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Mathematics Course OfferingsThe Mathematics Department offers a wide range of courses to provide students with opportunities to actively participate in learning the structure and the nature of mathematics, while developing analytic skills that will help them apply basic principles to other areas of study and everyday living. Students begin their mathematics program at FHS at different points, based on their middle school programs. The basic sequence of mathematics courses is Algebra I, Geometry, and Algebra II. Many students enroll in higher-level mathematics courses after successful completion of Algebra II. All mathematics courses make use of technology in the form of computer software and/or graphing calculators. Technology allows students to visualize the mathematics that they are learning as well as lessening the burden of voluminous and complicated numerical computation. Students should check with their current mathematics teachers for recommendations about appropriate types of graphing calculators. The Mathematics Department suggests students purchase their own calculators (which will be used throughout their math program at the high school and beyond). The Mathematics Department takes primary responsibility for the following Franklin High School academic expectations for student learning: (Students will) analyze and solve problems effectively by: · Locating, organizing, and processing information from various sources · Utilizing thinking skills and reasoning strategies Introduction to Algebra 200 College Preparatory Grade 9 Full Year 5.0 Credits Introduction to Algebra is the first course in a two-year sequence that will introduce students to the foundations of algebra and the principles of logical thinking used in higher mathematics. Because students develop at different rates, the mathematics department offers this course to students who would benefit from additional time reinforcing pre-algebraic concepts through the use of manipulative materials and cooperative group work. Introduction to Algebra will include the following concepts: properties of numbers and algorithms with numerals; concept of the variable and its applications; concept of function and its extensions; linear equations and inequalities; and systems of linear equations. For success in Introduction to Algebra, students will need facility with number facts and operations and a commitment to work hard both in class and on the daily homework (30 minutes or more). Students will be expected to participate actively in class, both as individuals and as team members. Because Introduction to Algebra includes work with the graphing calculator; students will benefit by having their own calculators to complete assignments both in class and at home. Grades in this class will be based on homework, classwork, tests, and quizzes. Students who successfully complete Introduction to Algebra will enroll in Concepts in Algebra and Geometry the following year. Completion of this two-year sequence will provide students with a solid foundation in a comprehensive algebra program as well as a foundation in the principles of geometry, which will afford them greater success in more advanced mathematics courses. Concepts in Algebra and Geometry 201 College Preparatory Grade 10 Full Year 5.0 Credits Concepts in Algebra and Geometry is the second course in a two-year sequence, which will continue the development of algebraic thinking established in Introduction to Algebra. Concepts in Algebra and Geometry will focus on the following concepts: polynomials and operations with polynomials, solving equations and inequalities, relations, systems of equations and inequalities, rational expressions, nomenclature of geometry, and deductive reasoning. For success in Concepts in Algebra and Geometry, students will need facility with number facts and operations and a commitment to work hard both in class and on the daily homework (30 minutes or more). Students will be expected to participate actively in class, both as individuals and as team members. Students will use graphing calculator to a greater extent than in Introduction to Algebra and will benefit by having their own calculators to complete assignments both in class and at home. Grades in this class will be based on homework, classwork, tests, and quizzes. Completion of Concepts in Algebra and Geometry will provide students with a solid foundation in a comprehensive algebra program as well as a foundation in the principles of geometry, which will afford them greater success in more advanced mathematics courses. Algebra 202 College Preparatory Grades 9, 10, 11, 12 Full Year 5.0 Credits Algebra I is an entry level course offered in the college preparatory program. The major topics to be covered include the properties of the real number system, polynomials and operations with polynomials, factoring, exponents, solving equations and inequalities, relations, functions, systems of equations and inequalities, and rational expressions. These algebraic topics will be integrated in real world problems that also explore topics from discrete mathematics, such as statistics, probability, graphs, and others. A major goal of the course is to introduce the language of algebra and foster the integration of geometry and technology in real world situations. Students will evaluate formulas, apply the Pythagorean Theorem, Triangle Sum Theorem, Triangle Inequality Theorem. They will determine algebraic expressions, solve linear equations and inequalities, graph solutions, interpret graphs, and other work that will prepare them with a foundation for further study in mathematics. Since algebra permeates all of mathematics, a strong foundation in this first course is essential