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 the internal memo and problem description from the client which establishes the need to develop a procedure for placing sprinklers around campus open spaces. Students individually begin to think about what factors need to be considered in designing a sprinkler system plan. The focus is on establishing what factors may be important to consider as the sprinkler system plan progresses.
  2. Team Activity � In teams of 4, students develop a memo to the client 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. They also include a preliminary procedure based on the information they do have. 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 adjusting their solution. Their preliminary solution is meant to be based on the information they have and provides one iteration of a multi-iteration solution
  3. Homework - Continuing in teams of four, students revise their procedure based on feedback and additional information they receive about various sprinkler head mechanisms.

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 – Properties of sprinklers such as distribution pattern and watering intensity, building/sidewalk/plant dimensions and locations
Operators – Minimum and maximum watering intensities allowed in a given area
Relationships – Additive properties of watering and resulting overwatering if watering is excessive or the resulting absence of water if not enough is present.
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. 		Systematic placement of objects, as well as trying to achieve an appropriate level between two boundaries, is commonplace
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 provided sample case allows students to test their procedure on a layout with many of the properties they may need to deal with in their final 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 client describing the procedure for placing sprinklers in the open spaces around buildings and walkways
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 client can use to update the current campus sprinkler system design.
Generalizable – the model should be general enough to handle placing sprinklers around any set of buildings and sidewalks with similar constraints.
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 concepts of geometry and units show up across a wide variety of circumstances. Furthermore, placement schemes of objects such as lights and sprinklers are common in many locations.

Author Information:

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

Files:

History:
Tested in ENGR106 - Fall 2004