MATHEMATICS COURSES OFFERED AT SUMMIT HIGH SCHOOL
In order to graduate from Summit High School, students must successfully complete three full-year mathematics courses including Algebra 1, Geometry, and Algebra 2 (or a third year of math that builds upon the concepts and skills of algebra and geometry and prepares students for college and 21st century careers )
Based on teacher evaluations and district assessments, students who have not demonstrated minimum proficiency in their mathematics skills will be assigned to the Mathematics Strategies course in addition to their regularly scheduled mathematics class.
ALGEBRA 1 - Modeling with Functions
Grades 9-11
NCAA
5 Credits
PREREQUISITE: Foundations of Algebra
H225: This course will focus on solving systems of equations, exploring linear, quadratic, exponential, and
rational functions, and manipulating radical, polynomial, and rational expressions. Emphasis will be placed on the
application of these concepts in real world settings and methods for modeling real world scenarios using these
functions. Graphing calculators will be used throughout this course to further develop each concept. Students
completing this course will take the NJSLA Exams in Algebra 1.
PREREQUISITE: Pre-Algebra 8
H224: Placement in this course is based on completion of Pre-Algebra 8. This course will focus on solving
systems of equations, exploring linear, quadratic, exponential, and rational functions, and manipulating radical,
polynomial, and rational expressions. Emphasis will be placed on the application of these concepts in real world
settings and methods for modeling real world scenarios using these functions. Graphing calculators will be used
throughout this course to further develop each concept. Throughout the course, the pacing and level of rigor is
designed to accommodate the diversity of learning styles in this class. Students completing this course will take
the NJSLA Exams in Algebra 1 and will take Geometry 3 the following year.
SHELTERED-ENGLISH ALGEBRA 1 - Modeling with Functions
Grade 9-11
NCAA
5 Credits
PREREQUISITE: Foundations of Algebra
This Algebra 1 - Modeling with Functions course is designed for English language learners. Emphasis is placed on learning the Algebra 1 content, while developing English language skills related to reading, writing, listening and speaking all within the context of developing mathematics skills. The course is intended for students who are prepared to continue their exploration of Algebra 1 – to obtain mastery of the skills, techniques, and concepts necessary for success in future mathematics courses. For a full description of the content see Algebras 1 - Modeling with Functions above.
GEOMETRY
Grades 9-12
NCAA
5 Credits
PREREQUISITE: Algebra 1
H232: This course is for the successful Algebra 1 student who wishes to continue his study of college preparatory mathematics. The course is Euclidean geometry and includes congruence, similarity, parallelism, perpendicularity, area, volume, and circles. Coordinates and transformations in both two and three dimensions are integrated throughout the course. There is a main sequence of proved theorems with many "originals" for the student to prove. Students completing this course will take the NJSLA Exams in Geometry and are eligible to take Algebra 2 or Algebra 2 with Trigonometry the following year.
H233: Placement in this course is the result of a teacher recommendation based upon a limited level of success in Algebra 1. The course is Euclidean geometry and includes congruence, similarity, parallelism, perpendicularity, area, volume, and circles. Coordinates and transformations in both two and three dimensions are integrated throughout the course. While the use of Algebra is required throughout the course, the level of rigor is designed to accommodate the diversity of learning styles in this class. The students will explore the process of presenting formal geometric proofs as an entry level topic. Students completing this course will take the NJSLA Exams in Geometry and are only eligible to take Algebra 2 the following year..
HONORS GEOMETRY
Grades 9-10
NCAA
5 Credits
Prerequisite: Algebra 1, performance on a placement test, and acceptance through the written application process outlined on page 55 of the student handbook.
The course is Euclidean geometry and includes congruence, similarity, parallelism, perpendicularity, area, and volume. Coordinates and transformations in both two and three dimensions are integrated throughout the course. There is a main sequence of proved theorems with many "originals" for the student to prove. The content includes that of the regular Geometry course but with an increased degree of rigor and greater depth of coverage. Students completing this course will take the NJSLA Exams in Geometry.
