Mathematics

MATHEMATICS

The Mathematics Department has pledged itself to prepare each and every student with a background in mathematics commensurate with his/her ability which will aid the student in pursuing the career goal of his/her choice. To graduate from Canton High School, each student must pass three years of mathematics, in addition to the MCAS Mathematics Exam. There are multiple advanced placement courses and several electives are offered. Mathematics courses offered to students address and align with the Massachusetts Curriculum Framework standards.

• Expectations of students taking classes at the “College Prep” level (CP): Students in classes taught at the College Prep level are expected to attain proficiency in the Massachusetts Curriculum Frameworks.

• Expectations of students taking classes at the “Honors” level (H): Honors level courses explore the same mathematical topics as a CP level course with a significant emphasis on theoretical concepts. Students are expected to interface with a more rigorous curriculum in an honors-level course.

• Expectations of students taking classes at the “Advanced Honors” level (H) *: Advanced Honors level courses explore all of the same mathematical topics as an Honors level course in addition to higher-level and more abstract concepts. Students are expected to interface with a more rigorous curriculum than an honors-level course. Additionally, students are expected to work more independently and to go beyond the presented material. Students must be recommended to take an Advanced Honors course by an instructor.

* Advanced Honors Pre-Calculus BC is weighted at the AP level 

• Expectations of students taking classes at the “Advanced Placement” level (AP): Students in classes taught at the “Advanced Placement” level are expected to be able to interface with college-level material. Each Advanced Placement class follows the published course description and syllabus given by the College Board. Advanced Placement courses incorporate a blend of advanced problem-solving techniques and theoretical concepts. The theoretical concepts are discussed more thoroughly and more rigorously than in a class that is taught at the honors or college prep level. Students must take the advanced placement exam that accompanies each course in May of the school year. Any student enrolled in an Advanced Placement course will be required to complete outside work over the summer prior to the start of the school year. 

Course Name:  Algebra 1

Course # 220

Level CP     

Grade  9               

Credits 6

Students will increase their algebraic fluency and increase their mastery of solving linear and quadratic equations and inequalities. Other topics include simplification of expressions with polynomials, exponents, and radicals; factoring; use of linear and quadratic equations as mathematical models; solution of linear systems; analytical geometry of the straight line and parabola; functions. Since this course approaches mathematics from a graphical perspective, students are encouraged to use a graphing calculator in class.

Course Name: Geometry

Course # 221/212

Level CP/H

Grade 9-10

Credits 6

This course is designed to develop deductive and inductive reasoning processes as the students develop an analytic approach to geometric problem solving and introductory proof. Major topics include parallelism and perpendicularity, triangles, quadrilaterals, polygons, congruence, similarity, circles, area, volume, and surface area. Ongoing preparation for the MCAS test is included.

Course Name: Algebra 2

Course # 222/211

Level CP/H

Grade Level 9-12

Credits 6

The course covers topics beyond that covered in Algebra 1. The goal is to increase knowledge of algebra and mastery of problem-solving. There is a brief review of linear equations and functions, factoring, polynomial equations, rational expressions, and irrational numbers. The course continues with complex numbers, quadratic equations, direct and inverse variation, conic sections, exponential and logarithmic functions, and sequences and series.

Course Name: Pre-Calculus

Course # 223/213

Level CP/H

Grade Level 11-12

Credits 6

This course builds upon the skills and concepts gained over previous courses in Algebra and Geometry. Among the topics to be covered are polynomial functions, conic sections, exponential and logarithmic functions, trigonometry, analytic geometry, systems of equations, matrices, complex numbers, inequalities and absolute value, and graphing algebraic functions. Time permitting, additional topics such as vectors, sequences and series, polar coordinates, and probability will be studied. It is expected that students will provide a graphing calculator.

Course Name: Algebra/Geometry/Statistics

Course # 243

Level H

Grade Level 9-12

Credits 6

This course is designed to develop an understanding of how the branches of mathematics connect to each other. Students will learn to reason quantitatively, interpret mathematical expressions, create equations to describe relationships, and use the concept and notation of functions. They will examine linear and exponential functions using algebraic and graphical approaches, and use these function types for modeling and problem-solving. Students will solve linear equations and inequalities, as well as systems of equations. They will use descriptive statistics to summarize, represent, and interpret one-variable and two-variable data involving categorical or quantitative variables. Students will develop knowledge of transformations of the plane, use transformations to establish triangle congruence criteria, and use coordinate geometry. 

