*Weighted Courses

The following charts show the transitions necessary for the implementation of changes in the math curriculum. These charts reflect the general sequence of both required and elective courses.

Course Descriptions

SUMMER MATH BRIDGE
One semester, one credit
This course is offered in summer school and is appropriate for students who have earned a C or D in Algebra I and who would like to get a head start on *AP Prep Algebra II: Advanced Systems. The course content will focus on formal logic, mathematical proof, and algebraic systems. The nature of this course will provide some review of Algebra I concepts and skills, but these will not be the focus of the course. Out-of-class homework assignments are part of the course requirements.
PSAE MATH
One semester, one credit
This is a required course for juniors who received a 15 or less on the math portion of the PLAN test administered during their sophomore year. This course provides students with strategies to effectively apply their knowledge and skills to solve mathematics problems in the areas of number sense, measurement, algebra, geometry, probability, statistics, and data analysis. The course will count for one elective credit.
MATH FUNDAMENTALS
One year, two credits
This course is designed to strengthen basic arithmetic skills and to provide a bridge from arithmetic to high school mathematics. Content includes: computation with the basic four operations, ratios, fractions, decimals, percents, problem solving, basic algebra, and basic geometry concepts and skills. Out-of-class homework assignments are part of the course requirements.
MATH APPLICATIONS
One year, two credits
Computational skills will certainly be necessary to solve problems and to complete assignments but they will not be the focus of instruction. This course will focus upon: authentic tasks such as meeting the expectations of employers; intricate tasks such as requiring more than substitution into formulas and multi-step procedures; interesting tasks that touch on the personal interests of students; and powerful tasks that connect graphical, numerical, symbolic, verbal, and technical approaches, and propel students into more advanced mathematics. Out-of-class homework assignments are part of the course requirements.
COLLEGE PREP ALGEBRA I
One year, two credits
The emphasis of this course is on problem solving, the use of spreadsheets, collaboration with other students in learning teams, and graphing. Content includes: simplifying, factoring, solving equations and inequalities, solving systems of equations, graphing, working with rational expressions, working with radical expressions, solving quadratic expressions, and problem solving. Out-of-class homework assignments are part of the course requirements.
*AP PREP ALGEBRA I
One year, two credits
This course is for advanced 8th grade students who wish to pursue advanced high school mathematics. The course is taught at the high school and may involve team teaching. The course content will focus on basic set theory, rigorous development of relations, and functions from a set theoretic perspective, basic algebraic systems, basic number theory, development of the system of integers, and an extension of topics included in the College Prep Algebra I course. Extensions of Algebra I topics will include: factoring, simplifying algebraic expressions solving linear and quadratic equations, graphing on number lines, graphing in a Cartesian coordinate system, solving systems of equations, and simplifying and using radical expressions. There will be an emphasis on higher order thinking through providing mathematical arguments and solving problems. Students who earn an A or B in this class are encouraged to take *AP Prep Algebra II: Advanced Systems their freshman year.
COLLEGE PREP ALGEBRA II
One year, two credits
Prerequisite: College Prep Algebra I or *AP Prep Algebra I.
This course extends the work of College Prep Algebra I. It includes: an introduction to logic and proof, a study of relations and functions as sets of ordered pairs, a study of the real numbers as a field, a study of the complex numbers as a field, solving systems of linear and quadratic equations, solving inequalities and systems of inequalities, a study of sets of polynomials (defined over a set of numbers) as systems and polynomial equations, introduction to and application of the binomial theorem, an introduction to circular functions, an introduction to arithmetic and geometric progressions, and basic analytic geometry. Out-of-class homework assignments are part of the course requirements.
*AP PREP ALGEBRA II: ADVANCED SYSTEMS
One year, two credits
Prerequisite: College Prep Algebra I or *AP prep Algebra I
This is an extremely rigorous course designed for the most mathematically talented students. The content of this course includes: rigorous development of circular functions, basic formal logic; rigorous mathematical proof that exhibits the syllogisms used in the argument, proof by contradiction, proof by contraposition, and proof by math induction; a rigorous, set-theoretic approach to the study of relations and functions; an introduction to abstract algebraic systems, rigorous study of the system of integers under addition and multiplication as an integral domain, rigorous study of the system of rational numbers under addition and multiplication as a field, introduction to and use of the real number field; number theoretic concepts of divisibility and factorability, and development and refinement of the computational skills and symbolic manipulation skills taught in a second year, high school algebra course. The second year algebra skills will include: solving linear and quadratic equations using various methods, graphing linear and quadratic equations, solving systems of linear equations using various methods including matrix solutions, an introduction to polynomials that are defined over specific mathematical systems, and factoring of specific types of polynomials The focus of this course is on higher order thinking skills including: analysis, synthesis, argument building and presentation, and problem solving. Students should expect to work with other students in study group situations both in class and outside of school. Students should expect to spend more than one hour per day outside of class to meet the learning demands of this course. Students should expect to have daily access to assistance.