for success in future courses. For students to experience success in algebra they will need facility with number facts and operations and a commitment to work hard both in class and on the daily homework (30 minutes or more). Students will be expected to actively participate in class, both as individuals and as team members. Since technology is becoming increasingly more important, it is integrated into our lessons. Students will benefit by having a graphing calculator to complete assignments both in class and at home. Algebra/Geometry 205 College Preparatory Grade 9 Full Year 5.0 Credits The content of this course is designed for those 9th grade students who need more time to assimilate the basic algebraic concepts necessary for the continuation of mathematical study. Topics will include exponents and powers, quadratic equations and radicals, polynomials, linear systems, factoring, and a more comprehensive analysis of some interesting and real world applicable functions. The curriculum will conclude with basic geometric definitions and postulates and preliminary concepts necessary to develop the Euclidean Geometry. Activities, real world applications, continual review and the use of graphics technology will be part of the pedagogical tools that will assist student learning. Students will be assigned homework daily and will be expected to actively participate in class activities and complete out-of-class projects. Successful completion of this course will prepare the students to continue the study of mathematics in Geometry CP or Geometry Honors. Geometry 211 Honors Grades 9, 10, 11, 12 Full Year 5.0 Credits Geometry Honors takes a formal approach to the discipline. Topics are developed with a high degree of rigor and precision and include angle relationships, line relationships, congruent and similar triangles and polygons, circles, quadrilaterals, constructions, and area and volume of plane and solid figures. The development of the course will integrate algebra and discrete topics that will also be examined analytically. Transformation functions will be employed in the analysis of plane figures that are reflected, rotated, dilated or translated. Three-dimensional figures, measurement and connection with other disciplines are also given much attention in the course. Developing the student’s mathematical power to explore, make conjectures, and reason logically is a major goal. Students who elect this course will be expected to work hard. Computer technology and other graphics utilities will be employed to explore, conjecture, and simplify learning. Activities, real world applications, continual review and the use of graphics technology will be part of the pedagogical tools that will assist student learning. Students will be assigned homework daily and will be expected to actively participate in class activities and complete out-of-class projects. Geometry 212 College Preparatory Grades 9, 10, 11, 12 Full Year 5.0 Credits The major topics covered in Geometry CP include angle relationships, perpendicular and parallel lines and planes, congruent triangles, quadrilaterals, similar polygons, circles, constructions, area of polygons and lateral area, surface area and volume of three-dimensional figures. Analytical relationships will be established, as topics from algebra and discrete mathematics are integrated, using transformations of points and figures on the Cartesian Coordinate system. Activities, real world applications, continual review and the use of graphics technology will be part of the pedagogical tools that will assist student learning. The use of applicable software will assist students in learning the vocabulary and the concepts of geometry along with the properties and characteristics of the plane figures. Students will be assigned homework daily and will be expected to actively participate in class activities and complete out-of-class projects for successful completion of the course. Applications in Geometry, Advanced Algebra, and Statistics 218 College Preparatory Grades 11, 12 Full Year 5.0 Credits This course includes a range of topics including geometry, functions and systems of equations, right triangle trigonometry, and probability. Students will investigate applications of these topics in real-world situations and will demonstrate their understanding through a variety of projects. They will have opportunities to strengthen existing mathematical knowledge and skills and develop an appreciation of the relevance and uses of mathematics in their daily lives. Graphing calculators will be used to support concept development. This course is an option for students who have completed Algebra I or Concepts in Algebra and Geometry. Students who have completed Geometry CP or Honors are not eligible to take this course for credit. Algebra II 219 Honors Grades 9, 10, 11, 12 Full Year 5.0 Credits Algebra II Honors extends and further explores topics already developed in Algebra I and Geometry, and the course includes new topics from both continuous and discrete mathematics. Concepts will be developed with rigorous and stringent attention to detail, processing and understanding. Topics will include: polynomial, exponential, logarithmic and trigonometric functions, matrices, graphs, systems of equations, inverses, sequences, series and combinations.. A real world orientation has guided both the selections of the content and the applications. Activities are included in many lessons, and up-to-date technology is used and integrated throughout the course. Students will explore, analyze and consider the mathematics from an algebraic, numerical and graphical approach in an effort to synthesize their newly acquired knowledge. Homework will be assigned daily. To be successful in this honors course