The Mathematics Department offers a four-year sequence of courses for all students, which accommodates students with varied background and aptitude in Mathematics. Curricula for our courses are constantly being updated and designed with input from the NCTM standards, the Massachusetts Frameworks and the College Boards; we believe, however, that all students should be taught many skills, concepts and applications that go beyond the expectations of these standards. Our goals are to lead our students into higher-level critical thinking and problem solving as well as to enable our students to apply previously learned mathematical concepts and skills into new situations

The Winchester High School graduation requirement for Mathematics is two years but the Math Department encourages all students to continue with the study of Mathematics throughout their four years. We believe this will better prepare them for college and their future careers.

We believe in a variety of instructional methods, which are not only appropriate to the material being taught but also appropriate to individual learning styles. Both colleges and the business world are expecting high school students to be more technology literate. By using graphing calculators and computers the math department addresses this demand. These technology tools are used for exploration and investigation as well as for the development and extension of mathematical topics. Technology provides a dynamic approach to the learning of Mathematics. A graphing calculator is an integral part of all courses beyond Algebra 1 and Geometry.

Within the Mathematics Department there are many levels of study. Prerequisites and levels of study are indicated in the individual course descriptions. Placement in courses is based on the student’s grades, the recommendation of the teacher, and performance on department exams. And student/parent input. Students and parents are always strongly encouraged to appeal any decisions which they feel is not in the student’s best interest.

See Math Directors web site for math course of studies flowchart/matrix

Year Courses:

0406 ALGEBRA 1 (C1) Y 5 (Prerequisite: Grade of C or better in grade 8 Pre-Algebra)

This is a first course in Algebra, using modern techniques and technology as an approach to problem solving. Algebraic structure and language as well as the development of basic skills will be emphasized. Algebraic topics include variables, linear equations and inequalities, the real number system, factoring, exponents, radicals, polynomials, rational expressions, graphs, systems of equations and an introduction to quadratic functions. Topics in probability and statistics will also be part of the course. Students successfully completing this course should follow with a Geometry course.

0401 GEOMETRY (C1) Y 5 (Prerequisite: Pass Algebra 1 open to 10,11 sonly)

The major concepts of the traditional Geometry curriculum will be covered in a concrete manner, with less emphasis on abstract concepts and proofs. Practical applications, informal language, exploration, constructions, and experiments will be the basis for the course. It is a stimulating approach for students who have demonstrated a need for a less abstract, approach to geometry. Topics include lines, angles, triangles, polygons, circles, perimeter, area, volume, Pythagorean Theorem and an introduction to the coordinate plane.

0402 GEOMETRY ADVANCED (C1) Y 5 (Prerequisite: Grade of C- or better in Algebra 1)

This Geometry course is designed to have each student develop the skills and concepts of visualization and spatial reasoning; to represent and analyze the characteristics and properties of two and three dimensional shapes and their relationships. It includes identifying and describing, moving and transforming geometric objects along with argument and proof. Right triangle trigonometry, circumference, area and volume will also be studied. There will be an emphasis on using algebraic skills to solve applications and analytic problems. Calculators and computers are used to enhance the mathematical understanding and improve problem-solving skills.

0403 GEOMETRY (H) Y 5 (Prerequisite: Grade of B or better in Algebra 1 (H or 8th grade adv))

This is an in-depth course designed for those students who have already displayed an aptitude in mathematics. It will cover all the traditional topics of Euclidean Geometry with particular emphasis on inductive and deductive reasoning. Formal geometric language, theorems, constructions and proofs will be emphasized. Algebraic skills and technology will be incorporated throughout the course. Calculators and computers are used to enhance the mathematical understanding and improve problem-solving skills.

0410 ALGEBRA 2 (C1) Y 5 (Prerequisite: Grade of C- or better in both Algebra 1 and Geometry)

This course further develops and reinforces the basic skills of first year Algebra and extends these skills and concepts into the traditional topics of Algebra 2. The course explores and develops the concept of mathematical functions, including linear, quadratic, and exponential functions. Other topics include polynomials, exponents, radicals and an introduction to complex numbers. Applications and problem solving using technology will be integrated into the course.