Course Name: Algebra 2/Geometry/Statistics

Course # 209

Level H

Grade Level 9-12

Credits 6

This course is designed to develop an understanding of how the branches of mathematics connect to each other. Students will examine functions of varied types, with an emphasis on quadratic functions and their use in modeling. They will develop skills in rewriting expressions, using exponent properties, and solving equations and inequalities. Students will understand the geometric concepts of congruence and similarity in terms of transformations. They will investigate geometry theorems about triangles, parallel lines, and circles, and prove them by writing deductive proofs and coordinate proofs. They will compute and interpret probabilities of compound events and conditional probabilities. 

Course Name: Algebra 2/Precalculus/Statistics

Course # 229

Level H

Grade Level 9-12

Credits 6

This course is designed to develop an understanding of how the branches of mathematics connect to each other. Students will expand their understanding of functions to include polynomial, exponential, logarithmic, and trigonometric functions. They will use trigonometric functions for general triangle solving, sinusoidal modeling, and other algebraic uses. They will extend their use of number systems to include complex numbers and make use of sequences and series. Students will apply methods from probability and statistics to draw inferences and conclusions from data. They will use functions and geometry to create and critique mathematical models and solve contextual problems.

ADVANCED HONORS COURSES

Course Name: Geometry Adv Honors

Course # 242

Level H

Grade Level 9

Credits 6

During the first semester topics that complete the honors geometry course, including introductory analytic geometry, are taught. Time permitting, investigations into transformations and non-Euclidean geometry are made. The second semester is devoted to a thorough study of all topics in trigonometry. Additional topics covered include complex numbers (in both algebraic and trigonometric form), sequences and series, and theory of equations.

Course Name: Algebra 2 Adv Honors

Course # 216

Level H

Grade Level 10

Credits 6

The concepts of sets and different number systems are reviewed. Elementary number theory is investigated. During the first semester, topics covered include exponents and radicals, factoring, rational expressions, and solving various types of equations. Second semester work revolves around coordinate geometry and the function concept. Specific topics include linear and quadratic functions, systems of linear equations in two and three variables, rational inequalities, absolute value inequalities, the quadratic formula, direct and inverse proportion, arithmetic, and geometric sequences. Solving verbal problems is included, where appropriate, throughout the course.

Course Name: Precalculus BC Adv Honors

Course # 218

Level H (weighted at the AP level for GPA calculations)

Grade Level 11

Credits 6

This course includes the study of the following topics: theory of equations, mathematical induction, determinants and matrices, analytic geometry, probability, permutations, combinations, conic sections, vectors, sets and logic, sequences and series, binomial theorem, and an introduction to calculus. Other topics include concepts of limit, derivatives of algebraic functions, applications of the derivative, units in sets and logic probability, geometric probability, matrices, and vectors. This course is intended to be the precursor to AP Calculus. 

MATHEMATICS ELECTIVES

Course Name: Calculus

Course # 214

Level H

Grade Level 12

Credits 6

This is an elective course offered to students who have mastered the prerequisite skills in Pre-Calculus. It is highly recommended that students take a math elective in their senior year in preparation for college. This course provides an excellent head start to many required college freshman math courses. Students use limits of infinite processes to develop differential and integral calculus (without the rigors of an AP course) and use these concepts to create mathematical models. The abstract properties of elementary functions are re-examined in light of these new techniques. Students apply these new concepts to problems drawn from the natural and social sciences.

Course Name: AP Precalculus

Course # 248

Level AP

Grade Level 11-12

Credits 6

AP Precalculus centers on functions modeling dynamic phenomena. This research-based exploration of functions is designed to better prepare students for college-level mathematics and science courses. In this course, students study a broad spectrum of function types that are foundational for careers in mathematics, physics, biology, health science, social science, and data science. The course content is organized into units of study that provide a suggested sequence. Units include Polynomial and Rational Functions, Exponential and Logarithmic Functions, Trigonometric and Polar Functions, Functions Involving Parameters, Vectors, and Matrices (this unit is not included on the AP Exam). 

