Course descriptions

• Pre-Algebra 6
  In Grade 6 Math, instructional time will focus on connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; writing, interpreting, and using expressions and equations; and developing understanding of statistical thinking. Students will learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students in Grade 6 will also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They will find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students will discuss, develop, and justify formulas for areas of triangles and parallelograms. Students will find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They will reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths.
  
  Pre-Algebra 7
  In Pre-Algebra 7, instructional time will focus on students extending their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students will use their understanding of ratios and proportionality to solve a wide variety of percent problems. Students will graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They will distinguish proportional relationships from other relationships. Students will develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. They will use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Students will continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8, they will reason about relationships among two-dimensional figures. They will solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. Students will build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They will begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.
  
  Pre-Algebra 7/8
  In Pre-Algebra 7/8, instructional time will focus on students developing a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students will recognize that every real number can be classified according to its characteristics. They will use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Students will work with numbers written in various forms, including powers and exponents. Students will extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students will graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They will distinguish proportional relationships from other relationships. Students will further their understanding of linear relationships to write and graph lines in the form y = mx + b and interpret the significance of the variables for real-world problems. Students will build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They will begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Students will continue their work with solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. They
  will solve real-world and mathematical problems involving area, surface area, and volume of two- and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. Students will complete their work on volume by solving problems involving cones, cylinders, and spheres.
  
  Pre-Algebra 8
  In Pre-Algebra 8, instructional time will focus on students using linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students will also use a linear equation to describe the association between two quantities in bivariate data (ex: arm span vs. height for students in a classroom). Students will grasp the concept of a function and using functions to describe quantitative relationships. They will understand that functions describe situations where one quantity determines another, and they will describe how aspects of the function are reflected in the different representations. Students will use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students will understand the statement of the Pythagorean Theorem and its converse, and will explain why the Pythagorean Theorem holds. They will apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students will complete their work on volume by solving problems involving cones, cylinders, and spheres.
  
  

ALGEBRA 1:  COLLEGE PREP (CP)                                                                                                Open to Grades 9, 10, 11, 12

Pre-requisites: none         

Criteria for admission: Recommendation of teacher based on need, Course Length: Year

The primary objectives of this college preparatory course are to help the students master the basic structure of algebra and to assist them in acquiring facility in applying algebraic concepts to the solution of problems.  Algebra 1 CP is a course designed for students who have demonstrated a need for greater support and remediation in mathematics. The course will present the same concepts outlined in the Algebra 1 CPE course. Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

ALGEBRA 1:  COLLEGE PREP ENRICHED (CPE)                                                                            Open to Grades 8, 9, 10, 11, 12

Pre-requisites: none                                                                                                                        

Criteria for admission: none, Course Length: Year

Through the Standards for Mathematical Practice outlined in the NJ Student Learning Standards, students will learn to understand the basic structure of algebra.   Connections between mathematics and other disciplines with realistic and relevant applications are provided.  This course includes work with expressions and equations through understanding quantities and the relationships between them.  Additionally, grade 8 concepts for linear and exponential relationships are built upon by modeling the mathematics.  Linear models are used to assess how a model fits data as students work with descriptive statistics.  Units extend to quadratic and exponential functions.  Solutions to quadratic equations are held to the real number system.  Further standards involve functions and extend the concepts of integer exponents to concepts of rational exponents.  Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

GEOMETRY:  COLLEGE PREP (CP)                                                                                                  Open to Grades 9, 10, 11, 12

Pre-requisite:  Algebra 1                                                                                  

Criteria for admission: Recommendation of teacher based on need, Course Length: Year

The primary objectives of this college preparatory course are to help the students master the basic structure of geometry and to assist them in applying geometric definitions and theorems both inductively and deductively for  logical analysis in mathematical proofs. Geometry CP is a course designed for students who have demonstrated a need for greater support and remediation in mathematics. The course will present the same concepts outlined in the Geometry CPE course. Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

