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. Reusability 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 Shareability:
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
ReTest / Evaluate Mathematical Model Team Final Solution (Homework)
Address TA Feedback
Incorporate Additional Information (as needed)
Revise Mathematical Model
Document Mathematical Model
ReTest / 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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 Fall '08
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 Das Model, the00, Document Mathematical Model

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