Mathematics

At Walker’s, mathematics instruction is guided by a desire to instill critical thinking and the integration of technology into classroom instruction. Our math faculty provide experiences that encourage and enable students to value mathematics, develop confidence in their mathematical ability, use mathematics to solve problems, and be able to reason and communicate mathematically.

Instruction is problem-based and focuses on the practice of new skills and concrete applications. Mathematical rigor is introduced at all levels, commensurate with the course level. Our lower level courses are taught with a great deal of structure, providing a solid foundation for abstract thinking, integration, and synthesis needed in the more advanced selections. We offer regular and honors sections for every grade level; 98% of our students take a 4-year mathematics program.

The traditional subjects of algebra, geometry and trigonometry provide the theoretical background for students intending to further their education. For students who plan to pursue careers in mathematics, science, and engineering, the pre-calculus and calculus courses are preparation for higher level mathematics courses.

Various teaching techniques are employed to address multiple learning styles in order to help each student find and develop her unique abilities and strengths in math. At the core of our mission is the determination to encourage our young women to find their own “unique voice” in our mathematics classrooms as students are encouraged to lead discussions, ask clarifying questions, and contribute alternative methods of problem solving.

MATHEMATICS COURSES

ALGEBRA 1 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.

HONORS ALGEBRA 1 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. They 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.

GEOMETRY Prerequisite: Algebra 1 Credit: 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 GEOMETRY Prerequisite: Honors Algebra 1 or departmental approval Credit: 1 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 will be included.

ALGEBRA 2 Prerequisite: Algebra 2 or departmental approval Credit: 1 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 ALGEBRA 2 Prerequisite: Honors Algebra 1 and Honors Geometry or departmental approval Credit: 1 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.

TRIGONOMETRY Prerequisite: Algebra 2 or departmental approval Credit: 1 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 and cosine graphs.

PRECALCULUS Prerequisite: Algebra 2 and Trigonometry Credit: 1 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 Prerequisite: Honors Algebra 2 Credit: 1 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.

HONORS CALCULUS Prerequisite: Precalculus or Honors Precalculus Credit: 1 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.

ADVANCED CALCULUS 1 Prerequisite: Precalculus or Honors Precalculus Credit: 1 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.

ADVANCED CALCULUS 2 Prerequisite: Completion of Advanced Calculus 1; departmental approval Credit: 1 This course will build on the skills and topics introduced in Advanced Calculus I and introduce students to topics including but not limited to: various techniques of integration, sequences and series, polar and parametric functions. This class would serve those students who have completed Advanced Calculus I 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.

ADVANCED MULTIVARIABLE CALCULUS Open to Grades 11-12 Prerequisite: Advanced Calculus 2 and departmental approval Credit: .5 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.

STATISTICS Open to Grades 11-12, and sophomores with approval of instructor Prerequisite: Algebra 2 and departmental approval Credit: 1 Topics will include: probability & statistics, sampling, data analysis, combinations/permutations, and notation. This class is best suited for students who are looking for a fourth year of math that would provide them with real world and applicable math skills.

INTRODUCTION TO COMPUTER SCIENCE Open to students who have completed Algebra 2 Credit: .5 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.

ADVANCED COMPUTER SCIENCE Open to Grades 11-12, and sophomores with approval of instructor Credit: .5 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.

ADVANCED STATISTICS Prerequisite: Honors Algebra 2 or departmental approval Credit: 1 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, and 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.