# Mathematics

The Mathematics Department at Saint Gertrude High School fosters the students’ personal and academic growth in a Christian learning environment by encouraging a strong sense of personal responsibility and a commitment to academic excellence. We believe the following:

• We believe that analytical reasoning and the ability to create logical arguments will enable our students to effectively process the ever-increasing amounts of information available to them.
• We believe that the skill of solving complex problems is honed through synthesizing multiple perspectives and evaluating a variety of approaches. Encouraging structured collaboration on assignments during and outside of class is the best means of providing our students exposure to diverse perspectives and approaches.
• We believe that appropriately integrated technology is an essential tool for manipulating multiple representations of mathematical models, for enhancing spatial reasoning, and for facilitating workflow.
• We believe that maintaining consistency of our department’s content, objectives and course offerings with the objectives of the science and social studies departments effectively conveys to our students that mathematics and analysis are tools that can further their proficiency with quantitative information in many disciplines.
• We believe that a firm grasp of mathematical notation and language is critical to learning to effectively and confidently communicate mathematical thoughts, questions and methods.
We believe that single-sex classrooms and our adherence to the Benedictine core values enhance our ability to provide a nurturing environment for our students and help them to develop a positive attitude toward learning. Such an environment allows young women to have the confidence and ability to succeed in advanced mathematical studies and to pursue careers in a male-dominated field.

## Mathematics Courses

#### Algebra 1

Algebra I consists of the application of the properties of real numbers to algebraic expressions and equations. Emphasis is placed on solving and graphing linear equations and inequalities, factoring and its applications, and developing and applying the properties of exponents and radical expressions. Students are taught to develop and use visual aids for problem solving, including charts, tables, graphs, and diagrams.  The graphing calculator is used as a tool for exploring and analyzing functions. Students must have a minimum year end course grade of C- to advance to Algebra II.

#### Algebra 2

In level II, the skills and concepts of Algebra I are strengthened and expanded to include complex numbers. Students will expand their knowledge of linear equations to include systems of linear equations and inequalities. Emphasis is placed on the properties of exponents and roots, quadratic equations and functions, and polynomial functions. Logarithms are introduced and there will be an introduction to arithmetic and geometric sequences and series.

#### Algebra 2 Honors

In level II, the skills and concepts of Algebra I are strengthened and expanded to include complex numbers. Students will expand their knowledge of linear equations to include systems of linear equations and inequalities.  Emphasis is placed on the properties of exponents and roots, quadratic equations and functions, and polynomial functions. Logarithms are introduced and there will be an introduction to arithmetic and geometric sequences and series.  Honors Algebra 2 will cover all of the material included in Algebra II but at a faster pace and with greater depth. It will provide more extensive coverage of rational, exponential and logarithmic functions and a greater emphasis will be placed on function analysis.  Students may register with department approval only.

#### AP Calculus AB

This college level course is designed for the students who excel in their study of mathematics.  It is an in-depth study of differential and integral calculus with a review of analytical geometry, a thorough analysis on the limit concept and applications of science and economics.  At the conclusion of the course, students are required to take a College Board Examination, which could determine the possibility of college credit.  Students may register by department selection only. The College Board defines the scope of this class. The teacher will determine the pace and order in which the topics are taught.

#### AP Statistics

The purpose of the AP course in statistics 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:

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

Students who successfully complete the course and exam may receive credit, advanced placement or both for a one-semester introductory college statistics course.

#### Geometry

This course presents the basic structure of Geometry. Emphasis is on the further development of deductive/logical reasoning and problem solving skills through applications and visual expressions. The student gains an understanding of coordinate geometry and thus recognizes how geometry and algebra complement one another. Topics include properties and relationships within the following categories: lines, planes, angles, polygons, circles, triangles, area, volume, right triangle trigonometry, constructions and proofs.

#### Geometry Honors

In addition to the course prescribed for geometry, honors geometry includes more extensive work with area, volumes of solids, coordinate geometry and proofs.  Honors geometry is designed to offer challenging and thought-provoking discussions/problems for the math-oriented student.  It also prepares the students for the rigor of honors precalculus.

#### Intro to Calculus

This is a one semester elective course used as an introduction to calculus and material beyond the scope of Pre-Calculus with Trigonometry.  Students will continue their analysis of functions and will utilize limits and derivatives to examine these functions and the characteristics of their graphs.  Students will use the behavior of functions to understand practical applications such as in science and business.

#### Pre-Cal/Trig Honors

In the Pre-Calculus portion of the course, students will analyze a wide variety of functions.  They will investigate the behavior of the graphs of these functions and identify connections between the algebraic formulas to their graphic representations.  In the Trigonometry section of the course, students will examine the connection between right triangles and the unit circle.  They will understand the six trigonometric functions, how they can be used for practical situations and how to manipulate them using identities.  The students will also draw connections between the algebraic functions and the trigonometric functions when they analyze the transformation properties of all the various types of functions.  Honors PreCalculus with Trigonometry will cover all of the material included in PreCalculus with Trigonometry but at a faster pace and with greater depth. It will provide more extensive coverage of rational, exponential and logarithmic functions and a greater emphasis will be placed on rigorous mathematical language.  Students may register with department approval only.

#### Pre-Calculus/Trig

In the Pre-Calculus portion of the course, students will analyze a wide variety of functions.  They will investigate the behavior of the graphs of these functions and identify connections between the algebraic formulas and their graphic representations.  In the Trigonometry section of the course, students will examine the connection between right triangles and the unit circle.  They will understand the six trigonometric functions, how they can be used for practical situations and how to manipulate them using identities.  The students will also draw connections between the algebraic functions and the trigonometric functions when they analyze the transformation properties of all the various types of functions.

#### Probability / Statistics

This is a one semester elective course used as an introduction to elementary probability and statistics.  In this course, students will learn techniques for collecting, representing, and processing data.  The course will have a focus on interpretation, manipulation and analyzation of data.  Students will utilize available technology and collaborative efforts in order to better understand and apply the material as well as to communicate their analytical results.  Application to practical situations will help the students relate the material to their own lives and to the world in general.

## Math Department Faculty

#### Sherry Panas

The Mathematics Department at Saint Gertrude High School fosters the students’ personal and academic growth in a Christian learning environment by encouraging a strong sense of personal responsibility and a [...]

#### Michael Gill

Teacher of: Algebra II, Pre-Calculus with Trigonometry, Introduction to Calculus, Probability & Statistics; Moderator of the SGHS Spirit Club First Year at SGHS: 2010 Hometown: Oakton, VA Athletics: Former varsity soccer and [...]

#### Susan Farmer

Teacher of: Algebra I, Algebra 1, Honors Algebra 2, and AP Calculus Started Teaching: 1986 Started at SGHS: 1989 Hometown: Marianna, AR Education: B.I.E. from Georgia Institute of Technology with [...]