Master Course Syllabus
PRINCE GEORGE'S COMMUNITY COLLEGEACADEMIC AFFAIRS
MASTER COURSE SYLLABUS
MAT 1150 Quantitative Modeling and Reasoning / Prof. Andy D. Jones May 23, 2013
Course Designator and Title / Prepared by Date
Prof. Joanne Weinberg May 23, 2013 / Dr. Christine Barrow May 23, 2013
Department Chairman Date / Instructional Dean Date
COURSE DESCRIPTION:
Intended for students who need only one general education mathematics course not specified in the program. This course includes support in intermediate algebra as needed to study concepts in modern mathematics and its applications. Linear, quadratic, exponential, and logarithmic functions are used to represent problems across a variety of contexts and disciplines. Structures and algorithms are used to model and make decisions in social choice, management science, art and nature, and consumer finance. Students must pass an algebra competency exam, offered mid-semester, to receive credit in this course. This course is a terminal course and will not serve as preparation or prerequisite for any other mathematics course. Credit will not be awarded for both MAT 1130 and MAT 1150. 4 credits. (3 class/2 lab/1 recitation)
Prerequisite: Math placement score and permission of the Mathematics Department.
CREDIT HOUR EXPLANATION
At Prince George’s Community College, for all credit courses, students are expected to spend a minimum of 37.5 combined hours of instructional time and related coursework time per credit hour. This course is a 4-credit course. This course achieves the minimum of 150 hours of instructional time by requiring 75 hours of instructional time and 165 hours of student work outside of instructional time.
(Even though MAT 1150 is a 4-credit course, it includes 3 lecture, 2 lab, and 1 recitation hours for a total of 6 equivalent hours of direct instruction per week.)
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Master Course Syllabus
COURSE OUTCOMES:
· Students passing this course will be able to accomplish all of the outcomes listed below.
· Students will demonstrate their attainment of these outcomes through the planned assessments. So, for each course learning outcome, indicate briefly the planned assessment tools, such as cases, essay, multiple choice questions, etc
· Courses seeking general education status must address all pertinent general education outcomes in the below alignment.
Upon successful completion of this course, the student will be able to:
Course Outcome / *Program Outcome # / MO # / **Planned Assessments1 / Solve linear, quadratic, exponential, and logarithmic equations by applying algebraic, numerical, graphing, and/or technology-based techniques. / 2.2, 4.3 / Homework, quizzes, exams, and labs.
2 / Express mathematical information, concepts, and ideas in verbal, numeric, graphical, and symbolic form while solving a variety of problems. / 2.2, 4.3, 1.1, 1.4 / Homework, quizzes, exams, and labs.
3 / Identify and interpret, in context, the key symbolic and graphical features of linear, quadratic, exponential, and logarithmic functions. / 2.2 / Homework, quizzes, exams, and labs.
4 / Apply algebraic, numerical, graphical, and/or technology-based techniques to model real world data and make predictions using an appropriate linear, quadratic, exponential, or logarithmic function. / 2.2, 4.3 / Homework, quizzes, exams, and labs.
5 / Calculate and interpret average rates of change, percentage growth and decay rates from data, formulas, and graphs. / 2.2, 1.3 / Homework, quizzes, exams, and labs.
6 / Select, use, and evaluate appropriate mathematical models to solve problems in consumer finance. / 1.1, 2.1, 3.1, 1.3 / Homework, quizzes, exams, labs, and projects.
7 / Select, use, and evaluate appropriate mathematical models and algorithms to solve problems in management and scheduling systems. / 2.1, 3.1, 1.3, 1.4 / Homework, quizzes, exams, labs, and projects.
8 / Select, use, and evaluate appropriate mathematical models and algorithms to solve problems in societal systems. / 2.1, 3.1, 1.1, 1.4 / Homework, quizzes, exams, labs, and projects.
9 / Identify, analyze, and model mathematical ideas found in art and nature. / 1.1, 2.1 / Homework, quizzes, exams, labs, and projects.
* Note: This course is not part of the math program. Therefore, this column is not applicable.
