## Mathematics

The mathematics department at SWWHS consists of six teachers offering courses which meet, not only the graduation requirements of DCPS, but the diverse needs of our student body. At Walls, we offer Algebra I, geometry, Algebra II, pre-calculus, calculus, AP calculus, statistics and AP statistics.

We make every effort to meet the needs of our students through teacher assistance and volunteer tutoring services. For students in Algebra I, geometry, and Algebra II who need additional tutorial support, we offer problem-solving (foundation) courses. Students who take Calculus in 10th grade or 11th grade may be eligible to enroll in math classes at The George Washington University.

**M21 Algebra 1 **

Algebra I provides the opportunity for students to learn algebra as a style of thinking for formalizing patterns, functions, and generalizations. In this course, students expand previously learned quantitative rational number relationships to include the irrational numbers. The focus is on students becoming proficient in recognizing and working effectively with linear relationships and their corresponding representations in tables, graphs, and equations; such proficiency also includes competence in solving linear equations, generating equivalent expressions, using formulas, and applying proportionality. Other key algebraic topics include operations with exponents, radicals, and polynomials and rational expressions and solving systems of equations and an introduction to quadratic equations. To develop proficiency in symbolic and graphical representations, students use physical models, visual models, and technology. While mathematical skills are addressed, teaching is focused on developing an understanding of concepts in depth, enabling students to apply the skills and make meaningful connections to life’s experiences. The use of graphing calculators is an integral part of the course.

**M31 Geometry **

Students in Geometry study Euclid’s postulates and theorems as the basis for an axiomatic system. Students explore geometry through inductive and deductive processes using proofs and making algebraic connections where appropriate. Topics of investigation include logic, angle and line relationships, triangles and other polygons, congruence, and similarity. Students also study coordinate geometry. Trigonometric ratios of sine, cosine, and tangent are used to solve triangle problems. Students use area, volume, geometric probability, and geometric relationships to solve real-life problems. Students use technology, constructions, and manipulatives to support their processes.

While mathematical skills are addressed, teaching is focused on developing an understanding of concepts in depth, enabling students to apply mathematical skills and make meaningful connections to life’s experiences.

**M41 Algebra II & Trigonometry **

The study of functions is the primary focus of Algebra II. Students study functions algebraically, as well as numerically and graphically, using technology and manipulatives. The student will become proficient in recognizing and solving everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, step, and trigonometric functions. The course emphasizes the concepts of complex numbers, matrices, systems of equations and inequalities, sequences and series, probability using permutations and combinations, and trigonometry.

**M46 Advanced Topics in Mathematics **

The study of functions is the primary focus of Algebra II. Students study functions algebraically, as well as numerically and graphically, using technology and manipulatives. The student will become proficient in recognizing and solving everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, step, and trigonometric functions. The course emphasizes the concepts of complex numbers, matrices, systems of equations and inequalities, sequences and series, probability using permutations and combinations, and trigonometry.

**M51 Pre-Calculus **

Areas of study for the Pre-Calculus course will include exponential, power, polynomial, rational, logarithmic, and piece-wise functions, along with trigonometric functions and their inverses.

Students investigate and explore mathematical ideas using methods that help them gain a deep understanding of fundamental concepts, develop multiple strategies for analyzing complex situations, and acquire appropriate technological skills. Students analyze situations verbally, numerically, graphically, and symbolically. Effective communication skills are developed so that students are able to discuss, explain, and justify their thoughts and ideas. While mathematical skills are addressed, teaching is focused on developing deep understanding of concepts that will enable students to apply mathematical skills and make meaningful connections to life’s experiences. The use of graphing calculators is an integral part of the course, allowing for exploration of a variety of approaches to solving problems.

**M54 Concepts & Context of Calculus **

This course builds on students’ experience with functions and introduces the basic concepts and skills of calculus. Students will investigate and apply the properties of polynomial, exponential, and logarithmic functions; broaden their understanding of the mathematics associated with rates of change; and develop facility with the concepts and skills of differential calculus as applied to polynomial, rational, exponential, and logarithmic functions. Students will apply these skills to problem solving in a range of applications.

**M61 AP Calculus AB **

This is a college level class with college level expectations. Areas of study for the AP- Calculus AB course will include limits, continuity, derivatives of functions, the definite integral, and their real-world applications, products, quotients, parametric functions, the calculus of exponential and logarithmic functions, the calculus of growth and decay, algebraic calculus techniques for the elementary functions the calculus of average, extreme and vector motion. Students investigate and explore situations graphically, numerically, and symbolically. The use of graphing calculators is an integral part of the course, allowing for exploration of a variety of approaches to solving problems. A comprehensive exam will be given at the end of each semester. The student will be required to take the AP Calculus Exam in May. Participation in study group is highly recommended.

**M64 AP Statistics **

The purpose of Advanced Placement Statistics course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

- Exploring Data: Describing patterns and departures from patterns
- Sampling and Experimentation: Planning and conducting a study
- Anticipating Patterns: Exploring random phenomena using probability and simulation
- Statistical Inference: Estimating population parameters and testing hypotheses.

Graphing calculators are an integral part of this course. Real world applications are heavily emphasized, and students are expected to actively participate in class discussions, complete projects, essays and presentations throughout the year. The student will be required to take the AP Statistics exam in May. Participation in study group is highly recommended.