## MCR 2 - Learning Support for Fundamentals of Reasoning at Piedmont Virginia Community College

### Course Description

Effective: 2017-08-01

Provides mathematical instruction for students who require minimum preparation for college-level but still need further preparation to succeed. Students in this course will be co-enrolled in college-level Fundamentals of Reasoning. Credits not applicable toward graduation and do not replace MTE courses waived. Successful completion of Fundamentals of Reasoning results in the prerequisite MTE modules being satisfied.

Lecture 1-2 hours. Total 1-2 hours per week.

1-2 credits

### General Course Purpose

To enable qualified students to enter into credit bearing courses sooner, with the appropriate support, and with equal or better success than those students meeting course prerequisite requirements. The course provides support and enhancement of foundational and course content required of the credit course.

### Course Prerequisites/Corequisites

Prerequisites: Completion of any one of the MTE 1-3 modules. Corequisite: MTH 130

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Use appropriate mathematical language in oral, written and graphical forms.
- Read and interpret real world advertisements, consumer information, government forms and news articles containing quantitative information.
- Use quantitative information from multiple sources to make or critique an argument.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Use multiple calculations to develop an answer to an open-ended question requiring analysis and synthesis of data.
- Develop personal problem solving processes and apply them to applications studied over an extended period of time.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Draw conclusions or make decisions in quantitatively based situations that are dependent upon multiple factors.
- Analyze how different situations would affect the decisions.
- Present written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.
- Recognize when additional information is needed or the appropriate times to simplify a problem.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Evaluate the validity and possible biases in arguments presented in real world contexts based on multiple sources of quantitative information for example; advertising, internet postings, or consumer information.
- Technology
- Use appropriate technology in a given context.
- Use a computer or calculator to organize quantitative information and make repeated calculations using simple formulas. This would include using software like Excel or internet-based tools appropriate for a given context for example, an online tool to calculate credit card interest.
- Basic Algebra through Application
- Solve real world application problems requiring basic operations and simple linear equations.
- Perform operations with signed numbers (including whole numbers, decimals, and fractions)
- Simplify and evaluate algebraic expressions using the order of operations
- Solve simple linear equations - one step equations, two step equations and some multi-step equations requiring distributive property
- Determine the reasonableness of answers using estimation
- Linear Graphing Applied
- Through contextualized perspective,
- Locate and plot points on the xy plane
- Interpret the concept of slope using real world examples (including vertical and horizontal lines)
- Graph lines using a table of values with and without the domain provided
- Graph lines using the slope-intercept method when lines are in y=mx+b form and Ax+By=C form
- Write the equation of a line in slope-intercept form that models a real world situation when given the rate of change and initial value
- Make predictions using the equation of a line
- Graph and solve a system of two linear equations in an applied context
- Financial Literacy using Percents, Ratios and Proportions
- Create and simplify ratios
- Solve given proportions
- Solve real world problems using proportions
- Calculate percents, sales tax and discounts
- Create a budget to include percentages and a pie chart using appropriate software
- Calculate simple and compound interest
- Interpret credit scores and how they affect opportunities to buy on credit
- Solve problems which involve buying on credit, including add-on interest rate loans and home buying
- Calculate FICA and federal income taxes (simple cases)
- Descriptive Statistics
- Compute and interpret statistics (mean, median, mode, range, quartiles/percentiles) for data displayed in various formats, such as a boxplot, stem-and-leaf plots, frequency distributions, histogram, pie/line/bar graph
- Compare sets of data by comparing similarities and differences in their graphical displays and/or descriptive statistics
- Create graphical displays of data using spreadsheet software such as Excel
- Compute and interpret descriptive statistics for a set of real-world data, including mean, median, mode, range, standard deviation using spreadsheet software or a calculator
- Identify graphical displays or arguments that are misleading or involve the incorrect use of statistical concepts
- Measurement & Geometry
- Solve problems by applying measurement and geometry topics (such as measurement conversions, area, perimeter, volume, etc) in a variety of real world contexts
- Logic (Optional topic to support certain CTE programs.)
- Identify statements and form compound statements and negations using "and", "or", and "not"
- Use truth tables to determine the truth value of compound statements and to determine whether statements are equivalent
- Identify conditional statements. Write and determine truth values for the converse, inverse, and contrapositive of a conditional statement.
- Use truth tables to determine the validity of a syllogistic argument
- Draw and interpret Venn diagrams
- Distinguish between inductive and deductive reasoning
- Use inductive reasoning to find a pattern or to disprove a statement by finding a counterexample
- Trigonometry (Optional topic to support certain CTE programs.)
- Understand/use terms related to an angle(s).
- Define the trigonometric functions and their values
- Solve right triangles and their applications
- Understand the signs of the trigonometric function of angles greater than 90?
- Determine trigonometric functions of any angle
- To achieve the above objectives, the support course will cover appropriate topics such as those suggested below in both planned review and just-in-time remediation:
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Math Skills Topics
- Operations with fractions, decimals, and integers
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Evaluating expressions/functions for given values of variables
- Excel or similar applications
- Formulas
- Ratios and Proportions
- Percents

### Major Topics to be Included

- Basic Algebra
- Linear Graphing
- Financial Literacy using Percents, Ratios, and Proportions
- Descriptive Statistics
- Measurement and Geometry
- Logic (Optional)
- Trigonometry (Optional)