Mathematics

A minimum of three credits is required in mathematics including successful completion of trigonometry, either as part of the full-year Algebra 2 with Trigonometry course or in a one-semester course (Algebra 3 with Trigonometry). A junior is required to take a full year of math and EHS strongly encourages students to take mathematics every semester. Seniors have several Advanced Placement math options.

Department Philosophy

The Mathematics Department at Episcopal High School strives to offer each student both a challenge and an opportunity to succeed. Emphasis is placed on using applications or "real world" problems to provide a context for students to develop not only the traditional facts and techniques of mathematics, but also the logical reasoning and problem-solving skills that will allow them to approach and solve unfamiliar problems. The Mathematics Department believes strongly that students should learn to use technology such as computers and graphing calculators as exploration problem-solving tools, and it expects students to pursue the study of mathematics throughout all four years of high school.

Objectives

  1. To create a positive attitude toward the study and learning of mathematics
  2. To foster confidence, competence, and creativity in the learning and execution of mathematics, so that students can become independent self-learners
  3. To expect mastery of identified course-specific skills in problem solving, algebraic manipulation, proof, and mathematical theory
  4. To teach the mathematical skills necessary to support other academic disciplines
  5. To provide students with frequent assessment and feedback so that faculty, students, and parents can get a good sense of a student’s progress at almost any time
  6. To encourage department members to continue their study of mathematics and education through coursework, workshops, and conferences
  7. To teach the "art of learning," including note taking, daily self-evaluation, test preparation, and using available resources to be a better learner of mathematics
  8. To achieve consistency of content and depth across the mathematics curriculum through detailed course syllabi, course meetings, and common examinations, while honoring the individual strengths and styles of department members

ALGEBRA 1

This course introduces the study of algebra. Beginning with a study of variables and algebraic expressions, it includes solving all types of linear and quadratic equations. It also focuses on the linear, absolute value, exponential, rational and quadratic functions, and systems of equations. Part of studying the functions is recognizing patterns within a table of values, emphasizing, where appropriate, the concept of "rate of change."

Content Objectives
  1. From Patterns to Algebra
  2. Operations in Algebra 1
  3. Equations
  4. Proportional Reasoning
  5. Linear Functions
  6. Inequalities and Absolute
  7. Systems of Equations and Inequalities
  8. Exponents and Exponential Functions
  9. Polynomials and Factoring
  10. Quadratic Functions
  11. Rational Functions
  12. Radicals and Coordinate Geometry
  13. Functions and Transformations
Skill Objectives
  1. Develop sound algebraic and arithmetic skills
  2. Develop problem-solving skills
  3. Help students understand the material beyond simply "how to do the problem"
  4. Help improve student work habits through regular homework evaluation and notebooks checks
  5. Give students working knowledge of the TI-84 graphing calculator and spreadsheets
Materials

Algebra 1, Schultz, Kennedy, Ellis, Hollowell [Holt, Rinehart and Winston 2001]
calculators (TI-84 is preferred)
laptops

Methods of Evaluation
  1. Daily homework
  2. Regular quizzes every 2–3 days
  3. Tests approximately every 2 weeks
  4. Projects

GEOMETRY

The purpose of this course is to familiarize students with the properties of two- and three-dimensional figures and to provide a foundation for the presentation of mathematical arguments and logical reasoning. In the first semester, the course focuses on triangles, proofs, and a general overview of geometric terms. During the second semester, the course makes a more in-depth examination of two- and three-dimensional figures with a special emphasis on trigonometry and circles. The year ends with a study of three-dimensional figures.

Once per week, the class works on labs which emphasize group work and projects.
Geometer’s Sketchpad is used extensively throughout the course. Other projects involve
work inside and outside the classroom. Technology is used in the classroom, including spreadsheets and graphing calculators. Much emphasis is given to creative, hands-on, cooperative projects that help students apply geometric concepts to more complex problems in the "real world."

