# Math

## Math Courses

- Math Concepts & Applications
- Algebra
- Geometry
- Pre Calculus
- Calculus
- Statistics
- Accuplacer Math
- Math in the Real World
- SAT Prep- Math

## Math Concepts & Applications

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 9 |

Prerequisite: | None |

NJ Course Code: |

This is the first course of a two-year Algebra 1 program. Students in Math Concepts and Applications will focus on the topics found in the first half of our Algebra 1 CP curriculum. These topics will focus on the description of the relationships between changing quantities using the language of symbols and graphs. Students will use symbols to represent situations, create and apply formulas, and make predictions or generalizations. Students will learn to create graphs, communicate ideas with graphs, and draw conclusions from graphs. Students will also understand how variables play a variety of different roles in symbolic expressions. Students will explore real-world contexts that involve developing flexible notions with uses of variables. In particular, students will use variables to represent constant rates of change and use algebraic expressions and equations to represent different aspects of a situation.

Overall, the course will draw from mathematical topics found in the New Jersey State Learning Standards and students will learn to apply them in a variety of contexts and situations, but students will also learn techniques of algebraic reasoning in the context of making justifications and drawing conclusions. Understanding and applying symbolic manipulation is an important outcome of the course, but students will also be expanding their ability to use verbal, graphical, and numerical ways to represent and justify situations as well. In addition, technology will be used to implement experiments, build understandings, and confirm written solutions.

## Algebra

## ALGEBRA I COLLEGE PREP

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 9 |

Prerequisite: | None |

NJ Course Code: | 02-052-E |

This course will focus on the description of the relationships between changing quantities using the language of symbols and graphs of linear functions as well as some nonlinear functions. Students will use symbols to represent situations, create and apply formulas, and make predictions or generalizations. Students will learn to create graphs, communicate ideas with graphs, and draw conclusions from graphs. Students will also understand how variables play a variety of different roles in symbolic expressions. Students will explore real-world contexts that involve developing flexible notions with uses of variables. Students will use variables to represent constant rates of change and use algebraic expressions and equations to represent different aspects of a situation.

Overall, the course will draw from mathematical topics found in the New Jersey State Learning Standards and students will learn to apply them in a variety of contexts and situations, but students will also learn techniques of algebraic reasoning in the context of making justifications and drawing conclusions. Understanding and applying symbolic manipulation is an important outcome of the course, but students will also be expanding their ability to use verbal, graphical, and numerical ways to represent and justify situations as well. In addition, technology will be used to implement experiments, build understandings, and confirm written solutions.

## ESSENTIALS OF ALGEBRA I

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 10 |

Prerequisite: | Math Concepts and Applications |

NJ Course Code: |

This is the second course of a two-year Algebra 1 program. Students in Algebra 1 Essentials will focus on the topics found in the second half of our Algebra 1 CP curriculum. These topics will be a continuation of finding relationships between changing quantities using the language of symbols and graphs, but with other nonlinear functions. Students will continue to use symbols to represent situations, create and apply formulas, and make predictions or generalizations, as well as learn to create graphs, communicate ideas with graphs, and draw conclusions from graphs. Students will also understand how variables play a variety of different roles in symbolic expressions. Students will explore real-world contexts that involve developing flexible notions with uses of variables.

Overall, the course will draw from mathematical topics found in the New Jersey State Learning Standards and students will learn to apply them in a variety of contexts and situations, but students will also learn techniques of algebraic reasoning in the context of making justifications and drawing conclusions. Understanding and applying symbolic manipulation is an important outcome of the course, but students will also be expanding their ability to use verbal, graphical, and numerical ways to represent and justify situations as well. In addition, technology will be used to implement experiments, build understandings, and confirm written solutions.

## ALGEBRA II

Course Level: | General |

Credits: | 5 |

Grade Level: | 11 |

Prerequisite: | Algebra 1 Essentials or Algebra 1 CP and refer to Level Placement Policy |

NJ Course Code: | 02-056-G |

This course focuses on mathematical models that employ variables and geometric relationships. Students study the behavior of graphs that result from such models, and the symbolic procedures needed to communicate about linear, quadratic, and exponential relationships between variables. Students use graphs to communicate about how quantities change, preparing for advanced mathematics courses and critical thinking in a technological world. In this second course in algebra, students use graphs as tools for posing, answering and communicating questions, and expand their ability to connect symbolic manipulations with graphical, numerical, and verbal representations. Students in this course use multiple representations to construct equations and communicate meanings about change and variation. Students learn techniques of symbolic reasoning involving factors, exponents, radicals, and quadratic expressions, and study the mathematical structure that underlies equation solving. Technology is used regularly by students and teachers to implement experimentation, build connections, confirm written solutions, and assist in interpreting results. By drawing from mathematical topics across the NJ Core Curriculum Standards, students see algebra as a set of powerful techniques and as a way to solve problems in a variety of contexts.

