MATHEMATICS

The Mathematics Department provides a curriculum to help students develop the knowledge and skills for entrance into and success in college as well as an awareness, which enables them to apply mathematical principles in other academic disciplines. Students begin by establishing a solid base in algebra and geometry, emphasizing logical reasoning, problem solving, the interpretation of data, functions, and the use of computers and calculators.  Students are exposed to different forms of technology throughout the curriculum.  Students are encouraged to collaborate with their peers, creatively communicate their knowledge, and learn to be independent thinkers and learners.

Algebra I (Prerequisite: Pre-Algebra)

This course serves as the first in the sequence of college preparatory mathematics.  Concepts are introduced in the context of real-world problems in order to increase the conceptual development of the student.  This course covers graphs in the coordinate plane, linear equations and inequalities, radicals, polynomials, quadratics, and data analysis. The concept of functions is emphasized using graphical, verbal, numerical, and algebraic methods.

Geometry (Prerequisite: Algebra I)

This class emphasizes two- and three-dimensional reasoning skills, coordinate and transformational geometry, the use of geometric models to solve problems, and algebraic connections in Geometry. Concepts are introduced in the context of real-world problems in order to increase conceptual development. A variety of application problems and problem-solving skills are included. This course covers properties of geometric figures, coordinate geometry, constructions, introduction to Trigonometry, informal proofs, and cultural, artistic and historical contexts of Geometry. Students will need a computer for this class and use of Geogebra and Google SketchUp.

Algebra II (Prerequisite: Geometry)

This course is a continuation of the Algebra I course. It is designed to give the student a strong connection between algebraic, numerical, verbal, and graphical representations of functions.  It includes a review of basic algebra skills at the start of this course.  A thorough study of advanced algebraic topics is done based on the study of functions, parent functions and their families, equations, inequalities, systems of equations, quadratics, radicals, exponents,  and logarithms.  Emphasis is placed on multiple representations of functions, including the use of technology. Students will also be expected to clearly communicate their understanding of the concepts in written form. The goals in this course are to develop a knowledge base of algebraic functions, types of equations, and the connections between the different formats these can be represented.

Algebra III (Prerequisite: Algebra II)

This is the second course in a two-year series for the study of Algebra II, Trigonometry, Probability and Intro to Statistics.  It is a continuation of the concepts from Algebra II.  There is a basic review of Algebra II topics at the start of this course.  Students continue with a study of polynomial functions, rational functions and exponential functions. Students will then study trigonometry content including right triangle trigonometry, general triangles, radian measures, arc length, area of sectors, circular motion, graphs of trigonometric functions and properties of trigonometric functions, polar equations and parametric equations. The final phase of the course will cover an introduction to probability and statistics. Topics will include independent and dependent events, conditional probability, discrete random variables, probability distributions, measures of central tendency, normal distributions curves, and organizing and displaying data.

Computer Programming  (Prerequisite: Algebra II)

This course introduces students to basic web design and programming using HTML (Hypertext Markup Language), CSS (Cascading Style Sheets) and Javascript and ProcessingJS (Processing JavaScript). The course does not require any prior knowledge of web design or programming but will require Algebra II as a prerequisite as there are many algebraic and geometric elements in programming. Students will learn how to create websites by structuring and styling their pages with HTML and CSS as well as learn the fundamentals of JavaScript, the programming language of the Web.  The course is designed to use Khan Academy’s Computer Programming Curriculum and Codecademy’s Curriculum to work through the modules and challenges in a self paced yet collaborative structure.  Students will create and share multiple projects and will develop a portfolio of work by the end of the course.  A computer will be required for this class.

Pre-Calculus (Prerequisite: 80+ Algebra II and Teacher Recommendation)

In this course students study functions introduced through their applications. Students will study linear, absolute value, piece-wise, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. They will initially investigate these functions in depth from the perspective of transformations without the use of technology. Subsequently an emphasis will be placed on the use of elementary functions to investigate and analyze applied problems and questions, supported by the use of appropriate technology and the effective communication of quantitative concepts and results.  The goals in this course are to learn how to manipulate functions and formulae, understanding the concepts involved in solving equations, and the ability to communicate this understanding clearly in written form.  Such understanding is best gained from the combined viewpoints of geometry, algebra, logic, and numerical experiment.  This course emphasizes the development of visual, numerical and logical intuition to complement the usual algebraic intuition.  

Calculus (Prerequisite: 80+ Pre-Calculus and Teacher Recommendation)

Standard Calculus is designed to be taught with the intention of learning the basic topics of Calculus without following the college level rigor and intensity of Advanced Placement Calculus.  Generally, the first semester is devoted to differential calculus while the second semester teaches integral calculus.  The primary aim of this class is to develop the student’s understanding of the concepts of calculus and provide experience with its methods and applications. Since there is no AP test to prepare for, this course will be able to spend more time with these topics, completing more hands on labs to help reinforce the methods and applications covered.  A graphing calculator is required for this course.

AP Calculus AB (Prerequisite: 85+ Pre-Calculus and Teacher Recommendation)

AP Calculus AB is designed to be taught with the intention that the student will earn college credit or placement.  This course follows the requirements set out by the College Board.  Generally, the first semester is devoted to differential calculus while the second semester teaches integral calculus.  The primary aim of this class is to develop the student’s understanding of the concepts of calculus and provide experience with its methods and applications. A graphing calculator is required for this course.

Statistics (Prerequisite: 80+ Alg II and Teacher Recommendation)

Statistics covers methods of data gathering, representation, analysis, and inference. Significant time is dedicated to design, administer, and tabulate results from surveys and experiments. Topics include correlation and regression, probability, binomial and normal distributions, and hypothesis testing.  A graphing calculator is required for this course.

AP Statistics (Prerequisite: 80+ Alg II and Teacher Recommendation)

AP Statistics is a year-long high school equivalent of a one semester, introductory college statistics course which follows the requirements outlined by The College Board and prepares the students for the AP exam in May. In this course, students develop strategies for gathering, representing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance phenomena. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests.  A graphing calculator is required for this course.

AP Calculus BC w/ Math Seminar* (Prerequisite: 90+ AP Calculus and Teacher Recommendation)

This advanced mathematics course is designed for those students wishing to continue their study of calculus after the AP Calculus AB course.  Students must be high achievers in the AP Calculus AB course, and they should wish to pursue their study of abstract mathematics further.  This course will cover the topics of the BC curriculum that were not covered in the AB course and will prepare students for the BC exam in the spring.  As time permits, interesting and relevant math topics will be covered including introduction to logic and proofs, elementary number theory topics, linear algebra introduction and applications as well as an introduction to complex analysis. *This course will be offered contingent upon adequate enrollment.

 

MEET THE DEPARTMENT

Ralf Melis Math Department Chair ✉︎ rmelis@millerschool.org ☏ 434-823-4805, ext. 244

Ralf Melis
Math Department Chair
✉︎ rmelis@millerschool.org
☏ 434-823-4805, ext. 244

John Macdonald Math ✉︎ jmacdonald@millerschool.org ☏ 434-823-4805, ext. 250

John Macdonald
Math
✉︎ jmacdonald@millerschool.org
☏ 434-823-4805, ext. 250

Gene Gartner Math ✉︎ ggartner@millerschool.org ☏ 434-823-4805, ext. 261

Gene Gartner
Math
✉︎ ggartner@millerschool.org
☏ 434-823-4805, ext. 261

Stephanie Crosby Math ✉︎ scrosby@millerschool.org ☏ 434-823-4805, ext. 247

Stephanie Crosby
Math
✉︎ scrosby@millerschool.org
☏ 434-823-4805, ext. 247