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 newspaper article and problem description from the client which establishes the need to identify the least expensive alternative for placing lights around campus buildings and walkways. Students individually begin to think about what factors need to be considered in evaluating the proposed lighting plans. The focus is on establishing what factors may be important to consider in the economic analysis.
  2. Team Activity � In teams of 4, students develop a memo to the board of trustees requesting any additional information need to develop a procedure, as well as a ranking of how important the requested items are and the intended use of those items. The goal is to get students thinking about not only what information they currently have, but also what information they think they may need and why they may need it for developing their solution.
  3. Homework - Continuing in teams of four, students develop a procedure for evaluating the economic viability different lighting proposals. Their procedure is intended to be general enough that it can be applied to multiple proposals with minimal adjustments to the procedure.

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 – Number/Type/Lifespan of lights, replacement schemes
Operators – How the replacement scheme interacts and depends on the lights
Relationships – The number and lifespan of a bulb and the replacement scheme options are related. A lower lifespan means having to replace more often, but if there are fewer bulbs in need of replacement then that may be acceptable.
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. 		Economic comparisons are commonplace in industry and evaluating options such as this are not rare.
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 proposed lighting schemes also allows students to test their procedure
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 Board of Trustees describing the procedure for evaluating the economic viability of various lighting alternatives and replacement schemes.
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 of Trustees can use to evaluate numerous proposals and replacement schemes.
Generalizable – the model should be general enough to handle evaluating any proposal and replacement scheme.
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? 		Economic analysis and comparison of alternative is a common problem. Furthermore, much of this problem is simply making multiple small related calculations, an exercise in basic problem solving.

Author Information:

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

Files:

History:
Tested in ENGR106 - Fall 2003