quantitive literacy final

for this Final Assessment, you will demonstrate successful use of quantitative reasoning appropriately within the context of a real-world situation.

Academic integrity is a core University of Massachusetts Global value. The University expects that students will conduct themselves in an honest and ethical manner and respect the intellectual work of others. Your Final Assessment submission will be checked for academic integrity, and violations may impact your standing within the program. Please refer to your Academic Catalog, Student Handbook, and/or contact your tutorial faculty regarding the standards of academic integrity.

Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Purpose of this Assessment
The purpose of the Final Assessment for this competency is to demonstrate successful use of
quantitative reasoning appropriately within the context of a real-world situation.
Item Required for Submission
A 4-6 page paper in APA format with the four distinct sections detailed below for any of the
investigations you select, following the guidelines for completing the paper completely.
Step ONE: Introduction (1 page)
Describe the investigation you selected from the Appendix: Investigations for Summative Assessment
options below. What is the problem about? What given information have you been provided? What
kind of solution are you expecting? What else might be relevant to consider in your problem situation?
Step TWO: Using Mathematics (1 page)
Any ‘plan’ for solving your problem should require using mathematics. What is the mathematics that is
appropriate to use for your particular problem? What should be the ‘plan’ for solving the problem using
that mathematics? Are there different approaches for how to solve the problem? If so, why did you take
the one you chose?
Final Assessment: Outline and Rubric
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Step THREE: Calculations (1-2 pages)
Effective communication requires organizing the calculations in such a way that the ‘plan’ is evident.
This would include the narrative discussing the calculations, as well as the calculations themselves. For
readability, individual portions of this section can be placed in an Appendix if it is also organized and
supports the ‘plan’ by presenting it that way.
Step FOUR: Solution and Recommendations (1 page)
What solution did you find? How confident are you about the answer? If possible, how accurate is your
answer, and how do you know? If there is another approach that could be used, would you get a better
answer? Based on the work you’ve done, what recommendation are you making about the problem you
described?
Step FIVE: Complete Checklist for Submission
Before you submit your work, check to see if you have met the criteria noted below. Did you:
✓
Make sure your introduction section contains the appropriate discussion for that section?
✓
Make sure your mathematics section contains the appropriate discussion for that section?
✓
Make sure your calculations section contains the appropriate discussion for that section?
✓
Make sure your solutions and recommendations section contains the appropriate discussion for
that section?
✓
For readability sake, label any figure (table, graph, picture) with a brief description (e.g. Figure
3. Graph of Variable Relationship), and use the title in discussing it (e.g., Refer to Figure 3 and
notice the positive slope exhibited)
✓
Demonstrate professional writing and presentation style by:
o Proof-reading your paper to ensure accurate spelling, grammar and punctuation?
o Meeting the specified requirements of length and formatting specifications? o
Providing citations using correct APA format if appropriate?
Step SIX: Submit Your Work
●
Your completed files should be submitted through the Final Assessment page of your
competency.
Final Assessment: Outline and Rubric
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
●
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Please note, for files smaller than 10MB (e.g., most Word documents), use the corresponding
“+UPLOAD STUDENT FILE” button to upload your Final Assessment documents. For larger files of
any type (e.g., voice over PowerPoint files, video presentations), please use the optional TEXT
EDITOR to provide a URL where your tutorial faculty can download your file.
How you create a download URL is up to you, but various free online providers, including Google
Drive and Dropbox, offer this service. Please make sure that the URL you provide can be accessed
by anyone with the link. For further instructions on how to create public links for uploaded files,
consult the support pages for your chosen provider.
List of Templates/Resources Needed
APA 7th edition is required for your assignment. Review this comprehensive tutorial, which also
contains a template that can be used for your assignment.
● UMass Global APA Manual – Student Resource
Scoring Rubric for Final Assessment
Criterion
EMERGING
DEVELOPING
PROFICIENT
EXEMPLARY
Introduction
Not enough detail
to understand the
problem. No given
information or no
expected solution.
The problem is
discussed, maybe
not enough detail,
or some missing
information or no
expected solution.
The problem is
discussed
sufficiently,
including given
information and
expected solution.
The problem is
discussed
completely,
including all given
information and
expected solution.
Mathematics
Mathematics
discussed is
inappropriate for
solving the problem
with the current
‘plan’.
Mathematics
discussed is
appropriate but not
developed
sufficiently to know
whether the
solution is
achievable.
Appropriate
concrete
mathematical
structures (e.g.,
tables, graphs) are
employed in
planning the
solution.
Appropriate
abstract
mathematical
structures (e.g.
equations and
geometric shapes)
are employed in
planning the
solution.
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Calculations
Calculations are
sufficiently
disorganized to the
point that it
impacts the
readability of this
section.
Calculations are not
organized. Three or
more mistakes in
calculations may be
noticed.
Calculations
are
organized and done
correctly. One or
two mistakes in
calculations may be
noticed.
Calculations
are
organized and done
correctly.
