**MICHAEL VANYA - **Math

A graduate of UT Austin, Mr. Vanya comes to the GW Community School with twenty years of experience at all levels of mathematics, from Pre-Algebra to Advanced Calculus. His familiarity with a wide variety of educational settings, from one-on-one tutoring to large public school classrooms, allows him to create classes which are lively, engaging and informative. In addition to loving math, Mr. Vanya is also a chess enthusiast and he has taught this touchstone of the intellect to students throughout his career. In his spare time, Mr. Vanya enjoys spending time with his children, delving into recreational math problems, reading science fiction and poetry, computer programming, camping and studying the stars.

COURSES TAUGHT

**Algebra I**

How does a car know how far it has traveled? If I have a recipe for a cake that asks for 1/2 cup of margarine but I want to make 25 cakes, how much margarine do I use? How can sportscasters predict how many touchdowns the Redskins will score each week with some accuracy? And just how does that Wifi remote work? All of these have one thing in common: Algebra. Algebra is your first step on your journey through the world of advanced math. Picking up where basic arithmetic and pre-algebra leave off, we will be studying variables, equation solving, graphing, the coordinate plane, drawing lines, and how all of these things are related to the world around us. While you might think that algebra is just a subject in school that won't help you in life, it is in fact used every day by many people in many different professions around the world.

You will study real life example problems to help you understand how algebra is used in the real world. The question, "Why do I need to learn algebra?" will be answered over the course of the year and you'll be prepared for the next step in your mathematical journey.

**Trigonometry I and Analytic Geometry**

Trigonometry is a two-semester course that provides students with a thorough treatment of Trigonometry through the study of trigonometric definitions, applications, graphing, and solving trigonometric equations and inequalities, with an emphasis placed on the connections between right triangle ratios, trigonometric functions, and circular functions.

Following the study of trigonometry, the analytic geometry part of the course studies the other transcendental functions. Throughout the course emphasis will be placed on using trigonometry and analytic geometry as a tool to solve real-life problems. Graphing calculators will be used to assist in teaching and learning and to enhance understanding of realistic applications through mathematical modeling. They will also aid in the investigation of functions and their inverses, as well as provide a powerful tool for solving/verifying equations and inequalities.

This course satisfies the Virginia Commonwealth Standards of Learning for Trigonometry and provides the foundation for students to pursue a sequence of advanced mathematical studies from Pre-calculus to Advanced Placement Calculus.

**Algebra II/Trigonometry**

Algebra II/Trigonometry is a one-session college-level course in which students combine the operational skills of Algebra I with the special and logical reasoning skills of Geometry to learn more about the ways patterns of numbers relate to each other numerically and visually. The overall focus of the course is the study of functions and their graphs, including polynomial, rational, exponential & logarithmic functions. Students learn to analyze a mathematical function and predict its behavior. They also learn how these function relationships exist in the natural and man-made world and how mathematical functions can model relationships in the real world.

Students are also introduced to the study of Trigonometry, both through the trigonometric ratios discovered in the Classical Period as well as through their analysis as functions introduced during the Enlightenment. The same analytical approach applied to earlier functions is applied to the trigonometric functions, including numerical, algebraic and graphical reasoning.

The course places a heavy emphasis on the use of graphing calculators, which help students visualize the graphs of functions and analyze numerical patterns. They also are used to powerfully demonstrate the value of matrix mathematics.

**AP Calculus AB**

Calculus is the mathematics of change. It allows us to model real life situations in the physical and life sciences and economics, as well as other fields.

Students will become adept in the use of graphing calculators to facilitate an intuitive understanding of the concepts, and to more efficiently solve difficult problems. AP Calculus AB is a rigorous college level course designed to prepare you for the AP exam in May. Doing well on this exam should get you credit or advanced placement in math when you start college. For science and engineering majors, this means getting right into your major topic during your first semester.

**Hours Available for Extra Help**

By appointment only.