The mathematics department encourages all students to take as many mathematics courses in high school as possible. Studying mathematics helps the student to develop problem solving abilities, abstract reasoning skills, and computational tools which are necessary for success in the world of work. There is a minimum fifteen credit mathematics graduation requirement including Algebra 1, Geometry, and a third year that builds on Algebra and Geometry. A student must have a grade of C or better in current course level to progress to the next course at the same level.** **College-bound students whose career goals may involve a curriculum requiring calculus, discrete math or statistics should absolutely take four years of advanced mathematics. Scientific and graphing calculators are required.

*Computer courses offered by the department receive Practical Arts credit. These courses are Computer Science Basics through Gaming, Intro to Programming, Python Programming, AP Computer Science Principles, AP Computer Science A and Data Structures.*

**501 ALGEBRA IA (CP) Gr. 9-12 5 cr., 36 wks**

Algebra IA (CP) is the first part of a two-year Algebra I course for students who may benefit from additional practice and support with prerequisite skills. This course will cover a solid review of pre-algebra skills and emphasize modeling and applications of linear functions. Real- life experiences and technology will be used to explore and enrich understanding. Students will not take the NJSLA-Mathematics Algebra I assessment at the conclusion of this course, but will take it the following year when they are taking Algebra IB (CP). Passing the NJSLA-Mathematics Algebra I assessment is a New Jersey graduation requirement.

**502 ALGEBRA IB (CP) Gr. 10-12 5 cr., 36 wks**

*Pre: 501*

Students will enroll in this course upon successful completion of Algebra IA (CP). This is the second part of the two-year Algebra I curriculum. Topics in this course include operations with polynomials, radicals, and quadratic and other non-linear functions. Students will take the NJSLA-Mathematics Algebra I assessment near the end of this course. Passing the NJSLA-Mathematics Algebra I assessment is a New Jersey graduation requirement.

**503** ** GEOMETRY (CP) Gr. 10-12 5 cr., 36 wks**

*Pre: 510, 512, 502*

Geometry is designed to help student who have successfully completed Algebra 1. Students will explore and discover key geometric properties using a more hands-on approach with Geometry computer software applications used at times to assist with exploring concepts. Sample topics to be covered include: reasoning and proofs, parallel and perpendicular lines, relationships within triangles, two and three-dimensional figures, transformations, right triangle trigonometry, and circles. This course is designed to help make sense of the mathematics they encounter in and out of class each day. It will allow students to learn geometric principles and how they are connected to one another and to students’ prior knowledge. This course prepares students for the New Jersey Student Learning Assessment in Geometry.

**504 INTEGRATED ALGEBRA (CP) Gr. 11-12 5 cr., 36 wks **

*Pre: 503, or 522*

Integrated Algebra is intended for students who have taken Algebra I and Geometry but who are not yet ready for Algebra II. This course will help solidify students’ understanding by bridging conceptual gaps giving them an introduction to many Algebra II topics. With Integrated Algebra, students will model real-world applications with a functions approach, netting a deeper grasp of key concepts helping to provide success for those students who choose to explore these topics more in depth in Algebra II.

**510 ALGEBRA I (CP) Gr. 9-12 5 cr., 36 wks **

Algebra I builds upon the knowledge and skills gained in a Pre-Algebra course and is designed for students who may need the concepts presented in a more concrete manner. It covers all Algebra 1 topics including operations with polynomials and matrices, creation and application of linear functions and relations, algebraic representations of geometric relationships, probability, and nonlinear functions. It will give the student the opportunity to apply their mathematical knowledge to a number of real life experiences. Technology is used to explore, research and present data. All incoming freshmen who enroll in this course must earn a qualifying score on the Scholastic Math Inventory assessment. This course prepares students for the New Jersey Student Learning Assessment in Algebra 1. Passing the New Jersey Student Learning Assessment for Algebra 1 is a New Jersey graduation requirement.

**512 ALGEBRA I (ADV) Gr. 9-12 5 cr., 36 wks **

This course is a rigorous College Preparatory course that includes work with variables, simple equations, and formulas, signed numbers, operations with polynomials, fractions and fractional equations, systems of linear equations, factoring, ratio and proportion, exponents, radicals, probability and statistics, and quadratic equations. This course helps the student develop a systematic approach to thinking while learning algebraic skills. All Incoming freshmen who enroll in this course must earn a qualifying score on the Scholastic Math Inventory assessment. This course prepares students for the New Jersey Student Learning Assessment in Algebra 1. Passing the New Jersey Student Learning Assessment for Algebra 1 is a New Jersey graduation requirement.