• This course concludes the traditional College Prep or Honors course sequence and is designed to be the final math course. It is not intended to prepare students for AP Calculus. Students who have completed Honors or Advanced Honors courses should consider Precalculus Honors or Precalculus BC Advanced Honors as preparation for AB/BC Calculus.

Course Name: AP Calculus AB/AP Calculus BC

Course # 215/204

Level AP

Grade Level 12

Credits 6

In the first half of the year, concurrent with the early topics in calculus, the curriculum includes all topics recommended for the Advanced Placement exam, as well as all topics listed in the Calculus AB and BC course description. This course covers differentiation, integration, and applications of the logarithmic exponential, trigonometric, inverse trigonometric functions, and parametric equations, arc length, polar coordinates, vectors, numerical approximations to integration, methods of integration, volumes of solids of known cross-sections, sequences, and infinite series, and introductory differential equations. Provisions exist for specific preparation for the advanced placement exam.

Course Name: AP Economics - Micro

Course # 245

Level AP

Grade Level 11-12

Credits 6

AP Microeconomics is an introduction to the study of the consumers and producers that make up the economy: households, firms, governments, and community organizations. The course provides particular emphasis on the function of consumers and producers within the economic system. The course also offers an analysis of the markets in which consumers and producers interact as well as non-market economics. This course prepares students to take the Advanced Placement Microeconomics Exam. Students wishing to take both the Advanced Placement Microeconomics Exam and the Advanced Placement Macroeconomics Exam should take AP Economics - Macro concurrently with this course.

Course Name: AP Economics - Macro

Course # 246

Level AP

Grade Level 11-12

Credits 6

AP Macroeconomics is an introduction to how the market system works, how prices are determined, why shortages and surpluses occur, and why incomes differ. Topics include national income, price determination, economic performance measures, economic growth, and international economics.  This course prepares students to take the Advanced Macroeconomics Exam. 

Course Name: AP Statistics

Course # 240

Level AP

Grade Level 11-12

Credits 6

This course is an introduction to statistics, with an emphasis on analyzing data and statistical thinking. Topics include sampling, organizing and analyzing data, distributions, correlation and regression, testing, and hypotheses. There will be many real-world applications interwoven throughout the course. 

• A TI-83 or better calculator is mandatory for this course. 

Course Name: Introduction to Probability/Statistics

Course # 227/228

Level CP/H

Grade Level 11-12

Credits 6

This course introduces students to the basic concepts and logic of statistical reasoning and gives the students introductory-level practical ability to choose, generate, and properly interpret appropriate descriptive and inferential methods. In addition, the course helps students gain an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study. The course does not assume any prior knowledge in statistics. The course focuses on probability through the lens of games and statistics through the lens of sports.

Honors: The honors course will be included in the CP level course and will require more detailed term projects.

Course Name: Financial Literacy

Course # 255/256

Level: CP/H

Grade Level 11-12

Credits 6

This comprehensive course equips students with essential financial management skills for post-graduation success. Students explore fundamental concepts including banking operations, credit management, personal budgeting, investment strategies, and career planning. Through practical exercises and real-world applications, students develop the knowledge and confidence to make informed financial decisions.

Learning Outcomes:

• Master personal banking and money management fundamentals

• Understand credit systems, scores, and responsible borrowing

• Create and maintain effective personal budgets

• Analyze investment vehicles and develop basic portfolio strategies

• Plan career paths and understand employment-related finances

Course Name: Applications in Mathematics

Course # 257/258    

Level: CP/H

Grade Level: 11-12 (consideration for other grades on an individual basis)

Credits: 6

This course provides students with opportunities to explore how mathematical concepts directly connect to real-world scenarios and practical problem-solving. Students will strengthen their foundational algebra, geometry, and statistics skills while learning to apply these concepts in contexts relevant to daily life, business, and social sciences. The course emphasizes mathematical modeling, data analysis, and logical reasoning to solve authentic problems. Students will develop their ability to approach complex situations systematically, represent problems using multiple mathematical representations, and communicate their solutions effectively. Through project-based learning and real-world applications, students will build confidence in their quantitative reasoning skills and prepare for both college mathematics and career-related mathematical challenges.