Content Objectives
  1. Reasoning
  2. Lines in a Plane
  3. Congruent Triangles
  4. Properties of Triangles
  5. Constructions
  6. Polygons
  7. Similarity
  8. Right Triangles
  9. Circles
  10. Planar Measurements
  11. Space Measurements
Skill Objectives
  1. Give students an overview of important geometric concepts
  2. Maintain algebra skills that are integrated into geometry
  3. Teach students to work together in projects and homework
Materials

Geometry: An Integrated Approach, by Larson et al.
laptops
graphing calculators

Methods of Evaluation

1. Mid-year and final exams
2. Test on each chapter
3. Weekly quizzes
4. Group projects

HONORS GEOMETRY

This class is designed to introduce geometric concepts to students in a non-traditional format. New concepts are frequently introduced in problem sets so students can learn by discovery. The depth of study of vectors, proofs, and trigonometry goes beyond the regular curriculum.

Content Objectives
  1. The Plane
  2. Proof
  3. Pairs of Lines
  4. Vectors
  5. Polygons
  6. Perpendicularity
  7. Angles
  8. Trigonometry
  9. Congruence
  10. The Rest of Trigonometry
  11. Area
  12. Inequalities
  13. Circles
  14. Lines and Planes in Space
  15. Volumes
Skill Objectives
  1. Train students in the mechanics of mathematics and deductive reasoning
  2. Teach students to use mathematical arguments and logical reasoning to solve problems
  3. Develop manipulation skills that apply to problem-solving situations
Materials

Geometry, An Algebraic Approach, Geer [1987], online version
graphing calculators
laptops
Geometer’s Sketchpad, and other software

Methods of Evaluation
  1. Mid-term and final exams
  2. Quizzes
  3. Homework
  4. Effort
  5. Group projects

ALGEBRA 2

This course continues the study of algebra and introduces work with coordinate geometry, matrices, and functions. Algebra 2 is designed for students who require more review of fundamental algebra than is provided in the Algebra 2 with Trigonometry course. Functions studied include: exponential, logarithmic, quadratic, polynomial, rational, and radical.

Content Objectives
  1. Data and Linear Representations
  2. Numbers and Functions
  3. Systems of Linear Equations and Inequalities
  4. Matrices
  5. Quadratic Functions
  6. Exponential and Logarithmic Functions
  7. Polynomial Functions
  8. Rational Functions and Radical Functions
  9. Counting Principles and Probability
Skill Objectives
  1. Train students in the mechanics of mathematics and deductive reasoning
  2. Teach students to use mathematical arguments and logical reasoning to solve problems
  3. Develop manipulation skills that apply to problem-solving situations
  4. Approach all concepts from numerical, algebraic, graphical, and verbal perspectives
  5. Develop confidence as problem solvers
  6. Learn to use available technology tools for exploration and problem solving
Materials

Algebra 2, Schultz, Ellis, Hollowell, Kennedy [Holt, Rinehart & Winston 2001]
graphing calculators (TI-84 preferred)
laptops
Microsoft Excel, Study Works, MathType 5.0, TI-SmartView, and other software.

Methods of Evaluation
  1. Tests
  2. Mid-term and final exams
  3. Quizzes
  4. Homework
  5. Individual and group projects

ALGEBRA 2 WITH TRIGONOMETRY

ALGEBRA 2 WITH TRIGONOMETRY

This course continues the study of algebra and introduces work with coordinate geometry, matrices, and functions. Functions studied include: exponential, logarithmic, quadratic, trigonometric, polynomial, rational, and radical.

Content Objectives
  1. Data and Linear Representations
  2. Numbers and Functions
  3. Systems of Linear Equations and Inequalities
  4. Matrices
  5. Quadratic Functions
  6. Exponential and Logarithmic Functions
  7. Trigonometric Functions
  8. Further Topics in Trigonometry
  9. Polynomial Functions
  10. Rational Functions and Radical Functions
  11. Conic Sections
  12. Counting Principles and Probability
Skill Objectives
  1. Train students in the mechanics of mathematics and deductive reasoning
  2. Teach students to use mathematical arguments and logical reasoning to solve problems
  3. Develop manipulation skills that apply to problem-solving situations
  4. Approach all concepts from numerical, algebraic, graphical, and verbal perspectives
  5. Complete the trigonometry section prior to SAT I in the spring so that juniors will be better prepared
Materials

Algebra 2, Schultz, Ellis, Hollowell, Kennedy [Holt, Rinehart & Winston 2001]
graphing calculators (preferably TI-83)
laptops
Microsoft Excel, Study Works, MathType 5.0, TI-SmartView, and other software.