INTEGRATED ALGEBRA
Grades 11-12
5 Credits
PREREQUISITE: Geometry
This course is designed for the student who has completed a course in Algebra 1 and Geometry yet would benefit from further developing algebraic skills and mathematical reasoning. As required by the State, this course offers a third-year of mathematics that “builds upon the concepts and skills of algebra and geometry and prepares students for college and 21st century careers”. Students will review, explore and extend their use and understanding of algebraic reasoning while they continue to apply problem solving techniques and build on the knowledge gained in previous mathematics courses. Graphing calculators are integrated throughout the course.
ALGEBRA 2 NCAA
Grades 10-12 5 Credits
PREREQUISITE: Geometry
This course is for the college-preparatory student with average mathematical ability who has successfully completed Algebra 1 and Geometry. Students with above-average mathematical ability who have an interest in mathematics (or science-related careers) should consider the Algebra 2/Trigonometry course. This course is a continuation of work begun in Algebra l. It emphasizes facility with algebraic expressions and forms, especially linear and quadratic forms, powers and roots, and functions based on these concepts. Students study exponential, logarithmic, polynomial, and other special functions for their abstract properties and as tools for modeling real-world situations. Geometric ideas are utilized throughout, and matrices are examined conceptually and applied. Students completing this course will take the NJSLA Exams in Algebra 2.
ALGEBRA 2/TRIGONOMETRY NCAA
Grades 10-12 5 Credits
PREREQUISITE: Geometry 232
This course is for the student with above-average mathematical ability who has maintained a "B" average or better in Geometry 232 and who wishes to continue his study of more advanced work in mathematics. The algebraic properties of the real number system are reviewed, as are equations and inequalities of the first and second degree. The real number system is extended to the complex number system. Coordinate geometry, systems of equations, and logarithmic, exponential, trigonometric, and polynomial functions are covered in detail. Students completing this course will take the NJSLA Exams in Algebra 2.
HONORS ALGEBRA 2/TRIGONOMETRY NCAA
Grades 10-11 5 Credits
PREREQUISITE: Geometry 232 or Honors Geometry and acceptance through the written application process outlined on page 5 of the student handbook.
The algebraic properties of the real number system are reviewed, as are equations and inequalities of the first and second degree. The real number system is extended to the complex number system. Conic sections are given a geometric application. Coordinate geometry, systems of equations, exponential, logarithmic, polynomial, trigonometric, and circular functions are studied in detail. Matrices and probability are covered as time permits. Students completing this course will take the NJSLA Exams in Algebra 2.
PRECALCULUS ESSENTIALS (Formerly Algebra 3/Trigonometry)
Grades 11-12
NCAA
5 Credits
PREREQUISITE: Algebra 2
This course is for the college-preparatory student with average mathematical ability who has successfully completed Algebra 2. It is designed for students who want and need to continue taking mathematics but who are not yet prepared for the rigors of the standard Precalculus course. The course integrates ideas of functions and trigonometry with statistics and data analysis. It reviews and extends ideas about polynomial, exponential, logarithmic, and trigonometric functions. Statistical and algebraic concepts are integrated as students display, describe, transform, interpret, and model numerical data. The study of counting, probability, and simulation is also included. Additional topics include rational functions, conic sections, sequences, and series.
PRECALCULUS
Grades 11-12
NCAA
5 Credits
PREREQUISITE: Algebra 2/Trigonometry, Precalculus Essentials
This course is for the student who has successfully completed Algebra 2/Trigonometry, maintained at least a "B-" average and wishes to continue the study of mathematics at a more demanding level. Students who have taken the Precalculus Essentials course and have maintained a B average may also enroll in this course. The course develops the ideas associated with circular, polynomial, exponential, logarithmic, and trigonometric functions. The various functions are applied to real world situations. Additional topics are rational functions, conic sections, polar coordinates, sequences and series, and an introduction to limits.
HONORS PRECALCULUS
Grades 10-12
NCAA
5 Credits
PREREQUISITE: Algebra 2/Trigonometry or Honors Algebra 2/Trigonometry and acceptance through the written application process outlined on page 5 of the student handbook.
