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 � Students individually begin to articulate what factors could be used to select songs from a database. The focus is on establishing what properties may be important to the client.
  2. Team Activity � In teams of four, students read the interoffice memo from the client, which establishes the need to create a procedure to more efficiently select songs from a large database based on the client's parameters. They document their procedure by developing a memo back to the client detailing their methodology.
  3. Homework - Continuing in teams of four, students revise their procedure based on TA feedback of the original procedure. As part of their new memo, students are asked to describe what changes were made from their original procedure and why, as well as to apply their new procedure to three additional test cases.

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 – Songs in the Database
Operators – Properties of songs in the database, such as length, tempo, and cost
Relationships – Desired properties of the CD the client is requesting
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. 		CD Song selection must occur for a "various artist" CD and is based on some desired characteristics for the final CD.
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 a playlist for the given subset of the database.
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 describing the procedure for processing the database to select songs.
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 company can use for any target CD based on the client's specifications of the target CD.
Generalizable – reducing a large dataset to a subset that meets a prescribed set of properties must be done in numerous applications outside of CD development.
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? 		The logical underpinings of selecting and handling ties while reducing a dataset are essential in numerous applications such as search engines.

Author Information:

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

Files:

History:
Tested in ENGR106 - Spring 2005 and Spring 2006