This modified algebra course will cover major topics detailed in Algebra II CP. However, the topics will be covered at a slower pace with the major emphasis on student understanding. More practice, technology, hands-on activities, small group interactions, diagrams, calculators and graphing applications will be employed to help students understand the mathematical concepts.

## ALGEBRA II COLLEGE PREP

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 10 - 12 |

Prerequisite: | Algebra 1 CP or Teacher Recommendation and refer to Level Placement Policy |

NJ Course Code: | 02-056-E |

This course focuses on mathematical models that employ variables and geometric relationships. Students study the behavior of graphs that result from such models, and the symbolic procedures needed to communicate about linear, quadratic, and exponential relationships between variables. Students use graphs to communicate about how quantities change, preparing for advanced mathematics courses and critical thinking in a technological world. In this second course in algebra, students use graphs as tools for posing, answering and communicating questions, and expand their ability to connect symbolic manipulations with graphical, numerical, and verbal representations. Students in this course use multiple representations to construct equations and communicate meanings about change and variation. Students learn techniques of symbolic reasoning involving factors, exponents, radicals, and quadratic expressions, and study the mathematical structure that underlies equation solving. Technology is used regularly by students and teachers to implement experimentation, build connections, confirm written solutions, and assist in interpreting results. By drawing from mathematical topics across the NJ Core Curriculum Standards, students see algebra as a set of powerful techniques and as a way to solve problems in a variety of contexts.

## ALGEBRA II HONORS

Course Level: | Honors |

Credits: | 5 |

Grade Level: | 9-10 |

Prerequisite: | Algebra 1 CP or Algebra 1 Honors and refer to Level Placement Policy |

NJ Course Code: | 02-056-H |

This course focuses on mathematical models that employ variables and geometric relationships. Students study the behavior of graphs that result from such models, and the symbolic procedures needed to communicate about linear, quadratic, and exponential relationships between variables. Students use graphs to communicate about how quantities change, preparing for advanced mathematics courses and critical thinking in a technological world. In this second course in algebra, students use graphs as tools for posing, answering and communicating questions, and expand their ability to connect symbolic manipulations with graphical, numerical, and verbal representations. Students in this course use multiple representations to construct equations and communicate meanings about change and variation. Students learn techniques of symbolic reasoning involving factors, exponents, radicals, and quadratic expressions, and study the mathematical structure that underlies equation solving. Technology is used regularly by students and teachers to implement experimentation, build connections, confirm written solutions, and assist in interpreting results. By drawing from mathematical topics across the NJ Core Curriculum Standards, students see algebra as a set of powerful techniques and as a way to solve problems in a variety of contexts.

In this course, students are challenged to find connections beyond those explored in Algebra II, and undertake mathematical investigations that extend across multiple class meetings. Students are expected to develop accurate recall of and facility with procedures, facility communicating with multiple representations, and the habit of using mathematical connections in problem-solving. Students deepen their understanding of the connections between graphical representations of functions and symbolic procedures through investigation of non-routine questions.

## Geometry

## ESSENTIALS OF GEOMETRY

Course Level: | General |

Credits: | 5 |

Grade Level: | 10-11 |

Prerequisite: | Algebra I CP or Math Concepts and Applications |

NJ Course Code: | 02-072-G |

This course focuses on visual, graphical, and spatial thinking, with particular attention to linking variables and shapes. Technology is used to model situations, make conjectures, implement experiments, and assist in interpretation and justification. Visual representations are a key to understanding mathematical symbols. Students in the course investigate contexts that involve shape, position, and measurement, using variables as a tool for reasoning. They also use diagrams as a tool to understand the uses of variables. The course is designed to encourage students to use diagrams, drawings, and spatial reasoning to reason about algebra. Students discuss mathematical reasoning to develop meanings for mathematical terminology. Activities in the course are chosen to motivate "why" questions that connect variables and shapes in a wide array of settings and contexts. By justifying their answers with deductive reasoning, students increase their capacity for logical and critical thinking in their daily lives and in later mathematics courses.

