Project 1 Introduction

This project is a chance for you to demonstrate your quantitative reasoning skills. In this project, you will first evaluate the written work of other students and then submit your own written work. The full project is worth 30 points, 5 of which will come from your evaluation of other projects and 25 of which will come from your own work.

Evaluating Projects

As you evaluate projects, you will be shown 3 projects and asked to rank them according to the project rubric in order from best (1) to worst (3). Make sure to take note of your rankings because you will need to justify your rankings in "Project Evaluation 1."

When you are evaluating, use theProject Rubricbelow to organize your thoughts and justifications. The TA's will grade your evaluations based on the correct rankings and your justifications for the way you rank the samples.

Tips for Success

The best way for you to do well is to follow the rubric below, both for your own submission and as you evaluate other projects. You will also want to clearly demonstrate the skills you learned in this unit and follow any specific instructions in the project outline. To begin you will need to come up with a problem or a question to solve using the quantitative skills you have acquired in this unit (Ratios and Rates).

Project Outline

Problem

Clearly state the problem you are exploring. Describe how you came up with it, and answer the following questions. Why does it qualify as a quantitative reasoning question? How does it relate to you, and why is the solution important or interesting to you? Having a unique, original question will make your paper more interesting. Make sure that there are multiple aspects to your question or that there are multiple solutions to explore, or both. This will show that your question has depth.

Gather Information

What information (measurements, facts, values, formulas, etc.) or data did you need to gather to answer the question? How and where did you get this information? If you couldn't find the needed information, give it your best estimate and explain why you think your estimate is reasonable.

Analyze

This is the main part of your paper. Describe the process you went through to make sense of the information you collected, to organize an approach to solve the problem, and to determine an answer to your question. Make sure your math is correct. A good quantitative reasoning analysis will discuss things that are not purely mathematical. Take into account and discuss other aspects of real life that will affect the question you are exploring and the decision you will make, even if these aspects aren't quantifiable (representable numerically). This section may include graphs or other visual representations of data.

Interpret and Act

Provide a clear and complete substantive answer to your question. Come to a clear conclusion or decision. Then interpret the answer: What does the answer mean for you? How does the answer solve the problem? How can you use the answer in your everyday life?

Reflect and Inquire Again

Do not forget to include this section in your project! Now that you have the answer, is there something you would do differently? What new questions arise from your answer? How could you extend this problem? What further questions could you now explore if you had more time?

Project Rubric

Category

Criteria

Points

Problem/Inquiry

1.The problem being explored is clearly stated.(1point)

2.The problem being explored is quantitative and meaningful to the writer.(1point)

3.The question is nontrivial, unique, and has multiple aspects (deep).(1point)

___/3

Gather Information

1.Student thoroughly explains their process of gathering data and information (e.g. measurements, facts, values, formulas, etc.), including where the data was collected from.(1point)

2.Information gathered makes sense in the context of the questions being asked.(1point)

3.Student accurately explains why this data/info was collected.(1point)

___/3

Analyze

1.Mathematical computation is accurate and correct.(4points)

**If the mathematical computations are incorrect, the student cannot get full points in the categories below.

2.Student presents an organized approach to walking the reader through each step of the problem-solving process.(1point)

3.The analysis takes into account any aspects of real-life that may affect their reasoning process.(1point)

___/6

Interpret and Act

1.Student's conclusion or answer to the question is clearly stated.(1point)

2.The student interprets the data.(3points)

3.The student discusses how this conclusion can be applied to their life.(1point)

**If the answer is unclearandthe student doesn't state any application to their life then the student receives a zero for this section.

___/5

Reflect and Inquire Again

1.Student reflects deeply on the results.(2points)

2.Student states how this problem can be further explored, extended, or analyzed.(1point)

**If the reflection is superficialandthe student does not mention how the problem can be further explored, extended, or analyzed then the student receives a zero for this section.

___/3

Total Points:

___/20 Points

*If any of these sections are missing from the student's project, the student will receive 0 points in that section.

The purpose of this assignment is to help you identify the strengths and weaknesses of the quantitative reasoning of others. In this unit, the projects you will evaluate use ratios and rates. Compare the three sample projects and rank them from top (strongest) to bottom (weakest) using theproject rubricand these guiding evaluation questions:

Was the question something that can be analyzed using quantitative reasoning?

Was the reasoning correct?

Was the math correct?

Was the math reasonable in context of the situation?

Does it have a justifiable conclusion?

Be prepared to justify your rankings.

This assessment can only be taken one time.

Project 1 Sample A

Problem

My husband and I are trying to decide whether or not we should buy a new car. We currently have a 2013 Altima and a 2005 Hyundai Sonata. We both drive 15 miles in separate directions for work and we are spending a fortune on gas! But we have to get to work, and we earlier calculated if it would cost more or less per month for my husband to ride public transit. We found that after the cost of gas and the car payment we would pay less per month to keep our 2005 Hyundai then to sell it and have him just ride public transit. But now my work requires me to travel back and forth twice daily. We also are starting to think about having a second child. We need a car that gets the same or better gas mileage as our Hyundai, and has more room in the back seat for two car seats and storage in the back for a stroller.

