I. General Information

1. Course Title:
Fundamentals of Mathematics

2. Course Prefix & Number:
MATH 0800

3. Course Credits and Contact Hours:

Credits: 3

Lecture Hours: 3

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:

III. Course Purpose

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

3. Other - If this course does NOT meet criteria for #1 or #2 above, it may be used for the purpose(s) selected 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 fluency with order of operations on real numbers through verbal and symbolic communication;
• Represent fractions, decimals, and percentages in equivalent forms;
• Demonstrate fluency when ordering real numbers;
• Demonstrate an understanding of large and small numbers by interpreting and communicating with different forms (including words, fractions, decimals);
• Describe quantitative relationships and solve problems in a variety of contexts;
• Analyze, represent, and solve authentic problems involving proportional relationships and percentages with appropriate use of units;
• 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;
• Express and interpret relationships using equality and inequality symbols;
• Graph inequalities on a number line;
• Solve linear equations;
• Calculate and interpret a rate of change as given by a symbolic, graphical, or numerical representation;
• Apply appropriate formulas to solve problems involving perimeter, area of 2D figures, and volume and surface area of 3D figures;
• Represent measurements with appropriate units;
• Convert among units of measurement;
• Evaluate polynomial and rational expressions at specified points in their domains;
• Add and subtract polynomials;
• Factor common monomial factors from polynomials;
• Use substitution to check the equality of expressions for some particular values of the variables;
• Use algebra to solve geometric problems;
• Represent and solve problems in various contexts using linear equations;
• Graph equations by creating a table of values;
• Identify intercepts, zeros, maximum, and minimum from the graph of a function;
• Translate between graphs, tables, and symbolic representations of linear functions;
• Apply the Pythagorean Theorem and its converse to solve problems;
• Determine the sine, cosine and tangent of an acute angle in a right triangle;
• Apply the trigonometric ratios sine, cosine and tangent to solve problems such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles; and
• Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts;

V. Topical Outline

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

1. Lecture Sessions

1. Geometric figures
   • Calculate the perimeter, circumference, and area of plane figures
   • Represent prisms, cylinders, and pyramids as nets in two dimensions and calculate the area of the nets
   • Calculate the surface area and volume of prisms, cylinders,pyramids, cones, and spheres
   • Explore and predict the effect of multiplying all sides of a figure by a scale factor on the perimeter, surface area, and volume
2.  Algebraic expressions
   • Apply the order of operations and the associative, distributive, and commutative properties to numerical and algebraic expressions to generate equivalent expressions
   • Verify that expressions are equivalent using substitution
   • Justify steps for creating equivalent expressions by indicating the properties used
   • Evaluate polynomial and rational expressions and expressions containing radicals and absolute values for given values of the variable
   • Add and subtract polynomials
   • Factor out a common monomial from a polynomial
3.  Applications of equations and inequalities
   • Write and solve linear equations and inequalities given in context
   • Use substitution to determine whether solutions are correct
   • Interpret solutions in context and assess their reasonableness in context
   • Write and solve equations for geometric relationships including angle relationships, polygon properties, and similarity
4. Interpreting graphs and identifying graph features
   • Create graphs for a variety of equations by creating a table of values and plotting points
   • Describe the rate of change of the graph of a function at different places along the graph
   • Interpret and draw conclusions from graphs in context
   • Given a graph, identify features including intercepts, zeros, and extreme values
   • Graph parabolas with technology and identify the vertex, line of symmetry, and intercepts
5. Introduction to lines
   • Graph linear equations and inequalities using a table of ordered pairs
   • Calculate slopes from graphs or equations in slope-intercept form
   • Convert linear equations into slope-intercept forms
   • Solve real-world problems involving slope
   • Graph a linear equation using slope and y-intercept
6. Right triangle trigonometry and the Pythagorean Theorem
   • Write and solve equations using sine, cosine, and tangent, and the Pythagorean Theorem to find missing sides of right triangles
   • Use inverse sine, cosine, and tangent to find missing angles in right triangles
   • Solve application problems with right triangle trigonometry and the Pythagorean Theorem