10-804-134Mathematical Reasoning
Course Information
Description
Making decisions about fiscal, environmental, and health issues requires using mathematical reasoning to solve complex problems.   This course explores numerical and algebraic relationships, graphical data displays, statistical measures, proportional and algebraic reasoning, translating contexts to mathematical models, and solving using linear, exponential and other mathematic models. This course may be used as the first of a two-part sequence that ends with Quantitative Reasoning as the capstone general education math requirement.
Total Credits
3
Course Competencies
  1. Apply number sense with operations and numeric formats
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use correct operation sense in algebraic expressions
    communicate verbally the effects of common operations on numbers
    communicate symbolically the effects of common operations on numbers
    explain the importance of scientific notation
    convert very large numbers from real-world problems to and from scientific notation
    convert very small numbers from real-world problems to and from scientific notation

  2. Apply estimation to evaluate reasonableness and detect errors
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify when to estimate results
    determine estimation technique for real-world scenarios
    use estimation to detect errors
    use estimation to check accuracy

  3. Solve quantitative problems in context
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    apply quantitative reasoning to solve problems involving quantities
    apply quantitative reasoning to solve problems involving rates
    apply quantitative reasoning to solve problems using formulas
    convert between different measurement units
    use measurement terms correctly

  4. Compute statistical measures
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    compute measures of central tendency
    use measures of central tendency to represent data
    compute mathematical models from data
    use mathematical models to represent data

  5. Analyze graphical data displays
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    read data from graphical displays
    interpret data from graphical displays
    determine reasonableness of data from display
    make decisions based upon data from graphical displays

  6. Apply proportional reasoning
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    compare ratios represented in different ways
    identify proportional relationships from verbal or written representations
    identify proportional relationships from numeric representations
    solve real-world problems with proportional relationships

  7. Apply algebraic relationships
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    explain the uses of variables to represent quantities
    explain the uses of variables to represent attributes
    describe the effect that a change in the value of one variable has on the value of other variables in an algebraic relationship
    construct equations to represent relationships involving one or more unknown or variable quantities
    construct inequalities to represent relationships involving one or more unknown or variable quantities
    use equations to solve problems
    use inequalities to solve problems

  8. Translate between contexts and mathematical models
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    translate a contextual description into a linear mathematical representation
    translate a contextual description into an exponential mathematical representation
    translate a contextual description into a quadratic mathematical representation
    translate mathematical representations back into contextual descriptions

  9. Evaluate functions and mathematical models
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    describe the behavior of common types of functions
    identify important characteristics of functions in various representations
    use appropriate terms and units to describe rate of change
    identify when a linear model or trend is reasonable for given data
    explore the applicability of other models when a linear model does not appear to be reasonable
    explain the limitations of mathematical models