students must have a strong algebraic foundation and fluency in algebra vocabulary. Students enrolling in Algebra II Honors should have a minimum grade of C in Geometry Honors or B+ in both Algebra I CP and Geometry CP. Willingness to work hard, to participate individually and in groups, and effectively communicate orally and in writing are requirements for success. Students should have a graphing calculator for the course. Algebra II 220 College Preparatory Grades 10, 11, 12 Full Year 5.0 Credits The Algebra II CP course includes all the topics covered in the honors program: linear relations, functions, graphs, matrices, systems of equations, powers, inverses, radicals, trigonometry, series, combinations, etc. The development of the course, however, is less rigorous and applies more intuitive understanding. The graphing calculator and other technology prompts will be used to clarify concepts and analyze the concepts from a graphical and numerical as well as an algebraic perspective. Algebra is an important component of all mathematics, and since students will be confronted with complex algebraic manipulations in any college math course they take, it makes sense to continue the development of algebraic algorithms and procedures. In this course students will develop skills in carrying out various algorithms; identify mathematical properties and relationships; apply mathematics in real-world situations; and produce graphical representations of concepts. Homework will be assigned daily. Students are expected to be active participants in class, both individually and in group work. A solid background in basic algebra and geometry is essential for success. Students should have a graphing calculator for this course. Pre-Calculus 231 Honors Grades 10, 11 Full Year 5.0 Credits This course has as its objective the development of a broad base foundation in mathematics upon which to build the concepts of calculus. A solid foundation in algebra and geometry is essential, and students are expected to have successfully completed both Algebra II Honors and Geometry Honors. Students will continue to develop and extend previously learned topics and encounter new concepts that are necessary in future study. All topics will be explored in detail and in depth, analyzing the concepts from an algebraic as well as from a numerical and graphical perspective. The topics include polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. Vectors, polar equations, parametric equations, systems, sequences, series and other topics from discrete mathematics, are also part of the curriculum. The concepts are explored and applied in real world problems integrated with graphics utilities and other technological prompts. Success in this course requires a great deal of focus and work, both in class and at home. Students enrolling in Pre-Calculus Honors should have a minimum grade of C in Algebra II Honors or B+ in Algebra II CP. Those students who successfully complete the course with a grade of B+ or better will be prepared for the AP Calculus course offered at the high school. Algebra III/Trigonometry 234 College Preparatory Grades 11, 12 Full Year 5.0 Credits This rigorous course concentrates on a variety of complex mathematical topics including trigonometry; polynomial, rational, exponential, and logarithmic functions; sequence and series; probability; and number theory. A solid foundation in algebra and geometry is essential, and students are expected to have successfully completed both Algebra II (minimum grade of a C) and Geometry. Extensive use of the graphing calculator allows students to extend previously learned topics and develop proficiency in new concepts that are necessary in future mathematics courses. Topics will be explored in detail and in depth and applied in real world contexts. Success in this course requires a great deal of focus and work, both in class and at home. Students who successfully complete this course will be prepared for Introduction to Calculus CP or Pre-Calculus H. Calculus 244 Honors Grades 11, 12 Full Year 5.0 Credits This calculus course will develop most of the topics that are on the syllabus of the Calculus Advanced Placement Program at a slower rate and with a less rigorous tone. The syllabus will include a preliminary review of polynomial, exponential, logarithmic, trigonometric transcendental and other functions, their properties, and applications. The concept of differentiation and integration, and their applications in real world problems are then explored, developed, and analyzed. The development of the course will encompass a theoretical approach as well as a concrete understanding. All topics are explored numerically, graphically and algebraically, always with application to the everyday real world. The course is demanding both with respect to class work and homework. Success in the course requires a strong and sound foundation in logic, algebra, geometry, trigonometry, and analytic geometry, plus a sincere devotion to hard work and persistent effort with a clear and focused mind. Students who complete this course successfully will be prepared to pass college entrance examinations in Mathematics. A graphing calculator is required for this course. Also, summer work is assigned, to complete during the summer, before entering the class. Calculus AB/AP 240 Advanced Placement Grades 11, 12 Full Year 5.0 Credits Calculus AB/AP develops all the topics, which are on the syllabus of the Calculus Advanced Placement Program. The topics include a preliminary review of polynomial, exponential, logarithmic, trigonometric transcendental and other functions, their properties, and applications. The concepts of differentiation and integration, and their applications to real world problems, are