Campus Sprinkler Design

Concepts

  • Geometry
  • Units and Unit Conversions
  • Additive Properties

MEA Description: The Campus Sprinkler Design MEA requires teams of students to develop a generalizable procedure for placing sprinkler heads around campus open spaces for a university. The motivation for developing this procedure is established using a realistic context in which the university would like to redesign the existing system to better distribute water for grass and plants and to reduce overwatering of these items. The client wishes to improve the current sprinkler system and provide a more efficient campus sprinkler system. The teams must take into account the size and strength of sprinklers and the effects of having too much or too little water in a given area. The student teams are required to (1) develop a reusable general procedure for sprinkler placement such that the minimum watering requirements are met but not exceeded to the point of causing overwatering and (2) use the procedure to provide a sample layout on a provided map of a sample building and the surrounding walkways and grassy areas.

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.

Files:

History:
Tested in ENGR106 - Fall 2004