**514 ALGEBRA II (CP) Gr. 12 5 cr., 36 wks **

*Pre: 512 AND 522 or 504*

Algebra II is designed for student who need more time to process mathematical ideas and is taught at a slower pace than the Algebra II ADV course. It builds and expands upon the concepts taught in Algebra, Geometry and Integrated Algebra such as fundamental operations, functions, systems of linear equations, exponents, radicals, and quadratic equations. Additional topics such as exponential, logarithmic, and rational functions, sequences and series, conics, matrices, probability and statistics, and trigonometry will be introduced. Technology is used to explore, research and present data. This course prepares students for the New Jersey Student Learning Assessment for Algebra II.

**516 ALGEBRA II (ADV) Gr. 10-12 5 cr., 36 wks **

*Pre: 512 and 522 *

Algebra II gives the student the mathematical background needed for continuing his/her studies in mathematics. The course increases understanding of facts and principles learned in Algebra I (ADV), including fundamental operations, functions, systems of linear equations, exponents, radicals, and quadratic equations. New topics, such as complex numbers, logarithms, advanced topics in trigonometry, and conic sections are taught. Word problems are used throughout, and a systematic approach to problem solving is emphasized. This course prepares students for the New Jersey Student Learning Assessment for Algebra II.

**518** **ALGEBRA II (H/Wt.) Gr. 10-12 5 cr., 36 wks **

*Pre: 523 *

This is an accelerated course which covers the topics of Algebra II. It thus requires that the student be able to solve problems rapidly and to spend additional time beyond that normally expected in mathematics courses to complete assignments. As an honors course, it is comprehensive and theoretical. This course prepares students for the New Jersey Student Learning Assessment for Algebra II.

**522** ** GEOMETRY (ADV) Gr. 9-12 5 cr., 36 wks **

*Pre: 512 *

An introduction to plane geometry is provided. Students learn the nature of proof, and develop methods of critical thinking. Definitions and postulates are used as the foundation for the basic plane geometry theorems concerning parallel and perpendicular lines, congruent triangles, right triangle trigonometry (including the Law of Sines and Cosines), similar polygons, and arcs, and angles in circles. Solid geometry is handled informally where applicable. The basic concepts of coordinate geometry and compass and straightedge construction are included. This course prepares students for the New Jersey Student Learning Assessment for Geometry.

**523** **GEOMETRY (H/Wt.) Gr. 9-10 5 cr., 36 wks **

This is a geometry course for the accelerated mathematics student. It thus requires that the student be able to solve problems rapidly and to spend additional time beyond that normally expected in mathematics courses to complete assignments. Methods of critical and logical deductive thinking will be developed and used to investigate and solve problems. Many complicated geometric proofs will be presented to the student who will ultimately be able to make presentations on his/her own. Both solid and analytical geometry will be treated on a sophisticated level. This course also includes right triangle trigonometry as well as the study of the Law of Sines and Cosines. Applications of geometry to other fields are emphasized. This course prepares students for the New Jersey Student Learning Assessment for Geometry.

**530** **DISCRETE MATHEMATICS (ADV) Gr. 12 5 cr., 36 wks **

*Pre: 504, 514, 516 *

Discrete Mathematics will use problem solving and reasoning skills to explore areas of mathematics not traditionally covered in earlier courses of study. It is the study of mathematics dealing with objects that have distinct separate values that lends itself to a wide variety of “real world” applications. Topics will include counting and sorting techniques, the exploration of combinations, game strategies, the appropriate use of building tree diagrams, and the many applications of networking. Additional topics to be included are the mathematics of voting, problem solving, set theory, logic, and cryptography. This course is designed for the liberal arts student, but may also be of interest to the math/science focused student and taken concurrently with another math class after having completed Integrated Algebra or Algebra 2.

**533** **PRECALCULUS (ADV) Gr. 11-12 5 cr., 36 wks **

*Pre: 516 *

Precalculus (ADV) is rigorous course designed to prepare juniors and seniors for a first course in Calculus. It builds upon the concepts taught in Algebra II (ADV) such as functions, trigonometry, polynomials, and rational expressions. Topics to be introduced include limits, unit circle trigonometry, graphs of trigonometric functions and their inverses, trigonometric identities and proofs involving those identities, and conic sections. Additional topics may include polar coordinates, sequences and series, matrices and work with continuity. The course will offer opportunities for students to build problem solving and mathematical modeling skills.

**534** **PRECALCULUS (H/Wt.) Gr. 10-12 5 cr., 36 wks **

*Pre: 518*

Precalculus (H/Wt.) is designed to continue, maintain, sharpen and improve mathematical skills attained through Algebra II and Trigonometry (H/Wt.). It also extends many of the topics in more depth than covered in previous math courses and prepares students for a formal course in AP Calculus. The course includes topics such as: functions, analytical geometry, vectors, and matrices, probability, statistics, limits, series, and introduction to Calculus. Some of the applications of the above topics will involve computer solutions.