Gather Information

We have two cars we need to look at, and the third car is what car we would potentially buy. Our 2005 Hyundai Sonata gets on average 26 miles per gallon. The gas tank holds 17.2 gallons. This means on average you can travel 447.2 miles on one tank of gas. We pay a monthly car payment of $77.56. We owe about $1,500 on this car and hope to sell it for $2,500. Our 2013 Nissan Altima gets on average 33 miles per gallon. The gas tank holds 20 gallons. This means on average you can travel 660 miles on one tank of gas. We pay a monthly car payment of $256. We would like to get a 2013 Jeep Compass because we need a smaller SUV to fit two car seats and room in the back to store the stroller. The average cost, according to Kelley Blue Book, for a used 2013 Jeep Compass is $10,721. This would give us a car payment of about $214 a month. The Jeep Compass gets on average 26 miles per gallon. The gas tank holds 13.6 gallons. This means on average you can travel 353.6 miles on one tank of gas. Currently at Costco gas is $2.28. Our Costco membership is paid for by his parents, so it does not factor into any costs here.

Analyze

First, we will analyze information from the Hyundai Sonata. One tank of gas at Costco is $39.22 and we pay $77.56 on a car payment. But, we fill up with gas twice a month. So currently, we spend $78.44 on gas. So, for the Hyundai we spend $156 a month. Now the Nissan Altima, which we fill up with gas three times a month. We spend $256 on a car payment and for one tank of gas at Costco we spend $45.60. So currently, we spend $136.80 on gas. So, for the Altima we spend $392.80 a month. Together with the Altima and Hyundai we spend on gas and car payments $548.80. With the Jeep Compass one tank of gas at Costco would be $31.01. Because this car would be replacing the Hyundai and the Compass gets less miles per gas tank, I would assume we would fill this car up 2.5 times a month (three times one month, two times the next for once every 2 weeks). We would spend $77.53 on gas and $214 on a car payment. So, for the Jeep we would potentially spend $291.53. If we were to sell the Sonata and buy the Compass, our total each month on gas and car payments with the Compass and Altima would be $684.33.

Interpret and Act

The cost of gas between the Hyundai and Jeep is within a dollar of each other with the Jeep being $0.91 less. No matter what car we get the Jeep Compass is very comparable and possibly a good choice for our family because the cost of gas is around the same.

Reflection

I was not able to take into account the cost of insurance and the difference that would make. I know it would be more expensive because of we would have an SUV, but I'm not sure how much more it would be. We would also need to make sure we could sell the Sonata so we have a down payment for our next car.

Project 1 Sample B

Problem

As part of my responsibilities at church, I was assigned to gather information about, and then purchase, refreshments for a youth and parent activity. What dessert items would be least expensive to purchase for our large group, while still having variety in flavors?

Gather Information

The information needed to solve this problem includes the number of people attending the event, the available budget, and the price of different refreshment options. I estimated 300 youth and parents would attend the activity, based on past events. My total budget to spend was $200. Pricing information came from BYU Food to Go where my church unit has a direct billing account. I narrowed down the dessert choices based on the options for variety and similar cost per unit. Cookie Tray: (5 flavors available, a mixed tray includes all five varieties) 7 dozen per tray = $39.50, 5 dozen per tray = $29.00. Brownie Tray: (12 flavors available, but only 1 flavor per tray) 18 inch tray cut into 30, 40, or 50 = $29.50. Donuts: (5 flavors available, 1 flavor per dozen) 1 dozen = $6.25. To figure out how much each unit costs, I need to know the number of units in each package and how much each package costs. I need to know my budget so I don't spend more than I should and I need to know how many people are attending so I make sure to have enough refreshments for everyone.

Analyze

To find out which dessert item would be the most inexpensive, I needed to calculate down to price per unit for each item. Then how many trays or dozen would I need for 300 units. And finally, the total cost of the amount of trays or dozen I calculated I would need. For the cookies, I needed to find out how many units are in the 7doz and 5doz trays. 7x12 = 84 and 5x12=60. I divided the total cost of a tray by how many units there were to find the price per unit: 7doz tray was $39.50/84 = $0.47 while the 5doz tray was $29.00/60 = $0.48. Then I needed to find out how many trays I would need to get as close to 300 units as possible. I divided 300 by the number of units on each tray: 7doz tray was 300/84 = 3.57 (so I needed to get 4 trays), 5doz tray was 300/60 = 5 trays. Four 7doz trays was 4x$39.50 = $158 while five 5doz trays calculates to be 5x$29 = $145. Brownies come in 18-inch trays that cost $29.50 and can be cut to 30, 40, or 50 units. I divided $29.50/30 = $0.98, $29.50/40 = $0.74, and $29.50/50 = $0.59 to find the cost per unit. Next was to divide 300 by the amount of units of the different sizes per tray to find out how many trays I would need. 300/30=10 trays, 300/40=7.5 (so 8 trays), 300/50=6 trays. Finally, I multiplied the total number of trays (in each size cut) by the total cost of a tray. 30-cut tray was $29.50x10=$295, 40-cut tray was $29.50x8 = $236, and 50-cut tray was $29.50x6=$177. Donuts were more straightforward to calculate. First was finding cost per donut by dividing the cost per dozen by 12 which was $6.25/12= $0.52 per unit. Next was to find out how many dozen were needed for 300 units which was 300/12=25 dozen. Finally to calculate the total cost was how many dozen I needed multiplied by the cost per dozen which was 25x$6.25=$156.25.

