## Curriculum: Mathematics

#### Web Design

Upper School

Mathematics

Credits: .5

In this course, students will learn to create, organize, and publish a website using a variety of software and coding techniques. Our first sites will be coded by hand with HTML. As students progress, they will study layout, take photos for their site, edit photos in Photoshop, write content for the site, and study fonts and multimedia.

#### Pre-Algebra

Middle School

Mathematics

Credits: 1

Prerequisite: Foundations of Math or Department Placement

This course is for students who have completed Foundations of Mathematics or an equivalent course. Topics include further exploration of decimals, factors, fractions, integers, exponents, ratios, proportions, and percents, as well as graphing on the coordinate plane, linear equations, algebraic expressions, and solving algebraic equations and inequalities.

#### Foundations of Mathematics

Middle School

Mathematics

Credits: 1

Prerequisite: Department Placement

Basic computational skills are reviewed, and problem solving, patterns, estimating, and mental math skills are emphasized. Topics introduced include decimals, fractions, exponents, scientific notation, ratios, rates, proportions, percents, measurement, graphing in the coordinate plane, and an introduction to variables and solving algebraic equations.

Upper School

Mathematics

Credits: 1

Prerequisite: Honors Algebra 2 or departmental approval

Advanced Statistics will closely mirror the content required in AP Statistics with some time dedicated to give students two distinct opportunities to conduct real research in areas that are meaningful to them. The course will begin with descriptive statistics including the organization and analysis of both univariate and bivariate data. The emphasis will always be on why we can make a specific generalization and what makes the generalization or description valid based on the data. Included in descriptive statistics will be methods of organizing and presenting data as well as methods of analyzing data, with an emphasis on linear regression, measures of strength for that correlation, Pearson’s r, the coefficient of determination, measures of center, measures of spread, skew or symmetry, and standard deviation about the least squares line. To prepare students for inferential statistics, the course will investigate probability and the laws of probability which students will use to simulate real-world situations. Finally, the course will cover inferential statistics, the formal hypothesis testing procedure, and all of the myriad tests that are expected even at the introductory level. A paper and oral presentation will substitute for both exams, giving students a true ability to determine the viability of statistics in areas where they might have interest. Students will be empowered to answer questions in ways that they were never able to prior to a course in statistics. They also will have the ability to critically read and evaluate the analytical process employed by others, recognizing good research, and pointing out flaws in poor research. Students who take this course will have the option of taking the Advanced Statistics Placement Test in the spring.

Upper School

Mathematics

Credits: .5

Open to Grades 11-12, and sophomores with approval of instructor.

Advanced Computer Science aims to introduce students to a broad array of concepts in computer science. Students will use the Javascript programming language to explore complex problem solving, algorithm design and implementation, and coding their own program. Topics include number systems, the internet, data visualization, and various programming concepts such as variables, loops, arrays, object, formal logic, and processing.

#### Introduction to Computer Science

Upper School

Mathematics

Credits: .5

Prerequisite: Open to students who have completed Algebra 2

This course focuses and engages the entire discipline of computer science. We will demystify computer hardware and how it works, use computer software, and explore design, coding and implementation. Students will problem-solve, develop software, and come to understand how computers, people, and society interoperate. Our goal is to build quantitative reasoning skills and a basis for future survival and exploration in our advancing world.

#### Statistics

Upper School

Mathematics

Credits: 1

Prerequisite: Algebra 2 and departmental approval

Open to Grades 11-12, and sophomores with approval of instructor.

This course will include extensive studies of probability and statistics, sampling, data analysis, combinations/permutations, and notation. Students will learn real-world applications of these concepts, completing numerous projects to learn the ways in which statistics frame the way we view the world around us. This course will provide students who have completed at least math through Algebra 2 with math skills that are readily applicable to their lives.

Upper School

Mathematics

Credits: .5

Prerequisite: Advanced Calculus 2 and departmental approval

This course will extend the study of calculus to functions with several variables. It will additionally cover topics that are not currently included in a traditional high school calculus course but may be included in a college-level calculus course. Students will explore topics including but not limited to partial derivatives, double and triple integrals, vector fields, and integration over curves and surfaces.

Upper School

Mathematics

Credits: 1

Prerequisite: Completion of Advanced Calculus 1; departmental approval

This course will build on the skills and topics introduced in Advanced Calculus 1 and introduce students to topics including but not limited to: various techniques of integration, sequences and series, and polar and parametric functions. This class would serve those students who have completed Advanced Calculus 1 prior to their senior year. Students are expected to be able to apply and understand the theory behind advanced mathematical topics. Students who take this course will have the option to take the Calculus BC Advanced Placement Test in the spring.

Upper School

Mathematics

Credits: 1

Prerequisite: Precalculus or Honors Precalculus

The methods and techniques of differential and integral calculus are developed and applied to algebraic, trigonometric, logarithmic, and exponential functions. Students are required to use a graphing calculator. This course is for the young mathematician looking to be challenged. Students who take this course will have the option to take the Calculus AB Advanced Placement Test in the spring.

