Mathematics Program
The Mathematics Department offers courses designed to help students develop skills in a number of areas in mathematics. The program attempts to achieve a balance of instruction in algebra, data representation, functions, geometry, and measurement, number systems and problem solving. The course sequences, with differences in rigor, pacing and methodologies, consider the areas of basic skills, algebra, geometry, trigonometry, analysis and calculus.
This course sequence chart which follows the listing of courses below, is intended to be a reference for a four-year math program for each ability level of students. Although the Mathematics Department is responsible for the placement of each student in the most appropriate course and sequence, it is hoped that sufficient information is provided in the description of each course and sequences so that the meaning of each student placement is understood.
Colleges, National Testing Services, and the business communities have placed new technological demands on our students. In response, the Mathematics Department has now integrated the TI-83 graphing calculator into all courses starting with Algebra II in each sequence. If students intend to purchase a calculator for use in mathematics and science courses, we strongly recommend that they obtain a TI-83 or TI-83 Plus graphing calculator.
The Mathematics Department also provides a Math Resource Center (MARC) which is available to students throughout the school day. The purpose of the MARC, which is staffed by regular math teachers, is to provide support to students who need assistance with math homework, with make-up assignments, or with a unit of work that needs to be reexamined because it was not mastered by the student in the assigned class.
Students are reminded that while successful completion of two years of mathematics is required for graduation from CCHS, many students need four years of mathematics to be prepared to matriculate at most colleges and universities.
The courses offered by the
Mathematics Department include:
Algebra I – Part I (Full Year) Advanced Topics in Math (Semester I)
Algebra I – Part 2 (Full Year) Advanced Topics in Math (Semester II)
CP Algebra I (Full Year) * CPIII Analysis (Semester I)*
CPIII Algebra 2 (Full Year)* CPII Analysis (Semester I)*
CPII Algebra 2 (Full Year)* CPI Analysis (Semester I)*
CPI Algebra 2 (Full Year)* CPIII Trigonometry (Semester II)*
Honors Algebra 2 (Full Year) CPII Trigonometry (Semester II)*
CPI Trigonometry (Semester II)*
Honors Analysis and Trigonometry (Full Year)
Statistics (Full Year)
AP Statistics (Full Year)
CPIII Geometry (Full Year)* Calculus (Full Year)
CPII Geometry (Full Year)* AP Calculus AB (Full Year)
CPI Geometry (Full Year)* AP Calculus BC (Full Year)
Honors Geometry (Full Year)
*CP= College Preparatory
The four levels in mathematics are designed to meet the different learning style needs of our students. To a large extent, the curriculum and the order in which the topics are taught remains constant across the four levels. The major difference among the levels is the way in which new material is presented, and the amount of review of previously learned topics. In most cases, the different levels use the same textbook. Instruction in each of the levels is intended to match the learning profile for each grouping. Students who are independent learners and have demonstrated high levels of proficiency in meeting the standards of prior courses will be recommended for honors or CPI classes. Those who lean best in an atmosphere offering more guided practice will be recommended for CPI or CPII classes. Students who perform best with a high degree of teacher-directed instruction will be recommended for CPII or CPIII classes. As teachers match their instructional approaches to the predominant learning styles of each class, a goal is also to enable students to become more self-directed and independent learners. In this way, students who, as freshmen, are grouped in classes that have a high level of teacher direction, will be able, in subsequent years, to gain access to courses where they will work more independently.
Students at this level are typically able to follow a model given concrete examples and experiences, master concepts with directed practice, and rely on the teacher’s assessment of understanding and performance. Instructional approaches are designed to meet the needs of the directed learner and include extending and refining types of activities/practice, explicit directions and modeling, extensive review of previous topics, direct teaching of how to use resources, direct instruction in reading the text, and extensive review of homework in class.
Students at this level are typically able to follow a model and reach an abstract level with guidance, learn well from periods of directed instruction in combination with in-class guided practice, select one of several models and master it, be willing to seek extra help when necessary, identify a problem in understanding or performance with guided questioning, and complete homework in a reasonable amount of time.
