## I. General Information

1. Course Title:

Math for Elementary Teachers II

2. Course Prefix & Number:

MATH 1512

3. Course Credits and Contact Hours:

**Credits:** 3

**Lecture Hours:** 3

**Lab Hours:** 0

4. Course Description:

This is the second 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 decimals, percents, topology, transformations, geometry, discrete mathematics, probability, and statistics.

5. Placement Tests Required:

6. Prerequisite Courses:

MATH 1512 - Math for Elementary Teachers II

There are no prerequisites for this course.
9. Co-requisite Courses:

MATH 1512 - Math for Elementary Teachers II

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

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

Ridgewater College, MATH 211: Introduction to Modern Mathematics II, 3 credits

Bemidji State University, MATH 1013: Math for Elem School Teachers II, 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.
- Relate patterns in one strand of mathematics to patterns across the discipline.
- Demonstrate an understanding of the properties and relationships of geometric figures.
- Demonstrate an understanding of geometry and measurement from both abstract and concrete perspectives and identify real world applications.
- Use geometric learning tools such as geoboards, compass and straightedge, ruler, protractor, patty paper, reflection tools, spheres, and platonic solids.
- Use a variety of conceptual and procedural tools for collecting, organizing, and reasoning about data.
- Interpret and draw inferences from data and make decisions in applied problem situations.
- Aid students in the understanding of quantitative and qualitative approaches to answering questions and developing their abilities to communicate mathematically.
- Use probability as a way of describing change in simple and compound events.
- Demonstrate an understanding of the role of randomness and sampling in experimental studies.
- Reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality.
- Demonstrate an understanding of how to integrate technological and non-technological tools with mathematics.
- Demonstrate an understanding of the relationship between mathematics and other fields.
- Demonstrate an understanding of and apply problem solving, reasoning, communication, and connections.

## V. Topical Outline

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

1. Lecture Sessions

- Proportional Reasoning
- The Concept of Ratio
- Proportional Variation and Solving Proportions
- Solving Percent Problems
- Definition of Percent
- Connecting Percents, Ratios, and Decimals
- Types of Percent Problems
- Estimating Percents

- Finding Simple and Compound Interest

- Analyzing Data
- Types of Data Displays
- Graphs, Stem-and-Leaf Plots, Pictographs, Histographs, Bar Graphs

- Data Displays that Show Relationships
- Displaying Two-Variable Data

- Describing the Average and Spread of Data
- Mean, Median, Mode, Midrange, and Range
- Interquartile Range
- Box-and-Whisker Plots

- Decision Making with Data

- Probability
- Understanding Probability
- Connecting Probability to Models and Counting
- Simulations
- Odds and Long-Term Behavior
- Random Variables and Probability Distributions
- Permutations and Combinations
- Solving Permuations
- Counting Combinations

- Introducing Geometry
- Basic Ideas of Geometry
- More About Points, Segments, and Lines
- Triangle Concurrency
- Euler Line
- Network Traversability

- More About Angles
- Angles in Intersecting Lines
- Angles in Polygons and Circles

- More About Triangles
- Congruent Triangles, Similar Triangles
- Pythagorean Theorem
- Special Right Triangles

- More About Quadrilaterals
- Properties of Quadrilaterals
- Quadrilaterals and Geometric Construction

- Extending Geometry
- Transformations
- Geometric Patterns
- Special Polygons
- Three-Dimensional Figures

- Measurement
- The Concept of Measurement
- Measuring the Perimeter and Area of Polygons
- Measuring the Surface Area and Volume of Solids

- Exploring Ideas of Algebra and Coordinate Geometry
- Variables, Expressions, and Equations
- Understanding Numerical and Algebraic Expressions
- Understanding Equations

- Solving Equations
- Solving Linear and Quadratic Equations

- Exploring Graphs of Linear Equations
- Relationships between Graphs and Equations
- Understanding Slope

- Connecting Algebra and Geometry
- Finding the Midpoint of a Line Segment
- Finding the Distance between Two Points
- Finding the Equation of a Line
- Developing the Equation of a Circle
- Describing Transformations

## I. General Information

1. Course Title:

Math for Elementary Teachers II

2. Course Prefix & Number:

MATH 1512

3. Course Credits and Contact Hours:

**Credits:** 3

**Lecture Hours:** 3

**Lab Hours:** 0

4. Course Description:

This is the second 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 decimals, percents, topology, transformations, geometry, discrete mathematics, probability, and statistics.

