Mathematics

(2) Semester Course  2.5 credits/semester

Open to:  Grade 9 

Prerequisites:  Grade 8 teacher recommendation

This course is designed to support the needs of students who benefit from a individualized environment or have foundational gaps in their knowledge base. It is structured to meet individual needs in terms of pacing, rigor, and scope. Ample scaffolding of topics and review will be incorporated to support mastery of the course content. Students will benefit from frequent and varied instruction/assessment so students will receive consistent feedback on their progress. Curriculum will focus on the same big ideas with reduced depth and complexity as College Prep Algebra I. In this course, students will: 1) Solve one variable equations, systems, and inequalities; (2) Examine linear, exponential, and quadratic functions graphically and algebraically (3) Perform operations on polynomials, including addition, subtraction, multiplication, and factoring; (4) Graph and analyze the graphs of linear, exponential, and quadratic functions and (5) Extend their understanding of the laws of exponents and apply them to simplify problems.

The course objectives are taught each year according to each student’s instructional level.

Curriculum Units and Learning Outcomes:

Pre-Algebra and Solving One Variable Equations
Solve Advanced One Variable Equations and Graphing Lines
Solving Systems of Equations
Solving and Graphing Inequalities and Special Equations
Exponential Expressions and Functions
Polynomials and Factoring
Graphing Parabolas and Solving Quadratic Equations
Functions
Statistics

(2) Semester Course  2.5 credits/semester

Open to:  Grade 9 

Prerequisites:  Grade 8 Math or Honors Grade 8 Math / teacher recommendation

The main areas of concentration of College Prep Algebra I are to 1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend.   Students will also summarize, interpret and represent one or two variable data distribution. All topics will be covered with rigor to ensure mathematical success at the college level. College prep students will benefit from frequent and varied instruction and assessment so students will receive consistent feedback on their progress. High expectations are coupled with many vehicles for success to ensure all students can reach their potential. Honors Algebra I students should possess a strong and consistent work ethic as well as an ability to learn independently. While some review of prerequisite topics will occur, the class depth and challenge of the class content requires students enter the course with a firm mathematical foundation from middle school.

(CP) Curriculum Units and Learning Outcomes:

Evaluate Expressions, Solve Equations, Graph Linear Equations
Write linear equations, solve and graph inequalities
Solving Linear Systems, Graphing Piecewise Functions
Exponents and Exponential Functions
Polynomials and Factoring
Functions
Quadratics, Graphing and Solving
Statistics

(Honors) Curriculum Units and Learning Outcomes:

Prerequisite Review/ Linear Functions
Inequalities
Linear Systems
Exponents and Exponential Functions
Polynomials and Methods of Factoring
Advanced Factoring, Quadratic Graphing, and Linear Regression
Solving Quadratics
Topics in Statistics

(2) Semester Course 2.5 credits/semester

Open to:  Grade 9 

Prerequisites:  H Algebra I / teacher recommendation

The main areas of concentration of Honors Accelerated Algebra I are to 1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend.   Students will also summarize, interpret and represent one or two variable data distribution. In addition, students simplify and solve rational expressions and equations using various operations. Lastly, students will explore some of the important aspects of functions that they will further develop in Algebra II including but not limited to composition, inverse, and operations.

It is important to understand that Accelerated Algebra I requires not only solid mathematical prerequisite skills, but also a strong and consistent work ethic. Mastery of all middle school math topics is necessary for success because in place of review and remediation are the extra topics covered necessary for Calculus preparation.