This course will prepare students for the rigorous AP Calculus AB curriculum. It will develop Precalculus topics in greater depth and at a challenging level that will expose students to the future demands of an Advanced Placement course. Topics that will be explored include circular, trigonometric, parametric, exponential, and logarithmic functions, vectors, conic sections, polar coordinates, sequences and series, and an introduction to limits and derivatives. This course may require a summer assignment.
HONORS INTRODUCTION TO ANALYSIS
Grades 10-12
NCAA
5 Credits
PREREQUISITE: Completion of Honors Algebra 2/Trigonometry with a B+ or better and acceptance through the written application process outlined on page 5 of the student handbook.
This course is for the student who has successfully completed Algebra 2/Trigonometry Honors and ultimately wishes to continue the study of advanced mathematics in the Advanced Placement Calculus BC. The first semester of this course explores pre-calculus topics such as polynomial functions, trigonometry, conic sections, exponents and logarithms, mathematical induction, and miscellaneous topics from advanced algebra and analytic geometry. The second semester includes a rigorous exploration of topics in calculus and includes limits, continuity, definition of derivative, derivatives of algebraic functions, and applications of derivatives. The calculus in this course is continued in the BC Calculus course. This course may require a summer assignment.
CALCULUS
Grade 12
NCAA
5 Credits
PREREQUISITE: Precalculus
This course is designed for those students who have completed a course in Precalculus and would like to continue their study of advanced mathematics. This course is offered as an alternative to the rigors of the Advanced Placement Calculus AB course. It includes an exploration of the concept of a limit, derivatives, definite integrals, and indefinite integrals. Students will investigate differentiation and integration using numerical, graphical, algebraic, and analytical methods. The use of a graphing calculator is expected as real-world applications are explored throughout the course.
AP CALCULUS AB
Grade 12
NCAA
5 Credits
PREREQUISITE: Precalculus or Honors Precalculus and acceptance through the written application process outlined on page 5 of the student handbook.
The work in this course is developed in conjunction with the syllabus of the Advanced Placement program. It includes the concepts of limit, differentiation of algebraic and transcendental functions, differentials, mean value theorem, Rolle's Theorem, integration of standard elementary forms, and transcendental functions. Geometric and physical applications include the area under a curve, volume of revolution, and velocity. Additional topics include differential equations and hyperbolic functions. All students enrolled in this class will be required to complete a summer curriculum assignment. This assignment is designed to review key mathematical topics that will be utilized throughout the course. Additionally, all students enrolled in an AP course will be required to prepare for and take the AP exam in May.
AP CALCULUS BC
Grades 11-12
NCAA
5 Credits
PREREQUISITES: Introduction to Analysis Honors, acceptance through the written application process outlined on page 5 of the student handbook and approval of the department supervisor.
This course is for the exceptional student who wishes to continue an exploration of advanced mathematics. The course is a continuation of the calculus work begun in Introduction to Analysis Honors. The course curriculum is based upon the College Board's Advanced Placement Calculus BC curriculum. It includes the concept of limit, differentiation of algebraic and transcendental functions, differentials, mean value theorem, Rolle's Theorem, integration of standard elementary forms, and transcendental functions. Geometric and physical applications include the area under a curve and between curves, volumes of revolution, length of a curve, surfaces of a revolution, and velocity. The BC syllabus covers the topics of the AB Calculus course in greater depth and with more rigor. Additional topics include polar graphs, infinite sequences and series, and differential equations.
All students in this course will be required to complete a summer curriculum assignment. This assignment is designed to review key mathematical topics that will be utilized throughout the course. Additionally, all students enrolled in this class are required to prepare for and take the Advanced Placement Calculus BC exam in May.
HONORS MULTIVARIABLE CALCULUS
Grade 12
NCAA
5 Credits
PREREQUISITES: AP Calculus BC, acceptance through the written application process outlined on page5 of the student handbook and approval of the department supervisor as an Independent Study opportunity.
