# Math Department

The Math Department strives to encourage each student to comprehend and execute the study of mathematics.Committed to supporting and assisting each student in their efforts, we believe students should be active learners who take risks and work collaboratively, enjoying the core concepts of mathematics and how it helps us to better understand the world around us.

##### Course Offerings

##### INTEGRATED MATH

This course is the first year of a three‐year integrated math sequence covering the topics traditionally covered in Algebra I, Algebra II, Geometry, and PreCalculus. This course uses an integrated approach to lay the conceptual and technical groundwork for the study of further algebra, geometry, statistics, and discrete mathematics. It is appropriate for students who have completed Pre‐Algebra. Topics from the traditional Algebra I curriculum include algebraic operations with variable expressions, solving and graphing linear equations and inequalities, and solving quadratic equations. Foundational concepts from geometry and statistics include transformations and similarity, right triangles and the Pythagorean theorem, calculating area, theoretical probability, and quantitative statistics. Throughout the course there is an emphasis on questioning and discovery in mathematics. Students contribute to group work, complete research and writing on unfamiliar mathematical concepts, complete tests and quizzes regularly, and are also graded on homework completion and class participation. Students take a final exam at the end of the year. The TI‐Nspire graphing calculator app or handheld is required. Freshman course

##### INTEGRATED MATH II (STANDARD/ACCELERATED/HONORS)

This course is the second year of a three‐year integrated math sequence covering the topics traditionally covered in Algebra I, Algebra II, Geometry, and PreCalculus. The goal of this course is to extend and apply the topics studied previously and to introduce higher‐level topics that will prepare students for future courses. This course is appropriate for students who have completed Pre‐Algebra and Algebra I (Integrated Math I). Throughout the course there is a focus on developing problem‐solving skills, evaluating the potential uses of technology in mathematics, and communicating methods and solutions. As a capstone project, students write and present a solution to an open‐ended problem that may incorporate content and technology skills from throughout the course. Topics in the Standard Level from the traditional Algebra II curriculum include linear equations, inequalities and systems, graphing and analyzing functions, exponents and radicals, and quadratic and polynomial functions. Concepts from geometry include parallel lines and transversals, polygon angles, triangle congruence and basic proofs, and properties of quadrilaterals. Additional topics in the Accelerated Level include exponential and logarithmic functions, right triangle and unit circle trigonometry, non‐right triangle trigonometry and 3D geometry. Further additional topics in the Honors Level include relationships within triangles, further proofs, and trigonometric functions on the coordinate plane. The TI‐Nspire graphing calculator app or handheld is required. Freshman-Senior course

##### INTEGRATED MATH III (STANDARD/ACCELERATED/HONORS)

This course is the third year of a three‐year integrated math sequence covering the topics traditionally covered in Algebra I, Algebra II, Geometry, and PreCalculus. The goal of this course is to integrate all previously learned math content, solidify retention of technical skills, and lead students into the deeper questioning that can be answered with higher‐level study of mathematics including calculus and statistics. This course is appropriate for students who have completed Algebra I, Geometry, and Algebra II (Integrated Math II). Throughout the course there is a focus on contextual analysis of math problems, comparison of methods and solutions, and self‐reflection on both conceptual and technical mastery. Students complete an investigation and write a paper on a mathematical concept or question at the level of this course or beyond, the answer to which may lie beyond their current mastery. Topics in the Standard Level from the traditional Algebra II and PreCalculus curricula include an integrated look at linear, quadratic, polynomial, exponential, logarithmic, radical and rational functions, an introduction to complex numbers, equations of circles, and an in‐depth study of trigonometry. Non‐algebraic concepts include one‐variable data analysis, graphical representations of two‐variable statistics, and area and volume calculations. At the standard level, technology is fully integrated throughout the course. Additional topics in the Accelerated Level include sketching parent functions and their transformations without technology, as well as sequences and series and an introduction to two‐ dimensional vectors. Further additional topics in the Honors Level include an introduction to limits and basic differential calculus for the analysis of functions. The TI‐Nspire graphing calculator app or handheld is required. Sophomore‐PG course