GEOMETRY:  COLLEGE PREP ENRICHED (CPE)                                                                           Open to Grades 8, 9, 10, 11, 12

Pre-requisites: Algebra 1                                                                                                 

Criteria for admission: none, Course Length: Year

Through the Standards for Mathematical Practice outlined in the NJ Student Learning Standards and moving towards formal mathematical arguments, the standards presented in this high school geometry course are meant to formalize and extend middle grades geometric experiences.   Triangle congruence conditions are established using analysis of rigid motion and formal constructions. Various formats will be used to prove theorems about angles, lines, triangles and other polygons and similarity.  The notion of similarity is extended to right triangles and the understanding of right triangle trigonometry.  The Laws of Sines and Cosines are utilized to find missing measures of triangles in general, not just right triangles.  This course also focuses on circles and using the rectangular coordinate system to verify geometric properties and to solve geometric problems. Concepts of similarity will be used to establish the relationship among segments on chords, secants and tangents as well as to prove basic theorems about circles.  Previous understandings of two- dimensional objects are used to explain, visualize, and apply geometric concepts to three-dimensional objects.  Informal explanations of circumference, area and volume formulas are analyzed. Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

Geometry CPE and Algebra 2 CPE may be taken concurrently, with teacher recommendation and the permission of the Mathematics supervisor.

GEOMETRY:  HONORS                                                                                                                                 Open to Grades 9, 10 

Pre-requisites: Algebra 1                                                                                                

Criteria for admission: Meets honors admission criteria, Course Length: Year

This course includes the concepts studied in the Geometry CPE course plus additional selected topics designed to broaden and strengthen a student’s insight and understanding of the nature of mathematics.  Additional emphasis is placed on mathematical proof, relevant application problems and SAT and ACT Preparation.  Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

ALGEBRA 2: COLLEGE PREP (CP)                                                                                                   Open to Grades 9, 10, 11, 12

Pre-requisites: Geometry                                                                                  

Criteria for admission: None, Course Length: Year

The primary objectives of this college preparatory course are to help the students master the connections between the basic structures of Algebra 1 and 2, and to assist them in acquiring facility in applying algebraic concepts to the solution of problems.  Algebra 2 CP is a course designed for students who have demonstrated a need for greater support and remediation in mathematics. The course will present the same concepts outlined in the Algebra 2 CPE course. Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

ALGEBRA 2: COLLEGE PREP ENRICHED (CPE)                                                                             Open to Grades 9, 10, 11, 12

Pre-requisites: Geometry                                                                                

Criteria for admission: None,  Course Length: Year

This is a traditional course in mathematics for the college bound student.  It follows Algebra 1 CPE and Geometry CPE and is a precursor to Pre-calculus.  Through the Standards for Mathematical Practice outlined in the NJ Student Learning Standards, students in Algebra 2 extend the basic structure of Algebra 1.   Building on the understanding of linear, quadratic and exponential functions from Algebra I, this course extends function concepts to include polynomial, rational, and radical functions. The standards in this course continue the work of modeling situations and solving equations.  Students explore the effects of the transformations on graphs of functions and include identifying an appropriate model for a given situation.  Additionally, students' previous knowledge of functions, trigonometric ratios and circles in geometry to extend trigonometry to model periodic phenomena are explored.  Lastly, students relate the visual displays and summary statistics learned in prior courses to different types of data and to probability distributions.  Samples, surveys, experiments and simulations are used as methods to collect data.  Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

Geometry CPE and Algebra 2 CPE may be taken concurrently, with teacher recommendation and the permission of the Mathematics supervisor.