No
mistakes
in
calculations
noticed.
Solution/
Recommendati
on
Solution may be
not related to the
calculations
involved, or there
is no analysis about
the scope of the
results.
Solution may be
incomplete or
somewhat fuzzy, or
the analysis about
the results is not
developed
completely.
Solution is
explained and
refers to the
calculations. It
provides
appropriate
analysis about the
results.
Solution is clearly
explained, refers to
the calculations
and
provides
appropriate
analysis about the
results.
Writing
Mechanics
The paper lacks
clarity and may be
confusing; too long
or short. Numerous
errors in spelling,
grammar and/or
punctuation.
No
evidence
of
adherence to APA
formatting.
The
paper
is
somewhat logical
and well-written;
too long or short.
Some errors in
spelling, grammar
and/or
punctuation. Some
deviation from APA
formatting may be
noticed.
The paper is logical,
well-written, and
the required
length. There may
be one or two
minor errors in
spelling,
grammar and/or
punctuation. APA
formatting is
followed.
The paper is logical,
well-written, and
the required
length. Spelling,
grammar and
punctuation are
accurate. APA
formatting is
followed.
Final Assessment: Outline and Rubric
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Appendix: Investigations for Summative Assessment
Investigation #1: Planning to Make Money
Some venture capitalists learned in economics that total revenue is the total receipts a
seller receives from selling goods to buyers, and that it can be written as P × Q, which is the
price of goods times the quantity of goods sold. They hold the plans to the next “hot”
technology gizmo that everyone will want to buy. In pricing the item, they made some
assumptions:
1)
For small quantities purchased, set the price low to invite people to get familiar with the
product.
2)
For large quantities purchased, set the price low as preferential treatment for your best
customers.
3)
Limit the number that can be purchased to a maximum of 1000 units.
4)
An analyst recommends that the selling price for 500 units be $2500, or you will price
yourself out of the market.
Therefore, they envision the pricing scheme shown in the graph as a rough model for projecting
revenue. They have hired you as a consultant to make a recommendation about what the maximum
revenue will be for the company under this business plan. Even though the units may be sold in
different quantities, the central question to ask is, “If all the purchases involved the same exact number
of items, what would be the revenue for the company under that condition, and when would the revenue
be as big as possible?” This would provide a ceiling figure to report back to the investors.
Investigation #2: Break-Even Point From Data
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
The Marketing Department has come up with the data shown in the graphs below. (Note: they
are showing trends in the company performance.) You can see that the revenue peaks and starts to
come back down, but the costs keep increasing, so the Management Team is concerned about when the
company will ‘break even’.
Your job is to make a recommendation to the Management Team about approximately how far off in
the future is the ‘break-even’ point for the company. Without using statistical tools, model what the
data indicates as a single cost equation and a single revenue equation. (If using specific points to model
the equations, be sure to communicate what those coordinates are.) Then use your equations to find
the ‘break-even’ point and communicate your findings.
Investigation #3: Time Series Analysis
In order to better understand the problem, an intern air traffic controller decides to simplify the
problem of describing objects in motion. She decides to pretend the planes are flying along the ground
at a constant height of 0 miles. Here is the simplified description of her problem, which uses Quadrant I
of the standard coordinate system:
One plane has starting coordinates (0, 80). It moves in a westerly direction at 20 miles
per hour and in a southerly direction of 10 mile per hour. Another plane has starting
coordinates (200, 0). That plane moves in an easterly direction at 15 mile per hour and
in a northerly direction of 30 miles per hour. A picture of the situation is shown below.
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Will the planes collide? Why or why not? Explain how you would adjust the starting conditions
of the problem in order to cause the collision to take place.
You may find the following “tools” helpful: time-series graphs show one directional motion over time,
state-space graphs show horizontal and vertical motion without showing time (actual motion), and
indicating the time at each point in a state-space graph produces a time sequence state-space graph.
Investigation #4: Comparing cell phone plans
LuckyUCalled is a company that offers several cellular service plans.
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Based on your past history, you expect to use your phone anywhere between 100 and 300 minutes per
month and it usually involves a data transfer of anywhere between 20 GB and 100 GB. If you restrict
your attention to just these three plans that LuckyUCalled offers, which one would you select? Why?
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #5: Football Team Revenues
In basic terms, the total revenue from a professional football team should come from three
sources: attendance at the live event, whether there is television revenue involved, and merchandising.
It is reasonable to assume that:
· attendance is related to the chance of success overall
· television exposure is related to the chance of success overall
·
marketing can be related to the chance of success overall, but doesn’t have to be. Star
power can drive sales from outside your local fan base region
Here is some basic information about two professional football teams: the Los Angeles Rams
and the Tampa Bay Buccaneers.
Los Angeles Rams
Stadium capacity (70,240) Field level: 20,000 Loge Level: 25,000
Upper Level: 25,240
Ticket prices: Field level: $250/game Loge Level: $150/game Upper Level: $75/game
Current COVID-19 restrictions: every 4th seat
Television revenue: $40M per minute per game (60 minutes per game)
Number of games per season to be televised: it could be 2 up to 8, based on chance of winning.
