## I. General Information

1. Course Title:

Math for Elementary Teachers I

2. Course Prefix & Number:

MATH 1510

3. Course Credits and Contact Hours:

**Credits:** 3

**Lecture Hours:** 3

**Lab Hours:** 0

4. Course Description:

This is the first of two math courses providing a background for teaching in the elementary school. It emphasizes the use of mathematics manipulatives for modeling the basic operations. Topics will include addition, subtraction, multiplication and division of whole numbers, number theory related to fractions, fractions, decimals, and integers.

5. Placement Tests Required:

6. Prerequisite Courses:

MATH 1510 - Math for Elementary Teachers I

There are no prerequisites for this course.
8. Prerequisite (Entry) Skills:

Fundamental algebra background and familiarity with a calculator.

9. Co-requisite Courses:

MATH 1510 - Math for Elementary Teachers I

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

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

Ridgewater College, MATH 210: Introduction to Modern Mathematics I, 3 credits

Bemidji State University, MATH 1011: Math for Elem School Teachers I, 3 credits

## III. Course Purpose

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:

Liberal Arts Elective

## IV. Learning Outcomes

1. College-Wide Outcomes

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

Assess alternative solutions to a problem |
Apply higher-order problem-solving and/or modeling strategies |

Analyze and follow a sequence of operations |
Explain what constitutes a valid mathematical argument |

Apply abstract ideas to concrete situations |
Clearly express mathematical/logical ideas in writing |

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

- Identify and justify observed patterns.
- Generate patterns to demonstrate a variety of relationships.
- Be able to relate patterns in one strand of mathematics to patterns across the discipline.
- Demonstrate an understanding of number sense and be able to use numbers to quantify concepts in the students’ world.
- Demonstrate an understanding of a variety of computational procedures and how to use them in examining the reasonableness of the students’ answers.
- Demonstrate an understanding of the concepts of number theory including divisibility, factors, multiples, and prime numbers, and know how to provide a basis for exploring number relationships.
- Demonstrate an understanding of the relationships of integers and their properties that can be explored and generalized to other mathematical domains.
- Demonstrate an understanding of how to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality.
- Demonstrate an understanding of the connections between mathematical concepts and procedures, as well as their application to the real world.
- Demonstrate an understanding of the relationship between mathematics and other fields.
- Demonstrate an understanding of and apply problem solving, reasoning, communication, and connections.
- Demonstrate an understanding of how to integrate technological and non-technological tools with mathematics.

## V. Topical Outline

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

1. Lecture Sessions

- Mathematical Processes
- Communicating Mathematically
- Reasoning Mathematically
- Mathematics for Problem Solving

- Sets and Whole-Number Operations
- Sets and Whole Numbers
- Addition and Subtraction of Whole Numbers
- Multiplication and Division of Whole Numbers
- Numeration

- Estimation and Computation
- Strategies and Procedures for Mental Computation
- Strategies and Procedures for Estimation
- Algorithms for Addition and Subtraction
- Algorithms for Multiplication and Division

- Number Theory
- Factors and Divisibility
- Prime and Composite Numbers

- Understanding Integer Operations and Properties
- Addition, Subtraction, and Order Properties of Integers
- Counter Method of Addition
- Charged-Field Method of Addition
- Properties of Integer Addition
- Absolute Value
- Multiplication, Division, and Other Properties of Integers
- Counter Method of Multiplication
- Charged-Field Method of Multiplication
- Number-Line Method of Multiplication
- Properties of Integer Multiplication

- Rational Number Operations and Properties
- Rational Number Ideas and Symbols
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Operations with Decimals
- Addition and Subtracting Decimals
- Multiplying and Dividing Decimals
- Comparing, Ordering, and Connecting Rational Numbers

## I. General Information

1. Course Title:

Math for Elementary Teachers I

2. Course Prefix & Number:

MATH 1510

3. Course Credits and Contact Hours:

**Credits:** 3

**Lecture Hours:** 3

**Lab Hours:** 0

4. Course Description:

This is the first of two math courses providing a background for teaching in the elementary school. It emphasizes the use of mathematics manipulatives for modeling the basic operations. Topics will include addition, subtraction, multiplication and division of whole numbers, number theory related to fractions, fractions, decimals, and integers.

5. Placement Tests Required:

6. Prerequisite Courses:

MATH 1510 - Math for Elementary Teachers I

There are no prerequisites for this course.
8. Prerequisite (Entry) Skills:

Fundamental algebra background and familiarity with a calculator.

9. Co-requisite Courses:

MATH 1510 - Math for Elementary Teachers I

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

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

Ridgewater College, MATH 210: Introduction to Modern Mathematics I, 3 credits

Bemidji State University, MATH 1011: Math for Elem School Teachers I, 3 credits

## III. Course Purpose

3. Other - If this course does NOT meet criteria for #1 or #2 above, it may be used for the purpose(s) selected below:

Liberal Arts Elective

## IV. Learning Outcomes

1. College-Wide Outcomes

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

Analyze and follow a sequence of operations |
Explain what constitutes a valid mathematical argument |

Apply abstract ideas to concrete situations |
Clearly express mathematical/logical ideas in writing |

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

- Identify and justify observed patterns.
- Generate patterns to demonstrate a variety of relationships.
- Be able to relate patterns in one strand of mathematics to patterns across the discipline.
- Demonstrate an understanding of number sense and be able to use numbers to quantify concepts in the students’ world.
- Demonstrate an understanding of a variety of computational procedures and how to use them in examining the reasonableness of the students’ answers.
- Demonstrate an understanding of the concepts of number theory including divisibility, factors, multiples, and prime numbers, and know how to provide a basis for exploring number relationships.
- Demonstrate an understanding of the relationships of integers and their properties that can be explored and generalized to other mathematical domains.
- Demonstrate an understanding of how to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality.
- Demonstrate an understanding of the connections between mathematical concepts and procedures, as well as their application to the real world.
- Demonstrate an understanding of the relationship between mathematics and other fields.
- Demonstrate an understanding of and apply problem solving, reasoning, communication, and connections.
- Demonstrate an understanding of how to integrate technological and non-technological tools with mathematics.

## V. Topical Outline

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

1. Lecture Sessions

- Mathematical Processes
- Communicating Mathematically
- Reasoning Mathematically
- Mathematics for Problem Solving

- Sets and Whole-Number Operations
- Sets and Whole Numbers
- Addition and Subtraction of Whole Numbers
- Multiplication and Division of Whole Numbers
- Numeration

- Estimation and Computation
- Strategies and Procedures for Mental Computation
- Strategies and Procedures for Estimation
- Algorithms for Addition and Subtraction
- Algorithms for Multiplication and Division

- Number Theory
- Factors and Divisibility
- Prime and Composite Numbers

- Understanding Integer Operations and Properties
- Addition, Subtraction, and Order Properties of Integers
- Counter Method of Addition
- Charged-Field Method of Addition
- Properties of Integer Addition
- Absolute Value
- Multiplication, Division, and Other Properties of Integers
- Counter Method of Multiplication
- Charged-Field Method of Multiplication
- Number-Line Method of Multiplication
- Properties of Integer Multiplication

- Rational Number Operations and Properties
- Rational Number Ideas and Symbols
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Operations with Decimals
- Addition and Subtracting Decimals
- Multiplying and Dividing Decimals
- Comparing, Ordering, and Connecting Rational Numbers