Instructional approaches at this level are designed to meet the needs of the guided learner who requires some direction and include reading the text with structured support to supplement lessons, considerable review of previous topics, moderate class time spent on reviewing homework built-in guided practice and guided questioning with some directed learning, and focus both on extending and refining knowledge with some performance tasks.
Students at this level are typically able to understand and analyze complex situations with guidance, respond well to criticism, sometimes apply concepts to model situations, almost always answer word problems of a type previously studied, know what she/he doesn’t know, have some metacognitive abilities, recall previous skills and topics, demonstrate proficiency with minimal review, understand alternative solutions when presented, understand and use several related models, be self-motivated in seeking extra help, complete homework in a reasonable amount of time, complete tests in the allotted time, and read the text to reinforce the lesson.
Instructional approaches at this level are designed to meet the needs of the guided learner and include minimal class time spent on reviewing homework, extended segments of guided instruction, instruction at a fast pace, and focus both on performance tasks and extending and refining knowledge.
Students at this level are typically able to think critically, analyze complex situations, and are comfortable with abstract concepts with an increasing level of abstraction and difficulty each year, be independently self-critical, be metacognitive, provide strong insight into algebraic thinking and visual relationships, miss a class and keep up, learn independently, learn at a fast pace, execute skills reliably, demonstrate proficiency of previous topics and skills, make use of available resources, for study groups, seek out others, complete homework in a reasonable amount of time, support answers appropriately, complete tests in the allotted time, and read the text to preview the lesson.
Instructional approaches are designed to meet the needs of the independent learner and include minimal class time spent in reviewing homework, instruction at a fast pace, and are focused on performance tasks.
Algebra I: Part I Full Year – 5.00 Credits Course #412
For students in grades
9 & 10
Prerequisites: C in Pre-Algebra or its equivalent
Description: This course is for students who need a preparatory program in mathematics for post-high school study, but who need to pursue mathematics at a slower pace. This course covers one-half of the topics covered in a standard first year of algebra, which include basic properties of the rational numbers, simple equations and inequalities, simple word problems, exponents, and algebra in a plane.
Evaluation: Evaluation will be based on homework, class participation, quizzes, tests, and semester examinations.
Algebra I: Part 2 Full
Year – 5.00 Credits Course
#422
For students in
Grades 9 & 10
Prerequisites: C- in Algebra I: Part I
Description: This course consists of the second half of the topics covered in a standard first year of algebra. The topics include work problems, linear systems, the real number system (including the quadratic formula), factoring trinomials, and simplifying and combining algebraic fractions.
Evaluation: Evaluation will be based on homework assignments, class participation, quizzes, tests, and semester exams.
For students in
grades 9 & 10
Prerequisites: Placement in this course is based on performance in previous courses and other assessments.
Description: This course consists of all the topics in a first year college preparatory algebra course. Such topics include the basic properties of the rational numbers, solving simple equations and inequalities, simple word problems, exponents, factoring trinomials, simplifying and combining algebraic fractions, algebra in a plane, linear systems, the real number system (including the quadratic formula), and, if time permits, quadratic equations and functions and relations.
Evaluation: Evaluation will be based on homework assignments, class participation, quizzes, tests, and semester exams.
College Preparatory
III Geometry Full Year – 5.00
Credits Course
#421
For students in
grades 10
Prerequisites: Placement in this course is based on
performance I previous course and other assessments.
Description: This numeric based course consists of all the topics generally included in an Euclidean Geometry course, such as geometric definitions and symbols, angles, triangles and congruencies, geometric inequalities, parallel lines in a plane, quadrilaterals, triangle similarity, areas of polygons, circles and spheres, solids an volumes. It treats geometry using primarily a numeric approach, with a heavy emphasis on the algebra skills needed to solve geometric problems.
Evaluation: Evaluation will be based on homework, class participation, quizzes, tests, and semester examinations.
College Preparatory II Geometry Full Year – 5.00 Credits Course #423
For students in
grades 9 & 10
Prerequisites: Placement in this course based on
performance in previous course and other assessments.
