# Mathematical Reasoning

MTH 098## Course Description

Prerequisite: MATH LEVEL 3. Develops conceptual understanding and acquires multiple strategies for solving problems using big mathematical and statistical concepts. Makes connections between concepts and applies previously learned material to new contexts. Practices using mathematical, statistical, and quantitative information to make decisions. Explores strategies for success in future courses; gains skills for the workplace and participating as citizens in our society. A graphing calculator is required. (60-0)

## Outcomes and Objectives

### Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.

#### Objectives:

- Use appropriate mathematical language.
- 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.
- Write 1 to 2 paragraphs using quantitative information to make or critique an argument or to summarize information from multiple sources.

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

#### Objectives:

- Demonstrate understanding of common types of consumer debt and explain how different factors affect the amount that the consumer pays.
- Demonstrate understanding of compound interest and how it relates to saving money.
- Identify erroneous or misleading information in advertising or consumer information.

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

#### Objectives:

- Use quantitative information to explore the impact of policies or behaviors on a population. This might include issues with social, economic, or environmental impacts.
- Identify erroneous, misleading, or conflicting information presented by individuals or groups regarding social, economic, or environmental issues.

### Develop strategies to find solutions and solve problems.

#### Objectives:

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

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

#### Objectives:

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

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

#### Objectives:

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

### Use appropriate technology in a given context.

#### Objectives:

- Use a spreadsheet to organize quantitative information and make repeated calculations using simple formulas.
- 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.
- Use internet-based tools appropriate for a given context (e.g., an online tool to calculate credit card interest).

### 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.

#### Objectives:

- Demonstrate operation sense and communicate verbally and symbolically with real numbers.
- 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.
- Solve problems involving calculations with percentages and interpret the results.
- 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.
- Use estimation skills, and know why, how, and when to estimate results.
- Solve problems involving measurement including the correct use of units.
- Use dimensional analysis to convert between units of measurements and to solve problems involving multiple units of measurement.
- 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).

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

#### Objectives:

- Represent, and use ratios in a variety of forms (including percentages) and contexts.
- Determine whether a proportional relationship exists based on how one value influences another.
- Analyze, represent, and solve real - world problems involving proportional relationships, with attention to appropriate use of units.

### 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.

#### Objectives:

- 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.
- Describe, identify, compare, and contrast the effect of multiplicative or additive change.
- Analyze real - world problem situations, and use variables to construct and solve equations involving one or more unknown or variable quantities.
- Express and interpret relationships using inequality symbols.
- 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.
- Represent mathematical models in verbal, algebraic, graphical, and tabular form.
- Recognize when a linear model is appropriate and, if appropriate, use a linear model to represent the relationship between two quantitative variables.

### 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.

#### Objectives:

- Interpret statements about chance, risk, and probability that appear in everyday media (including terms like unlikely, rare, and impossible).
- Identify common pitfalls in reasoning about risk and probability.
- 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.
- Demonstrate understanding of absolute risk and relative risk (percent age change in risk) by describing how each provides different information about risk.