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# Math Department

## FLHS Math Course Descriptions

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**Prerequisites are required for enrollment in all math courses.*

**Algebra 1 CP:** In Algebra 1, instructional time should focus on four critical areas: (1) Seeing Structure in Expressions; (2) Arithmetic with Polynomials and Rational Functions; (3) Creating Equations; and (4) Reasoning with Equations and Inequalities. Throughout the course, mathematical concepts will be taught with an emphasis on enduring understandings, essential questions, real-world application, technology, and cross-curricular interaction.

**NJSLS Algebra 1: **In NJSLS Algebra, instructional time should focus on supporting the Algebra 1 curriculum and the four critical areas: (1) Seeing Structure in Expressions; (2) Arithmetic with Polynomials and Rational Functions; (3) Creating Equations; and (4) Reasoning with Equations and Inequalities. Throughout the course, mathematical concepts will be taught with an emphasis on enduring understandings, essential questions, real-world application, technology, and cross-curricular interaction.

**Geometry CP:** In Geometry, the instructional time will focus on seven critical areas: (1) developing an understanding the basic terms of Geometry and the skill of writing a geometric proof; (2) transformations of geometric figures; (3) understand, apply and prove theorems about congruent triangles; (4) understand and apply theorems about similarity and right triangles; (5) understand and apply theorems about quadrilaterals; (6) understand and apply theorems about circles; (7) calculate area, surface area and volume of geometric figures; and (8) factoring, quadratic equations, linear equations, and simplifying radicals.

**Geometry H: **In Geometry Honors, the instructional time will focus on seven critical areas: (1) developing an understanding the basic terms of Geometry and the skill of writing a geometric proof; (2) transformations of geometric figures; (3) understand, apply and prove theorems about congruent triangles; (4) understand and apply theorems about similarity and right triangles; (5) understand and apply theorems about quadrilaterals; (6) understand and apply theorems about circles; (7) calculate area, surface area and volume of geometric figures; and (8) factoring, quadratic equations, linear equations, and simplifying radicals. The advanced level of geometry encompasses in greater depth all of the topics in Geometry.

**Algebra 2CP:** In Algebra 2, instructional time should focus on eight critical areas: (1) Review of Basic Algebra; (2) Polynomial Functions; (3) Advanced Functions; (4) Introduction to Trigonometry; (5) Probability and Statistics; (6) Sequences and Series. Throughout the course, mathematical concepts will be taught with an emphasis on enduring understandings, essential questions, realworld application, technology, and cross-curricular interaction.

**Algebra 2H:** In Algebra 2, instructional time should focus on eight critical areas: (1) Review of Basic Algebra; (2) Polynomial Functions; (3) Advanced Functions; (4) Introduction to Trigonometry; (5) Probability and Statistics; (6) Sequences and Series. Throughout the course, mathematical concepts will be taught with an emphasis on enduring understandings, essential questions, realworld application, technology, and cross-curricular interaction. The advanced level of geometry encompasses in greater depth all of the topics in Algebra 2.

**Pre-Calculus CP: **In Pre-Calculus CP, instructional time should focus on five critical areas: (1) furthering the understanding of Algebraic Function with Real-life Applications; (2) Studying the properties and applications of Exponential and Logarithmic Functions; (3) developing understanding of Conic sections and where they appear in the Universe; (4) The study of relationships within triangles; (5) Trigonometric Functions.

**Pre-Calculus H:** In Pre-Calculus Honors, instructional time should focus on five critical areas: (1) Trigonometric Functions and Applications of Trigonometry, (2) The study of relationships within triangles; (3) Developing an understanding of analytic geometry, specifically Conic sections and Polar Graphs; (4) Furthering the understanding of Algebraic Functions with Real-life Applications; (5) Introduction to Calculus topics including, limits, function decomposition, and derivatives.

**Calculus H:** In Calculus Honors, instructional time should focus on three critical areas: (1) Evaluating Limits and Continuity; (2) Derivatives of Functions; (3) Integration and Anti-Differentiation. Throughout the course, mathematical concepts will be taught with an emphasis on enduring understandings, essential questions, real-world application, technology and cross-curricular interaction.