Description: This course consists of all the topics generally included in a Euclidean Geometry course such as geometric definitions and symbols, angles, triangles and congruencies, geometric inequalities, parallel lines in a plane, quadrilaterals, triangle similarity, areas of polygons, circles and spheres, solids and volumes, and some geometry in three dimensions. It emphasizes the algebraic skills needed to solve geometric problems.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
College Preparatory I Geometry Full Year – 5.00 Credits Course
#424
Prerequisites: Placement in this course based on performance in previous course and other assessments (overrides only as space permits).
Description: This proofed-based course consists of all the topics generally included in a Euclidean Geometry course such as geometric definitions and symbols, angles, triangles and congruencies, geometric inequalities, parallel lines in a plane, quadrilaterals, triangle similarity, areas of polygons, circles and spheres, solids an volumes, and some geometry in three dimensions. It emphasizes the logic and abstract reasoning necessary to do paragraph proofs formal two column proofs, and indirect proofs.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework class participation, quizzes, tests, and semester examinations.
Honors Geometry Full
Year – 5.00 Credits Course
#425
For students in grade
9
Prerequisites: Placement in this course based on performance in previous course and other assessments. Placement into this course is by Mathematics Department recommendation only.
Description: This intensive, proof-based course consists of all the topics in a Euclidean Geometry course such as geometric definitions and symbols, angles, triangles and congruencies, geometric inequalities, parallel lines in a plane and in space, quadrilaterals, similarity, areas of polygons, circles, spheres, solids and volumes, three-dimensional figures and transformations. It emphasizes the logic and abstract reasoning necessary to do formal proofs, both direct and indirect.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, optional original exercises, class participation, quizzes, tests, and semester examinations.
College Preparatory III Algebra 2 Full
Year – 5.00 Credits Course
#431
Prerequisites: Placement in this course is based on
performance in a geometry course and an Algebra 2 placement examination.
Description: This course consists of all the topics in a standard second year college preparatory algebra course. Such topics include language of algebra, solving equations and inequalities, linear equations and system applications, absolute value, polynomials and factoring, rational numbers and expressions, quadratic relations, exponents and radicals, and arithmetic and geometric progressions.
Evaluation: Evaluation will be based on homework, class participation, quizzes, tests, and semester examinations.
College Preparatory II Algebra 2 Full Year – 5.00 Credits Course #433
For students in
grades 10 & 11
Prerequisites: Placement in this course is based on
performance in a geometry course and an Algebra 2 placement examination.
Description: This course consists of all topics in a standard second year college preparatory algebra course. Such topics include the language of algebra, solving equations and inequalities, linear equations an systems, applications, absolute value, polynomials and factoring, rational numbers and expressions, quadratic relations, exponents and radicals, complex number systems, conic sections, and arithmetic and geometric progressions.
Evaluation: Evaluation will be based on homework, class participation, quizzes, tests, and semester examinations.
College Preparatory I Algebra 2 Full Year – 5.00 Credits Course #434
For students in
grades 10 & 11
Prerequisites: Placement in this course is based on performance in a geometry course and an Algebra 2 placement examination. Overrides only as space permits.
Description: This course consists of all topics in a standard second year college preparatory algebra course. Such topics include the language of algebra, solving equations and inequalities, linear equations and systems, applications, absolute value, polynomials and factoring, rational numbers and expressions, quadratic relations, exponents and radicals, complex number systems, conic sections, and arithmetic and geometric progressions.
Evaluation: Evaluation will be based on homework, class participation, quizzes, tests, and semester examinations.
Honors Algebra 2 Full Year – 5.00 Credits Course #435
For students in grade
10
Prerequisites: Placement in this course is based on
performance in a geometry course and an Algebra 2 placement examination. Placement is by Mathematics Department
recommendation only.
Description: This intensive course features the more demanding proofs and problems in a second-year college preparatory course in Algebra. The topics studied include the language algebra, solving equations and inequalities, linear equations and systems, polynomials and factoring, rational numbers, quadratic relations, conic sections, complex number systems, radicals, exponents, logarithms and arithmetic and geometric progressions.
Evaluation: Evaluation will be based on homework assignments, optional original exercises, class participation, quizzes, tests, and semester examinations.