COLLEGE PREP GEOMETRY
One year, two credits
Prerequisite: College Prep Algebra II or *AP Prep Algebra II: Advanced Systems.
Geometry is the logical study of points, lines, angles, polygons, and circles with emphasis on the use of formal deductive reasoning to write proofs. Out-of-class homework assignments are part of the course requirements. The course is demanding in both time and effort. Students should be self-motivated and possess a high level of self-discipline. Continuation in the second semester of this course requires either a passing grade in the first semester or a grade of “conditional”.
*AP PREP GEOMETRY
One year, two credits
Prerequisite: College Prep Algebra II or *AP Prep Algebra II: Advanced Systems.
This course will cover all of the topics covered in Geometry. There will be an emphasis on the use of formal logic and the level of rigor in constructing proofs will be much higher that that in College Prep Geometry. This course will also include right triangle trigonometry, non-Euclidean geometries, and some analytic geometry.
STATISTICS
One semester, one credit
Prerequisite: College Algebra II or *AP Prep Algebra II: Advanced Systems.
This is an activity-based introduction to statistics. Content includes descriptive statistics, probability, sampling and tests of statistical significance, and other topics as time permits. It is recommended that students have their own TI-83+ calculator, or an equivalent model; however, calculators are available for use in the classroom. Out-of-class homework assignments are part of the course requirements.
COLLEGE ALGEBRA/TRIGONOMETRY
One year, two credits
Prerequisite: College Prep Algebra II or *AP Prep Algebra II: Advanced Systems.
This course is intended for college-bound students who desire four years of high school mathematics. It consists of an in-depth study of algebraic topics such as linear and quadratic equations, inequalities, functions and their graphs (including polynomial, exponential, inverse, logarithmic, and rational functions). The trigonometric component of the course begins with a review of functions and graphing. The course then covers circular, trigonometric, and inverse trigonometric functions, their graphs, and various applications including polar coordinates, solutions of triangles, and word problems. Students will use graphing calculators and a calculator such as the TI-83+ is recommended. Out-of-class homework assignments are part of the course requirements.
*PRE- CALCULUS/TRIGONOMERTY
One year, two credits
Prerequisite: College Prep Geometry or *AP Prep Geometry.
This course is intended to prepare strong math students for AP Calculus BC and to equip them with the mathematical tools they will find necessary for success in weighted physics (typically taken concurrently). It will serve as a bridge from high school-to college-level mathematics. This course is very rigorous in terms of the mathematical content and pace. Topics covered include: polynomial, rational, trigonometric, inverse trigonometric, logarithmic, and exponential functions along with their graphs; polar coordinates; parametric equations; sequences and series; proof by induction; vector operations; trig identities; limits and continuity; matrix transformations; analytic geometry including rotated conic sections; and polar representations of complex numbers. The course will also focus on applications and problem solving. A graphing calculator, such as a TI-83+ or TI-89, is highly recommended. Out-of-class homework assignments are part of course requirements.
*AP CALCULUS (AB & BC)
One year, two credits
Prerequisite: *Pre-Calculus/Trigonometry.
This is a very rigorous, university level course. Students are required to do summer preparatory work in pre-calculus and introductory calculus topics, including matrix theory, parameterizations, conic sections, and limits. Homework is assigned and collected regularly throughout the school year. The AB version of the course covers a full semester of university-level calculus, including limits, differentiation theorems, Riemann sums, business and scientific applications, optimization, differential equations, and antidifferentiation. The BC version of the course covers (in addition to the previous topics) infinite series, calculus using parametric and polar equations, advanced techniques of integration, and many other topics. Students should expect to do regular homework. Extra help will be available before and after school. Students can earn university credit for one of two calculus courses via the Advanced Placement Exam given near the end of the school year. A graphing calculator, such as a TI-83+ or TI-89, is highly recommended.
*Weighted Courses

Page Updated 8-24-05

Urbana High School
1002 S. Race Street
Urbana, Illinois 61801

Phone: 217-384-3505
Fax: 217-384-3532