##### DISCRETE MATH

As a senior/PG course, Discrete Math first provides an integrated review of the concepts in algebra, statistics, and probability that are traditionally covered in the first three or four years of a secondary math curriculum. The majority of the course then turns to more advanced probability, statistics, algebraic functions, and the financial applications of all three content areas. Each unit is designed to promote the ability to think and reason mathematically, collaborate creatively, and confidently apply mathematics to solve realistic industry‐driven challenges. Problem solving and critical thinking are emphasized in each topic. Students are accountable for quizzes and tests on the mathematical skills and content as well as project‐based major assessments on the overarching concepts that may be individual or team‐based. A capstone financial planning project is the culminating unit. Senior/PG course

##### INTEGRATED STATISTICS

This is a full‐year course designed for students with varied backgrounds and abilities in mathematics. This course is appropriate for students who have completed Algebra II (Integrated Math II) or further coursework and are looking for a course that does not heavily rely on prior algebraic concepts. Topics include number properties, number sets, Venn diagrams, introductory probability, conditional probability, logic and truth tables to evaluate the validity of arguments. Also covered are methods for displaying one‐ variable data and analyzing the center and spread of single variable data sets. Visual representations and qualitative/quantitative analysis of two‐ variable data sets are also covered. Students are expected to analyze problems using the appropriate notation, terminology, techniques, and graphical representations. Students should also expect to use graphing calculators on a daily basis. Students are expected to complete daily homework or classwork assignments and are assessed through periodic quizzes and tests at the 14 end of each unit. At least one major statistical investigation will be completed as a project‐based assessment of the content in the course. The TI‐ Nspire graphing calculator app or handheld is required. Junior-PG course

##### AP STATISTICS

AP Statistics is designed for students to complete studies equivalent to a non‐calculus‐based college course in statistics. Like the college course, the purpose of the AP course is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data drawn from a variety of disciplines. The course has two major themes: describing and displaying data and using probability models to develop the tools in statistical inference. A solid background in Algebra II (Integrated Math II), the recommendation of the math department, and good critical reading skills are prerequisites. In addition to mastery of specific statistical techniques, students will learn to think about the background of the data, the design of the studies that produce the data, the possible effect of outlying observations on conclusions from the data, the question of causation and the reasoning that lies behind the standard methods of inference. Students will become proficient in the statistical functions on their TI‐Nspire graphing calculators. Students are expected to contribute to group work and to complete homework daily. Take home quizzes based on prior years’ AP test questions will be assigned periodically. Chapter tests are generally given weekly. After the AP exam, students complete and present a project which investigates an advanced topic of their choice. The TI‐Nspire CAS graphing calculator iPad app or handheld is required. Senior/PG course

##### INTEGRATED CALCULUS

This is a one‐year course that is appropriate for students who have completed PreCalculus (Integrated Math III) or further coursework and are looking for a course to extend their mastery of algebraic concepts. The course begins with an integrated review of sequences and series, polynomial, exponential, logarithmic and rational functions, triangle trigonometry, and analytic trigonometry. It continues with the study of differential and integral calculus and the applications of these concepts to analysis of curves on the coordinate plane and the position, velocity, and acceleration of objects in motion. Technology will be utilized throughout the course, with an emphasis placed on identifying when and how to use calculators to develop and justify solutions. Student assessment includes chapter tests and quizzes, which require well‐developed problem‐ solving ability, integrated critical thinking skills, and the ability to write and reflect on solutions or approaches. The TI‐Nspire graphing calculator app or handheld is required. Junior‐PG course

##### AP CALCULUS AB

This is a fast paced, college level course in single variable calculus. The primary objective is to prepare students to do well on the AP exam and in their future math courses. Calculus is explored through the interpretation of graphs and tables as well as analytic methods. The primary topics are limits, derivatives and integrals. The TI‐Nspire graphing calculator is used extensively as students learn to work with functions presented numerically, algebraically and graphically and to discuss the connections among these representations. Students are expected to contribute to class discussions and group work and to complete homework daily. Take home quizzes based on prior years’ AP test questions will be assigned periodically. Chapter tests are generally given weekly. Several weeks, beginning in April, are devoted to review and preparation for the AP examination. After the AP exam, students complete and present a project which investigates an advanced topic of their choice. The TI‐Nspire graphing calculator app or handheld is required. Junior‐PG course