0411 ALGEBRA 2 ADVANCED (C1) Y 5 (Prerequisite: Grade of B- or better in both Algebra 1 and Adv. Geometry)

This course further explores and develops the concepts and skills of Algebra 1. Powers, roots, polynomials and other special functions (quadratic, exponential and logarithmic) are studied as tools for modeling real-world situations. Problem solving, which may incorporate geometry concepts, is stressed throughout the course. Calculators are used to enhance the mathematical understanding and improve problem-solving skills.

0412 ALGEBRA 2 (H) Y 5 (Prerequisite: Grade of B or better in both Algebra 1 (H) and Geometry (H) or permission of mathematics director)

This is a rigorous course that explores and develops the concept of mathematical functions, including linear, quadratic, exponential, logarithmic, and trigonometric functions. This course will include a unit on conic sections. Mathematical modeling and applications using technology will be an integral part of this course.

0413 ALGEBRA 3 (C1) Y 5 (Prerequisite: Grade of C– or better in Algebra 2)

Students who have completed Algebra 2 will continue with this course. Topics will include the further study of functions, including polynomial, exponential, and logarithmic functions, the nature of graphs, matrices, and trigonometry and its applications. Some topics from probability and statistics will also be introduced.

0414 PRE-CALCULUS ADVANCED (C1) Y 5 (Prerequisite: Grade of C+ or better in Algebra 2 Adv. or B or better in Algebra 3)

Students will continue their study and analysis of functions: linear, quadratic, polynomial, exponential and logarithmic. Right triangle trigonometry will be expanded to include circular functions, with applications. Complex numbers, polar coordinates, analytic geometry and conic sections will also be included. Emphasis is on applications and problem solving with the aid of graphing calculators.

0415 PRE-CALCULUS (H) Y 5 (Prerequisite: Grade of B- or better in Algebra 2 (H) or permission of mathematics director

This course seeks to develop the analytical ability of the student through the study of functions: linear, polynomial, rational, and exponential. Major emphasis is on the creation and analysis of graphs. Topics also include the study of conic sections, sequences and series, polar coordinates, and parametric equations. This course prepares students for the Advanced Placement Calculus BC course.

0417 INTEGRATED/ANALYSIS (C1) Y 5 (Prerequisite: Grade of D or better in Pre-Calculus Adv or Grade of D or better in Algebra III)

Topics include vectors, matrices, determinants, sequences and series. Probability and statistical analysis will also be covered as well as some discrete math. The study of functions: linear, polynomial, rational, and exponential will be continued. Advanced algebra topics will also be reviewed. Use of the graphing calculator will be an integral part of this course.

0419 AP STATISTICS (AP) Y 5 (Prerequisite: Grade of B or better in Pre-Calculus Adv or Grade of D or better in Pre-Calculus (H) and completion of
Summer work packet by the first day of school)

This course covers exploring data, sampling and experimentation (planning and conducting a study); anticipating patterns (exploring random phenomena using probability and simulation); and statistical inference (estimating population parameters and testing hypotheses). The use of graphing calculators is an integral part of the course, allowing the student to explore a variety of approaches to a problem. This course will prepare students for the Advanced Placement Statistics exam given in May. . All students are required to take the AP exam

0423CALCULUS (H) / 0424 AP CALCULUS AB (by contract) Y 5 (Prerequisite: Grade of B or better in Adv Pre-Calculus or Grade of D or better in Pre-Calculus (H) and completion of summer work packet by the first day of school is required for all students in either course).

The content of this course in differential and integral calculus is a rigorous HS level calculus course. The topics range from limits and continuity through derivatives and their applications to integrals and their applications. The course emphasizes a multi-representational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The use of graphing calculators is an integral part of the course, allowing the student to explore a variety of approaches to a problem. Additional assignments and assessments are required of those students taking the AP course. All students taking the AP course are required to take the exam.