#### Honors Calculus

Upper School

Mathematics

Credits: 1

Prerequisite: Precalculus or Honors Precalculus

This course is a survey of topics in Calculus from limits and continuity to basic differentiation and basic integration. It is an opportunity for students to integrate ideas from algebra and geometry, and to do analytical applications of trigonometry, rational functions, compositions, and logarithmic functions. It is a course geared toward deeper understanding of the material but without the focus on preparing for the standardized testing.

#### Precalculus

Upper School

Mathematics

Credits: 1

Prerequisite: Algebra 2 or Trigonometry

This course is for students who have a strong background in advanced algebraic topics. Students must make the challenging transition from a focus on algebraic skill building and processes to that of their application and conceptual analysis. In order to make connections and to contribute to class discussions and discoveries, students are expected to be quite proficient with a graphing calculator and to extract information from the textbook effectively. Topics reviewed and studied consist of various functions (including compositions, inverse, polynomial, rational, exponential, and logarithmic) and trigonometry.

#### Honors Precalculus

Upper School

Mathematics

Credits: 1

Prerequisite: Honors Algebra 2

This course is for students who have a strong background in advanced algebraic topics and have demonstrated a good aptitude for mathematical reasoning and intellectual curiosity. Students must make the challenging transition from a focus on algebraic skill building and processes to that of their application and conceptual analysis. Precise arithmetic and algebraic skills are essential to ensure accurate data for proper analysis, and to attain a strong level of command and understanding of the concepts studied. In order to make connections and to contribute to class discussions and discoveries, students are expected to be quite proficient with a graphing calculator and to extract information from the textbook effectively. Topics reviewed and studied consist of several types of functions (including compositions, inverse, polynomial, rational, exponential, logarithmic, and circular) and an introduction to limits.

#### Trigonometry

Upper School

Mathematics

Credits: 1

Prerequisite: Algebra 2 or departmental approval

This course consists of a review of advanced algebraic topics as well as an exploration of basic trigonometry. The algebraic topics include quadratic functions and their applications, composite and inverse functions, exponents, radicals, and logarithms. The study of trigonometry consists of right triangle and general triangle relationships and applications, the unit circle, and sine, cosine, and tangent graphs.

#### Honors Algebra 2

Upper School

Mathematics

Credits: 1

Prerequisite: Honors Algebra 1 and Honors Geometry or departmental approval

This course is for students who have a strong background in elementary algebra, including systems of equations, radicals, and quadratics. They must have demonstrated a good aptitude for mathematical reasoning. The course begins with an extension of Algebra 1 topics and continues with the study of complex numbers, quadratic functions, rational and polynomial functions, exponents, radicals, and logarithms.

#### Algebra 2

Upper School

Mathematics

Credits: 1

Prerequisite: Algebra 1 and Geometry

This course is for students who have completed a full year of elementary algebra and geometry. The year consists of a review and extension of Algebra 1 topics including inequalities, linear equations, operations with polynomials, and application of algebraic skills through verbal problems. Additional topics include functions, exponents, complex numbers, quadratic graphs, and an introduction to statistics.

#### Honors Geometry

Upper School

Mathematics

Credits: 1

Prerequisite: Honors Algebra 1 or departmental approval

This course is for students who have a strong mathematical background, good insight, and solid problem-solving skills. Plane geometry relationships will be explored in depth with algebraic and numerical applications provided. Units on congruence, similarity, polygons, right triangles, trigonometry, circles, plane and solid figures, and coordinate geometry are included.

#### Geometry

Upper School

Mathematics

Credits: 1

Prerequisite: Algebra 1

This course is for students who have completed a full year of elementary algebra. Plane geometry relationships are developed as part of a logical system, and the student learns to write short proofs based on these relations. Algebraic and numerical applications are provided, and units on right triangle trigonometry, three-dimensional figures, and coordinate geometry are included.

#### Honors Algebra 1

Middle School, Upper School

Mathematics

Credits: 1

Prerequisite: Pre-Algebra or Department Placement

This course is for students who have a strong background in arithmetic facts and skills, and in elementary algebra, including positive and negative numbers, the basic properties of numbers, and simple equations. Students must have demonstrated a good aptitude for mathematical reasoning. The course covers all topics of elementary algebra, including verbal problems, factoring, algebraic fractions, graphing of linear functions, radicals, solving linear and quadratic equations, systems of equations, variations, and the quadratic formula.

#### Algebra 1

Middle School, Upper School

Mathematics

Credits: 1

Prerequisite: Pre-Algebra or Department Placement

Students entering this class are expected to have studied positive and negative numbers, the basic properties of numbers, and simple equations. The course covers all topics of elementary algebra, including verbal problems, factoring, graphing of linear equations, radicals, solving linear and quadratic equations, and linear systems.