ALGEBRA 2:  HONORS                                                                                                                     Open to Grades 9, 10 ,11, 12

Pre-requisites: Geometry                                                                  

Criteria for admission: Meets honors admission criteria, Course Length: Year

This course includes the concepts studied in the Algebra 2 CPE course plus additional selected topics designed to broaden and strengthen a student’s insight and understanding of the nature of mathematics.  Additional emphasis is placed on discrete mathematics, conic sections, combinatorics, probability, logarithms and SAT and ACT Preparation. Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

STATISTICS                                                                                                                                                             Open to Grade 12, Dual Enrollment with FDU

Pre-requisite:  Algebra 2                                                                                                                  

Criteria for admission:  Prior approval and placement by Mathematics Supervisor, Course length:  Year

This course is an introduction to descriptive and inferential statistics, offering elementary probability as its background. Students will focus on organization and description of data, probability, probability distribution, inferences and hypothesis testing, correlation and linear regression through the use of real world data sets. The course will introduce students to the language and methodology of statistics through applications, and will serve to prepare students to apply statistics in college and in their careers. 

Through the analysis of real world data, students will be able to: (1) appropriately collect data, (2) display and analyze data, (3) make calculations and informed predictions about a population. Students will also be able to solve problems through probability calculations. The course will focus on algebraic analysis, as well as analysis through the use of appropriate technology, including the graphing calculator, and Microsoft Excel.

Click here for information about Dual Enrollment.

PRE-CALCULUS                                                                                                                                     Open to Grades  10, 11, 12

Pre-requisites: Algebra 2                                                                                                 

Criteria for admission: none, Course Length: Year

This course presents and develops the mathematics needed to prepare a student for a college level Calculus course by integrating algebraic and geometric concepts.  Extensive use of graphing calculators and web-based applications are made throughout the year.  The course stresses the application of mathematics to various fields.  This course includes a brief review of selected Algebra 2 topics, conic sections, exponential and logarithmic functions, and trigonometry.  Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.   Additional emphasis is placed on ACT and SAT preparation for the juniors and college placement examination preparation for the seniors.

PRE-CALCULUS:  HONORS                                                                                                                 Open to Grades  10, 11, 12

Pre-requisites: Algebra 2                                                                                                

Criteria for admission: Meets honors admission criteria, Course Length: Year

The course includes all the concepts in the college prep Pre-Calculus course plus several additional topics designed for the able student.  Additional topics from discrete math, data analysis, limits and introduction to calculus are introduced.  Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding. Additional emphasis is placed on SAT I and II and ACT preparation.

CALCULUS:  HONORS                                                                                                                                 Open to Grades 11, 12, Dual Enrollment with FDU

Pre-requisites: Pre-calculus                                                                                             

Criteria for admission: Meets honors admissions criteria, Course Length: Year

This honors level course is designed for students who have finished Pre-Calculus and would like to take a Calculus course without the rigors of an Advanced Placement course.  Some major concepts from Pre-calculus will be reviewed, but the emphasis will be on introducing and reinforcing the concepts of Calculus including limits, continuity, differentiation, and integration.  A student who completes this course successfully should be well prepared to take a college level Calculus course.  Manipulatives, graphing calculators and web-based learning are used to facilitate and enhance critical thinking activities, as well as conceptual understanding.

ADVANCED PLACEMENT CALCULUS AB                                                                                                 Open to Grades 11, 12

Pre-requisites: Pre-calculus, Course Length:  Year                                                                                          

Criteria for admission:   Meets honors admission criteria                                                                                                   

 This AP mathematics course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry.  It is a college level course in introductory calculus with elementary functions.  Some colleges may grant exemption from required basic courses and/or credit when mastery is demonstrated by results on an Advanced Placement examination or other criteria.  Students should check with individual colleges as to their policies regarding this process.  Topics in this course include:  functions and derivatives with a variety of applications, limits the differential, techniques of integration and the definite integral.   Graphing calculators and web-based applications are used extensively to enhance conceptual understanding.

ADVANCED PLACEMENT CALCULUS BC                                                                                                      Open Grades 11, 12

Pre-requisites: Honors Pre-calculus, Course Length:  Year                                                                             

Criteria for admission:                                                                                                      

1.       Mid-year average of 90% in the present honors mathematics; mid-year grade of

98% in the present academic mathematics course.

2.       Demonstrates proficient levels of the Standards for Mathematical Practice.

3.       Recommendation of the present mathematics teacher.

 This AP mathematics course is intended for superior mathematics students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry and trigonometry.