**536** **AP STATISTICS (H/Wt.) (AP/Wt.) Gr. 11-12 5 cr., 36 wks**

*Pre: 518 Sug. Pre/co: 534 *

The Advanced Placement course in statistics is equivalent to a one-semester, introductory, non-calculus based, college course in statistics. Upon successful completion of the course, students will take the Advanced Placement Exam for possible college credit. The purpose of the course 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: exploratory analysis, planning a study, probability, and statistical inference.

AP Statistics is a laboratory-like course which engages students in explorations and analysis of data. *Note: Students taking this Advanced Placement course will be encouraged to take the AP examination near the conclusion of the course. Please see the explanation of the Advanced Placement Program under General Information in this Course Selection Guide. *

**537** **CALCULUS (ADV) Gr. 12. 5 cr., 36 wks**

*Pre: 533 or 534*

This course is an introductory calculus course which covers the equivalent material of a first semester college calculus course. Students study limits, differential and integral calculus, and applications of the above. Topics include properties of continuity and limits, the slope of a curve, the rate of change of a function, techniques for finding derivatives of algebraic and trigonometric functions, extrema, the Mean Value Theorem, integration, area, and volume. This course is does not prepare students for an AP examination in calculus.

**538** **AP CALCULUS AB (H/Wt.) (AP/Wt.) Gr. 12 5 cr., 36 wks**

*Pre: 534 **
*AP Calculus AB is equivalent to a college-level Calculus course primarily concerned with developing the students’ understanding of the concepts of calculus and providing experiences with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being represented geometrically, numerically, analytically, and verbally. Topics covered include functions, limits, derivatives and their applications, Riemann sums, definite and indefinite integrals and their applications, the Fundamental Theorems of Calculus, and numerical approximations to integrals. The work is exceptionally rigorous and demanding and covers the topics included in the nationally approved Advanced Placement curriculum. In connection with the Common Core Standards, this course examines the concepts of; Number and Quantity, Algebra, Functions, Modeling and Probability and Statistics. This course will also incorporate the Eight Standards for Mathematical Practices as identified by the Common Core.

*Note: Students taking this Advanced Placement course will be encouraged to take the AP examination of the Advanced Placement near the conclusion of the course. Please see the explanation program under the General Information section of this Course Selection Guide.*

**540** **AP CALCULUS BC (H/Wt.) (AP/Wt.) Gr. 12 5 cr., 36 wks **

*Sug. Pre: 534 *

Calculus BC has the same general objectives as Calculus AB and it covers all the topics of Calculus AB plus the following topics: derivatives of parametric, polar and vector functions, slope fields, Euler’s Method, L’Hopital’s Rule and its applications, length of a curve, integration by parts, integration using partial fractions, improper integrals, logistic modeling, series, series of constants and Taylor series. The content of the BC course is designed to qualify a student for placement and credit in a college course that is one course beyond that granted for the AB course.

*Note: Students taking this Advanced Placement course will be encouraged to take the AP examination of the Advanced Placement near the conclusion of the course. Please see the explanation program under the General Information section of this Course Selection Guide. *

**544** **COMPUTER SCIENCE BASICS THROUGH GAMING 2.5 cr in Practical Arts 18 wks **

*Pre/co-requisite: 512* *
*This STEM based course engages students with project-based learning to introduce students to programming and design concepts through the development of computer games. Students will learn technical skills like programming, graphic design, and animation, testing/debugging and other computer programming skills. They will also learn how to form and work in project development teams, and how the same engineering cycle used to design bridges and buildings is used to design games and solve many types of problems. In addition to the programming aspect of this class, students will be provided with an “Overview” framing the bigger picture of Computer Science fundamentals including career opportunities. There are no programming prerequisites for students who take this course but they should have a strong background in algebra and experience in problem solving.

**545** **INTRO TO COMPUTER PROGRAMMING (ADV)**

**Gr. 9-12 2.5 cr. in Practical Arts, 18 wks**

*Pre/co-requisite: 512 *

The course is designed to introduce the student to the computer approach to solving problems. The Java language will be taught that will directly transfer to future coursework in computer science. The students will get “hands-on” experience with the computer from the earliest stages of the course. They will work on a wide variety of problems, many of which will reflect the students’ backgrounds and interests, as they cover the topics in the course outline.

