Math

The sequences listed above provide options for students at each grade level. Math instruction and coursework have been created to allow for flexibility between levels. The math department encourages all students to challenge themselves with rigorous courses, and will provide support as needed. Prior to moving levels, students are advised to have discussions with teachers, guidance counselors, and families, as well as examining their entire schedule.

There are opportunities to “double up” on math courses at certain points in the curriculum.  However, due to the cumulative nature of mathematics, these opportunities are limited by the need for specific prerequisite skills before enrolling in certain courses.

The following criteria must be met in order for a student to take two math courses simultaneously:

• The student must have a teacher recommendation and department head approval before enrolling in two math courses.

• Taking two math courses simultaneously should not be coupled with a level change, as taking two courses at the same time is a challenge unto itself.

The Mathematics curriculum is based on the Massachusetts Mathematics Curriculum Framework and attempts to provide learning experiences for all students consistent with their academic abilities, needs, and aspirations. The program offered by the Mathematics Department reflects an awareness that we live in a complex age in which mathematics plays an increasingly important role for society and the individual alike. The intent of the curriculum is to present mathematics as a useful, exciting, and creative area of study that can be appreciated, enjoyed, and mastered by all students. Particular emphasis is placed on understanding mathematics with the goal of preparing students to adapt in a continuously changing, technical world. Students will be challenged to achieve mathematical power through critical thinking, problem solving, communicating mathematically, reasoning, and making connections.

CORE CURRICULUM

ALGEBRA I HONORS

Year Course 5 credits

Prerequisite: Above Level Grade 8 Math; grade of B or above Open to: Fr.

Grade 8 Math; grade A 

This course is the first in a three-year sequence of courses that prepares students for AP Calculus in their senior year. Instructional time will focus on the following critical areas: deepening and extending understanding of linear and exponential relationships; solving systems of linear equations and inequalities; contrasting linear and exponential relationships with each other and engaging in methods for analyzing, solving, and using quadratic functions; applying linear models to data that exhibit a linear trend. Concepts will be explored in greater depth and extended to include the study of additional topics such as multi-variable and non-linear systems of equations, complex numbers, radical equations, and inverse functions.

ALGEBRA I CP

Year Course 5 credits

Prerequisite: Open to: Fr.

This course formalizes and extends the mathematics that students learned in the middle grades. Instructional time will focus on the following critical areas: deepening and extending understanding of linear and exponential relationships; solving systems of linear equations and inequalities; contrasting linear and exponential relationships with each other and engaging in methods for analyzing, solving, and using quadratic functions; applying linear models to data that exhibit a linear trend. Other topics to be studied include sequences, piecewise-defined functions, rational exponents, and statistical data displays.  

ELE ALGEBRA I

Year Course 5 credits

Open to: Foundational MLs in the ELE Program

ELE Algebra I is designed to provide the language and content of Algebra I to foundational students in the ELE (English Language Education) program. Through this course, students will work toward the progression of their interpretive and expressive English language and literacy proficiencies within the Algebra I content area. Advancement in the use of linguistic complexity, language conventions, and academic vocabulary in English through the Algebra I content will be the focus of this course.

GEOMETRY HONORS

Year Course 5 credits

Prerequisite: Algebra Honors; grade B or above, Open to: So

Algebra I CP1; grade of A

This course is the second in a three-year sequence of courses that prepares students for AP Calculus in their senior year.  Instructional time will focus on the following critical areas: establishing criteria for congruence of triangles based on rigid motions; establishing criteria for similarity of triangles based on dilations and proportional reasoning; developing explanations of circumference, area, and volume formulas; applying the Pythagorean Theorem in the coordinate plane; proving basic geometric theorems.  Other topics to be studied include right triangle trigonometry and working with conditional and compound probability.  Concepts will be explored in greater depth and extended to include the study of additional topics such as the Laws of Sines and Cosines and their various applications.

GEOMETRY CP1

Year Course 5 credits

Prerequisite: Algebra I CP1 Open to: So.

This course is designed to develop good habits for valid deductive and inductive reasoning through the study of the size, shape and position of figures, their measurements and relationships. Instructional time will focus on the following critical areas: establishing criteria for congruence of triangles based on rigid motions; establishing criteria for similarity of triangles based on dilations and proportional reasoning; developing explanations of circumference, area, and volume formulas; applying the Pythagorean Theorem in the coordinate plane; proving basic geometric theorems.  Other topics to be studied include right triangle trigonometry and working with conditional and compound probability.  Concepts will be explored in greater depth and may be extended to include the study of additional topics.

