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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 involving mathematical modeling a difficult
problem to solve?
T
roubleshooting
Find the error and correct it!
The graduation party was going to be a special event. We had four generations of family represented
and with a guest list totaling 95 people. The seating arrangements were designed to seat 10 people at
each round table. The tables were supposed to provide a comfortable “home base” for people to last four
hours, the total duration of the party. Unfortunately, many guests were not satisfied with the party. The
parents complained because they couldn’t spend time with their children or the new grandchild. Your
friends felt trapped with your cousins. Unmarried couples were separated. What went wrong?
Use the link available on the companion website to access a seating arrangement model.
M
aking it Matter
Solving problems in your life
Take a personality test such as the one found at the link provided on the companion website. Tests
such as these often determine in which job an individual will thrive. After the test, perform a thorough
analysis of themodel based on themethodology provided earlier in this section.Additionally, compare
the career choices suggested by the site to a field you have been, or are considering pursuing.
●
You have a group project with five other classmates, all with busy schedules. Describe an ideal model
with the purpose of finding times during the week that maximize the number of group members
available to meet. Find a mathematical model already developed for this purpose and use the model
to determine the output for your group.
●
The weather is perhaps the complex dynamic system we deal with in life. Despite the efforts of
several generations to model this system, forecasts rarely provide reliable predictions beyond a week.
To explore this situation in more detail you will find three different sources that model the weather.
Compare and contrast the inputs, outputs, and relationships for each of the models. Determine
the results of the forecast for the next 3 days with each model for the same location and compare
the results. Can we attribute the disparity to different inputs or different relationships between the
models?
9.1 Analyzing and Using Mathematical Models