This course will cover the major topics detailed in Geometry CP. However, topics will be covered at a slower pace with major emphasis on student understanding.

## GEOMETRY COLLEGE PREP

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 9 - 10 |

Prerequisite: | Algebra I College Preparatory and refer to Level Placement Policy |

NJ Course Code: | 02-072-E |

This course focuses on visual, graphical, and spatial thinking, with particular attention to linking variables and shapes. Technology is used regularly to model situations, make conjectures, implement experiments, and assist in interpretation, justification, and proof. Visual representations are a key to understanding mathematical symbols. Students in the course investigate contexts that involve shape, position, and measurement, using variables as a tool for reasoning. They also use diagrams as a tool to understand the uses of variables. The course is designed to encourage students to use diagrams, drawings, and spatial reasoning to reason about algebra, discrete mathematics, and ideas that underlie calculus. Students discuss mathematical reasoning to develop meanings for mathematical terminology. Activities in the course are chosen to motivate "what if" questions that connect variables and shapes in a wide array of settings and contexts. By justifying their answers with deductive reasoning, students increase their capacity for critical thinking in their daily lives and in later mathematics courses.

## GEOMETRY HONORS

Course Level: | Honors |

Credits: | 5 |

Grade Level: | 9 |

Prerequisite: | Algebra I CP or Algebra I Honors, refer to Level Placement Policy |

NJ Course Code: | 02-072-H |

This course focuses on visual, graphical, and spatial thinking, with particular attention to linking variables and shapes. Technology is used regularly to model situations, make conjectures, implement experiments, and assist in interpretation, justification, and proof. Visual representations are a key to understanding mathematical symbols. Students in the course investigate contexts that involve shape, position, and measurement, using variables as a tool for reasoning. They also use diagrams as a tool to understand the uses of variables. The course is designed to encourage students to use diagrams, drawings, and spatial reasoning to reason about algebra, discrete mathematics, and ideas that underlie calculus. Students discuss mathematical reasoning to develop meanings for mathematical terminology. Activities in the course are chosen to motivate the "why" questions. By justifying their answers with deductive reasoning, students increase their capacity for logical and critical thinking in their daily lives and in later mathematics courses.

In this level of the course, students are challenged to find connections beyond those explored in Geometry, and undertake mathematical investigations that extend across multiple class meetings. Students are expected to develop accurate recall of and facility with procedures, facility communicating with multiple representations, and the habit of using mathematical connections in problem-solving. Students learn how to use formal proof in a variety of contexts and apply higher-level algebraic computations to justify their reasoning.

## Pre Calculus

## PRE-CALCULUS COLLEGE PREP

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 10-12 |

Prerequisite: | Geometry College Preparatory and Algebra II College Preparatory and refer to Level Placement Policy |

NJ Course Code: | 02-109-E |

This course focuses on the study of the properties of functions, with specific attention to fundamental ideas about change and variation. Students learn to reason with symbols and graphs, make decisions about mathematical structure, and construct functions as models for relationships between independent and dependent variables.

The course introduces students to the use of mathematical representations – definitions, graphs, and symbols – needed to model situations from physics, chemistry, engineering, pharmacy, architecture, economics, medicine, and ecology. Students taking this course should have an interest in pursuing the study of calculus in high school or college.

## PRE-CALCULUS HONORS

Course Level: | Honors |

Credits: | 5 |

Grade Level: | 11-12 |

Prerequisite: | Geometry Honors or College Preparatory and Algebra II Honors or College Preparatory and refer to Level Placement Policy |

NJ Course Code: | 02-110-H |

This course focuses on the study of the properties of functions, with specific attention to fundamental ideas about change and variation. Students learn to reason with symbols and graphs, make decisions about mathematical structure, and construct functions as models for relationships between independent and dependent variables.

The course introduces students to the use of mathematical representations – definitions, graphs, and symbols – needed to model situations from physics, chemistry, engineering, pharmacy, architecture, economics, medicine, and ecology. Students taking this course should have an interest in pursuing the study of calculus in high school or college.

