MTH 151 – Mathematics for the Liberal Arts I
Sets Application Directions

Purposes
This assignment will help you practice applying what you have learned about set theory to real problems or situations, and communicating about mathematical ideas with others.

Directions
Pick a problem:
Option 1:  Find a problem in your home, school, or work life that you can solve using what you learned about set theory in this unit.  For example, suppose you are coordinating a youth group event to make sub sandwiches to sell as a fund raiser.  You might have tuna subs, regular subs, and vegetarian subs.  Some of the ingredients will be used in several or all three types, while other ingredients will be unique to one kind of sub.  You could use set theory to think through how many portions of each ingredient you will need.  This use of set theory could apply to many different product assembly situations. 
Option 2:  Find an example of the use of set theory in the news.  Data from studies of new medicines, the U. S. Census, and opinion surveys can often be analyzed by applying set theory.
Solve the problem or analyze the use of set theory in an example:
If you picked a problem from your own experience, use set theory to find a solution.  If you picked an example from the news, analyze how theory was or could be used to answer questions about the data.  The better you use the appropriate mathematics to correctly solve the problem or analyze the example, the more points you will earn.
Present the problem or example and your solution or analysis to the others in the class:
Post a message in the application discussion forum for this unit.  In your message, describe the problem or example and how you solved or analyzed it.  Use the equation editor as necessary to show the mathematical operations.  The better you communicate, the more points you will earn.  If you enjoy and know how to use multimedia, such as video, audio, and graphics, you may use those as well, but this is not required.
View and respond to the applications submitted by your classmates.
Pick two of your classmates’ applications that were particularly helpful to you.  Write a response to each, explaining in a paragraph or two why their applications helped you better understand the mathematics for this unit or better understand how the mathematics for this unit could be used outside of class.
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Example:  
Statement of the problem
I am going to have a joint face-to-face meeting of my MTH 151 class and MTH 152 class, and space is limited. Therefore, I want only enough chairs to seat everyone. Some students are enrolled in both classes. How many chairs will I need?
                    
Solution of the problem
Assume that there are 30 MTH 151 students, 25 MTH 152 students, and 4 students taking both classes.  I need to find the number of students in the union of the two classes.  The Cardinal Number Formula is what we need.

For any two sets, .
Let A = the set of MTH 151 students.
Let B = the set of MTH 152 students.
Then, 
I need 51 chairs for my students.
I can either stand or obtain a 52nd chair for me.

Other Topics:  scheduling classes, choosing a restaurant/movie/pizza/baby name, planning a party, iPod management, book distribution, menu planning

Grading Rubric:
Grading Criteria	Points Possible	
The problem:
•	Is it a real-life problem?
•	Is it challenging, not trivial?	5	
The strategies:
•	Are one or more general problem solving strategies used?
•	Are the strategies correctly identified?	5	
The presentation:
•	Is the problem explained well?
•	Are the problem solving strategies explained well?
•	Are the appropriate terms used?	3	
Your responses:
•	Did you post at least two responses?
•	Did you explain how the examples helped you better understand the math in this unit?
•	Did you ask questions for clarification or make suggestions on how to change or improve the original application posting or any other follow-up postings?	2