Curriculum Units and Learning Outcomes:

Evaluate Expressions, Solve Equations, Graph Linear Equations
Write linear equations, solving and graphing inequalities, systems of equations
Linear Programming and Rules of Exponents
Polynomials
Quadratics
Radicals and Rationals
Statistics

2) Semester Course  2.5 credits/semester

Open to:  Grade 10

Prerequisites:  9th grade teacher recommendation

This course is designed to support the needs of students who benefit from a more supported environment or have foundational gaps in their knowledge base. Students are expected to take notes, create study guides, build models and use manipulatives that can be utilized during assessments.  Curriculum will focus on the same big ideas with reduced depth and complexity as College Prep Geometry. In addition, there will be an emphasis on MCAS prep throughout the year. Exams, pacing, and instruction are adapted and modified to meet the needs of the students in the class. In this course, students will cover topics of congruence, transformations, similarity, constructions, algebraic proofs, modeling, classifications of polygons, introductory trigonometry, measurement (area, volume distance, etc.), and probability.

The course objectives are taught each year according to each student’s instructional level.

Curriculum Units and Learning Outcomes:

Points, Lines, Planes and Angles
Logic and Reasoning
Parallel / Perpendicular Lines and an Introduction to Triangles
Congruent Triangles
Similarity
Right Triangles and Trigonometry
Circles and Area and Volume of Two / Three Dimensional Figures

(2) Semester Course 2.5 credits/semester

Open to:  Grade 10 

Prerequisites:  Algebra I, Teacher Recommendation

The fundamental purpose of the high school Geometry is to formalize and extend students’ geometric experiences in the areas of congruence, transformations, similarity, constructions, theorem and algebraic proofs, circle theory and application, coordinate geometry, modeling, introduction trigonometry, measurement, and probability. Upon completion of this course, the student will be able to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; and apply transformations to analyze mathematical situations; use visualization, spatial reasoning, and geometric modeling to solve problems; understand measurable attributes of objects and the units, systems, and processes of measurement; and apply appropriate techniques, tools, and formulas to determine measurements.

Honors Geometry will include the derivation and application of trigonometric formulas and employ much algebra to solve geometric problems. Note: Geometry and Algebra II may be taken concurrently.

Curriculum Units and Learning Outcomes:

Tools of Geometry and Logic and Reasoning
Parallel and Perpendicular Lines andCongruent Triangles
Special Segments in Triangles
Quadrilaterals; Ratio and Proportions and Similarity; Probabilty and Measurement
Right Triangles and Trigonometry
Transformations and Circles
Extending Surface Area and Volume and Areas of Polygons

(2) Semester Course 2.5 credits/semester

Open to:  Grade 9 or 10 

Prerequisites:  Algebra I / teacher recommendation

The fundamental purpose of the high school Geometry is to formalize and extend students’ geometric experiences in the areas of congruence, transformations, similarity, constructions, theorem and algebraic proofs, circle theory and application, coordinate geometry, modeling, introduction trigonometry, measurement, and probability. Upon completion of this course, the student will be able to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; and apply transformations to analyze mathematical situations; use visualization, spatial reasoning, and geometric modeling to solve problems; understand measurable attributes of objects and the units, systems, and processes of measurement; and apply appropriate techniques, tools, and formulas to determine measurements.

Honors Geometry will include the derivation and application of trigonometric formulas and employ much algebra to solve geometric problems. Honors Geometry students require a mastery of Algebra I content (including quadratics). Students in honors should also be able to work independently and solve rigorous problems.

Note: Geometry and Algebra II may be taken concurrently.

Curriculum Units and Learning Outcomes:

Tools of Geometry and Logic and Reasoning
Parallel/Perpendicular Lines and Congruent Triangles
Proportions/Similarity and Probabilty
Right Triangles, Trigonometry and Areas of Polygons
Transformations and Circles
Extending Surface Area and Volume

(2) Semester Course  2.5 credits/semester

Open to:  Grades 9-10 

Prerequisites:  Grade 9 Accelerated Algebra I or Grade 8 Advanced Algebra / teacher recommendation

Accelerated Honors Geometry focuses on six critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability. A rigorous study of triangle trigonometry, evaluating with the unit circle, conic sections, introduction to graphing sinusoids, and an in-depth study of circles and their properties are explored. It is important to understand that Accelerated Geometry requires not only solid mathematical prerequisite skills, but also a strong and consistent work ethic. Self-motivation and the ability to work independently are also required.