explored, developed and analyzed in detail, and with a high degree of rigor and sophistication. The development of the course will encompass a theoretical approach as well as a concrete understanding. All the topics are explored numerically, graphically and algebraically—always with application to the everyday experiences of the real world. The course is demanding with respect to class work and homework. Success in the course requires a strong and sound foundation in logic, algebra, geometry, trigonometry, and analytic geometry, plus a sincere devotion to hard work and persistent effort, with a clear and focused mind. Students completing this course take the Advanced Placement Examination for college credit, and/or advanced placement. A graphing calculator is essential for a student enrolled in this course. Also, summer work is assigned, and to be completed during the summer, before entering the class. Prerequisite: Refer to information and requirements on pages six and seven. Calculus BC/AP 230 Advanced Placement Grade 12 Full Year 5.0 Credits This course is offered to those students who have completed the Calculus AB syllabus. The course will complete the remaining topics of a second semester of college calculus. The topics to be covered will include a review and an extension of the differential and integral topics covered in the AB syllabus and will expand the applications of these concepts. Additional topics to be included are: Parametrics, polar and vector functions and their derivatives, series including Taylor Maclaurin and the applicable calculus, and polynomial approximations of series, power series. Also included will be improper integral, convergence and divergence tests, etc. This course will be demanding and will require students to do summer work before entering in September. Prerequisite: Completion of Calculus AB with a grade of C or better. Discrete Mathematics 243 Honors Grades 11, 12 Full Year 5.0 Credits Pre-Calculus and Discrete Mathematics covers a wide-scope curriculum. Interwoven with the pre-calculus topics of continuous mathematics, generally taught at this level, are topics from discrete mathematics. Topics such as logic, properties of integers, sequences, induction, recursion, combinatorics, graphs, and networks are all discrete topics important in understanding current mathematics and its uses, particularly relative to computers. The mathematics of continuous and infinite processes includes the study of all types of functions, coordinate systems, trigonometry, vectors, limits, and an introduction to the calculus of the derivative and the integral. All of the content is studied in detail for its application to real-world problems using methods and applications settings that are reality oriented. The course also gives strong attention to the reasoning process used by mathematicians and those that use mathematics. Since complex algebraic manipulations are necessary in virtually all college mathematics courses that students will encounter, we continue to practice these skills, and develop an appreciation for the deductive approaches used in many fields of study. The instructional methods used are designed to maximize the student’s acquisition of skill and concept. The ability to analyze and carry out algorithms, the ability to develop and use mathematical properties and relationships, the ability to apply mathematics to real situations, and the ability to represent or picture mathematical concepts are all goals for students. Students enrolled in this honors course must have a solid understanding of the algebra, geometry, trigonometry, and analytic geometry of their previous courses (minimum grade of a C in Pre-calculus Honors or a B+ in Algebra III/Trigonometry). Students will be required to do homework daily, along with other out-of-class projects. To be successful students must be persistent with their work, must assume responsibility for the content, and must be actively involved in the process. A graphics calculator is a essential for a student enrolled in the course. Intro to Calculus CP 242 College Preparatory Grade 12 Full Year 5.0 Credits Introduction to Calculus is a rigorous course designed to strengthen and extend students’ mathematical background. Admittance to this class requires successful completion of Algebra III/Trigonometry or Pre-Calculus. Topics presented are from continuous as well as discrete mathematics and include probability, polynomial and logarithmic functions, sequences, series, and an introduction to the derivative and integral concept of calculus. Since complex algebraic manipulations permeate all college mathematics, it is reasonable to continue skill development with patterns and algebraic algorithms at this stage of the student’s education. Students will find that the review and extension of the previously encountered concepts will connect their knowledge and help them assimilate new understandings. The use of the graphing calculator to explore the mathematical concepts will further clarify and deepen their understanding and generate more questions for exploration. Introduction to Calculus will further connect topics and extend the application of mathematics to real world problems. This course is appropriate for students who have achieved a minimum grade of C in Algebra III/Trigonometry. To experience success the student must do daily homework, explore out-of-class projects and actively participate in class. Statistics/AP 260 Advanced Placement Grades 10, 11, 12 Full Year 5.0 Credits The Advanced Placement Statistics course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, probability, and statistical inference. Students who successfully complete the course and examination may receive credit and/or advanced placement for a one-semester