In this course, students are challenged to find connections beyond those explored in pre-calculus, and undertake mathematical investigations that extend across multiple class meetings. Students are expected to develop accurate recall of and facility with procedures, and use multiple representations and mathematical connections in problem solving. Students extend their ability to justify mathematical conclusions with formal arguments, and to invent solutions to non-routine questions. Students learn terminology and develop facility with symbols to speak meaningfully about contexts. The derivation of mathematical results is motivated by contexts from social and physical sciences.

## Calculus

- CALCULUS COLLEGE PREP
- CALCULUS ADVANCED PLACEMENT AB
- CALCULUS ADVANCED PLACEMENT BC
- ADVANCED TOPICS IN CALCULUS

## CALCULUS COLLEGE PREP

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 11-12 |

Prerequisite: | Pre-Calculus College Preparatory and refer to Level Placement Policy |

NJ Course Code: | 02-121-E |

This course is concerned with the development of students' understanding of the concepts of calculus and students' experience with its methods and applications. Questions, concepts, and results are approached and expressed graphically, numerically, analytically, and verbally. Connections between these representations are used to aid students in forming concepts about rates and accumulation.

Students learn the symbolic manipulations that are part of calculus through activities that focus upon ways of representing relationships between changing quantities. In these activities, students focus on the meaning and reasonableness of solutions, interpretations of information and results, and the verification of conjectures.

Students use technology to explore and reinforce the relationships between different representations of functions. Technology is also used to focus students on the underlying methods that produce the results of calculus. Rather than study a broad taxonomy of methods, students learn how to produce a core set of results, and how to use basic principles to draw conclusions.

Using technology, students investigate contexts of interest that are beyond the scope of the symbolic approaches students learn to perform by hand. Regardless of the approach, students learn how to communicate the ideas of calculus orally and using well-written sentences. Students explain their solutions and the meanings of the representations they use in their answers.

## CALCULUS ADVANCED PLACEMENT AB

Course Level: | Advanced Placement |

Credits: | 5 |

Grade Level: | 11-12 |

Prerequisite: | Pre-Calculus Honors and refer to Level Placement Policy |

NJ Course Code: | 02-124-H |

This course follows the AP Calculus syllabus detailed by the College Board. It is expected that students who take this course will seek college placement, college credit, or both, from institutions of higher learning, through the AP Exam or other method employed by the institution.

Graphing calculators are necessary for this course. The purchase of a graphing calculator is recommended for at-home use in this course.

More information can be found about this course at www.collegeboard.com

## CALCULUS ADVANCED PLACEMENT BC

Course Level: | Advanced Placement |

Credits: | 5 |

Grade Level: | 12 |

Prerequisite: | Calculus Advanced Placement AB and refer to Level Placement Policy. |

NJ Course Code: | 02-125 |

This course follows the AP Calculus BC syllabus detailed by the College Board. This course is a continuation of AP Calculus AB and is the equivalent of a second semester college calculus course. It is important to note that since Calculus AB as a prerequisite for this class, not all AP Calculus AB topics will be covered. Instead, students will go deeper into Calculus 2 topics and therefore expected to be proficient in all Calculus AB topics. Students will have the opportunity to gain college placement, college credit or both, for two semesters of calculus from institutions of higher learning through the AP exam.

The purchase of a graphing calculator is recommended for at home use in this course.

More information can be found about this course at www.collegeboard.com

## ADVANCED TOPICS IN CALCULUS

Course Level: | Honors |

Credits: | 5 |

Grade Level: | 12 |

Prerequisite: | Calculus Advanced Placement BC and refer to Level Placement Policy. |

NJ Course Code: |

This course will challenge students to explore topics beyond those covered in AP Calculus BC. Subject matter to be explored will include a variety of college-level Calculus 3 topics as well as introductory topics in Linear Algebra and Elementary Differential Equations. This course will also explore applications of calculus through engineering and the physical world and undertake mathematical investigations that extend across multiple levels of calculus. Students are expected to develop accurate recall of calculus topics previously covered and use multiple representations and mathematical connections in problem solving. Students will extend their ability to justify mathematical conclusions with formal arguments, and to invent solutions to non-routine questions and real world scenarios. Students will continue to learn new terminology and develop an understanding of new symbols in order to represent, solve and justify the application of higher level mathematics.