** Note: Quizzes and exams will contain free response questions with required explanation and shown work.
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Master Course Syllabus
RANGE OF SUBJECT MATTER -- MODEL COURSE OUTLINE:I. Analysis of Growth
A. Measurement of Growth
i. Intuitive Notion of Function
ii. Percentage Change
iii. Average Growth Rate
iv. Interpolation and Extrapolation
B. Visualizing and Interpreting Growth with Graphs
i. Scatterplots
ii. Line Graphs and Smoothed Line Graphs
C. Misleading Graphs
II. Functions
A. Linear Functions
i. Formulas for Linear Functions
ii. Slope
iii. Trend Lines and Regression
B. Exponential Functions
i. Formulas for Exponential Functions
ii. Relating Percentage Growth and Base
iii. Exponential Decay and Half-Life
C. Logarithms
i. Definition of Logarithm
ii. Applications of Logarithms
a. Richter Scale
b. Decibels
iii. Solving Exponential Equations
iv. Doubling Time
D. Quadratic Functions
i. Solving Quadratic Equations and Finding Zeros
a. Factoring
b. Quadratic Formula
ii. Parabolas
iii. Finding maximum/minimum values in applications of quadratic functions
ALGEBRA COMPETENCY EXAM
III. Voting and Social Choice
A. Voting Power
i. Coalitions
ii. Banzhaf Power Index
iii. Swing Votes
iv. Shapley-Shubik Power Index
B. Voting Systems
i. Plurality
ii. Run-offs
iii. Preferential Voting
iv. Borda Counts
v. Condorcet’s Paradox
vi. Arrow’s Impossibility Theorem
C. Fair Division
i. Divide-and-Choose procedure
ii. Adjusted Winner procedure
iii. Method of Sealed Bids
D. Apportionment
i. Apportionment History, Problems, and Issues
ii. Hamilton Solution
iii. Jefferson Solution
iv. Adams and Webster Method
v. Huntington-Hill Method
IV. Personal Finance
A. Saving Money
i. Simple Interest
ii. Compound Interest
iii. APR vs. APY
B. Borrowing Money
i. Installment Loans and Payments
ii. Amortization Tables and Equity
iii. Home Mortgages
C. Retirement Planning
i. Making Regular Deposits
ii. Annuities
D. Credit Cards
i. Basics of Credit Cards
ii. Minimum Payments
iii. Abuses of Credit Cards
E. Inflation, Taxes, and Stocks
i. CPI and the Inflation Rate
ii. Buying Power
iii. Income Taxes
iv. The Dow
V. Graph Theory
A. Drawing Graphs
B. Euler Paths and Circuits
C. Hamilton Paths and Hamilton Circuits
D. “Traveling Salesman”-type Problems
E. Trees
VI. Geometry
A. Perimeter, Area, and Volume
i. Applications of Basic Geometry Formulas
ii. Heron’s Formula
iii. Three-dimensional measurements
B. Proportionality and Similarity
i. Golden Ratio
ii. Golden Rectangles in Art and Architecture
iii. Similar Triangles
iv. Other Types of Proportionality
C. Symmetries and Tilings
i. Rotational Symmetry
ii. Reflectional Symmetry
iii. Regular Tilings
iv. Irregular Tilings
v. Escher Tilings
Suggested Course Timeline for 15-week Course:
I. Analysis of Growth / 1.5 weeksII. Functions / 4.0 weeks
Algebra Competency Exam
III. Voting and Social Choice / 2.5 weeks
Exam suggested
IV. Personal Finance / 2.0 weeks
Exam Suggested
V. Graph Theory / 2.0 weeks
Exam Suggested
VI. Geometry / 2.0 weeks
Review, Final, Project Presentations, etc. / 1.0 week
EVALUATION OF STUDENT PERFORMANCE:
Generally classes will be a mixture of lecture/discussion sessions, group activities, calculator or computer demonstrations, hands-on experience with both, and student presentations.
Course grades must include the following components:
· Algebra competency exam*
· At least three other examinations in addition to the algebra competency exam
· At least one written project (which may also be presented orally) on topics such as consumer finance, voting theory, fair division, or art.
· At least 70% of the course grade must be based on proctored assessments to include exams and quizzes.
Other un-proctored assessments (up to 30%) may contribute to the course grade, These may include
· Written homework assignments
· Laboratory activities
· Recitation activities
· Additional projects and presentations
· Portfolio
· Attendance
· Technology assignments
· Quizzes
*To receive credit for this college-level course, students must pass an algebra competency exam. This will verify that the student has met the “beyond the scope of intermediate algebra” requirement for a college-level course. Students who do not pass the algebra competency exam will be given a time period for self-remediation, and a second algebra competency exam opportunity will be provided. If the student does not pass the algebra competency exam, the student will earn a grade of F in the course no matter the current grade.
ACCOUNTING FOR CREDIT HOUR REQUIREMENT
*(THIS SECTION APPEARS ONLY ON MASTER SYLLABI, AND IS NOT TO BE DISTRIBUTED TO STUDENTS)
Face-to-face classes
Assignment/Assessment Clock Hours
In class instruction including lab activities, recitation, and final exam / 75 hours
Project(s) / 15 hours
Out-of-class Assignments including but not limited to
· Textbook Homework
· Assigned Readings from Textbook
· Instructor created worksheets
· Study and Exam Preparation Time
· Outside Testing Time / 150 hours minimum (10 hours per week x 15 weeks)
TOTAL: / 240 hours minimum
INSTRUCTIONAL MATERIALS:
Quantitative Literacy: Thinking Between the Lines, Crauder, Bruce, et al, W. H. Freeman, 2012.
· Must include Portal access.
· ISBN-10: 1-4641-2578-3 ISBN-13: 978-1-4641-2578-2.
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