Methods of Evaluation
  1. Common tests
  2. Mid-term and final exams
  3. Quizzes
  4. Homework
  5. Individual and group projects

HONORS ALGEBRA 2 WITH TRIGONOMETRY

A continuation of the first-year course in algebra; students review topics from Algebra 1 and then move on to those topics essential to the study of precalculus and calculus.

Content Objectives
  1. Equations and Inequalities
  2. Functions and Their Graphs
  3. Polynomial Functions
  4. Rational Functions and Conics
  5. Exponential and Logarithmic Functions
  6. Trigonometry
  7. Analytic Trigonometry
  8. Additional Topics in Trigonometry
  9. Systems of Equations and Inequalities
  10. Matrices and Determinants
  11. Sequences, Series, and Probability
Skill Objectives
  1. To be well prepared for precalculus
  2. To see math from different perspectives. The NAGV approach is used, hoping to get students to see each topic from numeric, algebraic, and graphical perspectives. Students should be able to explain what they are doing and why they are doing it, both in written and verbal form.
Materials

Algebra and Trigonometry, Larson & Hostetler. [7th edition: Houghton-Mifflin, 2007]
graphing calculators (TI-84 preferred)

Methods of Evaluation
  1. Quizzes
  2. Tests
  3. Homework
  4. Effort
  5. Individual and group projects

ALGEBRA 3 WITH TRIGONOMETRY/ADVANCED MATHEMATICS

This course continues the study of advanced algebra begun in Algebra 2. Students will complete a full study of trigonometry, assuming no prior knowledge or experience with trigonometric functions. Students may complete only the first semester of the course, finishing with trigonometry, or may continue to the second semester Advanced Mathematics portion of the course, which is an introduction to precalculus topics.

Content Objectives
  1. Number Patterns
  2. Equations and Inequalities
  3. Functions and Graphs
  4. Trigonometric Functions
  5. Trigonometric Graphs
  6. Solving Trigonometric Equations
  7. Applications of Trigonometry
  8. Polynomial and Rational Functions
  9. Exponential and Logarithmic Functions
  10. Systems and Matrices
  11. Statistics and Probability
Skill Objectives
  1. Continue to train students in the mechanics of mathematics and deductive reasoning
  2. Help students learn to apply multiple concepts to solve more complex problems
  3. Further develop algebraic manipulation skills that apply to problem-solving situations
  4. Approach all concepts from numerical, algebraic, graphical, and verbal perspectives
  5. Learn to use available technology tools for exploration and problem solving
  6. Help students to develop the confidence necessary to study precalculus without trepidation
Materials

Precalculus (A Graphing Approach) [Holt, Rinehart & Winston, 2002]
TI-84 graphing calculators
laptops
Microsoft Excel

Methods of Evaluation
  1. Quizzes 1–2 times per week
  2. Tests
  3. Daily homework
  4. Group projects

PRECALCULUS

This course studies functions as models of change. The central theme involves using functions as models for real-world applications. Linear, exponential, power, and periodic functions are introduced first, followed by the study of polynomial and rational functions. Once introduced, each function is compared and contrasted with each function group. Small group work is encouraged, as students learn how to create mathematical models that model the world in which we live.

Content Objectives
  1. Review of Algebra Fundamentals
  2. Functions
  3. Polynomial and Rational Functions
  4. Exponential and Logarithmic Functions
  5. Trigonometric Functions of Angles
  6. Analytic Trigonometry
  7. Polar Coordinates and Vectors
  8. Systems of Equations and Inequalities
  9. Analytic Geometry
  10. Sequences and Series
  11. Limits and Introduction to Calculus
Skill Objectives
  1. Train students to work singly or in small groups
  2. Allow students to present their work to the class and use mathematical arguments and logical reasoning to solve problems
  3. Prepare students for SAT II Level 2 test in the spring
  4. Prepare the students for calculus
Materials

Precalculus: Mathematics for Calculus Enhanced Review Edition. [5th edition,
Brooks/Cole, 2007]
TI-84 graphing calculators
laptops
Microsoft Excel

Methods of Evaluation
  1. Quizzes 1–2 times per week
  2. At least three common tests each quarter
  3. Daily homework
  4. Graphing art project

HONORS PRECALCULUS

This course continues the study of Algebra 2 with Trigonometry and prepares the student for calculus. The course is designed for students to learn and discover on their own rather than through direct lecture. Teachers of Calculus and Precalculus are strongly encouraged to devote more than their usual amount of time to homework review and small group work. Student daily assignments and problem presentation are also strongly encouraged. While the topics covered are the same as the Precalculus course, the Honors course covers them to greater depth and applies the concepts to more complex problems.