This course is offered as an independent study for the exceptional student who has successfully completed a course in single variable calculus (our BC Calculus course). The course will only be offered as an online experience. Students are assigned a specific class period during which they view the online tutorials and complete specific assignments. Details of the expectations for this course can be obtained through the department supervisor. The course is a rigorous study of Multivariable Calculus. It is a challenging exploration of functions of several variables and includes the examination of such functions through the use of vectors and matrices, differentiation and integration, optimization, parametric curves and surfaces, and vector fields while exploring real world applications. Students will receive a graphing calculator for their use throughout the course.
MATHEMATICS ELECTIVES
INTRODUCTION TO COMPUTER PROGRAMMING
Grades 9 -12
NCAA
2.5 Credits
PREREQUISITE: Algebra 1
This elective course has been developed to simultaneously introduce students to computer programming and to prepare them for an introductory course in the formal JAVA language Students will learn to program stories and games in the Alice programming environment. Students will learn the basics of programming languages with a focus on critical knowledge and skills that may be applied in future classes. Students will learn to create and manipulate object classes and to use these manipulations to develop program animations. As they progress, students will learn to program using a variety of diverse techniques including if/else statements, loops, while and for statements as well as techniques unique to the Alice program. Completion of this class will prepare students to enroll in a follow up course that will introduce them to the Java programming language.
INTRODUCTION TO JAVA PROGRAMMING
Grades 9-12
NCAA
2.5 Credits
PREREQUISITE: Introduction to Computer Programming
This course is for the student who has successfully completed Introduction to Computer Programming, maintained at least a "B" average, and wishes to continue the study of computer programming at a more sophisticated level. The course serves as a direct follow up to the “Introduction to Computer Programming” course and introduces to students the Java programming language. Over the course of the semester students will develop strong Java programming skills through a series of programming and written assignments. Topics discussed in this class will mirror those taught in the “Introduction to Computer Programming” course. By building a student’s Java abilities in a fashion similar to their Alice experiences in the prerequisite course, students will develop a strong, core set of fundamental skills. Topics that will be taught include a wide variety of techniques such as if/else statements, loops, while and for statements. In addition, students will learn about object-oriented programming and public and private classes.
AP COMPUTER SCIENCE PRINCIPLES
Grades 10-12
NCAA
5 Credits
PREREQUISITE: Introduction to JAVA Programming and acceptance through the written application process outlined on page 5 of the student handbook.
This course is for the student who has successfully completed Introduction to Programming in JAVA, maintained at least a "B" average, and wishes to continue the study of computer programming at an advanced level. From the College Board AP website: AP® Computer Science Principles introduces students to the central ideas of computer science, instilling the ideas and practices of computational thinking and inviting students to understand how computing changes the world. The rigorous course promotes deep learning of computational content, develops computational thinking skills, and engages students in the creative aspects of the field. This course is designed to broaden technical programming knowledge by examining a multitude of programming languages from historical periods of time. Students will explore the development and design of these languages, highlighting both positive and negative aspects of those languages. Students will examine and analyze the features each language contributed to the programming world. This course is designed to challenge and develop computational thinking skills and creative design ability. In addition, the course will expand the view of computer programming by examining the historical significance of recent computer advances. All students enrolled in an AP course will be required to prepare for and take the AP exam in May.
AP COMPUTER SCIENCE A Grades 11-12
NCAA
5 Credits
PREREQUISITE: Successful completion of the course AP Computer Science Principles as well as a passing grade on the AP Computer Science Principles exam.
The Advanced Placement Computer Science class is designed to prepare students for the AP Computer Science A examination. Instruction is based upon the College Board's Advanced Placement Computer Science A curriculum. In this class, students will learn how to develop and write Java programs utilizing object-oriented program design. Topics include implementation techniques, programming constructs and programming analysis with an overall focus on top-down development. In addition, students will learn how to test and debug their programs as well as utilize error handling to address runtime errors. This course is equivalent to a semester of college level computer programming. All students enrolled in an AP course will be required to prepare for and take the AP exam in May.
DESIGN PROJECTS IN COMPUTER SCIENCE
Grade 12
2.5 Credits
PREREQUISITE: Successful completion of the course AP Computer Science Principles as well as a passing grade on the AP Computer Science Principles exam.