Interpret and Act

Trays of 50-cut brownies, donuts, and the 5doz cookie trays were within my budget. However, after estimating the size of a brownie from a 50-cut 18 inch tray, I thought it too small of a dessert piece and ruled it out even though it would give slightly more variety. The closest in cost with only an $11.25 difference and totaling 300 units exactly were the donuts and 5doz cookie trays. Both also had 5 different flavor options. I decided to purchase 5 trays of 5doz cookies, each tray with an assortment of flavors because it was the less expensive of the 2 choices left. My total cost was $145, which was $55 under budget.

Reflect and Inquire Again

My analysis and interpretation gave me the information I needed to choose refreshments that fit my budget and had some variety. I was surprised to see that the famous BYU brownies are quite a bit more expensive than other dessert options. Even though the cookies in a tray of 7 dozen was less expensive per cookie, because I could get exactly 300 cookies with trays of 5 dozen, the best price over all was to go with the 5 dozen cookie trays. After my decision, I wondered if I could have purchased milk or punch to drink with the remaining $55 of my budget. I would have needed to continue my research on milk and punch prices per gallon, ounces per gallon, and how many gallons I would need for 300 people.

Project 1 Sample C

Problem

I got in a playful argument with my brother the other day whether or not it's better financially to own only one pair of shoes at a time and replace as needed (my brothers' preferred method), buy multiple pairs (let's say 7) at once and cycle them around (my preferred method), or if they were equal. After both of us threw out a few unsupported ideas to back up our argument, I really did want to know which method was better.

Gather information:

I did some research to find the data for a couple of the variables I needed to plug into my equation. I read through a study from 2013 that found the average shoe cost for males was $65.08. Accounting for a cumulative rate of inflation of 5.8% from 2013 to 2018, the average shoe cost today should be $68.87. However, this is only calculating for the value of shoes. Since we are purchasing shoes, we need to apply Utah's sales tax of 4.7% giving us a grand total of $72.11. As for the life of a typical shoe, I found that it varies from 1,000 miles to 1,500 miles. The two of us take very good care of our shoes so I'm picking the high end of the spectrum at 1,500 miles. The average US male walks 5,117 steps per day and has an average stride of 2.5 feet. That equals 2.42 miles walked per day on average. There is a shoe store 2.4 miles from my house and my 2010 Honda Civic gets an average of 26mpg in the city. I also found that the current national average for gas prices is at $2.538.

Analyze:

I'm going to play out both scenarios from the average age of my brother and I, 26, until the average death of a US male, 76. Individual 1: 1 pair of shoes at a time With a max life of 1,500 miles divided by a daily walking rate of 2.42 miles, a cycle of shoes in this scenario will only last 619.83 days. This means that approximately every 620 days this individual would have to spend $72.11 on new shoes. There will be 18,200 days from the age of 26 to 76 meaning this individual will buy new shoes a total of 29.36 times in their life. You can't pay for 0.36 of a shoe so they would need to buy shoes 30 times. Each trip, 2.4 miles in a car getting 26mpg, will use 0.092 gallons of gas one way. A round way trip, using 0.185 gallons of fuel, will cost $0.46 if the fuel costs stay the same forever at $2.538 per gallon. With 30 shoe purchases at $72.11 a pop for a total of $2,163.30, plus 30 trips costing $0.46 for a total of $13.80, the lifetime expense on shoes is $2,177.10. Individual 2: 7 pairs of shoes at a time If this individual owns 7 pairs of shoes at time, assuming they alternate each shoe every day, they will only need to go shopping 7 times as frequently as individual 1 (619.83 days) which is every 4,338.84 days. However, each shopping spree costs 7 times as much, coming in at $504.77. With the same 18,200 days from age 26 to 76, they would go on a total of 4.19 shopping trips. The same rule applies, you can't buy 0.19 of a shoe, so it be 5 total shopping trips. 5 trips at $0.46 equals $2.30, plus the cost of the 5 trips at $504.77 for shoes equalling $2,523.85, the lifetime expense ends up being $2,526.15.

Interpret and Act:

Assuming that all of the averages are correct and that it's a perfect scenario, it makes more sense to only buy one pair of shoes at a time. If you were a person that valued being able to have more choices of shoes, and are willing to pay an extra ~$350 over your lifetime for that privilege, then scenario 2 would be better for you.

Reflect and Inquire Again:

I think there are still a lot of factors to the equation. You could invest money if you were only buying shoes one at a time which would make it a cheaper option, shoes could wear out faster if you wear them consecutively vs. giving them a break and letting them breathe. I still stick to my opinion of it making sense to own more shoes at one time rather than upgrading the same one pair every time you need to, even if it does make less financial sense.