college course in introductory statistics. AP Statistics is an excellent option for any student who has successfully completed a second year course in algebra, regardless of the student’s intended college major. At least one statistics course is typically required for majors such as engineering, mathematics, psychology, sociology, health science, and business. This course will explore examples in diverse fields. Appropriate use of technology, student projects, and alternative assessments will be incorporated. This is a non-calculus based introductory course. A graphing calculator is essential for success in this course. Summer reading will be assigned. Prerequisite: Refer to information and requirements on page six and seven. Statistics 262 Honors Grades 11, 12 Full Year 5.0 Credits Statistics Honors will explore and develop the four conceptual themes of the Advanced Placement Statistics program in less depth. Successful completion of this course will give students a preview and a firm foundation for any college statistics course. Students will complete group projects, including a culmination project employing inference. A graphing calculator will be used in class and for the daily homework assignments. Statistics is an excellent option for any student who has successfully completed Algebra II. Statistics 263 College Preparatory Grades 10, 11, 12 Full Year 5.0 Credits Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Emphasis will be placed upon statistical applications relative to data and concepts, rather than formal probability and theory. Through active learning students will learn ideas and skills that will allow them to integrate their knowledge with other disciplines. Technological student projects and other forms of assessment will be incorporated, making Statistics an excellent option for any student who has successfully completed a second year of algebra. A student who is enrolled in the course will benefit by having a graphing calculator. Homework is assigned daily. Introduction to Statistics 264 College Preparatory Grades 11, 12 Full Year 5.0 Credits Introduction to Statistics is designed to provide real-world understanding of three of the four major statistical concepts: exploring data, planning a study (including surveys and experiments), and probability. The fourth statistical concept, methods of inference, will not be covered. Students will apply statistics in other disciplines through projects, computer programs, and graphing calculator simulations. This course is an option for students who have completed Algebra I and Geometry and will prepare them to master statistics concepts included in the Massachusetts State Frameworks in Mathematics, which are included in the MCAS exam. Students who have completed Algebra III/Trigonometry should enroll in Statistics 262-263 at either the college preparatory or honors level. Introduction to Statistics includes daily homework and at least one project per term. Students will benefit from having their own graphing calculator. Computer Science I 294 Honors Grades 10, 11, 12 Full Year 5.0 Credits Students entering into the Computer Science I (CSI) course will be exposed to many of the concepts essential in the understanding and construction of computer programs. These concepts will be introduced and explored using the Java programming language. The course will cover a number of key topics crucial to software development including: variables, branching, looping, arrays, objects, sorting, data structures, and software engineering techniques. Students, upon successful completion of this course, will be able to design, build and modify Java components. Work will be primarily project-based, with a concentration on developing actual hands-on skills. Most work and exams will be on the computers and will be completed in class. Students entering this course should have successfully completed Advanced Algebra Honors with a grade of C or better. Additionally, students wishing to enter this course may enter by successfully passing a programming entrance exam. To be successful in this course, students are expected to do 30 minutes of homework per day. Computer Science II/AP 296 Advanced Placement Grades 11, 12 Full Year 5.0 Credits The second course of the Computer Science series focuses upon preparing the student for the Advanced Placement Test in Computer Science AB. The course will begin with a review of CSI. Additional concepts will be introduced, such as analysis of algorithms, and advanced topics in sorting, data structures, algorithms, and software engineering. The class will participate in a full-lifecycle development project, with a goal of completed application by the end of the year. The course will expand beyond simple programming to involve homework, research, and reports, as students begin to explore more of the history and theory behind computer Programming. Students electing this course must have successfully completed Computer Science I with a grade of C or better. To be successful in this course, students are expected to do 30 minutes of homework per day. Prerequisite: Refer to information and requirements on page six and seven. Computer Hardware and Technologies 298 College Preparatory Grades 11, 12 Full Year 5.0 Credits This course is an intensive introduction to modern personal computer hardware and operating system software. Topics covered include computer hardware maintenance, troubleshooting, configuration, and upgrading. Operating system fundamentals, installation, configuration, troubleshooting, and upgrading will be covered. Basic networking topics will be introduced. The goal of this course is to prepare students for industry-standard information technology certification. |
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