Note: Geometry and Algebra II may be taken concurrently.

Curriculum Units and Learning Outcomes:

Points, Lines and Planes, Logic, and Parallel Lines
Triangles and their Relationships
Quadrilaterals/Polygons and Proportions/Similarity
Probability
Right Triangle Trigonometry and Transformational Geometry
Circles and Conic Sections
3D Solids and Intro to PreCalculus

(2) Semester Course  2.5 credits/semester

Open to:   Grade 11

Prerequisites: 10th  grade teacher recommendation

This course is designed to support the needs of students who benefit from a more supported environment or have foundational gaps in their knowledge base. Students will receive more in-class time spent on instruction and student practice for various topics, a significantly smaller class size and access to a lead teacher and support staff during class.   Curriculum will focus on the same big ideas with reduced depth and complexity as College Prep Algebra II. Students will have more frequent formative assessment feedback opportunities than college preparatory level. Students will demonstrate their understanding of curriculum taught on assessments with support of their own graphing calculator (or class notes, as applicable) and test items are scaffolded when multiple understandings are required within the same question (for example, separating one question into two or more questions each assessing only one or two discrete skills).  In this course, students will: (1) investigate and understand the characteristics of quadratic graphics; (2) use various methods for solving quadratics; (3) simplify exponential expressions and (4) perform operations on, as well as graph, polynomials and rational functions.

The course objectives are taught each year according to each student’s instructional level.

Curriculum Units and Learning Outcomes:

Solve One Variable Equations
Functions, Quadratic Functions, Exponential Functions
Matrices
Quadratic Equations, Quadratic Formula, Complex Numbers
Polynomials, Zeros, Complex Numbers
Right Triangle Trigonometry
Composition of Functions, Inverse Functions
Logarithm and Exponential Functions

(2) Semester Course  2.5 credits/semester

Open to:  Grade 11 

Prerequisites:  Algebra I / teacher recommendation  

In second year course, students will explore algebra in symbolic and graphical contexts. Upon completion of this course, the student will investigate and understand the characteristics of quadratic graphics and use various methods for solving quadratics.hey will simplify exponential expressions and perform operations on, as well as graph, polynomials functions.  Right triangle trigonometry, as well as, exponential and logarithmic functions are also discussed. Students will understand meanings of operations and how they relate to one another; compute fluently and make reasonable estimates; understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships and organize and display relevant data.  Honors Algebra will also include topics in piecewise and composite functions; series and simplifying rational expressions.

Note: Geometry and Algebra II may be taken concurrently.

(CP) Curriculum Units and Learning Outcomes:

Right Triangle Trigonometry
Relations and Family of Functions
Polynomials and Graphing Quadratics
Radicals
Solving Quadratics and Factoring
Exponential and Inverse Functions
Logarithms
Directed Angles

(Honors) Curriculum Units and Learning Outcomes:

Quadratic Functions
Relations and Functions
Polynomials
Rational Exponents
Exponential and Logarithmic Funcitons
Rational Functions

(2) Semester Course 2.5 credits/semester

Open to:  Grades 10-11 

Prerequisites:  Accelerated Geometry / teacher recommendation  

This course extends the completed content in Accelerated Geometry and Algebra I by deepening students’ understanding polynomial, rational/radical, exponential, logarithmic, trigonometric, and composite functions using a graphic and symbolic approach. Students will further their study of trigonometry to include identities, inverses and equations. In addition, matrices, piecewise functions, and the complex number system operations, and limits are explored.

It is important to note that all topics traditionally covered in precalculus will be covered in Accelerated Algebra II ensuring students are prepared for Calculus following this course.