Content Objectives
  1. Review of Algebra Fundamentals
  2. Functions
  3. Polynomial and Rational Functions
  4. Exponential and Logarithmic Functions
  5. Trigonometric Functions of Angles
  6. Analytic Trigonometry
  7. Polar Coordinates and Vectors
  8. Systems of Equations and Inequalities
  9. Analytic Geometry
  10. Sequences and Series
  11. Limits and Introduction to Calculus
Skill Objectives
  1. Train students to work singly or in small groups
  2. Allow students to present their work to the class and use mathematical arguments and logical reasoning to solve problems
  3. Allow students to gain experience in hypothesizing and discovering the next concept when learning new material
  4. Prepare students for SAT II Level 2 test in the spring
  5. Prepare the students for calculus
Materials

Precalculus: Mathematics for Calculus, Enhanced Review Edition. [5th edition,
Brooks/Cole, 2007]
TI-84 graphing calculators
laptops
Microsoft Excel, Study Works, MathType 5.0, and other software.

Methods of Evaluation
  1. Common tests
  2. Mid-term and final exams
  3. Quizzes
  4. Homework

CALCULUS

This course is an introduction to the techniques and applications of calculus. Students will study both differential and integral calculus and their applications, including problems in the area of business, physics, and geometry. Students in Calculus will follow the AP Calculus AB syllabus to the same depth as the Advanced Placement course, but not at the same pace. The role of calculus as a tool for problem solving is emphasized. This course is open to all students who have successfully completed Pre-Calculus or Honors Pre-Calculus.

Content Objectives

1. Functions
2. Limits
3. The Derivative
4. Derivative Applications, Including Related Rates
5. The Definite Integral
6. The Indefinite Integral

Skill Objectives

1. Be well-prepared to succeed in college Calculus
2. Develop a strong grasp of the underlying logic of calculus beyond the ability to solve problems
3. Be able to understand all concepts from numerical, algebraic, graphical, and verbal perspectives
4. Be able to perform all of the standard techniques of both differential and integral calculus
5. Appreciate the important of calculus within the greater context of mathematics and its applications

Materials

Calculus, Concepts and Applications, Paul A. Foerster [2nd edition; Key Curriculum Press, 2005]
graphing calculators (TI-84 preferred)

Methods of Evaluation

1. Quizzes
2. Tests
3. Homework
4. Effort
5. Take-home pledged problem sets
6. Projects and presentations including at least
   a. A presentation of research on the history and development of calculus
   b. Construction and presentation of a physical model of Volumes of Solids of Revolution

AP CALCULUS AB

A first-semester course in college calculus, taught at an accelerated, Advanced Placement pace. While the syllabus as provided by ETS makes up the majority of the topics covered, other topics are added to allow for a more complete introduction to differential and integral calculus.

Content Objectives
  1. Functions
  2. Limits
  3. The Derivative
  4. Derivative Applications, Including Related Rates
  5. The Definite Integral
  6. The Indefinite Integral
  7. Differential Equations and Slope Fields
Skill Objectives
  1. Be well-prepared for the AP Calculus exam
  2. Develop a strong grasp of the underlying logic of calculus beyond the ability to solve problems
  3. Be able to understand all concepts from numerical, algebraic, graphical, and verbal perspectives
  4. Be prepared to move on to and succeed in a Calculus 2 course the following year, be it at EHS or in college
Materials

Calculus, Concepts and Applications, Paul A. Foerster [2nd edition; Key Curriculum
Press, 2005]
graphing calculators (TI-84 preferred)

Methods of Evaluation
  1. Quizzes
  2. Tests
  3. Homework
  4. Effort
  5. Take-home pledged problem sets

AP CALCULUS BC

Following the AP Calculus BC course description, this course is a complete study of both differential and integral calculus, along with a focus on vectors, parametric and polar equations, and infinite series. Students will be prepared for the AP exam in May as well as further study in mathematics and science.