## Statistics

## PROBABILITY AND STATISTICS COLLEGE PREPARATORY

Course Level: | College Preparatory |

Credits: | 5 |

Grade Level: | 11-12 |

Prerequisite: | Algebra II College Preparatory and refer to Level Placement Policy |

NJ Course Code: | 02-201-E |

This course focuses on the development of students' ability to build mathematical models using variables to gain insight into and develop intuition about random processes. Using functions and graphs that result from such models, students connect graphical representations of data with algebraic methods to extend and refine their ability to make inferences. Students who learn statistical methods with meaning are prepared for thinking quantitatively in a data-driven economy and technological world. Consequently, problems and examples are drawn from contexts including games of chance, sports, science and medicine, and marketing, while techniques are developed using algebra, geometry, discrete mathematics and ideas of calculus. Facility with symbolic reasoning is important to the extent that it increases students' capacity for analyzing data and designing meaningful experiments. Ideas and models are expressed geometrically, numerically and verbally. Technology is used regularly by students to perform experiments, assist in interpreting and presenting results, and to coordinate algebraic results. Students in this course build ideas about chance and randomness through active involvement in constructing and justifying statistical results. They learn how to make choices about the procedures they use to analyze data, formulate statistical models, and write about the validity of methods and results.

## STATISTICS ADVANCED PLACEMENT

Course Level: | Advanced Placement |

Credits: | 5 |

Grade Level: | 11-12 |

Prerequisite: | Pre-Calculus Honors and refer to Level Placement Policy |

NJ Course Code: | 02-203 |

This course follows the course description in Statistics defined by the College Board. It is designed for students who wish to complete studies equivalent to a one semester, introductory, non-calculus-based, college course in statistics. Students who successfully complete the course and the AP Exam may receive credit, advanced placement, or both. The course depends heavily on technology used inside and outside of class, for the interactive, investigative aspects of data analysis.

More information can be found about this course at www.collegeboard.com.

## Accuplacer Math

Course Level: | College Preparatory |

Credits: | 2.5 |

Grade Level: | 12 |

Prerequisite: | Algebra II or Algebra II College Preparatory and Geometry Essentials or Geometry College Preparatory |

NJ Course Code: | 02-993-G |

This course is for students planning to attend any two or four year college. County College of Morris and many four year colleges, require students to take the NextGen Accuplacer test in order to determine the student's prior knowledge. Students do not pass or fail the test but rather place into a particular knowledge group as a result of the test score. Scoring well on this exam will prevent students from taking remedial math courses in college. Students often must pay for these remedial math courses, but they do not count as credits towards the student's degree.

The goal of the class is to help prepare students to be successful on the NextGen Accuplacer exam and attain a score on the test that will allow the student to register for college level Mathematics courses that will count towards the student's degree. The curriculum of the course will follow the three areas that the students will be tested on. Students will review prior math learned through Algebra 2 and practice test-like questions. Since the test does not permit the use of a calculator, one of the requirements of this course is that NO CALCULATORS will be used in the classroom

## Math in the Real World

Course Level: | College Preparatory |

Credits: | 2.5 |

Grade Level: | 12 |

Prerequisite: | Algebra II or Algebra II College Preparatory and Geometry Essentials or Geometry College Preparatory |

NJ Course Code: | 02-157-G |

This course will prepare students to succeed with 21st Century Math Skills when they graduate. Major topics will include solving linear programming, quadratic equations, and three-dimensional geometry. These topics will be applied to real world applications; assessments will include three projects: Salsa Project, Fireworks Project, and Doghouse Project. This course will show students how math is used in the real world!

## SAT Prep- Math

Course Level: | College Preparatory |

Credits: | 2.5 |

Grade Level: | 10-11 |

Prerequisite: | Geometry Essentials, College Preparatory, or Honors |

NJ Course Code: | 02-993-G |

This course is intended for students who plan to take the College Entrance Examination Board's Scholastic Aptitude Test (SAT) and want to review and prepare for the test. It is also designed for students who wish to improve their math SAT score. College Board materials will be used in this course. Test taking strategies, test content and sample problems will be reviewed. Students will take practice SAT exams and analyze their results.

Department Chair

**Keith Lucid**

@keith.lucid@motsd.org

973-927-2208 ext. 7623

Department Staff

**Mr. Fike**