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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
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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
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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
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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
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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
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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, et.c) 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
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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
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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
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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