I. General Information

1. Course Title:
Math Pathways

2. Course Prefix & Number:
MATH 0810

3. Course Credits and Contact Hours:

Credits: 3

Lecture Hours: 3

Lab Hours: 0

4. Course Description:

5. Placement Tests Required:

6. Prerequisite Courses:

9. Co-requisite Courses:

II. Transfer and Articulation

1. Course Equivalency - similar course from other regional institutions:

American River College (CA) and 21 other, Statway, 3 credits

III. Course Purpose

Program-Applicable Courses – This course is required for the following program(s):

Other - If this course is not required in a program or is not part of the MN Transfer Curriculum, it may be used for the purpose(s) listed below:
Developmental Course

IV. Learning Outcomes

1. College-Wide Outcomes

2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of the course:

• Solve authentic problems by applying two or more mathematical strategies or concepts and using multiple steps;
• Interpret and communicate quantitative information and mathematical concepts using appropriate language for the context;
• Present written or verbal justifications that include appropriate discussion of the mathematics involved;
• Use estimation skills to predict and check answers to mathematical problems in order to determine reasonableness of solutions;
• Make sense of problems, develop strategies to find solutions, and persevere in solving them;
• Read and interpret authentic texts containing quantitative information;
• Use technology when appropriate for a given context;
• Demonstrate an understanding of large and small numbers by interpreting and communicating with different forms (including words, fractions, decimals, standard notation, and scientific notation);
• Describe quantitative relationships and solve problems in a variety of contexts;
• Read, interpret, and make reasoned conclusions about data that is summarized in a table or a graphical display
• Use the Cartesian coordinate system to graph points and equations;
• Use and interpret variables as unknowns, in equations, in simplifying expressions, and as quantities that vary;
• Evaluate algebraic expressions for a given value or values;
• Model and solve applied problems involving both linear and nonlinear relationships;
• Express and interpret relationships using equality and inequality symbols;
• Graph inequalities on a number line;
• Recognize when a linear model is appropriate;
• Solve linear equations;
• Apply linear models to solve problems using tables, graphs, words and/or equations;
• Calculate and interpret a rate of change as given by a symbolic, graphical, or numerical representation;
• Review basic properties and definitions with graphing calculators;
• Complete basic sequences, series, and summations problems;
• Use Venn diagrams and set notation;
• Demonstrate an understanding of counting principles;
• Demonstrate an understanding of basic probability rules;
• Use basic statistics with calculator list entry and compute measures of central tendency;
• Solve linear inequalities in one variable;
• Develop tables using linear equations in two variables and graph; and
• Demonstrate an understanding of basic quadratic, logarithmic, and exponential equations and graphs;

V. Topical Outline

Listed below are major areas of content typically covered in this course.

1. Lecture Sessions

1. Basic properties and definitions
   • Review properties of real numbers
   • Using graphing calculator, review fractions, complex fractions, decimals, square roots, and order of operations with real numbers
   • Simplify numerical expressions
   • Use scientific notation
2. Basic sequences, series, and summation
   • Define sequence and series and explore basic examples
   • Introduce summation notation and apply to finite sequences
3. Venn diagrams and set notation
   • Introduce sets, cardinal numbers, union, and intersection
   • Use Venn diagrams to illustrate examples
4. Counting principles
   • Introduce factorials and the Fundamental Principle of Counting
   • Introduce the permutation and combination formulas 
   • Practice using the formulas on non-application problems and basic applications
5. Probability
   • Introduce terminology (outcome, event, sample space, etc.)
   • Introduce basic rules of probability
6. Basic statistics
   • Introduce “STAT” key on TI-83/84
   • Enter data into lists on calculator
   • Calculate measures of central tendency using calculator
7. Linear equations and inequalities in one variable
   • Simplify algebraic expressions
   • Solve equations, including strictly numerical problems and applications
   • Solve equation applications involving percents
   • Solve literal equations and formulas, including area, volume, and interest formulas
   • Introduce inequality symbols, graphs, and interval notation
   • Solve inequalities, including compound inequalities
8. Linear equations in two variables
   • Find slopes and equations of lines using points on the line
   • Develop tables and graphs for linear equations
   • Graph lines on graphing calculator
   • Create scatter plots of 2-variable data and introduce regression on the TI-83/84
9. Introduce other equations and graphs
   • Quadratic equations and parabolas
   • Exponential equations
   • Logarithmic equations