Content Objectives
  1. Library of Functions
  2. Limits and Continuity
  3. Derivative Techniques
  4. Applications of Derivatives
  5. The definite Integral
  6. Differential Equations and Mathematical Modeling
  7. Applications of Definite Integrals
  8. Sequences, l’Hopital’s Rule, and Improper Integrals
  9. Infinite Series
  10. Parametric, Vector, and Polar Functions
Skill Objectives
  1. Teachers follow the "rule of four"; numeric, algebraic, geometric and verbal
  2. Students will learn to use technology as tools for problem solving and discovery
  3. Students will learn to apply calculus concepts to unfamiliar problems
Materials

Calculus, Graphical, Numerical, Algebraic, Finney, Thomas, Waits, Kennedy [3rd edition; Pearson Prentice Hall, 2007]
graphing calculators (preferably TI-84 or TI 89)
laptops
Microsoft Excel, Study Works, MathType 5.0, and other software.

Methods of Evaluation
  1. Quizzes
  2. Tests
  3. Mid-term and final exams
  4. Homework
  5. Individual and group projects

HONORS MULTIVARIABLE/VECTOR CALCULUS

This course is a continuation of AB/BC Calculus. This course begins with a review of the topics included in the BC Calculus syllabus which are not covered in AB Calculus. Students then complete a full standard course in Multivariable Calculus. The last few weeks of the school year will involve a study of topics chosen by the teacher in collaboration with the class. Topics covered in past years have come from many areas, including Linear Algebra, Discrete Mathematics, Topology, and Symbolic Logic. By department permission.

Content Objectives

1. Infinite Series, including Taylor and Maclaurin Series
2. Calculus of Parameter, Polar, and Vector Functions
3. Vectors and Analytic Geometry in Space
   a. Dot and Cross Products
   b. Lines and Planes
   c. Cylindrical and spherical coordinates
4. Vector-valued Functions and Motion in Space
   a. Curvature
   b. Torsion
5. Multivariable Function Derivatives, including Partial Derivatives and Lagrange Multipliers
6. Multiple Integrals, Area, Volume, Mass, and Moments
7. Integration in Vector Fields
   a. Green’s Theorem
   b. Stokes’s Theorem
   c. Divergence Theorem

Skill Objectives

1. Fully understand the concepts and application of Multivariable Calculus
2. Be able to approach novel problems and find solutions through experimentation and proof
3. Develop the ability to visualize multi-dimensional functions and their relationships
4. Be able to work collaboratively with a group to solve more complex problems

Materials

Calculus, A Complete Course, Finney, Demana, Waits, & Kennedy [Pearson Custom Publishing, 2007]
graphing calculator (TI-84 or TI-89)

Methods of Evaluation

1. Class discussion
2. Tests
3. Take-home pledged problems
4. In-class collaborative investigation of more challenging problems
5. Presentation of problem solutions to the class

AP STATISTICS

A first-semester college course in statistics focusing on four main themes: exploring and analyzing data; planning a study and experimental design; anticipating patterns; and statistical inference. The course is designed to fulfill the College Board’s syllabus for the AP examination, and uses the graphing calculator as a tool for exploring data.

Content Objectives
  1. Exploring and Understanding Data
  2. Exploring Relationships Between Variables
  3. Gathering Data
  4. Randomness and Probability
  5. Probability Distributions
  6. Introduction to Inference
  7. Inference for Distributions
  8. Inference for Proportions
  9. Inference for Tables: Chi-square Procedures
  10. Inference for regression
Skill Objectives
  1. To be able to evaluate and interpret both data and decisions based upon that data
  2. To appreciate the power of statistical methods in describing patterns and making decisions
  3. To prepare for and score as high as possible on the Advanced Placement examination
Materials

Stats: Modeling the World. Bock, Velleman, DeVeaux. [2nd edition. Pearson Prentice
Hall, 2007]
graphing calculators (TI-84 preferred)

Methods of Evaluation
  1. Quizzes
  2. Tests
  3. Homework
  4. Effort
  5. Individual and group projects