Curriculum Units and Learning Outcomes:

Rate of Change, Functions, Matrices, and Systems
Quadratics, Polynomials, Radicals, and Rationals
Exponentials, Logarithms, and Limits
Right Triangle Trigonometry
Trigonometric Identities

(2) Semester Course

Open to:  Grade 11-12 2.5 credits/semester

Prerequisites:  Algebra II and Geometry / teacher recommendation

This advanced course will thoroughly cover functions and trigonometry in preparing students for future studies in calculus. This course is approached from both graphic and symbolic perspectives. The student will explore polynomial, rational, exponential, logarithmic, and trigonometric functions in great depth. This course requires that students compute fluently, work independently, have mastered prerequisite algebra skills and are well-versed in efficient use of graphic calculators.  

(CP) Curriculum Units and Learning Outcomes:

Applications of Trigonometry
Intro to Trigonometry Vocabulary
Circular Trigonometry
Sinusoidal Models
Analytic Trigonometry
Polynomial and Rational Functions
Exponential and Logarithmic Functions
Matrices

(Honors) Curriculum Units and Learning Outcomes:

Trigonometric Functions and Vectors
Trigonometric Graphs
Trigonometric Identitites
Trigonometric Equations
Polar and Parametric
Rational Functions
Advanced Functions
Rational Exponents and Radical Functions
Exponential and Logarithmic Functions
Conics (Time Permitting)
Sequence, Series, Probability (time permitting)
Limits, Intro to Calculus

(2) Semester Course  2.5 credits/semester

Open to:  Grade 12 

Prerequisites:  Algebra I / teacher recommendation

This course is designed to support the needs of students who benefit from a more supported environment or have foundational gaps in their knowledge base. Students will receive more in-class time spent on instruction and student practice for various topics, a significantly smaller class size and access to a lead teacher and support staff during class. This course is intended for grade 12 students. Placement in this course is based on the recommendation of classroom teacher and guidance counselor. Students are required to participate in a combination of in-class activities and online, self-paced studies. Class activities will include project-based and real-world applications.  

(2) Semester Course 2.5 credits/semester

Open to:  Grade 12 

Prerequisites:  Algebra II and Geometry / teacher recommendation

This course is designed as a mathematics course alternative to pre-calculus. Throughout Quantitative Reasoning, students are encouraged to continue their study of mathematical ideas in the context of real-world problems and decision-making through the analysis of information, modeling change, and mathematical relationships. Topics include analysis of quantitative data, modeling with a variety of functions, applying concepts of vectors and matrices, advanced algebra, and applications of trigonometry.

Curriculum Units and Learning Outcomes:

Fractions
Matrices
Geometry
Right Triangle Trig
Rational Functions
Vectors
Statistics

2) Semester Course 2.5 credits/semester

Open to:  Grade 12

Prerequisites:  Acc. Algebra II or H Algebra II & H Pre-Calculus recommended  / teacher recommendation

Key topics in this course include: analysis of graphs, limits of functions, asymptotic and unbounded behavior, continuity, the concept of a derivative, the derivative at a point, the derivative as a function, second derivatives, applications of derivatives, and the computation of derivatives, interpretations and properties of definite integrals, applications of integrals, the Fundamental Theorem of Calculus, techniques of antidifferentiation, applications of antidifferentiation, and numerical approximations to definite integrals.  Honor Calculus is intended for those students who will take calculus in college. Students enrolled in Honors Calculus show interest in algebra-based mathematics and have mastered simplifying algebraic expressions, factoring, and graphing polynomial, rational and trigonometric functions.

Students are expected to work questions involving basic trigonometry, factoring and graphing without having to rely on the assistance of a graphing calculator.

Curriculum Units and Learning Outcomes:

Prerequisites and Limits
Derivative Concept, Rules and Introductory Applications
Advanced Derivatives / Applications of a Derivative
Optimization
The Antiderivative and Basics of Integration
Methods of Integration
Topics in Calculus

(2) Semester Course 2.5 credits/semester

Open to:  Grades 11-12 

Prerequisites:  Acc. Algebra II / teacher recommendation

This course will prepare students to take the Advanced Placement Calculus AB Examination in May, which may allow them to be awarded credit or a course waiver in college.  The material covered in this course is the Calculus AB curriculum published by The College Board. The basic ideas of differential and integral calculus are developed. Work is assigned for the student to do during the summer before taking the course.

