### Junior High One & Two

Students consolidate and expand arithmetic skills to include problem-solving with percents. They build on their previous study of geometry, probability, statistics, and signed numbers, and proceed to algebraic topics such as solving equations and graphing functions. Careful consideration and evaluation take place continually in order to analyze the readiness and motivation of each student to work on advanced and abstract topics.

### Junior High Three

#### Algebra, Part II

*How does understanding the rules of algebra allow us to solve unfamiliar problems?*

*What are the similarities and differences between linear and non-linear functions?*

*How does one analyze and interpret mathematical information given in different representations? What types of data are better suited to which representations?*

Students in this course continue the study of algebra that was begun the previous year. In addition to a review of linear equations and systems, the course content includes quadratic equations, polynomials, functions, rational expressions, and radicals. Emphasis is placed on applications and conceptual development, as well as the building of skills.

#### Geometry

*What is proof? How do you use deductive reasoning to demonstrate the validity of previously accepted ideas?*

*How can you use the formulas for the areas of traditional plane figures to find the areas of nontraditional plan figures?*

*How does the concept of similarity lead to trigonometry and proportions in a circle?*

This course covers geometric theory, its methods and applications. A careful development of deductive reasoning is presented. Constructions and coordinate geometry are considered. Students use the Geometer’s Sketchpad, constructions, and other hands-on activities to explore concepts and theorems. Basic elements of right triangle trigonometry are introduced.

### Senior High One

#### Geometry

*What is proof? How do you use deductive reasoning to demonstrate the validity of previously accepted ideas?How can you use the formulas for the areas of traditional plane figures to find the areas of nontraditional plan figures?How does the concept of similarity lead to trigonometry and proportions in a circle?*

This course covers geometric theory, its methods and applications. A careful development of deductive reasoning is presented. Constructions and coordinate geometry are considered. Students use the Geometer’s Sketchpad, constructions, and other hands-on activities to explore concepts and theorems. Basic elements of right triangle trigonometry are introduced.

#### Algebra II/Trigonometry

*How can you solve, graph, and formulate mathematical functions?What are the advantages and limits when using mathematical functions to model real-life situations?What good are graphs if you can create a table of values for any function? Or: Do graphs of functions lie?*

This course reviews and builds on topics presented in Algebra I and goes on to the study of llinear programming and imaginary numbers. Students explore the behavior and applications of polynomial, exponential, logarithmic, and trigonometric functions.

### Senior High Two

#### Intermediate Algebra/Trigonometry

*How do** the rules of algebra enable us to solve unfamiliar problems?What are the similarities and differences between linear and non-linear functions?How are different representations of mathematical information analyzed and interpreted?Are different types of data better suited to certain representations?*

This course reviews and builds on basic algebraic skills and concepts and goes on to the study of matrices and imaginary numbers. Students explore the behavior and applications of polynomial, exponential, logarithmic, and trigonometric functions.

#### Pre-Calculus and Discrete Mathematics

*Why do certain functions better model data than others?How can basic functions be transformed to represent complicated phenomena?How can graphing calculators lead us astray?Continuous functions vs. discrete mathematics: what, when, why?*

This course expands the study of applications of polynomial, exponential, logarithmic, and trigonometric functions. Additional topics include sequences, series, conic sections, polar graphs, probability, and statistics. Students who successfully complete this course are prepared for the study of calculus.

### Senior High Three

#### Probability and Statistics

*How can probability be useful in making effective and logical decisions?How do we make numerical results more meaningful to others who are unfamiliar with the language of statistics?How do we use a sample to make inferences about a population? When can we trust those inferences?*

In this course students are introduced to methods of counting, probability theory, and descriptive and inferential statistics. Topics include permutations, combinations, measures of central tendency, measures of dispersion, normal distribution and sampling.

#### Advanced Calculus II

*How do derivatives and integrals inform us about functions?How can the calculus of single-variable functions be applied to parametric functions and polar curves? What are the pitfalls?When and why would we use power series to represent functions?*

This course is for students who have successfully completed Advanced Calculus I. It expands the study of differential and integral calculus to parametric functions and polar curves. Additional material includes advanced methods of integration and infinite series.

#### Mathematical Modeling

*How are regression models computed and interpreted?How do we write and analyze a mathematical function?Why do certain functions better model data than others?*

Through regression analysis and mathematical functions, algebraic and trigonometric concepts are reviewed, extended, and applied to scientific, economic, and geometric situations. Additional topics include analysis of annuity and loan formulas using geometric series, spreadsheets, and the graphing calculator.

#### Physical Applications of Calculus

*How do the tools of Calculus apply to the study of Physics and to solving Physical problems?What is it about Physics that can’t be solved by using algebraic methods?*

This course combines Physics applications and advanced topics in Calculus. We will consider realistic solutions to Physical problems and we will weave in some of the historical connections between Physics and Math. This is a college level course that will require approval from both the Science and Math departments. The course will include selected topics from among these:

- General kinematics (differentiation)
- Vectors
- Center of mass (integral calculus)
- Rotational inertia (integral calculus)
- Non-free fall (integral Calculus/DE)
- Biot-Savart law (integral calculus; dot and cross products)
- Maxwell’s equations (electricity and magnetism; surface and line integrals)
- Simple harmonic motion (2nd order DE)
- Schrodinger’s wave equation (2nd order DE)

#### Statistical Methods and Applications

*How can statistics be used to predict the future? How certain can we be about our predictions?How do we use a sample to make inferences about a population? When can we trust those inferences?How do we make numerical results more meaningful to others who are unfamiliar with the language of statistics?*

This is a fast-paced college-level course in which students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The topics are divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference.

Departmental approval is required.