This semester-course is designed for students who have completed an AP computer science course and want to design a full program in a choice of their programming language such as Java or Python. From planning to implementing, this course will allow students the opportunity to build a full program from start to finish around a topic of their choice. Computer science and design thinking standards will be utilized in this course, as students recognize and design computational problems, develop and use abstractions, create computational artifacts, and test and refine those artifacts. The class culminates with the presentation of running each student's computer program.
STATISTICS AND DISCRETE MATHEMATICS
Grade 12
NCAA
5 Credits
PREREQUISITE: Algebra 2
This course explores many facets of data analysis. Topics include descriptive statistics for univariate and bivariate data, experimental design, probability, probability distributions, anticipating patterns and inferential statistics. Examples will be taken from various fields and student-created projects will be utilized throughout the course. Topics in Discrete Mathematics (the study of mathematical structures whose solutions are limited to distinct, separated values) include graph theory, network theory, voting theory, fair division and Euler circuits. Discrete Mathematics offers another opportunity to have students experience the application of mathematics in real world settings. Technology will be used extensively.
AP STATISTICS
Grade 12
NCAA
5 Credits
PREREQUISITE: Precalculus and acceptance through the written application process outlined on page 5 of the student handbook.
The course will explore the many facets of data analysis. Topics will include descriptive statistics, experimental design, probability, probability distributions, anticipating patterns and inferential statistics. Examples will be taken from various fields and student-created projects will be utilized throughout the course. Technology will be used extensively. Students interested in business, economics, politics, sports and social sciences will be well served with this course. This course will require a summer assignment. All students enrolled in this class are required to prepare for and take the Advanced Placement Statistics exam in May.
FINANCIAL LITERACY AND PERSONAL FINANCE
Grades 11-12
2.5 Credits
PREREQUISITE: N/A
This course is designed for students who are interested in exploring a wide range of topics in financial literacy as they pertain to personal finances. Successful completion of this course will fulfill the State of New Jersey financial literacy requirement for graduation. Using project-based instruction and real-world simulations, this course will provide students the opportunity to explore the key aspects of personal finances necessary to be successful now and throughout their adult lives. The primary structure of this class will focus on the examination of real-world situations. Through these experiences, students will develop skills, gather data, and formulate strategies needed to gain personal and financial responsibility related to financial planning, savings, investments, and charitable giving in the global community. By exploring the relationships among income and careers, money management, credit and debt management, risk management and investing, insurance, and taxes the student will become an educated and critical consumer.
MATHEMATICS STRATEGIES
Taken concurrently with Algebra 1 (H225) or (H224)
Grades 9-10
2.5 or 5 Credits
PREREQUISITE: N/A
Based on teacher evaluations and district assessments, students identified as demonstrating minimum proficiency in their mathematics skills will be assigned to this course. This program is designed to help prepare students to perform successfully on required state tests for the course in which students are enrolled. Course content is based on the proficiencies and performance objectives described within the Common Core State Standards in Mathematics.
MATHEMATICS FOR PERSONAL FINANCE
Grades 12
5 Credits
PREREQUISITE: N/A
This course is for students who demonstrate proficiency in basic skills, yet evidence a need for practical rather than abstract mathematics, and seek an alternative to the college preparatory mathematics options. The course is intended to further develop mathematical skills, to increase one’s ability to make personal decisions based on mathematical or business concepts, and to increase one’s ability to manage personal business (consumer) affairs. Enrollment in this course will fulfill the State of New Jersey financial literacy requirement for graduation.
EXPLORING YOUR WORLD THROUGH MATHEMATICS
Grade 11-12
2.5 Credits
PREREQUISITE: Algebra 2
This one-semester course is designed to provide students with the opportunity to explore mathematical topics of their own choosing. Students will complete a series of individual projects through which they will research and explore topics of interest. Students will have opportunities to present their findings and share the ways in which their topic can be applied in real-world settings. Potential topics include using mathematics to analyze stock market trends, mathematics applied in music, statistical analysis in sports, as well as advanced mathematical topics such as the use of matrices, polar coordinates, and topology.