ALGEBRA II/PRECALCULUS HONORS

Year Course 5 credits
Prerequisite: Geometry Honors, grade of B or above Open to: Jr.
or Geometry CP1; grade of A

This course is the third in a three-year sequence of courses that prepares students for AP Calculus in their senior year.  Instructional time will focus on the following critical areas: relating the arithmetic of polynomial and rational expressions to the arithmetic of rational numbers; expanding understanding of functions and graphing to include trigonometric functions; synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions.  Other topics to be studied include data displays and summary statistics, probability, and data collection methods.  Concepts will be explored in greater depth and extended to include the study of additional topics such as binomial expansion, graphs of rational functions, exposures to limits, and solving trigonometric identities. .

ALGEBRA II CP1

Year Course       5 credits

Prerequisite: Geometry CP1 grade of C or above                                             Open to: Jr.

or Geometry CP2; grade of A

This course builds on the work done in Algebra I and extends the repertoire of functions to include logarithmic, polynomial, rational, radical, and trigonometric functions.  Instructional time will focus on the following critical areas: relating the arithmetic of polynomial and rational expressions to the arithmetic of rational numbers; expanding understanding of functions and graphing to include trigonometric functions; synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions.  Other topics to be studied include data displays and summary statistics, probability, and data collection methods.  Concepts will be explored in greater depth and extended to include the study of additional topics; such as, graphs of rational functions and trigonometric equations.

ALGEBRA II CP2

Year Course 5 credits
Prerequisite: Geometry CP2 Open to: Jr.

This course builds on the work done in Algebra I and extends the repertoire of functions to include logarithmic, polynomial, rational, radical, and trigonometric functions.   Instructional time will focus on the following critical areas: relating the arithmetic of polynomial and rational expressions to the arithmetic of rational numbers; expanding understanding of functions and graphing to include trigonometric functions; synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions.  Other topics to be studied include data displays and summary statistics, probability, and data collection methods.

 MATH ELECTIVES

DISCRETE MATH CP2

Year Course 

5 credits

Prerequisite: Algebra II CP2 

Open to: Sr. 

Discrete mathematics requires problem-solving strategies be applied to real-world application, develops verbal and written skills in the process of problem-solving, and promotes mathematical connections across disciplines. Course content includes but is not limited to management science, probability and counting techniques, voting and social choice, fairness and game theory, identification numbers and information science, and number theory.

CALCULUS HONORS

Year Course 5 credits

Prerequisite: Algebra II Honors, grade of B or above Open to: Sr.

Calculus Honors is a challenging course provided for students who have shown above average ability and motivation in mathematics. The focus is on developing an understanding of the concepts of calculus and providing practice with its methods and applications. Graphing calculators are used regularly to explore and to assist in interpreting results. The main topics of the course include limits, rates of change, derivatives, graphical analysis, and applications of the derivative, and integration.

STATISTICS HONORS

Year Course 

5 credits

Prerequisite: Geometry HR; grade of B or above, co-requisite: 

Algebra II             

Open to: Sr.

Algebra II Honors, grade of B or above,

• Or Geometry CP1; grade of A, co-requisite: Algebra II

• or Algebra II CP1; grade of A

This course is recommended for seniors who are thinking about careers in business, the sciences, or social sciences.  The course will move at a faster pace and will expect more independent learning than Statistics CP1. Topics to be studied include, but are not limited to, descriptive statistics, correlation and linear regression, data collection and analysis, experimental design, normal distributions, probability and inferential statistics including confidence intervals and significance tests.  A TI-83 or TI-84 calculator is required for the class.

STATISTICS CP1

Year Course 5 credits

Prerequisite: Algebra II CP1; grade of C or above Open to: Sr. 

or Algebra II CP2; Grade of A

This course is recommended for seniors who are thinking about careers in business, the sciences, or social sciences. Topics to be studied include, but are not limited to, descriptive statistics, correlation and linear regression, data collection and analysis, experimental design, normal distributions, probability and inferential statistics including confidence intervals and significance tests.