##### IB MATH STUDIES 1

IB Math Studies 1 is the first year of a two‐ year course designed for students with varied backgrounds and abilities in mathematics. In the first year, students begin by studying number properties, number sets and methods for measurement and approximation. Students go on to develop a deeper understanding of linear, quadratic, exponential and polynomial functions and how these can be used to model algebraic word problems. Students master the use of trigonometric ratios and analysis of trigonometric functions needed for the future study of calculus. In addition, students review methods for displaying data and learn more advanced statistics for the analysis of data. Students are expected to analyze problems using the appropriate notation, terminology, techniques, and graphical representations. Students should also expect to use graphing calculators on a daily basis. Students are required to maintain a well‐ organized binder, complete daily homework assignments, and are assessed through periodic quizzes and tests at the end of each unit. The TI‐Nspire non‐CAS graphing calculator app or handheld is required. Junior course

##### IB MATH STUDIES 2

IB Math Studies 2 is the second year of a two‐ year IB course. In the second year, students review functions, including quadratic and exponential functions, sequences and series, financial math, probability, and introductory statistics. They also study more advanced statistics, and are introduced to calculus. Students are expected to analyze problems using the appropriate notation, terminology, techniques and graphical representations. Students are required to complete homework on a daily basis and are assessed through periodic tests and quizzes. In addition, students are required to complete a project that demonstrates an understanding of the practical applications of mathematics. The project requires students to organize and present information and data in tabular or graphical form and is the culmination of the statistics portion of the course. In late spring, students sit for the IB examination, which consists of two written papers given over two days. The TI‐Nspire non‐CAS graphing calculator app or handheld is required. Senior course

##### IB MATH SL 1

IB Math SL 1 is the first year of a two‐year course. The first year covers a wide range of topics including number sets, function analysis, sequences and series, exponential and logarithmic functions, probability, descriptive statistics, two‐ variable statistics, triangle trigonometry and analytic trigonometry. Technology will be fully utilized throughout the course including use of graphing calculators for function and statistical analysis. Students learn to set up and solve complex word problems and to describe their methods in writing. Student assessment includes chapter tests and quizzes, which require well‐ developed problem‐solving ability and integrated critical thinking skills. The TI‐Nspire non‐CAS graphing calculator app or handheld is required. Junior course

##### IB MATH SL 2

This course completes the IB Standard Level Mathematics curriculum, including the study of differential and integral calculus, applications of calculus, vectors and probability distributions, as well as a comprehensive and integrated review of the material from year one. To satisfy the Internal Assessment component of the IB curriculum, students will complete an in‐depth mathematical exploration on a topic of their choice. The exploration allows students to work without the time constraints of a written 15 examination and to develop the skills they need for communicating their mathematical ideas. Student assessment includes chapter tests and quizzes, which require well‐developed problem‐ solving ability and critical thinking skills. In late spring, students sit for the IB examination, which consists of two written papers given over two days. The TI‐Nspire non‐CAS graphing calculator app or handheld is required. Senior course

##### IB MATH HL 1

IB Math HL 1 is a rigorous, fast‐paced course that begins with a comprehensive review of traditional PreCalculus topics, including exponential, logarithmic, and rational functions, sequences and series, and analytical trigonometry through an integrated problem‐solving lens. The course then moves on to the study of complex numbers and a comprehensive treatment of limits, derivatives, integrals, and applications of differential calculus. The year concludes with the study of vectors. The primary objective is to prepare students to do well on the end‐of‐course exam after two years. A graphing calculator is used extensively as students learn to work with functions presented numerically, algebraically, and graphically and see the connections among these representations. Students are expected to contribute to class discussions and group work, complete homework daily, and are assessed regularly through cumulative quizzes and tests. The TI‐Nspire non‐CAS graphing calculator app or handheld is required. Junior course

