Class1b -   Have Homework 1 out in front of you...

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Unformatted text preview:   Have Homework 1 out in front of you   Bring MATLAB text to next class At the end of this topic, you will be able to:   Define “model”   Describe a model development process   Identify a user   Identity the user’s needs from a problem statement in terms of a deliverable, criteria for success, and constraints   Describe the characteristics of a high quality mathematical model solution in terms of generalizability: share ­ability, re ­ usability, and modifiability A model is a system for interpreting, explaining, describing, thinking about …. another system A mathematical model uses mathematics (e.g. geometry, statistics, logic, …) to interpret another system 1.  2.  Understanding the Context of the Problem / System to be Modeled Express / Test / Revise a Working Model       3.  4.  Express (develop the model) the procedure Test (evaluate the model) the procedure Revise (re ­develop model) the procedure Evaluate the Working Model Document the Working Model Define the problem Test and implement solu2on Analyze & select a solu2on Gather informa2on Generate mul2ple solu2ons Adapted from Steven K. Howell, Engineering Design and Problem Solving, 2/e, 2002. Explore options for constructing model Gather information, make assumptions Identify a system to be explained by a model Define the goals for the model What are the conditions of its performance? e.g. limits, precision Revise Model Model does not predicts specific conditions or is incomplete Anticipate and select which version of a model will be used Compare results of model with actual performance of a “system” Build model and test for specific conditions Accept Model for use as a Tool (under specific conditions) Model predicts specific conditions   Realistic open ­ended problems with direct and indirect users in need of a problem solution   Require team of problem solvers   Product is the process for solving the problem   End product is a mathematical model that the direct user can use Homework 1: MEA  ­ Sports Equipment – Part A   Your method for determining the maximum number of hexagons that fit on a piece of 8 ½ in. x 11 in. paper   Your answers to these questions:   Who is the direct user of the deliverable your team is being asked to create?   In one or two sentences, what does the direct user need?   Who are the other stakeholders / indirect users? What do each of them need?   Describe at least two issues that need to be considered when developing a solution for the direct user.     Introduce Yourselves to Your Team Assign Team Member Roles           Meeting Coordinator Recorder Timekeeper Encourager/ Gatekeeper Come to consensus on these questions: (5 min)   Who is the direct user of the deliverable your team is being asked to create?   In one or two sentences, what does the direct user need?   Who are the other stakeholders / indirect users? What do each of them need?   Describe at least two issues that need to be considered when developing a solution for the direct user Scoping the Problem/Problem Identification   Who are the stakeholders? Memo: •  … Newpaper Article: •  … Scoping the Problem/Problem Identification   Who are the stakeholders? Memo: Newpaper Article: •  Tracey Kelly, CEO •  Tahira & her mother •  Ultimate (the company) •  Children in Pakistan •  Ultimate’s computer •  Manufacturers programmers •  International Labor Organization   What do each of them need? ▪  ▪  ▪    What are the roles of these stakeholders? How will they interact with or benefit from a solution to this problem? Are they direct or indirect users? Who is the direct user of the deliverable your team is being asked to create? Scoping the Problem/Problem Identification   In one or two sentences, what does the direct user need? Scoping the Problem/Problem Identification In one or two sentences, what does the direct user need? To minimize material waste, the Ultimate’s computer programmers (direct user) need a procedure to determine the maximum number of a specified shape that can be cut from a piece of material of known dimensions. Anatomy of a good response:   Deliverable the direct user wants   Criteria for success   Describes what this deliverable is for and how it should function   Quantify the performance needed when it is possible   Constraints   Describes how the problem is bounded Scoping the Problem/Problem Identification Describe at least two issues that need to be considered when developing a solution for the direct user. What are issues that are within the scope of the problem your team has been asked to solve? Scoping the Problem/Problem Identification Describe at least two issues that need to be considered when developing a solution for the direct user. What are issues that are within the scope of the problem your team has been asked to solve? Who are the issues you’ve identified related to? Memo: •  Tracey Kelly, CEO •  Ultimate (the company) •  Ultimate’s computer programmers Newpaper Article: •  Tahira & her mother •  Children in Pakistan •  Manufacturers •  International Labor Organization Team Activity (15 min)     Read each team member's individual procedure for hexagons  ­ come to consensus about a procedure that can be applied to any shape Draft a memo to Tracey Kelly that includes:   Your team’s procedure for determining the maximum number of shapes   Results – the maximum number of hexagons with other appropriate quantitative measures Team Activity (15 min)     Test your procedure using pentagons Note which steps work well   Note which steps do NOT work well   Make modifications to your model that make it better able to handle both shapes               Restates the task  ­ clarifies who the direct user is and what the direct user needs Provides an overarching description of the procedure States assumptions and limitations about the use the procedure Lists the steps of the procedure with clarifying explanations (e.g. sample computations) for steps that may be more difficult for the direct user to understand or replicate Contains acceptable rationales for critical steps in the procedure Clearly states assumptions associated with individual procedural steps Provides quantitative results of applying the procedure to specified data Mathematical Model   Specific to the MEA and the mathematical concepts expected to be employed to address the complexity of the problem. Generalizability   Share ­ability   Share ­ability means that the direct user can apply the procedure and replicate results.   