**Math**

Welcome to the Mathematics Department at Moreau Catholic! Our department believes in and delivers a comprehensive as well as applicable foundation of mathematics skills for students in order to prepare them for any of the different postsecondary directions they may choose. We provide a strong and broad curriculum ranging from Basic Algebra to both AP Calculus and AP Statistics. While we will continue to teach basic math concepts and skills that have been part of our curriculum for years, we recognize the need to be aware of the latest trends in mathematics education and implement the most effective ones. An emphasis on a multi-representational approach to functions is made in all of our classes, while also highlighting the importance of group work and hands-on problem solving. In keeping with our commitment to the school-wide initiative of improving the technology skills of our students, we include level-appropriate activities that involve graphing calculators, Geometer’s Sketchpad, and statistical software. All of this takes place with the goal of improving the critical thinking, problem solving, and communication skills of every student at Moreau.

## Teach to One Math

Moreau Catholic is the first high school and the first Catholic school in the nation to embrace the practice of personalized math instruction via Teach to One. Students in TTO always receive instruction that is tailored to their learning needs. Leveraged technology, in the form of an advanced algorithm, identifies what students should be learning and how they can best learn it.

There are eight methods of instruction in TTO, and each one is intended to identify and enhance how your student best learns. Lessons can be taught via live investigation, in small group, peer-to-peer, coached virtual instruction, one-to-one, virtual practice, independent practice and then applied in task sessions.

Task sessions take place over multiple days and students use a variety of related skills in real-world applications. For example, students might analyze the costs and benefits of purchasing a hybrid car and use the skills they acquire through this work (e.g., multiplication, estimation, calculating gas mileage) to defend a purchasing decision.

This cutting edge program is a strong example of how Moreau is a thought-leader in the educational community and a mission-driven institution determined to meet the needs of all learners.

## Department Members

Katie Hansen '08 (Chair), Eric Kaufman, Stephanie Nielsen, Ahmed Rangchi, Caitlin Riley, Michael Tsan, Efe Umukoro

## Math Courses

For students interested in more challenging course work, the department offers honors math classes as well as Advanced Placement courses (application required).

Note regarding honors placement: Any grade requirements cited are year averages, i.e., the average of both semester grades.

Graduation Requirements*

40 units

*(1 semester = 5 units)

#### 202. Algebra 1

**Full year, 10 units**

**Comment**: This course is UC approved.

Students will need a scientific calculator.

This course deals with basic algebraic concepts: sets, equations, inequalities, functions, and the operations and applications for real numbers. Methods and applications stressing word problems are presented throughout the course, using linear equations and inequalities, simultaneous and quadratic equations.

#### 203. Algebra Enrichment (Teach To One)

**Full year, 10 units **

Prerequisite: Placement based on performance on the placement test and/or the Algebra Diagnostic Exam.

Students will be required to take a mandatory summer bridge math course. Comment: This course does not meet the UC “c” requirement. Algebra Enrichment will covers and reviews math concepts needed for success in Algebra 1. Additionally, time will be taken to focus on enhancing study skills and effective use of laptops as a learning tool in mathematics. Completion of this course will prepare students for Algebra 1 their sophomore year. This course does not fulfill any mathematics units needed for graduation for students graduating in 2017 or 2018.

#### 206. Geometry

**Full year, 10 units**

**Prerequisite**: Successful completion of Algebra 1 or 1b with a C- or better in the second semester.

**Comment**: This course is UC approved.

Students will need a scientific calculator.

The concepts of congruence, similarity, and the Pythagorean theorem and its applications will be studied, including an introduction to trigonometry. Coordinate geometry will be covered, as well as geometric applications of algebra. There will be some geometric proof.

#### 208. Honors Geometry

**Full year, 10 units**

**Prerequisite**: Successful completion of Algebra 2 Honors with a B- or better or Completion of Algebra 1 with an A.

This course explores Euclidean Geometry from identifying geometric figures to proving relationships related to these figures. Students will be challenged to think creatively, reason logically and communicate effectively. In addition, students will explore the interdependence between algebra and geometry.

#### 212. Algebra 2

**Full year, 10 units**

**Prerequisite**: Completion of one year of Algebra and one year of Geometry with a C- or better in the second semester.

**Comment**: This course is UC approved.

Students will need a scientific calculator.

Topics of first year algebra are intensified and expanded with an emphasis on problem solving. The course deals with coordinate systems, systems of linear inequalities and systems of linear equations in three variables, logarithms, complex numbers, quadratic relations and conics.

#### 213. Honors Algebra 2 (Frosh)

**Full year, 10 units**

**Prerequisite**: Placement based on performance on the placement test and/or the Algebra Diagnostic Exam

**Comment**: This course is UC approved.

Students will need a scientific calculator.