Likelihood of a cancellation due to COVID-19: 40%
Projected chances of winning 2022 Super Bowl (scale of 0 – 10): 7
Fan Base: 13,131,000
Merchandising History: when “hot”, sales of $100M; when “not”, sales of $10M
Tampa Bay Buccaneers
Stadium capacity (65,890) Field Level: 25,000 Loge Level: 25,000 Upper Level: 20,890
Ticket prices: Field level: $200/game Loge Level: $100/game Upper Level: $50/game
Current COVID-19 restrictions: every 5th seat
Television revenue: $50M per minute per game (60 minutes per game)
Number of games per season to be televised: it could be 4 up to 8, based on chance of winning.
Likelihood of a cancellation due to COVID-19: 20%
Projected chances of winning 2022 Super Bowl (scale of 0 – 10): 9
Fan Base: 4,000,000
Merchandising History: constant nationally at $50M due to the Brady phenomena
Compare these two cornerstone franchises of the National Football League. Based on this information
alone, which team will make more revenue?
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #6: Comparing job offers
There are many factors to consider when comparing job offers – the salary and benefits, the taxes, the
cost of living, the cost of leaving, and other costs incurred by taking the new job. Here are three job
offers for similar types of work for which you are eminently qualified. You currently hold the job in
Silicon Valley, but you are considering choosing the offers elsewhere.
Location
Silicon Valley, CA
Seattle, WA
Austin, TX
Salary Offer
$250K
$200K
$150K
Retirement Benefits
8% contributed by
employer
6% contributed by
employer
7% contributed by
employer
Other Benefits
Stock option worth
$200K
Tax Rate
13%
12%
7%
Cost of Living
60% above national
average
40% above national
average
20% above national
average
Cost of Leaving
Not vested yet. You
lose 4 years of
retirement accrued
To break the contract
will cost $50,000
penalty.
Not vested yet. You
lose the stock option.
Relocation Costs
Up to $10,000
reimbursed
Up to 4% of salary
Compensated an
amount of $3000
You currently spend around $6000 per month in living expenses; you would live a similar lifestyle
wherever you work. Project your total earning for five years into the future whether you stay put or
take one of the other job offers. Which scenario provides the greatest accumulated earnings after five
years?
Investigation #7: Tile Counter Design
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
The classic Victorian tile pattern shown in the figure features green regular octagons and yellow squares
in a tiling pattern that leaves no space between individual tile pieces. The pattern has been in such big
demand that the manufacturer can no longer provide the green tiles to customers. The management
thinks that it can design smaller pieces that can be fit together exactly to look like the original shapes,
and the process can even be applied to the squares.
The management team has asked you to work on the problem, keeping the size of the pieces (number
of sides) as small as possible. Imagine that you can manufacture as many pieces as you want, so supply
will no longer be a problem. How many different shapes of each color would you want to start with?
What would be their dimensions relative to the original tiling pattern?
Investigation #8: Total Cost of a College Education
Think about when you were graduating from high school. If you knew everything you know now about
going to college, would you still make the same decision? Specifically, what is the cost of getting a
college education – the total cost? Imagine a graduating senior who is wrestling with a similar problem
— “Should I go to college, or not?” Analyze the situation using both your experience and what ‘experts’
say about the problem. Then write a report to the student explaining the benefits as well as the costs of
continuing with her/his education. Be sure to consider the total cost of getting an education – the
explicit and implicit costs involved. If you didn’t go to college, you could get a job that pays $12/hour (if
you’re lucky). On the other hand, once you graduate, you can get a job that pays $40/hour to start.
Consider all the lost revenue as well as the costs in your explanation.
Final Assessment: Outline and Rubric
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Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #9 – Considering Combinations of Postage Stamps
Suppose you have 4-cent stamps and 9-cent stamps in unlimited quantities, and you can combine them
to produce certain amounts of postage. For example, you can make 40 cents of postage by using four 9cent stamps and one 4-cent stamp, or by using ten 4-cent stamps. However, there are some amounts of
postage that you cannot make with those stamps, such as 10 cents.
What is the largest amount of postage that you cannot make exactly from a combination of 4- and 9cent stamps? How do you know?
If you consider other types of stamps, are there combinations where you cannot answer the question,
“What is the largest amount of postage that you cannot make exactly from combinations of those types
of stamps?”
When you have done investigating this problem, you will be able to describe working with two generic
types of stamps whose face values are ‘a’ cents and ‘b’ cents, and can tell the conditions under which
the problem can and cannot be solved, and if it is possible to solve the problem, what the largest
amount of postage that you cannot make exactly from combinations of those types of stamps. For
example, if a = 4 and b = 9, then the problem can be solved and the largest amount of postage you
cannot make would be 23 cents. But your description should output that answer from knowing the
values for a and b.
Final Assessment: Outline and Rubric
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