College Preparatory III Analysis Semester I – 2.50 Credits Course #440
For students in
grades 11 & 12
Description: This semester course is an introduction to topics to be covered in a math analysis course. It relates ideas originating in geometry to those studied in algebra through the use of co-ordinate methods. It strengthens the concepts of conic sections and functions, an introduces complex numbers as well as exponential, logarithmic, and polynomial functions. Emphasis is placed on preparation for a strong college course in math and analysis.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
College Preparatory III Trigonometry Semester II – 2.50 Credits Course #441
For students in
grades 11 & 12
Prerequisites: C- in Algebra 2
Description: This semester course in trigonometry covers the basic concepts of radian measure, polar coordinates, graphs and values of trigonometric functions, use of algebra to solve trigonometric identities and equates, laws of sines and cosines, half and double angle formulas.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
College Preparatory II Analysis Semester I –
2.50 Credits Course #442
Description: This semester course treats the topics generally included in a math analysis course including limits, and extensive treatment of polynomial functions which include graphing, finding zeros and intercepts, end behavior, and asymptotes. Probability, exponential and logarithmic functions are also studied
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
College Preparatory II Trigonometry Semester II – 2.50 Credits Course #443
For students in
grades 11 & 12
Prerequisites: C in College Preparatory Algebra 2
Description: This semester course consists of all topics generally included in a trigonometry course with an analytic approach. The treatment of the circular functions is based on the wrapping function and the unit circle. Specific topics covered are solutions of trigonometric equations, trigonometric identities, graphs of the trigonometric functions, inverse trigonometric functions, Law of Sines, and the Law of Cosines.
Evaluation: Students will be evaluated based on their level of achievement of the learning standard as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
College Preparatory I Analysis Semester I
–2.50 Credit Course
#444
For students in
grades 11 & 12
Prerequisites: C in College Preparatory I Algebra 2. Overrides only as space permits.
Description: This semester course treats the topics generally included in a math analysis course including limits, an extensive treatment of polynomial functions which includes graphing, finding zeros and intercepts, end behavior, asymptotes, and an introduction to polynomial derivatives and their applications. Probability, exponential and logarithmic functions are also students.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
College Preparatory I Trigonometry Semester II – 2.50
Credits Course #445
Prerequisites: C in College Preparatory I Algebra 2. Overrides only as space permits.
Description: This semester course consists of all topics generally included in a trigonometry course with an analytic approach The treatment of the circular functions is based on the wrapping function and the unit circle. Specific topics covered are solutions of trigonometric equations, trigonometric identities, graphs of the trigonometric functions, inverse trigonometric functions, Law of Sines, Law of Cosines, polar coordinates, and DeMoivre’s Theorem.
Evaluation: Students will be evaluated on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
Honors Analysis and Trigonometry Full
Year – 5.00 Credits Course
#446
Prerequisites: B- or better in Honors Algebra 2 or superior
performance in College Preparatory I Algebra 2. Placement is by Mathematics Department recommendation only.
Description: This is an intensive course which provides an in-depth study of trigonometry and completes all the topics generally included in a pre-calculus course such as complex number systems, polynomial functions, and exponential and logarithmic functions at an abstract level at an accelerated pace. Additional topics include limits, introduction to derivatives, probability, vectors, sequences, and series.
Evaluation: Student will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, optional original exercises. Quizzes tests, and semester examinations.
Advanced Topics in Math Semester I –2.50 Credits Course #451
For students in grade
12
Prerequisites: Analysis and Trigonometry
Description: This course is an elective for seniors who wish to continue their study of mathematics. The class is heterogeneously grouped and open to any senior who has met the prerequisites. The goal of this course is to give student a fresh perspective on the structure and history of mathematics and to see real applications of mathematics. The course will include topics in discrete mathematics and number theory, topology, applications of topics in Algebra 2 and Pre-Calculus and other topics as they arise.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
Advanced Topics in Math Semester II
– 2.50 Credits Course
#452
For students in grade
12
Prerequisites: Analysis and Trigonometry
Description: This course is the second half of a senior elective. It may be taken independently of the first semester offering. The class is heterogeneously grouped and open to any senior who has met the prerequisites. The goal of this course is to give students a fresh perspective on the structure and history of mathematics and to see real applications of mathematics. The topics will include fractal geometry, chaos theory, topology, network theory, computer architecture and HTML, and other topics as they arise. Extensive use will be made of computer simulations and other software in the PC Lab.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
Statistics Full Year – 5.00 Credits Course #449
For students in grade
12
Prerequisites: Successful completion of a pre-calculus or
introduction to mathematical analysis course.
