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

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:

III. Course Purpose

Program-Applicable Courses – This course fulfills a requirement for the following program(s):

Fundamentals of Math is a course designed within the framework of the 2007 Minnesota Department of Education K-12 Mathematics Standards to meet the needs of students whose placement test scores are too high to make them eligible for ABE assistance, but are not high enough for MATH 0810 Math Pathways or MATH 0820 Intermediate Algebra.

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:

• Use formulas to calculate surface area and volume of 3D figures;
• 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;
• Assess the reasonableness of a solution in its given context;
• Use coordinate geometry to determine slopes of lines;
• Graph equations by creating a table of values;
• Make qualitative statements about the rate of change of a function based on its graph or table of values;
• Graph quadratic functions with technology and identify the vertex, line of symmetry, and intercepts of the parabola;
• 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