This course will cover the content of Algebra 1 and Algebra 2 at an accelerated pace. This course is designed for students who have a strong background in Algebra.

#### 214. Honors Algebra 2

**Full year, 10 units**

**Prerequisite**: One of the following:

-Completion of Geometry with an A, if preceded by Algebra 1

-Completion of Honors Geometry with a C- or better, if preceded by Algebra 1 or Algebra 1B

**Comment**: This course is UC approved.

Students will need a scientific calculator.

This course will thoroughly cover Algebra 2 with additional problems and exercises of a more difficult type.

#### 215. Math Modeling

**Full year, 10 Units, Grade 12 **

Prerequisite: Completion of three years of math with a grade of C- or better in Algebra 2.

Comment: This course is pending UC approval.

In this course, students will be exposed to mathematics through critical thinking and problem solving with selected topics from Geometry, Analysis and Trigonometry, Algebra 2 and Statistics through real-life applications. Throughout this course, students will learn to think with and apply mathematics and will show mastery through culminating projects. Students will also learn to apply previously learned concepts to make decisions, studying financial mathematics concepts and inferential statistics through the lens of their own environment.

#### 216. Analysis and Trigonometry

**Full year, 10 units**

**Prerequisite**: Completion of Algebra 2 with a C- or better average for both semesters.

**Comment**: This course is UC approved.

Students will need a scientific calculator.

This course will study relations and functions, matrices, sequences and series, vectors, trigonometric functions and identities, elementary plane analytic geometry, conic sections, functions and their graphs, and exponential and logarithmic functions. Statistics and probability will also be covered.

#### 218. Honors Pre-Calculus

**Full year, 10 units**

**Prerequisite**: One of the following:

-Completion of Honors Geometry with a B- or better, if preceded by Freshman Honors Algebra 2

-Completion of Honors Algebra 2 with a B- or better

-Completion of Algebra 2 with an A

-Completion of Analysis & Trigonometry with a C- or better

**Comment**: This course is UC approved.

Students will need a scientific calculator.

Success in a Calculus course depends upon having acquired a thorough understanding of functions. In this course, considerable emphasis will be given to functions and their graphs. Polynomial, logarithmic, exponential, and trigonometric and circular functions and their inverses will be treated extensively.

#### 220. AP Calculus AB

**Prerequisite**: Completion of Honors Pre-Calculus with a B- or better average for both semesters.

Topics covered include limits and continuity, differentiation, applications of the derivative, integration, methods of integration and applications of the integral to surfaces revolution. Practical applications, particularly from Physics, will be emphasized. Students enrolled in this course must take the Advanced Placement test in Calculus AB.

#### 224. AP Calculus BC

**Full year, 10 units **

**Prerequisite**: One of the following: • Completion of Calculus AB with a B- or better or • Completion of Calculus AB with a C- or better and an AP Calculus AB score of 3 or higher

This course covers the topics of a second semester college-level Calculus course. After a review of the content of AP Calculus AB, the courses moves on to cover new types of derivative calculations using Euler’s method and L’Hopital’s rule. New integration methods are partial fractions, improper integrals, and logistic integration. Polar, parametric, and vector functions, as well as their derivatives and integrals are analyzed. Numerical integration methods are polynomial approximations and Taylor series. Students enrolled in this course must take the Advanced Placement test in Calculus BC.

#### 232. AP Statistics

**Full year, 10 units**

**Prerequisite**: One of the following: Completion of Honors Geometry with a C- or better, if preceded by Freshman Algebra 2 Honors

-Completion of Algebra 2 with an A

-Completion of Algebra 2 Honors with a B- or better

-Completion of Analysis & Trigonometry with a C- or better

-Completion of Honors Pre-Calculus with a C- or better

**Comment**: This course is UC approved.

Students will need a scientific calculator.

The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will work on projects involving the hands-on gathering and analysis of real world data. Ideas and computations presented in this course have immediate links and connections with actual events. Computers and calculators will allow students to focus deeply on the concepts involved in statistics. Students enrolled in this course must take the Advanced Placement test in Statistics.

#### 233. Multivariable Calculus

**Full Year, 10 units**

**Prerequisite**: One of the following: • Completion Calculus BC with a B- or better or • Completion of Calculus BC with a C- or better and an AP Calculus BC score of 3 or higher 9

This course covers topics such as vector and geometry of space, vector functions, space curve derivatives and integrals of vector functions and motion of particle in space. Further, double and triple integrals, volume under a surface with double and triple integrals, as well as partial derivatives, gradient, divergence, and curl will be discussed. The course will also look at forms of derivatives in multi directions, line integral of scalar and vector valued functions, Green theorem, 2-D divergence theorem, surface integrals, Stokes theorem, parameterizing a surface integral, divergence theorem intuition, and proof of regions in 3-D.