5. Placement Tests Required:

6. Prerequisite Courses:

MATH 1512 - Math for Elementary Teachers II

There are no prerequisites for this course.
9. Co-requisite Courses:

MATH 1512 - Math for Elementary Teachers II

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

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

Ridgewater College, MATH 211: Introduction to Modern Mathematics II, 3 credits

Bemidji State University, MATH 1013: Math for Elem School Teachers II, 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.
- Relate patterns in one strand of mathematics to patterns across the discipline.
- Demonstrate an understanding of the properties and relationships of geometric figures.
- Demonstrate an understanding of geometry and measurement from both abstract and concrete perspectives and identify real world applications.
- Use geometric learning tools such as geoboards, compass and straightedge, ruler, protractor, patty paper, reflection tools, spheres, and platonic solids.
- Use a variety of conceptual and procedural tools for collecting, organizing, and reasoning about data.
- Interpret and draw inferences from data and make decisions in applied problem situations.
- Aid students in the understanding of quantitative and qualitative approaches to answering questions and developing their abilities to communicate mathematically.
- Use probability as a way of describing change in simple and compound events.
- Demonstrate an understanding of the role of randomness and sampling in experimental studies.
- Reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality.
- Demonstrate an understanding of how to integrate technological and non-technological tools with mathematics.
- Demonstrate an understanding of the relationship between mathematics and other fields.
- Demonstrate an understanding of and apply problem solving, reasoning, communication, and connections.

## V. Topical Outline

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

1. Lecture Sessions

- Proportional Reasoning
- The Concept of Ratio
- Proportional Variation and Solving Proportions
- Solving Percent Problems
- Definition of Percent
- Connecting Percents, Ratios, and Decimals
- Types of Percent Problems
- Estimating Percents

- Finding Simple and Compound Interest

- Analyzing Data
- Types of Data Displays
- Graphs, Stem-and-Leaf Plots, Pictographs, Histographs, Bar Graphs

- Data Displays that Show Relationships
- Displaying Two-Variable Data

- Describing the Average and Spread of Data
- Mean, Median, Mode, Midrange, and Range
- Interquartile Range
- Box-and-Whisker Plots

- Decision Making with Data

- Probability
- Understanding Probability
- Connecting Probability to Models and Counting
- Simulations
- Odds and Long-Term Behavior
- Random Variables and Probability Distributions
- Permutations and Combinations
- Solving Permuations
- Counting Combinations

- Introducing Geometry
- Basic Ideas of Geometry
- More About Points, Segments, and Lines
- Triangle Concurrency
- Euler Line
- Network Traversability

- More About Angles
- Angles in Intersecting Lines
- Angles in Polygons and Circles

- More About Triangles
- Congruent Triangles, Similar Triangles
- Pythagorean Theorem
- Special Right Triangles

- More About Quadrilaterals
- Properties of Quadrilaterals
- Quadrilaterals and Geometric Construction

- Extending Geometry
- Transformations
- Geometric Patterns
- Special Polygons
- Three-Dimensional Figures

- Measurement
- The Concept of Measurement
- Measuring the Perimeter and Area of Polygons
- Measuring the Surface Area and Volume of Solids

- Exploring Ideas of Algebra and Coordinate Geometry
- Variables, Expressions, and Equations
- Understanding Numerical and Algebraic Expressions
- Understanding Equations

- Solving Equations
- Solving Linear and Quadratic Equations

- Exploring Graphs of Linear Equations
- Relationships between Graphs and Equations
- Understanding Slope

- Connecting Algebra and Geometry
- Finding the Midpoint of a Line Segment
- Finding the Distance between Two Points
- Finding the Equation of a Line
- Developing the Equation of a Circle
- Describing Transformations