Re ­Usability   Re ­usability means that the procedure can be used by the direct user in new but similar situations.   Modifiability   Modifiability means that the procedure can be modified easily by the direct user for use in different situations. Characteristics of a high quality MEA solution: Share ­ability Share ­ability means that the direct user can apply the procedure and replicate results Results from applying the procedure to the data provided are presented in the form requested. (If not included: D ­level work)   The procedure is easy for the direct user to understand and replicate. All steps in the procedure are clearly and completely articulated.     Spelling and grammar are not distracting   Clear and organized (e.g. numbered steps may be appropriate)   No extraneous information Characteristics of a high quality MEA solution: Re ­usability Re ­usability means that the procedure can be used by the direct user in new but similar situations. A re ­usable procedure:   Identifies who the direct user is and what the direct user needs in terms of the product, criteria for success, and constraints   Provides an overarching description of the procedure   Clarifies assumptions and limitations concerning the use of procedure Characteristics of a high quality MEA solution: Modifiability Modifiability means that the procedure can be modified easily by the direct user for use in different situations. A modifiable procedure:   Contains acceptable rationales for critical steps in the procedure and   Clearly states assumptions associated with individual procedural steps. Characteristics of a high quality MEA solution: Mathematical Model     The procedure fully addresses the complexity of the problem. The procedure takes into account all types of data provided to generate results OR justifies not using some of the data types provided. To: Tracey Kelley From: Team 12 Re: Machine Made Sports Equipment Date: 1/28/09 To minimize material waste, the Ultimate’s computer programmers need a procedure to determine the maximum number of a specified shape that can be cut from a piece of material of known dimensions. The procedure below will enable the programmers to establish a range for the maximum number of shapes. This procedure requires that at least one shape fit on the material and that the material is rectangular in shape. Re-usability Check:   Identifies who the direct user is and what the direct user needs in terms of the product, criteria for success, and constraints   Provides an overarching description of the procedure   Clarifies assumptions and limitations concerning the use of procedure This part of the procedure is used to determine a minimum bound for the maximum number of shapes that can fit on the material. 1. Inscribe the shape in a rectangle. (why? – approximate the shape as a common shape the dimensions of which can be easily determined) 2.  Find the height and width of the rectangle. For the hexagon provided: height = 1.75 in; width = 2.00 in 3.  Take the width of the material and divide by the rectangle width and round this number down to get X. (why? – yields the whole number of shapes that can fit along the width of the material) X = 8.5/2 = 4 4. Take the height of the material and divide by the rectangle height and round this number down to get Y. (why? – yields the whole number of shapes that can fit along the height of the material) Y = 11/1.75 = 6 5. Multiply X and Y to yield the minimum bound for the number of shapes that can fit on the material LOWER BOUND: 4 x 6 = 24 NOTE: This sample is more cryptic than your team’s solution will be. Your team will need to present the solution with complete sentences. This part of the procedure is used to determine a minimum bound for the maximum number of shapes that can fit on the material. 1. Inscribe the shape in a rectangle. (why? – approximate the shape as a common shape the dimensions of which can be easily determined) 2.  Find the height and width of the rectangle. For the hexagon provided: height = 1.75 in; width = 2.00 in Modifiability Check:   Contains acceptable rationales for critical steps in the procedure and   Clearly states assumptions associated with individual procedural steps (Not always needed; depends on the solution method) This part of the procedure is used to determine a minimum bound for the maximum number of shapes that can fit on the material. 1. Inscribe the shape in a rectangle. (why? – approximate the shape as a common shape the dimensions of which can be easily determined) 2.  Find the height and width of the rectangle. For the hexagon provided: height = 1.75 in; width = 2.00 in Share-ability:   Results are presented in form requested   All steps in the procedure are clearly and completely articulated ☺ Numbered steps ☺ Sample calculations for complex steps   No extraneous information             Always work towards meeting the direct user's needs Need to decide when you have a solution that meets the direct user's needs Verify your solution  ­ does it make sense? Contribute to your team’s solution Employ effective teaming techniques Critically evaluate the MEA solutions of other teams   Facilitate your team's solution path not impose their own           What is your team doing? Why are you doing it? Is it working? How do you know? Provide constructive feedback to your team   Guide you to a share ­able, re ­usable, and modifiable procedure for the direct user   Enable you to develop your problem ­solving skills   Foster effective teaming   Ensuring individual participation   Staying on task Individual Reading & Questions (Homework) Setting the context of the problem Team First Draft (Class) Construct Mathematical Model Document Mathematical Model Test Mathematical Model Peer Critique Calibration (Homework) Peer Critique Calibration Comparison to Expert (Homework) TA Feedback & Grade on Individual Questions Team First Draft Peer Critique (Homework) Team Second Draft (Homework) Address Peer Feedback Incorporate Additional Information (as needed) Revise Mathematical Model Document Mathematical Model Re-Test / Evaluate Mathematical Model Team Final Solution (Homework) Address TA Feedback Incorporate Additional Information (as needed) Revise Mathematical Model Document Mathematical Model Re-Test / Evaluate Mathematical Model TA Feedback and MEA Final Grade Peer Feedback on Your Peer Critique (PFYPC) (Homework) MEA Reflection (Homework) TA Feedback and Assessment ...
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This note was uploaded on 08/25/2011 for the course ENGR 195 taught by Professor Staff during the Fall '08 term at Purdue University.

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