# PROBABILITY, STATISTICS, & QUANTITATIVE PROBLEM SOLVING

SUBDOMAIN 212.1 – NUMERACY, ALGEBRA, & GEOMETRY

SUBDOMAIN 212.2 – PROBABILITY, STATISTICS, & QUANTITATIVE PROBLEM

SOLVING

Competency 212.1.2: Solving Algebraic Equations – The graduate solves algebraic

equations and constructs equations to solve real-world problems.

Competency 212.2.1: Applying Probability and Statistics – The graduate understands

and applies elementary probability and statistics concepts and knows the relationship

between them and sampling and inference.

Competency 212.2.3: Interpreting and Communicating Quantitative Information –

The graduate interprets documents and materials containing quantitative information and

effectively communicates mathematical arguments and quantitative results.

Competency 212.2.4: Applying Technology to Quantitative Problems – The graduate

uses appropriate technological tools, including regular and graphing calculators, databases,

and/or statistical analysis programs, to solve problems involving computation, graphical

information, and informational technology in a wide range of areas.

Introduction:

“Mathematical literacy is an individual’s capacity to identify and understand the role that

mathematics plays in the world, to make well-founded judgments, and to use and engage

with mathematics in ways that meet the needs of that individual’s life as a constructive,

concerned, and reflective citizen” (2003).

Individuals encounter countless situations in day-to-day life that require a strong

mathematical foundation in order to make informed decisions.

Shown below are four real-world scenarios that one might encounter in day-to-day life. For

this task you will choose one of the scenarios below. Each situation requires a mathematical

comparison of cost options in order to determine which is best for a consumer (e.g.,

customer or person).

Scenario 1:

A parent is looking for the best option for daycare for a child. A home-based option charges

a flat rate per hour. A center-based option charges a fixed fee per week for a certain

number of hours and then a fixed rate per hour for any hour provided over the set amount.

Determine which option is most advantageous for the parent based upon the parents’

needs.

Scenario 2:

A downtown employee is looking for the best option for parking a car during a 5 day work

week. One parking garage offers unlimited parking at a flat rate per month. Another garage

offers an hourly rate for parking. Which option is best for the employee on a monthly basis?

Scenario 3:

A family is looking for the best option for moving the family’s belongings into a new home.

Moving company A charges its customers a flat rate per mile. Moving company B charges its

customers a fixed amount for a certain number of miles and then a fixed rate per mile for

any miles over the set amount. Determine which company would best serve the needs of the family.

Scenario 4:

A student is looking to secure a hardcopy textbook for an upcoming course. Compare a

weekly textbook rental option with a purchase option to determine which option is most

advantageous for the student based upon the student’s needs.

Task:

Note: Part A, B, and D of this task should be completed in a word-processing program;

hand-written artifacts are not acceptable for this task. Part C should be completed in

approved graphing software; hand-drawn graphs and graphs crafted as art within a

computer program are not acceptable for this task

A. Develop a story problem using the real-world scenario you have selected from the four

provided above by doing the following:

1. Develop a cost comparison problem that can be solved according to the task

instructions that follow by supplementing your chosen scenario with additional

information.

2. Explain all needs (e.g., financial, non-financial, situational) of the hypothetical

consumer.

3. Discuss two cost options that are being considered.

B. Analyze the cost of each option algebraically by doing the following:

1. Develop an algebraic equation(s) with clearly defined variables to represent the cost

of each option.

Note: In some circumstances, a single cost option may require two equations

2. Explain the reasoning process used to translate the written description of each cost

option into algebraic equations.

3. Solve the system of equations algebraically to determine where the two cost options are

equivalent, showing all work.

a. Explain each step used to solve the system of equations. Include the following in

your explanation:

• All mathematical operations used to solve the system of equations

• The solution(s) of the system of equations in ordered-pair notation

C. Depict the real-world problem on a single graph, within a spreadsheet application using

integrated graphing tools (e.g., Microsoft Excel, OpenOffice Calc, LibreOffice Calc).

Include the following details in your graphical representation of the real-world problem:

• Label each axis of the coordinate plane with descriptive labels.

• Label all graphical solution(s) of the system of equations as “solution” and include

the ordered pair.

• In a legend, indicate which cost option corresponds with each line.

• Save and submit your spreadsheet as an *.xls, *.xlsx, or *.ods file.

D. Discuss a decision-making process that is based on both mathematical reasoning and

non-financial, or situational, considerations. Your discussion should include the

following:

• How financial information gleaned from your algebraic and graphical analyses can be used to determine the conditions for choosing cost option A over cost option B

and vice versa

• How non-financial, or situational, considerations can impact the decision-making

process

1. Discuss a final recommendation that states the option that most closely meets the

consumer’s financial needs and non-financial considerations.

E. When you use sources, include all in-text citations and references in APA format.

Note: When bulleted points are present in the task prompt, the level of detail or support

called for in the rubric refers to those bulleted points.

Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link

included in the Evaluation Procedures section.

Note: When using sources to support ideas and elements in a paper or project, the

submission MUST include APA formatted in-text citations with a corresponding reference list

for any direct quotes or paraphrasing. It is not necessary to list sources that were consulted

if they have not been quoted or paraphrased in the text of the paper or project.

Note: No more than a combined total of 30% of a submission can be directly quoted or

closely paraphrased from sources, even if cited correctly. For tips on using APA style, please

refer to the APA Handout web link included in the General Instructions section.

Reference List:

Note: This reference list refers only to direct citations in the task above and may be

different from those you need to complete the task. Consult your course of study for a list of

suggested learning resources.

(2003). Mathematical Literacy. Retrieved March 19, 2009, from OECD Programme for

International Student Assessment (PISA) website:

http://www.oecd.org/pages/0,3417,en_32252351_32235968_1_1_1_1_1,00.html