**546** **AP COMPUTER SCIENCE PRINCIPLES (H/Wt.) (AP/Wt.)**

**Gr. 10-12 5 cr in Practical Arts 36 wks**

Students who enroll in this course will be introduced to the foundational concepts of computer science and will challenge them to explore how computing and technology can impact the world. This course is unique in its focus on student creativity. There are seven main ideas that will be explored throughout the course: Creativity, Abstraction, Data Information, Algorithms, Programming, Internet, and Global Impact. With a unique focus on creative problem solving and real-world applications, AP Computer Science Principles prepares students for college and career.

*Note: Students taking this Advanced Placement course will be encouraged to take the AP examination of the Advanced Placement near the conclusion of the course. Please see the explanation program under the General Information section of this Course Selection Guide.*

**547** **AP COMPUTER SCIENCE A (H/Wt.) (AP/Wt.)**

**Gr. 11-12 5 cr. in Practical Arts 36 wks **

**Pre: 545 AND 516 with a minimum grade of C or 518 with a minimum grade of C or better**

AP Computer Science using the Java programming language emphasizes object-oriented programming methodology with a concentration on problem solving and algorithm development, and is meant to be the equivalent of a first-semester college-level course in computer science. Students will write computer programs that should be understandable, adaptable, and, when appropriate, reusable. At the same time, the design and implementation of computer programs is used as a context for introducing other important aspects of computer science, including the development and analysis of algorithms, the development and use of fundamental data structures, the study of standard algorithms and typical applications, and the use of logic and formal methods. In addition, the responsible use of these systems is an integral part of the course. This is rigorous course that requires time and commitment outside of the classroom.

*Pre: 545 with a C or better and/or 516 with a C or better*

**550** **PYTHON PROGRAMMING ADV Gr. 9-12 2.5 cr. in **

**Practical Arts, 18 wks**

*pre/Co-requisite: 512*** **

Python is a language with a simple syntax, and a powerful set of libraries. It is an interpreted language, with a rich programming environment, including a robust debugger and profiler. While it is easy for beginners to learn, it is widely used in many scientific areas for data exploration. This course is an introduction to the Python programming language for students with limited programming experience. We cover data types, control flow, object-oriented programming, and graphical user interface-driven applications. The examples and problems used in this course are drawn from diverse areas such as text processing, simple graphics creation and image manipulation, HTML and web programming, and genomics.

**551** **DATA STRUCTURES H/WT Gr. 12 (NHHS) 5 cr. in **

**Practical Arts, 36 wks **

*Pre: 547 or recommendation of teacher*

This year-long course continues and deepens students’ understanding and practice of object oriented programming. Students are expected to have familiarity with programming in Java at the AP Computer Science A level. Core topics in the context of the Java programming language include practical implementations of fundamental and more advanced data structures (linked lists, hash encoded storage, binary search tree and red-black trees, algorithms for organizing and manipulating data – including sorting, searching, and traversal algorithms), and time complexity of algorithms in a problem-solving oriented context. In-depth exploration of graph traversal algorithms (depth first search, breadth first search, shortest paths, and connected components) and string processing algorithms (substring search and string compression) is also included. Much of the course is project-based, with assignments stressing the design of classes and algorithms appropriate to a particular problem.

**495** **ROBOTICS AND AUTOMATION Gr. 9-12 2.5 cr. in **

**Practical Arts, 18 wks **

*Note: Description in Technology on pg. 52*

**499** **INTRODUCTION TO STEM **

**Grade 9-12, Credits 2.5 cr. ,18 weeks**

Introduction to STEM encourages students to develop basic skills across the curriculum, including basic literacy in reading, writing, listening, speaking, informational literacies, economics, science, technology, mathematics, and visual studies. Students will gain the skills and knowledge necessary to become lifelong learners. The methods of instruction will include collaboration, consensus building, and cooperative learning. This course will focus on developing literacy through the fields of science, technology, engineering and mathematics. The purpose of this semester long course is to introduce students to Science, Engineering and Technology in a real-world context. Starting with a foundational investigation of the engineering process, students will explore how their world is affected by Science, Engineering and Technology. Students will collaborate on projects and build critical 21st Century and College and Career Readiness skills.

**893** **ALGEBRA 1 WORKSHOP **

** Gr. 10-12 Semester Directed Study**

The directed study is for students who have not yet passed the Algebra 1 state assessment. During this workshop, students will review Algebra 1 topics in preparation to retake the Algebra 1 state assessment during the re-test window near the end of the first semester.

**893 S** **SENIOR MATH WORKSHOP Gr. 12 0 cr., Directed Study**

This workshop is designed for seniors who have not yet met their math graduation requirement and who will need to meet it using the Portfolio Appeal Process. Students will remain in this directed study until the Portfolio Appeal has been submitted and accepted by the state for graduation.