## Tor Academy - Mathematics

## Organization

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## Descriptions and credit recommendations for all evaluated learning experiences

**Versions 1 and 2:** Varies; self-study format.

**Version 1:** March 2016 - July 2021. **Version 2:** August 2021 - Present.

**Version 1 and 2:** Upon successful completion of the course, students will be able to: identify examples of the pervasiveness and importance of mathematics in the world around them; investigate challenging applied problems found in disciplines such as biology, ecology and finance; understand the fundamental ideas in descriptive statistics and recognize how statistics can be used and misused; think critically about real-world problems and be a more critical consumer of information; transfer real world information into a mathematical model accurately use problem-solving techniques, logical reasoning, algorithms and/or theorems to produce correct and useful results; apply analytical, numeric, descriptive, and graphical representations to aid in problem-solving; use technology effectively (including the Microsoft Excel) to experiment, solve problems, create and interpret graphs, and verify results; collaborate responsibly and productively; and clearly communicate mathematical findings in writing and through oral presentations.

**Versions 1:** Basic Concepts in Mathematics covers elementary mathematical ideas in order in order to gain a better appreciation and broader view of what mathematics is all about. The final exam assesses students’ problem solving and critical thinking skills in applying a number of applications of mathematics to real world problems. Major topics include: the mathematics of Voting, Sharing, Apportionment, Logistics, Touring, Spiral Growth in Nature, Money, Symmetry, Statistics, and Normal Distribution. **Version 2:** All topics in Version 1, additionally, extra reading material to cover topics involving algorithmic problem solving; Venn diagrams to relate methods of representing mathematical formulas in areas such as voting, profit sharing, logistics, resource allocations and more; further exploring the science of statistics in terms of identifying key factors, collecting data, interpreting the results; reading graphs; interpreting data relating to distance calculation; identifying and understanding arithmetic sequences; working with the nth Fibonacci sequence, and understanding how to apply percentages to real life equations such as sales and tax equations.

**Version 1:** In the lower division baccalaureate/associate degree category, 4 semester hours in Mathematics, Business, Marketing, or Finance (3/16). **Version 2: **In the lower division baccalaureate/associate degree category, 6 semester hours in Mathematics, Business, Marketing, or Finance (8/21 revalidation).

Varies; self-study format.

March 2016 - Present.

Upon successful completion of the course, students will be able to: identify the properties of functions, including domain and range, operations, compositions, and inverses; identify, interpret, and solve problems of various types of functions and their graphs, including but not limited to linear, quadratic, polynomial, rational, exponential, and logarithmic functions; apply graphing techniques for various functions; identify and develop basic sequences and series; and solve systems of equations with various methods including elimination, substitution, and matrices.

College Algebra covers the foundations of Algebra expressed in the applications of quadratics, polynomial, rational, exponential and logarithmic functions, and systems of equations. The final exam assesses students’ problem-solving skills and knowledge relating to functions and requires them to identify, interpret, and solve problems of various types of functions and their graphs, apply graphing techniques for various functions, identify sequences and series, and solve systems of equations with various methods including elimination, substitution, and matrices.

In the lower division baccalaureate/associate degree category, 4 semester hours in Mathematics, Business, Marketing, or Economics (3/16) (8/21 revalidation).

Varies; self-study format.

March 2016 - Present.

Upon successful completion of this course, students will be able to: construct and analyze logical arguments based on the rules of inference; define financial management and compound interest; correctly use statistical reasoning and proficient tin the use of statistical graphs and tables; correctly determine correlation and causality; explain the concept of data distribution and determine measures of variations; define the fundamentals of mathematical modeling and how they represent exponential growth, doubling-time, and half-life; and demonstrate proficiency in linear and quadratic modeling.

The course deals with the use of mathematics to model change in the real world. Major topics include: ratios, percentages, averages, estimation, and financial mathematics. The final exam assesses students’ skills in analyzing linear and exponential models of growth, basic geometric measurements and scaling, logical arguments based on the rules of inference, basic financial management and compound interest. Other topics include: statistical reasoning, statistical graphs and tables, data distribution, mathematical modeling, exponential growth, and linear and quadratic modeling.

In the lower division baccalaureate/associate degree category, 4 semester hours in Business, Marketing, or Finance (3/16) (8/21 revalidation).