MTH 098 - Mathematical Reasoning

Credits: 4

     A.          Use appropriate mathematical language.

     B.          Read and interpret short, authentic texts such as advertisements, consumer information, government forms, and newspaper articles
                   containing quantitative information, including graphical displays of quantitative information.

     C.          Write 1 to 2 paragraphs using quantitative information to make or critique an argument or to summarize information from multiple sources.

2.    Develop strategies to find solutions and solve problems.

     A.           Solve multistep problems by applying strategies in new contexts or by extending strategies to related problems within a context.

3.   Reason, model, and make decisions with mathematical, statistical, and quantitative information.

     A.           Make decisions in quantitatively based situations that offer a small number of defined options. The situations will not be limited to contexts
                    in which there is a single correct answer based on the mathematics (e.g., which buying plan costs less over time), but will include
                    situations in which the quantitative information must be considered along with other factors.

     B.           Present short written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.

4.    Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.

     A.          Identify mathematical or statistical errors, inconsistencies, or missing information in arguments.

5.    Use appropriate technology in a given context.

     A.          Use a spreadsheet to organize quantitative information and make repeated calculations using simple formulas.

     B.          Use the Internet to find quantitative information on a given subject. The topics should be limited to those that can be researched with a
                   relatively simple search.

     C.          Use internet-based tools appropriate for a given context (e.g., an online tool to calculate credit card interest).

6:    Demonstrate a number sense and the ability to apply concepts of numeracy to investigate and describe quantitative relationships and solve real - world problems in a variety of contexts.

     A.          Demonstrate operation sense and communicate verbally and symbolically with real numbers.

     B.          Demonstrate an understanding of fractions, decimals, and percentages by representing quantities in equivalent forms, comparing the size
                  of numbers in different forms and interpreting the meaning of numbers in different forms.

     C.          Solve problems involving calculations with percentages and interpret the results.

     D.          Demonstrate an understanding of large and small numbers by interpreting and communicating with different forms (including words,
                   fractions, decimals, standard notation, and scientific notation) and compare magnitudes.

     E.          Use estimation skills, and know why, how, and when to estimate results.

     F.           Solve problems involving measurement including the correct use of units.

     G.          Use dimensional analysis to convert between units of measurements and to solve problems involving multiple units of measurement.

     H.           Read, interpret, and make decisions about data summarized numerically (e.g., measures of central tendency and spread), in tables, and
                    in graphical displays (e.g., line graphs, bar graphs, scatterplots, and histograms).

7.    Use proportional reasoning to solve problems that require ratios, rates, proportions, and scaling.

     A.          Represent, and use ratios in a variety of forms (including percentages) and contexts.

     B.          Determine whether a proportional relationship exists based on how one value influences

     C.          Analyze, represent, and solve real - world problems involving proportional relationships, with attention to appropriate use of units.

8.    Demonstrate ability to transition from specific and numeric reasoning to general and abstract reasoning using the language and
       structure of algebra to investigate, represent, and solve problems.

     A.          Demonstrate understanding of the meaning and uses of variables as unknowns, in equations, in simplifying expressions, and as quantities
                  that vary, and use that understanding to represent quantitative situations symbolically.

     B.          Describe, identify, compare, and contrast the effect of multiplicative or additive change.

     C.          Analyze real - world problem situations, and use variables to construct and solve equations involving one or more unknown or variable
                  quantities.

     D.          Express and interpret relationships using inequality symbols.

     E.          Construct and use mathematical models to solve problems from a variety of contexts and to make predictions/decisions. Representations
                   will include linear and exponential contexts.

     F.           Represent mathematical models in verbal, algebraic, graphical, and tabular form.

     G.          Recognize when a linear model is appropriate and, if appropriate, use a linear model to represent the relationship between two quantitative
                   variables.

 9.    Demonstrate an understanding of and critically evaluate statements that appear in the popular media (especially in presenting medical
        information) involving risk and arguments based on probability.

     A.          Interpret statements about chance, risk, and probability that appear in everyday media (including terms like unlikely, rare, and impossible).

     B.          Identify common pitfalls in reasoning about risk and probability.

     C.          Interpret in context marginal, joint, and conditional relative frequencies in context for data summarized in a two - way table and identify
                   which relative frequency is appropriate to answer a contextual question.

     D.          Demonstrate understanding of absolute risk and relative risk (percent age change in risk) by describing how each provides different
                   information about risk.10.

10. Demonstrate an understanding of, interpret, and make decisions based on financial information commonly presented to consumers.

     A.          Demonstrate understanding of common types of consumer debt and explain how different factors affect the amount that the consumer
                   pays.

     B.          Demonstrate understanding of compound interest and how it relates to saving money.

     C.          Identify erroneous or misleading information in advertising or consumer information.

11. Demonstrate an understanding that quantitative information presented in the media and by other entities can sometimes be useful and
      sometimes be misleading.

     A.          Use quantitative information to explore the impact of policies or behaviors on a population. This might include issues with social, economic,
                   or environmental impacts.

     B.           Identify erroneous, misleading, or conflicting information presented by individuals or groups regarding social, economic, or environmental
                    issues.