases
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? 		Choice models and Trade-offs
Utility – also applicable to business

Author Information:

  • Original Author(s):
    • Carla Liguore
    • Ben Eick

Files:

History:
Tested in ENGR106 - Spring 2006 Originally written - Spring/Summer 2005