0425 CALCULUS AB/BC (AP) Y 5 (Prerequisites: Grade of C+ or better in Pre-Calculus (H) or an A in Pre-Calculus Adv (C1) , permission of the Mathematics Director and completion of summer work packet by the first day of school

The content of this course in differential and integral calculus is comparable to a college level calculus course. The topics range from limits and continuity through derivatives and their applications to integrals and their applications. The course emphasizes a multi-representational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The use of graphing calculators is an integral part of the course, allowing the student to explore a variety of approaches to a problem. This course will prepare students for the Advanced Placement Calculus AB exam given in May. With additional optional assignments students will be prepared for the BC exam all students are required to take the exam.

0426 AP CALCULUS BC (AP) Y 5 (Prerequisites: Grade of B or better in Pre-Calculus (H), completion of summer work packet by the first day of school; and permission of the Mathematics Director.)

Calculus BC is an extension of Calculus AB using a more theoretical approach. It covers all of the topics of Calculus AB, and in addition will cover the calculus of parametric, polar, and vector functions, tests for convergence and divergence of series, and Taylor and Maclaurin series. The course emphasizes a multi-representational approach to calculus with concepts, results and problems being expressed graphically, numerically, analytically, and verbally. The use of graphing calculators is an integral part of the course, allowing the student to explore a variety of approaches to a problem. This course will prepare students for the Advanced Placement Calculus BC exam given in May. All students are required to take the exam

0430 MATH LAB (9, 10, 11, 12) S 2 1/2 Approval of the math director is required in order to register for a math lab.

Programs of study that will be accommodated within the math lab environment include: an entry course for students who plan to strengthen their arithmetic skills before beginning the MCAS sequence, an entry course for ninth graders who aspire to take and pass the regular MCAS exam in 10th grade and whose performance in 8th grade indicates that they are not yet ready for a rigorous traditional Algebra 1 program. A follow up course for students who aspire to take and pass regular MCAS in spring of current school year, A life skills course for students who have passed MCAS and who desire a math course geared toward independent living, a course for students who have passed MCAS and desire a course geared toward mastering the content in college level developmental math. (These are the courses unprepared college students are required to take for no credit). Math Lab can be taken for credit an unlimited number of times. These courses fulfill the HS math graduation requirements.

ELECTIVE COURSES

0422 AP COMPUTER SCIENCE (AP) (11, 12) Y 5 (Prerequisite: Grade of B- or better in Honors ALGEBRA 2, grade of A- or better in Algebra 2 Adv., Grade of B- or better in Pre-Calculus Adv or Grade of C- or better in Pre-Calculus (H). This course must be taken concurrently with another math course. It does not satisfy the math requirement of WHS or most colleges. Completion of summer work packet by the first day of school is required.

This is an introductory computer science course with Computer Programming utilizing the programming language of JAVA. The major topics include computer concepts, control structures, functions, arrays, pointers and strings and an introduction to object oriented design and implementation. All students are required to take the exam

0419 AP STATISTICS (AP) (11, 12) Y 5 (Prerequisite: Grade of B or better in Honors ALGEBRA 2 or Grade of B or better in Pre-Calculus Adv or Grade of D or better in Pre-Calculus (H) and completion of summer work packet by the first day of school)

This course covers exploring data, sampling and experimentation (planning and conducting a study); anticipating patterns (exploring random phenomena using probability and simulation); and statistical inference (estimating population parameters and testing hypotheses). The use of graphing calculators is an integral part of the course, allowing the student to explore a variety of approaches to a problem. This course will prepare students for the Advanced Placement Statistics exam given in May. All students are required to take the exam

0400 MCAS PREP MATH SEM 2 (1 ¼ credits)

This course meets three times a cycle and is taken by those 10th graders who are determined to need additional math instruction in preparation for the math MCAS exam. This course is always taken in addition to another math class.