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A
Successful Performance
Successful application of your learning looks like this
As you begin to apply what you’ve learned, you should have a good idea of what success looks like.
A SUCCESSFUL
PERFORMANCE
When I am given a problem, I can construct a model to solve the problem. I...
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Verify that the purpose of the mathematical model aligns with the current situation
and that there is no appropriate model already available
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Generalize and then formulate the mathematical relationships relating input and
output variables
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Compare model output to known data and make adjustments for accuracy as part of
the refinement process
D
emonstrate Your Understanding
Apply it and show you know in context!
1. Construct a spreadsheet to calculate your overall grade in this class.
2. Construct a tool that determines your income tax due at the end of last year.
3. Suppose each individual at a company needs to have a private conference with each other individual
in order to effectively communicate the different parts of a project they are working on. Create a
model to determine how many conferences are necessary.
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Models, the Methodologies, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not.
What are the conditions and parameters that make a problem where you must create a mathematical
model a difficult problem to solve?
T
roubleshooting
Find the error and correct it!
The votes are in and no one is satisfied
. We had a committee of individuals all place preference ballots,
ranking each of the three candidates (X, Y, Z) running for the position of committee head from first (1
point) to last (4 points). The candidate with the most points, Y, was then declared the winner. The results
of the election revealed some inconsistencies. One member claimed that Z should be the winner since
they had the most first place votes. Another argued that when comparing the results of only X and Y,
the winner is X. What is wrong with the election model? Can it be fixed to satisfy both complaints? If
so who is the winner? Research the mathematical theory of election methods and fairness criteria to
troubleshoot this situation.
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9.2 Constructing a Mathematical Model