Calculus BC is considerably more extensive than Calculus AB as the course expands upon the AB topics and also includes such topics as:   the study of vector functions and parametrically defined functions, graphs in polar coordinates, integration, and the study of infinite sequences and series.  Graphing calculators and web-based applications are used extensively to enhance conceptual understanding.

MULTIVARIABLE CALCULUS                                                                                                                            Open to Grade  12, Dual Enrollment with Seton Hall University

Pre-requisites: Advanced Placement Calculus BC, Course Length:  Year                                                    

Criteria for admission:                                                                                                      

1.       Mid-year average of 90% in the present honors mathematics; mid-year grade of

        98% in the present academic mathematics course.

2.       Demonstrates proficient levels for the Standards of Mathematical Practice.

3.       Recommendation of the present mathematics teacher.

Multivariable Calculus is the equivalent of a typical third semester college calculus course.  It is a continuation and extension of the BC Calculus course.  Single-variable calculus concepts will be applied to vector and parametric functions, as well as explaining single-variable calculus concepts to functions of more than one variable.  Units in this course include:  Vectors and Geometry in R 3 , Vector – Valued Functions, Partial Derivatives, Multiple Integrals, Applications of Multivariable Calculus, and Differential Equations.  Graphing calculators and web-based applications are used extensively to enhance conceptual understanding.

ALGEBRA 1 ACCELERATOR                                                                                                                          Open to Grades 9, 10

Co-requisites: Algebra CP                                                                                                               

Criteria for admission: Mandatory course based upon proficiency, Course Length:  Year

Algebra 1 Accelerator is designed to strengthen content and process skills with respect to Algebra 1 NJ Student Learning Standards.  This course focuses on understanding mathematical expressions, polynomial, exponential, logarithmic and trigonometric functions, and statistics.  The functions will be analyzed with respect to their multiple representations and their real world applications.  Instructional strategies will incorporate technology and cooperative learning to foster students’ ongoing development in independent mathematical thinking and perseverance.  These skills will not only help students to succeed in their high school courses, but will also help to prepare them for the NJSLA-M, SAT and ACT assessments.  Students are placed into this course based on test scores, as well as by teacher recommendation.

COLLEGE & CAREER READINESS ALGEBRA 1/GEOMETRY                                                                        Open to Grades 9, 10, 11, 12

Pre-requisites: none                                                                                                           

Criteria for admission: Mandatory course based upon proficiency, Course Length: Semester

This course is designed to strengthen content and process skills needed for successful completion of Algebra 1  CP/CPE and/or Geometry CP/CPE.  This course focuses on understanding mathematical expressions, linear equations and inequalities, systems of equations, and quadratic and exponential functions as outlined in the Algebra 1 CP/CPE and/or Geometry CP/CPE course descriptions.   This course also focuses on understanding the relationships between geometric definitions and theorems as they using them in inductive and deductive proofs. Instructional strategies will incorporate technology and cooperative learning to foster students’ ongoing development in independent mathematical thinking and perseverance.  These skills will not only help students to succeed in their high school courses, but will also help to prepare them for the NJSLA-M, SAT and ACT assessments.  Students are placed into this course based on test scores, as well as by teacher recommendation.

COLLEGE & CAREER READINESS ALGEBRA 2                                                                                        Open to Grades 10, 11, 12

Pre-requisites: none                                                                                                          

Criteria for admission: Mandatory course based upon proficiency, Course Length: Semester

This course is designed to strengthen content and process skills needed for successful completion of Algebra 2 CP/CPE. This course focuses on understanding mathematical expressions, linear equations and inequalities, systems of equations, and quadratic and exponential functions. Instructional strategies will incorporate technology and cooperative learning to foster students’ ongoing development in independent mathematical thinking and perseverance.  These skills will not only help students to succeed in their high school courses, but will also help to prepare them for the NJSLA-M, SAT and ACT assessments.  Students are placed into this course based on test scores, as well as by teacher recommendation.