##### IB MATH HL2

In the second year of this course, offered senior year, students finish their study of the topics of the IB Higher Level curriculum, complete their internal assessment, and review for the IB examination which is cumulative on two years’ worth of material. The topics studied are further integration techniques, sequences and series (from the calculus option for the course), complex numbers, matrices, vector geometry in two and three dimensions, and introductory statistics and probability. The connections between these new areas of study and the calculus studied junior year are explored. The TI‐Nspire (non‐CAS) graphing calculator is used extensively. Students will tackle examinations from previous years and use these as a basis for review of the topics of the course. Grading is based on homework, tests and quizzes, and the internal assessment which involves an open‐ended investigation into an advanced topic of a student’s choice. The internal assessment is graded by the classroom teacher and samples are sent to IB for moderation. In late spring, students sit for the IB examination, which consists of three written papers given over two or three days. The TI‐Nspire non‐CAS graphing calculator app or handheld is required. Senior course

##### CODING

This semester course is an introduction to the exciting, rapidly growing world of coding and aims to teach structured program logic. Students will understand the role computation can play in solving problems. They will learn the process of writing and debugging a program through algorithms and simulation. Good style and logical thinking will be emphasized throughout the semester. A laptop computer is required. Algebra 1 is a prerequisite. Freshman-PG course

##### WEB DESIGN

This semester class is intended for students who want to learn about creating websites. Students learn how to create HTML documents, format text, add graphics and multimedia to web pages. Students will use open source internet resources to create, design, implement and manage websites. A laptop computer is required. Freshman-PG course

##### BIG DATA

What do Google and Amazon do with all the data they collect every day? Data Science is booming. Learn some of the tools that data scientists use to get value from huge amounts of data. You’ll do your own research on data of interest and create your own statistics using software such as Stata, R, and SQL. A unit of this semester class will also focus on managing data with Excel. A laptop is required. Algebra 1 is a prerequisite. Freshman-PG course

##### IB COMPUTER SCIENCE SL 1

(Co-seated with Java and Program Design) This two year course teaches computing system fundamentals, program construction using Java, systems life cycles and software development. Students will understand the use of computers in a variety of disciplines, learn methods to analyze problems and plan computer solutions, appreciate the technical and social consequences of developments in technology and acquire skills which can be transferred to future problems. The development of solutions lies at the heart of the subject. A laptop is required. Junior course

##### IB COMPUTER SCIENCE SL 2

This is the second year of a two-year course that teaches computing system fundamentals, program construction using Java, systems life cycles and software development. Students will understand the use of computers in a variety of disciplines, learn methods to analyze problems and plan computer solutions, appreciate the technical and social consequences of developments in technology, and acquire skills which can be transferred to future problems. The development of solutions lies at the heart of the subject. A laptop is required. Senior course

##### JAVA AND PROGRAM DESIGN

(Co-seated with IB Computer Science SL 1) This full-year course teaches computing system fundamentals, program construction using Java, systems life cycles and software development. Students will understand the use of computers in a variety of disciplines, learn methods to analyze problems and plan computer solutions, appreciate the technical and social consequences of developments in technology and acquire skills which can be transferred to future problems. The development of solutions lies at the heart of the subject. A laptop is required. Although not required, it is recommended that freshmen and sophomores take the Coding semester class first if they intend to enroll in this course in the future. Junior-PG course.

### Math Department Faculty

#### Rachel Wright

Math Department Chair, Advising Co-Coordinator

#### Daniel Casella

Math Teacher

#### Sue Eident

Dean of Academics and Math Teacher

#### Nathaniel Gartner

Math Teacher

#### Nicholas Joaquin

Computer Science Teacher

#### Thomas Marshall

Math Teacher

#### Andrew McBreen

Math Teacher, 11,12 & PG Dean, and Coordinator of Citizenship Committee

#### Melanie Dexter Morlath

Math Teacher

#### Michael Ropke

Math Teacher