Curriculum Units and Learning Outcomes:

We follow the AP College Board curriculum

(2) Semester Course  2.5 credits/semester

Open to:  Grade 11-12 

Prerequisites:  AP Calculus AB / teacher recommendation

This high-level course will prepare students to take the Advanced Placement Calculus BC Examination in May, which may allow them to be awarded credit or a course waiver in college.   The material covered in this course is the Calculus BC curriculum published by The College Board. It is more extensive than the AB course. The student contemplating a career in engineering or mathematics will find this course an essential preparation. The basic ideas of differential and integral calculus will be developed. Work is assigned for the student to do during the summer before taking the course.

Curriculum Units and Learning Outcomes:

We follow the AP College Board curriculum

(2) Semester Course  2.5 credits/semester

Open to:  Grades 11-12 

Prerequisites:  Algebra II / teacher recommendation

The purpose of this statistics courses is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. In this full year course, students learn to organize data,  interpret data, study elementary probability theory, and use random variables with binomial, normal, and standard distributions. The student later concentrates on inferential statistics. The student learns sampling principles and how to apply various tests to determine validity of the samples and implications to the entire population. Hypothesis testing, including t-tests, chi-square tests, and analysis of variance will also be covered. The course concludes with a section on nonparametric statistics.

Curriculum Units and Learning Outcomes:

We follow the AP College Board curriculum

(2) Semester Course 2.5 credits/semester

Open to: Grades 9-12 

Prerequisites: Teacher recommendation

The general math curriculum enables students to develop skills and work toward progression of their math skills. The course objectives are taught each year according to each student’s instructional level.

(2) Semester Course 2.5 credits/semester

Open to:  Foundational ELs and SLIFE 

Prerequisites:  None

ELE Math is designed to provide the language of the content area of mathematics to foundational and SLIFE students in the English Learner Education program.  Through this course, students will work toward progression of their English language and literacy proficiencies in the domains of listening, speaking, reading, and writing within the mathematics content area.  Advancement in usage of linguistic complexity, language conventions, and academic vocabulary will be the focus of this course for English learners.

Content for this course is based on WIDA standards and tailored to the needs of the students who are assigned.

* EL = English Learner            *SLIFE = Students with Limited or Interrupted Formal Education

Semester Course
Open to:  Grades 11-12
2.5 credits
Prerequisites:  Algebra II 

In this course, students are introduced to the cornerstones of mathematical modeling: problem identification / formulation/ investigation, development and refinement of  model, experimentation, and interpretation of results. This course fosters both logical and creative thinking through a project-based curriculum. Projects are chosen based on student interests.

Semester Course
Open to:  Grades 11-12
2.5 credits
Prerequisites:  Algebra II 

Sports analysis immerses students in the analysis of sports through a mathematical lens. Students will use their statistical toolbox to examine sports performance, records, and strategy. Contemporary methods of data organization and sorting will be employed to teach students computational efficiency. This course focuses on math application and inquiry. Students will engage in project based learning based on their interests.

Two Semester Course
Open to:  Grade 12
2.5 credits per semester
Prerequisites:  Algebra I / teacher recommendation

In this course, students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  Students learn methods for gathering and summarizing data, computing measures of central tendency and variation, and making inferences about a population. Students also study elementary probability theory and use random variables with binomial and normal distributions.  At the end of the semester, students design, implement, and present a statistically-based research project. 

This second part of this course will concentrate on inferential statistics.  The student will learn sampling principles and how to apply various tests to determine validity of the samples and implications to the entire population.  Hypothesis testing, including t-tests, chi-square tests, and analysis of variance will also be covered.  The course will conclude with a section on nonparametric statistics.