STATISTICS CP2

Year Course 5 credits

Prerequisite: Algebra II CP2 Open to: Sr.

This is an introductory course in statistics. Topics to be studied include, but are not limited to, data exploration, correlation and linear regression, probability and random behavior, sampling distributions, estimating and bias, modeling, and normal distributions.

SAT MATH

Semester Course 2.5 credits

Prerequisite: Geometry (or taken concurrently) Open to: So. (2nd semester), Jr..

The SAT Math course is designed to help students prepare for the rigors of taking the SAT tests offered by the College Board.  The primary goal is to identify and implement test taking strategies using prerequisite knowledge. Emphasis will be placed on strengthening knowledge of essential math topics specific to the SAT in order to improve student performance.  Students are expected to register for the SAT prior to the conclusion of the course.

STATISTICS AND MATHEMATICS OF FINANCE CP

Semester  Course 5 credits

Prerequisite: Completion of Algebra 2                Open to: Seniors in Work Study Program                                 

This course is designed for students in the Work Study program. It contains an online introductory Statistics component that includes data exploration, correlation and regression, probability and normal distributions, and sampling and bias. Students can work on this during the summer. The Mathematics of Finance component focuses on applying mathematical concepts to personal finance applications. Various functions, including linear and exponential, will be used to investigate credit, banking, investments, and other topics. Technology, including spreadsheets, will be used to supplement the curriculum. 

AP MATH COURSES

AP CALCULUS AB

Year Course 5 credits

Prerequisite: Algebra II Honors; grade of B or above Open to: Sr.

This course closely parallels a freshman college course. The focus is on understanding 

calculus  concepts. A multi-representational approach is emphasized. Concepts, results, and problems  will be expressed geometrically, numerically, analytically and verbally.  A TI-84 calculator is required for this course, as it will be used regularly to reinforce the relationships among the multiple representations of  functions, to confirm written results, and to explore and assist in interpreting results. The  themes of the course include derivatives, integrals, limits, approximation, and applications. All  students taking this course must take the AP exam. Failure to take the exam will result in  removal from the AP course.

AP CALCULUS BC

Year Course 5 credits

Prerequisite: Algebra II H; Teacher Recommendation Required Open to: Sr. 

This course addresses all of the concepts in Calculus AB and includes additional concepts not  addressed in the AB curriculum. These topics include Euler’s method, L’Hopital’s rule,  advanced integration techniques, improper integrals, logistic differential equations,  polynomial approximations and series. A thorough analysis of planar curves given in  parametric, polar, and vector forms is explored, including their derivatives. The course  moves at a significantly faster pace than Calculus AB and requires a high level of student  motivation and independence. A TI-84 calculator is required for this course.  Completion of a prerequisite summer assignment is  expected. All students taking this course must take the AP exam. Failure to take the exam  will result in removal from the AP course.

AP PRECALCULUS

Year Course 5 credits

Prerequisite:  Grade of B- in Algebra II CP1 or B+ in Algebra II CP2       Open.  to: Sr                                

This course is designed to prepare students for Calculus and other college level math and science courses.  Algebra II topics will be examined in greater detail, including polynomial, rational, exponential, logarithmic, and trigonometric functions. Transformations, composition, inverses, and rates of change of these functions will be covered. Polar functions will be examined, along with a brief look at parametric functions, conic sections, vectors, and matrices. Students will be asked to model and manipulate functions in various forms, including graphical, numerical, analytical, and verbal representations. A TI-84 calculator is required for this course.  All students taking this course must take the AP exam. Failure to take the exam will result in removal from the AP course. Students seeking to take this course concurrently with Calculus must receive Department Chair approval.

AP STATISTICS 

Year Course 

 5 credits

Prerequisite: Algebra I Honors, grade of B or above, co-requisite: Geometry Or Geometry Honors, grade of B or above, co-requisite: Algebra II Or Algebra II Honors, grade of B or above

Open to: So.,Jr., Sr.

The AP Statistics course introduces students to the major concepts and tools for formulating questions, collecting and analyzing data, and interpreting results from data. The practices and skills for the course have been aligned to help students understand the statistical problem solving process based on the American Statistical Association (ASA) recommendations. The content, skills, and assessments in the AP Statistics course focus on exploring data, sampling and experimentation, probability and simulation, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.