## I. General Information

1. Course Title:

Pathway to Mathematical Reasoning

2. Course Prefix & Number:

MATH 0815

3. Course Credits and Contact Hours:

**Credits:** 3

**Lecture Hours:** 3

**Lab Hours:** 0

4. Course Description:

This course is closely aligned with MATH 1442 Mathematical Reasoning, providing prealgebra, elementary algebra, graphing, geometry, and other topics to supplement the set theory, probability, statistics, geometry and finance concepts that are taught in the college-level course. Use of the TI-84 Plus graphing calculator and/or Excel software will be introduced. This course is designed to be taken prior to or concurrently with MATH 1442 Mathematical Reasoning.

5. Placement Tests Required:

**Accuplacer (specify test):** |
Next Gen QAS |
**Score:** |
240 |

6. Prerequisite Courses:

MATH 0815 - Pathway to Mathematical Reasoning

There are no prerequisites for this course.
7. Other Prerequisites

or MATH 0800

9. Co-requisite Courses:

MATH 0815 - Pathway to Mathematical Reasoning

There are no corequisites for this course.
## II. Transfer and Articulation

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

Various Minnesota State institutions and others nationwide are developing co-requisite developmental courses for liberal arts math courses, using guidance from the Dana Center, which is supported by the American Mathematical Association of Two-Year Colleges (AMATYC) and the Mathematical Association of America (MAA).

## 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

College-Wide Outcomes/Competencies |
Students will be able to: |

Analyze and follow a sequence of operations |
Write and justify steps in the process of solving algebraic equations. |

Apply abstract ideas to concrete situations |
Apply appropriate geometric and algebraic formulas to solve applications problems. |

Utilize appropriate technology |
Use a graphing calculator and determine when the technology is appropriate to use. |

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; and

- Calculate and interpret a rate of change as given by a symbolic, graphical, or numerical representation.

## V. Topical Outline

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

1. Lecture Sessions

- Preparation for, and practice of Set Theory
- Set terminology
- Physical examples
- Basic Venn diagrams
- Solving linear equations using the addition property of equality

- Preparation for, and practice of Probability
- Probability terminology
- Identification of outcomes of a probability experiment
- Equivalent fractions, decimals, and percents
- Number sense (relative size), estimation
- Number sense (order of decimals)
- Evaluating algebraic expressions
- Solving linear equations
- Reading tables and graphs
- Fraction multiplication, addition

- Preparation for, and practice of Statistics
- Reading skills (Statistics terminology, recognizing bias or error, reading graphs)
- Number sense (sorting data, reading graphs)
- Evaluating algebraic expressions (order of operations)
- Calculator or computer software statistics applications
- Graphing paired data in scatter plots by hand and with technology
- Graph inequalities on a number line (solutions to statistical applications)

- Preparation for, and practice of Geometry
- Evaluating algebraic expressions, including exponents and radicals
- Measurement of angles (protractors) and lengths (rulers)
- Hands-on practice with prisms, spheres, and cylinders
- Equivalent fractions, solving proportions
- Sketching right triangles for trigonometric applications

- Preparation for, and practice of Finance
- Equivalent fractions, decimals, and percents
- Graph linear equations in two variables (simple interest)
- Graph exponential equations (compound interest)
- Solving formulas for a variable
- Evaluating algebraic expressions
- Reading applications for understanding
- Understanding spreadsheets

## I. General Information

1. Course Title:

Pathway to Mathematical Reasoning

2. Course Prefix & Number:

MATH 0815

3. Course Credits and Contact Hours:

**Credits:** 3

**Lecture Hours:** 3

**Lab Hours:** 0

4. Course Description:

This course is closely aligned with MATH 1442 Mathematical Reasoning, providing prealgebra, elementary algebra, graphing, geometry, and other topics to supplement the set theory, probability, statistics, geometry and finance concepts that are taught in the college-level course. Use of the TI-84 Plus graphing calculator and/or Excel software will be introduced. This course is designed to be taken prior to or concurrently with MATH 1442 Mathematical Reasoning.

5. Placement Tests Required:

**Accuplacer (specify test):** |
Next Gen QAS |
**Score:** |
240 |

6. Prerequisite Courses:

MATH 0815 - Pathway to Mathematical Reasoning

There are no prerequisites for this course.
7. Other Prerequisites

or MATH 0800

9. Co-requisite Courses:

MATH 0815 - Pathway to Mathematical Reasoning

There are no corequisites for this course.
## II. Transfer and Articulation

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

Various Minnesota State institutions and others nationwide are developing co-requisite developmental courses for liberal arts math courses, using guidance from the Dana Center, which is supported by the American Mathematical Association of Two-Year Colleges (AMATYC) and the Mathematical Association of America (MAA).

## 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

College-Wide Outcomes/Competencies |
Students will be able to: |

Analyze and follow a sequence of operations |
Write and justify steps in the process of solving algebraic equations. |

Apply abstract ideas to concrete situations |
Apply appropriate geometric and algebraic formulas to solve applications problems. |

Utilize appropriate technology |
Use a graphing calculator and determine when the technology is appropriate to use. |

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; and

- Calculate and interpret a rate of change as given by a symbolic, graphical, or numerical representation.

## V. Topical Outline

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

1. Lecture Sessions

- Preparation for, and practice of Set Theory
- Set terminology
- Physical examples
- Basic Venn diagrams
- Solving linear equations using the addition property of equality

- Preparation for, and practice of Probability
- Probability terminology
- Identification of outcomes of a probability experiment
- Equivalent fractions, decimals, and percents
- Number sense (relative size), estimation
- Number sense (order of decimals)
- Evaluating algebraic expressions
- Solving linear equations
- Reading tables and graphs
- Fraction multiplication, addition

- Preparation for, and practice of Statistics
- Reading skills (Statistics terminology, recognizing bias or error, reading graphs)
- Number sense (sorting data, reading graphs)
- Evaluating algebraic expressions (order of operations)
- Calculator or computer software statistics applications
- Graphing paired data in scatter plots by hand and with technology
- Graph inequalities on a number line (solutions to statistical applications)

- Preparation for, and practice of Geometry
- Evaluating algebraic expressions, including exponents and radicals
- Measurement of angles (protractors) and lengths (rulers)
- Hands-on practice with prisms, spheres, and cylinders
- Equivalent fractions, solving proportions
- Sketching right triangles for trigonometric applications

- Preparation for, and practice of Finance
- Equivalent fractions, decimals, and percents
- Graph linear equations in two variables (simple interest)
- Graph exponential equations (compound interest)
- Solving formulas for a variable
- Evaluating algebraic expressions
- Reading applications for understanding
- Understanding spreadsheets