10804xxxQuantitative Reasoning with Applications
Course Information
Description
This course is intended to develop analytic reasoning and the ability to solve quantitative problems. Topics to be covered may include: construction and interpretation of graphs; descriptive statistics; geometry and spatial visualizations; math of finance; functions and modeling; probability; and logic. Appropriate use of units and dimensions, estimates, mathematical notation, and available technology will be emphasized throughout the course. 
Total Credits
3
Course Competencies
  1. Analyze logical arguments
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you identify logical fallacies in popular arguments
    you recognize arguments as inductive or deductive
    you construct a short deductive proof
    you identify inconsistencies in statistical arguments
    you identify necessary assumptions and/or conditions for statistical techniques
    you test conditions and/or reasonableness of assumptions

  2. Employ counting principles
    Assessment Strategies
    in the solution on a quiz, homework, project or exam
    Criteria
    you apply permutations in determining the cardinality of ordered subsets
    you apply combinations in determining the cardinality of unordered subsets
    you determine the size of intersections, unions, and complements of sets
    you apply rules of counting in solving applied contexts

  3. Utilize probability models and rules
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you distinguish between theoretical and empirical probability
    you compute probability using the basic definition
    you compute the probability of joint and disjoint events
    you compute conditional probabilities
    you determine if two events are independent

  4. Employ descriptive statistics
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you generate frequency distributions from a given data set
    you calculate the mean, median, and mode of a distribution
    you interpret the mean, median, and mode as measures of central tendency
    you calculate quartile and percentile ranks as measures of position
    you calculate range, standard deviation, and interquartile range as measures of spread for a distribution
    you identify and interpret outliers
    you use measures of central tendency and spread to compare and contrast two distributions
    you construct a modified box-and-whisker plot to summarize comparisons
    you use the language of probability to describe and evaluate statements involving risk

  5. Apply inferential statistics
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you evaluate sampling strategies
    you determine sources of bias
    you describe the difference between correlation and causation
    you distinguish between discrete and continuous probability distributions
    you interpret probability as an area under the probability distribution
    you identify confounding variables
    you compute probabilities of events for discrete random variables
    you compute probabilities of events for normally distributed random variables
    you interpret normal distribution probabilities in solving applied contexts
    you construct a confidence interval to estimate a population parameter
    you interpret the error term for a confidence interval

  6. Apply non-linear mathematical models
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you identify appropriate models for given data sets and applications
    you develop piecewise, exponential, logarithmic, and logistic models to fit source data from real contextual applications
    you identify reasonable domain and range for a non-linear or piecewise function model
    you analyze model break-down conditions
    you employ solution techniques to solve for an unknown value in the function model
    you utilize solutions to interpret results in an applied context
    you identify important characteristics of models (increasing/decreasing, cyclic, piecewise, etc.) that represent real world contexts
    you understand that abstract mathematical models used to characterize real-world scenarios or physical relationships are not always exact and are subject to error
    you create and use exponential models of real-world situations including growth and decay models
    you compute interest amount and compound amount in compound interest financial models
    you compute present and future values for compound interest applications
    you compute the amount and payment of an annuity
    you calculate the present and future value of an annuity

  7. Develop graphical representations
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you plot points to construct the graph of a given equation
    you evaluate graphs in an applied context
    you construct pie charts, bar graphs, and line graphs
    you construct appropriate charts or graphs to depict distributions
    you utilize function tables
    you employ calculators, spreadsheets, or other technological tools for construction of various graphs
    you construct scatterplots of bivariate data

  8. Apply principles of geometry
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you use appropriate units
    you convert units as needed
    you use precision and accuracy to round values appropriately
    you apply circumference, perimeter and area of plane figures to physical applications
    you apply volumes of three dimensional figures to physical applications

  9. Apply linear mathematical models
    Assessment Strategies
    in the solution to a problem on a quiz, homework, project or exam
    Criteria
    you assign variables as needed
    you develop linear equations which express inherent relationships in an applied context
    you describe the behavior of linear models using words, algebraic symbols, graphs, and tables
    you identify reasonable domain and range for a linear model
    you use appropriate terms and units to describe rate of change
    you compute the slope and intercept for a regression line
    you interpret the slope and intercept for a regression line in an applied context
    you analyze model break-down conditions
    you employ solution techniques to solve for an unknown value in the functional model
    you utilize solutions to interpret results in an applied context
    you compute principal, rate, and time in simple interest financial models