This course covers topics in algebra and geometry with a focus on problem-solving, understanding the mathematical properties being used, justifying steps, and interpreting results. Connections between these two branches of mathematics will be made as students study graphing equations, apply the Pythagorean Theorem, and solve equations involving right triangle trigonometry, among other applications.

5. Placement Tests Required:

Accuplacer (specify test):

Arithmetic Exam

Score:

40

6. Prerequisite Courses:

MATH 0800 - Fundamentals of Mathematics

There are no prerequisites for this course.

9. Co-requisite Courses:

MATH 0800 - Fundamentals of Mathematics

There are no corequisites for this course.

II. Transfer and Articulation

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

III. Course Purpose

Program-Applicable Courses – This course is required 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

College-Wide Outcomes/Competencies

Students will be able to:

Analyze and follow a sequence of operations

Use formulas to calculate the surface area and volume of 3-dimensional figures.

Apply abstract ideas to concrete situations

Write and solve equations involving geometric relationships.

Utilize appropriate technology

Utilize scientific or graphing calculators appropriately.

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

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

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

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

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

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

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

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:

This course covers topics in algebra and geometry with a focus on problem-solving, understanding the mathematical properties being used, justifying steps, and interpreting results. Connections between these two branches of mathematics will be made as students study graphing equations, apply the Pythagorean Theorem, and solve equations involving right triangle trigonometry, among other applications.

5. Placement Tests Required:

Accuplacer (specify test):

Arithmetic Exam

Score:

40

6. Prerequisite Courses:

MATH 0800 - Fundamentals of Mathematics

There are no prerequisites for this course.

9. Co-requisite Courses:

MATH 0800 - Fundamentals of Mathematics

There are no corequisites for this course.

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):

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.

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

College-Wide Outcomes/Competencies

Students will be able to:

Analyze and follow a sequence of operations

Use formulas to calculate the surface area and volume of 3-dimensional figures.

Apply abstract ideas to concrete situations

Write and solve equations involving geometric relationships.

Utilize appropriate technology

Utilize scientific or graphing calculators appropriately.

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

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

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

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

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

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

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