I have attached what I would like help on. 2 Questions and 6 Responses

or my homework assignment I am suppose to answer 3 Discussion Questions (I have attached the instruction). Next I am suppose to respond to 4 Questions that have already been solved by one of my classmates. So the part where I stated “Problem Question 1-6 – I would like to respond to” those are the discussion questions that my classmates did and I am suppose to respond to them. The one highlighted in “red” I was showing you a response from another classmate about the problem that another student did to show you that the response can be kind of short as long as it covers the following: 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?

Discussion Questions – General Problem Solving Strategies Application Directions

– Sets Application Directions

– Logic Application Directions

sets-directions.rtf

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.

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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.

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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:

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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.

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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,

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.

Let A = the set of MTH 151 students.

Let B = the set of MTH 152 students.

Then,

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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

logic-directions.rtf

MTH 151 – Mathematics for the Liberal Arts I

Logic

Application Directions

Purposes

This assignment will help you learn to apply what you have learned about logic to real problems or situations, and to communicate about mathematical ideas with others.

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Directions

Pick a problem:

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People try to make logical arguments all around us every day in, for example, citizen comments at government hearings, television commercials, and political speeches. Sometimes the argument is explicit (a and b and c, therefore d), and sometimes it’s implied and you have to restate it in logical terms. You also make logical arguments yourself, such as in writing a paper for an English or history class, or in making a difficult decision. Pick a real logical argument from your own experience to analyze and show whether or not it is valid. The more real and challenging the argument you pick, the more points you will earn.

Solve the problem:

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Use what you have learned in this unit to analyze the validity of the argument you chose. What are the statements? What are the connectors and conditionals? Can you construct a truth table or Euler diagram to determine validity? The more you correctly apply the logical terms, symbols, and analytical techniques from this unit, the more points you will earn.

Present the problem and your solution to the others in the class:

Post a message in the application discussion forum for this unit. In your message, describe the problem and how you solved 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.

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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:

I have a track record of falling ill every autumn. Some say change in weather, some say allergies. All I know is that I’m on good terms with my general practitioner from October onward.

Using Reasoning by transitivity I think my argument is sound.

p=It is fall

q=I am sick

r=I will need antibiotics

If it is fall, then I am sick.

If I am sick, then I will need antibiotics.

If it is fall, then I will need antibiotics

p->q

q->r

______

p->r

Valid argument form.

I’ll go make than appointment now!

Other Topics: Euler diagrams with political examples, consequences of not doing homework

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

Discussion Questions x

Problem 1

– In a roster of 73 NFL football players, 25 were drafted in the 1st and 2nd round for defense and 25 were drafted in the for 1st and 2nd round for offense. Of the remaining players, are 23 vying for a position . How many players will make the team ?~

This problem can be solved with a Venn diagram. First, we find out how many students are on defense (40) and then offense (30). Then we have: Total = defense + offense+ both + neither; 73 = (25-23) + (25-23) + 23 + neither. Answer: Players to make the team= 27

Problem 2

– My husband and I recently decided to start our three year old son in daycare. We were concerned about the financial impact of the daycare fees and had to adjust my husband’s work hours to compensate for the additional expense. We were first faced with the number of days we wanted our son to attend and could choose between three days, four days, or five days. Then we had to determine how many additional hours he could pick up at work to help offset the new expense.

For five days a week the cost was $320.00 weekly and $1,280.00 per month

Four days a week the cost was $280.00 weekly and $1,120.00 per month

Three days a week the cost was $240.00 weekly and $960.00 per month

My husband then discussed the needs for additional help at his gym and was offered an additional 10 hours of work per week. At roughly $25.00 per hour this equated to an addtional weekly income of $250.00 before taxes or $1,000.00 per month before taxes. We calculated taxes to be roughly 28% which meant that his hours would cover about 56% of the full five day week expense of daycare, 64% of the four-day option, and 75% of the three day option.

We ultimately selected the four day option, since the remaining out of pocket expense to us less the additional income my husband would earn was just $400.00 a month.

We backed into our decision, by identifying the expenses first, the additional income available to us second, and identifying how much money we were able to commit out of our current income.

Example of a student responding to this response – Kristy this problem that you solved is similar to one that many families with young children have faced. My son’s mother and I also had to do some budget planning when my son was born. Initially we didnt put a ton of thought into it because we were both working in the military and we knew that she would have six weeks of maternity leave. Needless to say that six weeks flew by and the reality of the child care expenses set in pretty quickly. I didnt have the option of working extra hours, but between the two of us we did have to calculate where we could cut back on miscellaneous expenses in order to cover the cost of weekly day care which amounted to about $1000 per month.

Problem Question 3 – I would like to respond to:

I like to plan out our dinners a month in advance so that I don’t buy too many groceries. I need to figure out how many dinners I need to make over the next 2 weeks. On Fridays we eat leftovers. On Saturdays we eat out. How many dinners will I need to make?

Solution: Let U = All the days we eat dinner. I will use the first 14 days of the month, if the month starts on Sunday, so each number is the date. Ex: 1=april 1st, 2=april 2nd, etc.

{1,2,3,4,5,6,7,8,9,10,11,12,13,14}

Let A = The days we eat leftovers or eat out

{6,7,13,14}

If we find the complement of Set A, we can count how many numbers are in the set to know how many dinners I need to make.

