The CPS Mathematics Curriculum

Mathematics I

1 Unit

Concepts and applications of algebra, problem-solving, and geometry are the main topics in this course, designed to prepare students with diverse mathematial backgrounds for Math II. Students learn how to use the scientific calculator to solve problems and use manipulatives extensively to develop spatial visualization skills. They often work together in small groups in the classroom, developing their collaborative skills and their ability to explain mathematics clearly. Students review and practice algebra skills in a wide variety of situations. Topics include proportional reasoning, geometric similarity and transformations, area and perimeter, linear and quadratic equations, and introductory statistics and probability. This course is coordinated with Science I.

Mathematics II

1 Unit

The development of more formal mathematical reasoning provides the theme for this course, which stresses the distinction between inferences from examples and patterns (inductive reasoning) and a convincing logical argument (deductive reasoning). Coordinate methods, transformations, and algebraic problems concerning figures in two and three dimensions serve as vehicles to develop this theme in a context rich in both geometry and algebra. Students are motivated through the assembly and use of models, which help their spatial visualization and make abstract ideas more concrete. Taught at the honors level, the course includes more algebra, three-dimensional geometry, geometric transformations, coordinate geometry, statistics, and probability than a typical geometry course.

Mathematics III

1 Unit

The concept of function serves as a framework for this course. Mathematical modeling (deriving a mathematical expression from real-world data) is introduced, and students do experiments and use graphing calculators to gather information. Students purchase a course-specific graphing calculator and are instructed in its use. Algebraic skills are practiced within the context of solving problems, and geometric interpretations and graphing are emphasized. Students continue the study of linear and quadratic equations begun in Math I and Math II, adding new functions to their repertoire: polynomials, trigonometric functions, exponentials, and logarithms. The statistics and probability topics introduced in Math II are deepened and extended.

This course is offered at two levels: Math IIIA and Math IIIB. Both are college preparatory and cover functions and applications. Math IIIA covers topics usually included in algebra II honors, trigonometry and precalculus and includes quite challenging problems. It prepares students for Level IIC of the College Board SAT II Test in Mathematics. Math IIIB covers topics normally taught in algebra II and trigonometry. It prepares students for Level IC of the College Board SAT II Test in Mathematics.

Mathematics IV

1/2 Unit Each Semester

This class is offered at two levels, Math IVA and Math IVB. Both are two-semester courses that prepare students for a standard, first-year college mathematics or statistics course.

Math IVA covers honors precalculus topics and introduces important calculus concepts and techniques. It has four major themes: calculus; algebra, geometry and trigonometry; discrete mathematics; and mathematical objects and representations (such as polar coordinates and matrices). Topics are introduced through discovery when possible to enhance motivation. Instruction in the graphing calculator continues, though students also solve many problems without using calculators.

Math IVB is a traditional precalculus course. It covers functions, graphs and their applications, trigonometry and discrete mathematics. Students learn the material through lecture, group work, and homework.

Mathematics V: Calculus AB (AP) & Calculus BC (AP)

1/2 Unit Each Semester

This two-semester course covers differential and integral calculus at the college level; there are two versions. Math VAB is the basic course, covering techniques and applications of derivatives and integrals. It prepares students for the "AB" Advanced Placement Examination. Designed for the strongest math students, Math VBC covers the same material, often in a more theoretical form, as well as topics like infinite series and multivariable calculus. It prepares students for the "BC" Advanced Placement Examination. The department advises students on which course to take based on their previous math work at CPS.

Advanced Placement Statistics

1/2 Unit Each Semester

This two-semester course is equivalent to a one-semester college course in statistics. It is particularly suitable for anyone interested in a science or social science major in college. Students gain a knowledge and understanding of various formulas and techniques used in basic statistics. There are also wide-ranging discussions designed to give students an appreciation of how statistics are used in academic settings, the workplace, and daily life. Students may take this course after or at the same time as Math IVA, or, with permission, after Math IVB.