Description: This course addresses the field of statistics from a non-calculus –based perspective. It allows students to develop both an intuitive and rigorous understanding of statistical concepts and applications. This course will increase students’ ability to model quantitatively real-life situations, interpret and analyze data, and make necessary inferences. Students will develop competency with several appropriate technologies, including the TI-83, Excel, and other statistics software applications. Topics covered include descriptive statistics, probability, discrete probability p-distribution, normal probability distributions, confidence intervals, hypothesis testing with one sample, hypothesis testing with two samples, correlation and regression, chi-square tests and f-distribution, non parametric test.
Evaluation: Evaluation will be based on homework, completion of problem sets and take home questions, class participation, quizzes, tests, and semester examinations.
AP Statistics (Honors) Full
Year – 5.00 Credits Course
#TBA
For students in grade
12
Prerequisites: C+ in Honors Analysis and Trigonometry or
superior performance in College Preparatory Analysis and Trigonometry. Placement is by Mathematics Department
recommendation only.
Description: This course is for students who are able to proceed at an accelerated pace. The course consists of the topics covered in a semester 1 statistics course such as interpreting data, exploring bivariate data, methods of data collection, planning and conducting surveys and experiments, random variables, the normal distribution, other sampling distributions, confidence intervals, and tests of significance. Problem solving and interpretation of results will be stressed in the course, as both skills are an important component of the AP Statistics Exam. While not a requirement, students who enroll in this course should be prepared to take the Advanced Placement College Board examination in statistics near the end of the school year.
Evaluation: Students will be evaluation based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
Calculus Full
Year – 5.00 Credits Course
#454
For students in grade
12
Prerequisites: C+ in College Preparatory I Analysis and Trigonometry, or superior performance in College Preparatory II Analysis and Trigonometry.
Description: This course is for students who are able to proceed at an accelerated pace. The course consists of the topics included in a semester 1 college calculus course, and provides exposure to calculus for those students who are planning to take calculus in college.
Evaluation: Students will be evaluation based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
AP Calculus AB (Honors) Full
Year – 5.00 Credits Course
#455
Prerequisites: C+ in Honors Analysis and Trigonometry, or
superior performance in College Preparatory I Analysis and Trigonometry. Placement is by Mathematics Department
recommendation only.
Description: This course is for students who are able to proceed at an accelerated pace. The course consists of the topics included in a semester 1 college calculus course such as limits, derivatives, marginal analysis, maxima and minima, curve sketching, chain rule, inverse and implicit functions, transcendental functions, rate of proportional change, and differential equations. This course provides a non-rigorous approach to calculus, stressing application as opposed to theory. While it is not a requirement, students who enroll in this course should be prepared to take the Advance Placement College Board Examination in mathematics near the end of the school year.
Evaluation: Students will be evaluated based on their level of achievement of the learning standards as demonstrated through homework, class participation, quizzes, tests, and semester examinations.
AP Calculus BC Full Year – 5.00 Credits Course #456
For students in grade
12
Prerequisites: Superior performance in Honors Analysis and Trigonometry. Placement is by Mathematics Department recommendation only.
Description: This intensive, advanced placement course consists
of a full year of college calculus and analytic geometry. This course is recommended only for students
who have completed “Honors Analysis and Trigonometry” or its equivalent with
confidence in their ability to handle this material. Successful completion of this advanced placement course will
enable students to begin sophomore or other more advanced mathematics at most
high competitive colleges. Students who
enroll in this course should be prepared to take the Advanced Placement College
Board Examination in mathematics near the end of the year.
Evaluation: Evaluation will be based on the student’s level of achievement of the learning standards as demonstrated through homework, class participation, and quizzes, tests, and semester examinations.