A’ = {1,2,3,4,5,8,9,10,11,12}

I will need to make 10 dinners over the next two weeks.

Problem Question 4 – I would like to respond to: Last year I was involved with a church feeding the homeless around the holidays. The lines was set up for those who came in with their own bags, or rather used the boxes and plastic bags that were supplied by the church. . The last program showed that the people preferred bringing their own bags, rather than using boxes and plastic bags . Three Hundred people showed up that morning. About 100 people brought their own bags, 60 people brought boxes, 100 people used both boxes and plastic bags. I needed to find out what each family prefers to use, then how many people need bags that would be provided by the church?

Let A = the set of people who brought their own bags

Let B = the set of people who prefer boxes and plastic bags.

n(A) = 100, n(B) = , n(A ∩ B) = 100

n(AUB) = n(A) + n(B) – n(A ∩ B)

Plugging-in all the values,

n(AUB) =100 + 60 – 100

n(AUB) = 100

Problem Question 5 – I would like to respond to: In my classroom I have a great ELL (English Language Learner) population. With parent teacher conferences, we are often setting up our meetings with interpreters. I want to find out how many of my students’ parents are both ELL and Spanish speaking so that I can interpret for those meetings myself and know how many I will be doing.

Let A= all ELL students in my class

Let B= just Spanish ELL students

Let C= just Arabic ELL students

Let D= other language ELL students

A= {

a, b, c, d, e, f, g, h, i, j, k, l, m}

B= {

a, c, e, f, j, k, m}

C= {

b, d, l}

D= {

g, h, i}

A∩B= {

a, c, e, f, j, k, m}

A∩C= {

b, d, l}

A∩D= {

g, h, i}

Since I can interpret for the Spanish speaking parents, and I can just use one interpreter for the parents who speak Arabic, I know that I will need to request, at the most, 4 interpreters (not including myself).

I can give the information to the secretary at my school to arrange for 4 interpreters to come in for my parent teacher conferences.

Problem Question 6 – I would like to respond to: Last year I was involved with a church feeding the homeless around the holidays. The lines was set up for those who came in with their own bags, or rather used the boxes and plastic bags that were supplied by the church. . The last program showed that the people preferred bringing their own bags, rather than using boxes and plastic bags . Three Hundred people showed up that morning. About 100 people brought their own bags, 60 people brought boxes, 100 people used both boxes and plastic bags. I needed to find out what each family prefers to use, then how many people need bags that would be provided by the church?

Let A = the set of people who brought their own bags

Let B = the set of people who prefer boxes and plastic bags.

n(A) = 100, n(B) = , n(A ∩ B) = 100

n(AUB) = n(A) + n(B) – n(A ∩ B)

Plugging-in all the values,

n(AUB) =100 + 60 – 100

n(AUB) = 100

strategies-directions.rtf

MTH 151 – Mathematics for the Liberal Arts I

General Problem Solving Strategies

Application Directions

Purposes

This assignment will help you practice applying what you have learned about general problem solving strategies to real problems or situations, and communicating about mathematical ideas with others.

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Directions

Pick a problem:

Option 1: Pick a real problem that you need to solve and use the different general problem solving strategies to try to find a solution. For example, perhaps you need to figure out how to pack an awkward item in your car trunk, or decide what to spend the most time studying for an exam in another class, or plan the assignments and schedule for a charity clean-up project you are organizing.

Option 2: Pick a real problem that someone else has solved and describe the general strategies they used. This could be a friend or relative who solved a problem like the ones described in Option 1, or it could be a historical person, like George Washington Carver, who invented peanut butter and many other things, or Mary Anderson, who invented the windshield wiper.

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Option 3: Pick a currently unsolved problem, like curing cancer or finding better energy sources, and analyze how people are using the different problem solving strategies to find a solution.

Solve the problem or analyze the solution:

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If you are solving your own problem, use the different general problem solving strategies that you learned about in this unit to try to solve it. If you are analyzing a problem someone else solved, or is trying to solve, identify the different general problem solving strategies used.

Present the problem, the general problem solving strategies used, and the solution to the others in the class:

Post a message in the application discussion forum for this unit. In your message, describe the problem and how you solved it. Use the equation editor as necessary to show any 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.

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View and respond to the application problems 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

:

Background: This Saturday is the annual chocolate chip cookie bake sale event. At each of the last 2 bake sale events, there were 600 people who attended. Every annual bake sale must receive 600 attendees. Every attendee eats 5 cookies each.

Problem: We must raise $1,500 for our daughter’s team travel expenses. How many cookies must we make and how much money must each cookie sell for in order to raise the appropriate money?

Solution: 1) The amount of cookies to make are 600 (attendees) times 5 (cookies eaten per person) equals 3,000 cookies to make. 2) 3,000 (cookies made) divided by $1,500 (money needed) equal 50 cents per cookie.

Other

Topics: shipping textbooks, pattern recognition, MPG, budgeting, transportation, metric/English conversions, lottery, time management, retail sales, volume of dirt on a softball field, tipping at a restaurant, yard sales, auto part manufacturing, room design, rate of change, estimate the square root of 3 to two decimal places with a calculator without square root key

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