**AP Calculus (AB): **AP courses in calculus consist of a full high school academic year of work and are comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement or both from institutions of higher learning. Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. Students must take the Advanced Placement Calculus AB examination.

**AP Calculus (BC): **(7 periods per week includes 2 lab periods). This course includes all of the topics taught in AP Calculus (AB), but is more extensive and includes an emphasis on theory. Additional topics are complex integration, infinite series, vectors, and polar coordinates. Students must take the Advanced Placement AP examination.

**Multivariable Calculus:** Multivariable Calculus is the final course in the Fair Lawn High School accelerated mathematics course sequence. Students of Multivariable Calculus will learn to extend the tools they learned in AP Calculus BC to help understand more complex problems that cannot be addressed using the techniques of single‐variable Calculus. In their first year of Calculus, they were limited to problems in two‐dimensions, or three‐dimensional shapes that could be easily seen as manipulations of two‐dimensional shapes. Multivariable Calculus opens up the greater reality of three‐dimensional space and of functions of more than one variable, giving the students tools to better understand a three‐dimensional world. This course will prepare students for further study in all branches of higher mathematics, science and related fields. Technology and laboratory work are used as appropriate to reinforce these approaches Topics included in this course are: Vectors and the Geometry of Space, Vector-Valued Functions, Functions of Several Variables, Multiple Integration, and Vector Analysis. Vectors have many applications in geometry, physics, engineering, and economics. The student builds on many of the ideas of calculus of a single variable to calculus of several variables.

**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 must take the Advanced Placement AP examination.

**Statistics H: **This course will cover all the topics of AP Statistics without the rigor and depth required in AP Statistics. The purpose 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

**Advanced Algebra & Statistics: **The Advanced Algebra & Statistics math curriculum develops mathematical skills designated by the High School Specific NJ Student Learning Standards. Throughout the year, students will explore multiple concepts in both Advanced Algebra and Statistical analysis. The students will cover the Discrete topics of Election Theory, Cryptography, Coding, Circuits, Paths, Map Coloring, Vertex Coloring, and Scheduling. In Statistics students will cover measures of central tendency, normal distribution, standard deviations, and ways to present statistical findings through plots and graphs. In addition, students will complete project based assignments to demonstrate their understanding of the models and what they represent.

**Visual Basic Computer Programming*:** This semester course serves as an introduction to computer science via the use of the Visual Basic programming language. Students design and debug interactive programs that allow them to improve their problem-solving skills and deductive reasoning skills. Students learn about project design, the Visual Basic toolbox, and many elements of the Visual Basic language, using examples and several detailed computer projects the student will build, debug, and run. No prior programming experience is necessary, but familiarity with doing common tasks using Microsoft Windows is helpful.

**Can be taken as semester (half year) or full year course. Semester (Half year) is paired with Personal Financial Literacy (see Business Department Website for Personal Financial Literacy description)*

**AP Computer Science A: **AP Computer Science is a college level course that asks the student to design programs that are understandable, adaptable, and where appropriate, reusable. Students will write their own classes, modify existing classes and develop algorithms using standard data structures. Students must take the Advanced Placement Computer Science A examination.

**AP Computer Science Principles: **AP Computer Science Principles offers a multidisciplinary approach to teaching the underlying principles of computation. The course will introduce students to the creative aspects of programming, abstractions, algorithms, large data sets, the Internet, cyber-security concerns, and computing impacts. AP Computer Science Principles will give students the opportunity to use technology to address real-world problems and build relevant solutions. Together, these aspects of the course make up a rigorous and rich curriculum that aims to broaden participation in computer science. Students must take the Advanced Placement Computer Science Principles examination, which includes the submission of a digital portfolio.

**Robotics Honors: **Robotics Honors is a course that asks the student to develop, design and build machines to perform a specific task. Students are encouraged to work independently and as a team with a variety of devices. Students learn to plan and organize their thoughts before approaching a project, and after completion, will present their project to the class in a professional fashion. Students learn the importance of, as well as the difficulties associated with working a group.