ALGEBRA 1
Instructor: Brian McColgan
Algebra I is a course that reviews and further develops the concepts learned in previous math courses. In addition, students are introduced to new concepts that bridge from the concrete to the abstract. An emphasis is placed on problem solving and real world applications. Algebra is considered a foundation course for all subsequent higher-level high school and college math courses. Knowledge and mastery of the course is assessed through homework, class activities, projects, quizzes, tests and a cumulative final assessment.
Topics:
- Introduction to Algebra
- Integers and Rational Numbers
- Equations
- Inequalities
- Cumulative Review
- Cumulative Assessment
- Exponents and Polynomials
- Polynomials and Factoring
- Graphs and Linear Equations
- The Pythagorean Theorem
- Triangles in Algebra
- Systems of Equations
- Inequalities and Absolute Value
- Radical Expressions and Equations
- Quadratic Equations Texts: Algebra : The University of Chicago Mathematics Project
- functions
- variation and graphs
- linear functions
- matrices
- systems
- quadratic functions
- powers
- inverses and radicals
- exponential and logarithmic functions
- trigonometry
- polynomials
- quadratic relations
- series and cominbations
- Geometric Art
- Introducing Geometry
- Reasoning in Geometry
- Using the tools of Geometry
- Discovering and proving triangle properties
- Discovering and proving polygon properties
- Discovering and proving circle properties
- Transformations and Tessellations
- Area
- The Pythagorean Theorem
- Volume
- Similarity
- Trigonometry
- Geometry as a mathematical system
- Work with functions represented in a variety of ways and understand the connections among these representations.
- Examine models of functions and graph these same functions.
- Show an understanding of new and different types of functions, such as:
- circular functions
- trigonometric functions
- Root functions
- Power functions
- Logarithm functions
- Polynomial functions
- Communicate mathematics both orally and in well-written sentences to explain solutions to problems.
- Use technology to help solve problems, experiment, interpret results, and verify conclusions.
- work with functions represented in a variety of ways and understand the connections among these representations.
- understand the meaning of the derivative in terms of rate of change and local linear approximation, and use derivatives to solve a variety of problems.
- understand the relationship between the derivative and the definite integral.
- communicate mathematics both orally and in well-written sentences to explain solutions to problems.
- model a written description of a physical situation with a function, a differential equation, or an integral.
- use technology to help solve problems, experiment, interpret results, and verify conclusions.
- determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
- G: Graphical analysis (where a graph is known, but not an equation)
- N: Numerical analysis (where data points are known, but not an equation)
- A: Analytic/Algebraic analysis (traditional equation and variable manipulation)
- W: Written/Verbal methods of representing problems (story problems and written justification of problem-solving methods.
Level: This course is for freshmen.
Prerequisite: None.
ALGEBRA 2
Instructor: Alexis Spina
Advanced Algebra is what every high school graduate should know about mathematics that has not been learned in previous courses. It contains the mathematics that educated people around the world use in conversations and that most colleges want or expect students to have studied. There will be familiar ideas present, such as properties of numbers, graphs, expressions, equations, and inequalities throughout the course. In addition, we will be studying many new topics such as matrices, logarithms, trigonometry, and conic sections. The content of this course is related to what students have learned in their first year of algebra. We will extend on their previously learned knowledge, asking harder questions and solving more difficult problems.
The topics listed below are a brief overview of what we will cover in this course:
Level: Algebra II is the most challenging math class that some of the most advanced algebra students will ever take. Most of the students in Algebra II are a mix of sophomores and juniors. This is a year-long class and, therefore, it does fulfill a year of math requirement for college.
Prerequisite: Algebra 1 and Geometry
ESL ALGEBRA 2
Instructor: Jeff Narva
GEOMETRY
Instructor: Brian McColgan
The word "Geometry" comes from Latin geometria and from Greek geometrein, meaning "to measure the land". Essentially, geometry is the study of 2 and 3 dimensional shapes and the components of these shapes: line, points, angles and space. In this class students will use explorations and investigations to develop resoning skills and to study geometry and discover relationships among the different components of geometric figures. The primary tools will be a pencil, compass, protractor and straight edge. Students will learn to recognize geomtric principles in nature, art, and architecture and to view geometry as a mathematical system. Knowledge and mastery of the course is assessed through homework, class activities, projects, quizzes, tests and a cumulative final assessment.
Topics:
Level: This course is primarily for freshmen or sophomores.
Prerequisite: Algebra 1
PRE-CALCULUS
Instructor: Katie O'Shaughnessey
Pre-calculus at Besant Hill School integrates functions and trigonometry and applies the algebra and geometry that students have studied in the previous years. As the course progresses, we will more closely explore the tools used in further calculus classes. Topics that are discussed in this course can be found below. Students will use the mathematics they have learned to examine and discuss the theorems studied during the course.
By successfully completing this course, students will be able to:
Precalculus: Graphs & Models and Graphing Calculator Manual Package, by Bittinger, Beecher, Ellenbogen, and Penna. 4th Edition.
Level: Typically a junior-and senior-level class.
Prerequisite: Algebra II
ADVANCED PLACEMENT CALCULUS AB
Instructor: Katie O'Shaughnessey
Advanced Placement Calculus at Besant Hill School analyzes functions and their behavior and goes in-depth with trigonometric functions studied previously. As the course progresses, we will more closely explore the derivative of a function, and what it means in terms of rate of change and appoximation. The relationship between the derivative and the integral will be probed, and an understanding of the reasonableness of solutions will be gained. Students completing AP Calculus will be able to use technology to help solve problems, experiment, interpret results and verify conclusions, and communicate mathematics both orally and in well-written sentences to explain solutions to problems.
By successfully completing this course, students will be able to:
This class will focus on a variety of ways to solve problems. These four approaches are easily remembered as "GNAW"ing on Calculus. This refers to:
Level: Advanced.
Prerequisite: Pre-calculus (or an equivalent).
ADVANCED PLACEMENT CALCULUS BC
Instructor: Katie O'Shaughnessey
This two-semester course sequence continues to explore calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and series. During this course, students will gain further experience in the use of calculus methods and learn how calculus methods may be applied to practical applications.
Level: Advanced.
Prerequisite: Advanced Placement Calculus AB.