PHILOSOPHY OF THE MATHEMATICS DEPARTMENT


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1 PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building of mathematical skills through highquality instruction Mastery of material aligned with state and national standards Courses offered within the Mathematics curriculum help students learn challenging mathematics ideas through a variety of teaching techniques. The department is committed to properly integrating technology into all facets of the mathematics curriculum. Based on their abilities and course level, students shall reach the following National Council of Teachers of Mathematics standards, which are outlined in Principles and Standards for School Mathematics: Numbers and Operations Standard Algebra Standard Geometry Standard Measurement Standard Data Analysis and Probability Standard Problem Solving Standard Reasoning and Proof Standard Communication Standard Connections Standard Representation Standard Grading Standards: Student grades are determined based on their performance on homework and final examinations, as well as cumulative proficiency. Note: A graphing calculator is required for all courses in the mathematics curriculum; students should consult with their instructors for more details. In order to select the proper Mathematics courses, students should consult the math flow chart, which may be viewed on the Lemont High School Web site. CORE COURSES  MATHEMATICS PreAlgebra Prerequisite: None Description: This course is an introduction to high school level mathematics, and prepares students to enroll in Algebra I. The course covers basic operations involving integers, decimals and fractions; algebraic expressions and equations; linear equations and inequalities; number line and coordinate graphing; exponents; exponential expressions; and absolute value. Students are expected to use a graphing calculator. Lemont High School Program of Studies 39
2 Algebra I Applications Grades Course Open To: Credit: 1.0 Prerequisite: Successful completion of one mathematics course Description: This course is designed to investigate and develop algebraic concepts through the use of technology. Problems from the areas of linear, polynomial and exponential functions, systems of equations, series and sequences, graph analysis and trigonometry involve applications from business, finance, economics and consumer education. Both algebraic and graphical interpretation of data are stressed, as is the connection between the algebraic and graphical representations of data. Note: This course satisfies the Consumer Education requirement. Algebra I AB Grades Course Open To: Credit: 2.0 Prerequisite: Successful completion of PreAlgebra or by result of placement test Description: This course covers the four fundamental operations with rational numbers, which are then applied to the solutions of equations in one variable. Students study axioms of inequalities, which is followed by work with inequalities in one variable. Solution sets and graphs of open sentences in two variables are presented, studied and solved. Multiplication and factoring of polynomials are discussed and equations in one variable are solved. Graphs are used to represent data and mathematical modeling. The course helps students appreciate the need for precision of language and lays the groundwork for the study of advanced algebra. The course meets daily, which allows students to develop a proficiency in basic skills in addition to comprehension of the mathematics language. Algebra I Prerequisite: Successful completion of PreAlgebra or by result of placement test Description: This course covers the four fundamental operations with rational numbers, which are then applied to the solutions of equations in one variable. Students study axioms of inequalities, which is followed by work with inequalities in one variable. Solution sets and graphs of open sentences in two variables are presented, studied and solved. Multiplication and factoring of polynomials are discussed and equations in one variable are solved. Graphs are used to represent data and mathematical modeling. The course helps the student appreciate the need for precision of language and lays the groundwork for the study of advanced algebra. Algebra II AB Grades Course Open To: Credit: 2.0 Prerequisite: Successful completion of Algebra I or Algebra I AB Description: This course provides a review of the basic terminology, concepts, skills and applications presented in Algebra I, and emphasizes theory and sophistication in mathematics. A number of new topics are introduced and studied in depth, including absolute value equations, matrices, quadratics, irrational numbers, complex numbers, rational expressions, logarithms and statistics. The course provides students with the terminology, skill and algebraic background necessary for success in college mathematics. Major units of study include equations and inequalities, linear equations and functions, linear systems and matrices, quadratic functions and factoring, polynomials, rational exponents and radical functions, exponential and logarithmic functions, rational functions, and data analysis and statistics. The course meets daily, which provides students with better retention and an opportunity for additional tutoring in the subject matter. 40 Lemont High School Program of Studies
3 Algebra II Prerequisite: Successful completion of Algebra I or Algebra I AB Description: This course provides a review of the basic terminology, concepts, skills and applications presented in Algebra I, and emphasizes theory and sophistication in mathematics. A number of new topics are introduced and studied in depth, including absolute value equations, matrices, quadratics, irrational numbers, complex numbers, rational expressions, logarithms and statistics. The course provides students with the terminology, skill and algebraic background necessary for success in college mathematics. Major units of study include equations and inequalities, linear equations and functions, linear systems and matrices, quadratic functions and factoring, polynomials, rational exponents and radical functions, exponential and logarithmic functions, rational functions, and data analysis and statistics. Accelerated Algebra II Honors Grades Course Open To: 910 Credit: Honors credit Prerequisite: Result of placement test Description: The first in the accelerated math sequence, this course consists of challenging material designed for aboveaverage students. The course moves through material at a quick pace, requires students to apply knowledge to new mathematical and practical situations, and stresses the analysis of mathematical functions through a rigorous curriculum. A number of new topics are introduced and studied in depth, including linear and quadratic equations and inequalities, linear and quadratic functions, systems of equations and inequalities, matrices, factoring, polynomials, radicals and irrational numbers, exponential and logarithmic functions, complex numbers, and an introduction to counting problems and probability. The course provides students with the terminology, skill and algebraic background necessary for success in college mathematics. Geometry Applications Grades Course Open To: Credit: 1.0 Prerequisite: Successful completion of one mathematics course Description: This course is designed for students who may be apprehensive about the content in the standard geometry course or who may not have found success in previous math courses. Basic geometry topics and concepts are introduced and reinforced, as students experience hands on projects and applications and observe real life uses of geometry. Concrete examples and projects provide additional opportunities for students to understand geometric concepts and gain success with the material. The student is familiarized with basic terms, useful language, symbolism and definitions common to a geometry course. Some topics include geometric art, angles, perpendicular lines; congruent and right triangles, similarity, circles, area, perimeter, volume, transformations and tessellations. This course may be taken concurrently with Geometry. Lemont High School Program of Studies 41
4 Geometry Prerequisite: Successful completion of Algebra II Description: This course introduces and studies in depth the concepts of geometry, and is recommended for all collegebound students. The coursework includes basic geometric definitions and shapes, triangle congruence, similar triangles, parallel and perpendicular lines, quadrilaterals, circles, area and volume of geometric figures, and proofs. Students become familiar with all basic terms and definitions in relation to the coursework, which are of value in later mathematics courses and applications. This course may be taken concurrently with PreCalculus. Accelerated Geometry Honors Grades Course Open To: Credit: Honors credit Prerequisite: Grade of B or better in Accelerated Algebra II Honors; concurrent enrollment in Accelerated Trigonometry Honors Description: This advancedlevel course is the second in the accelerated mathematics sequence, and is designed to develop and enhance students ability to analyze a problem while maintaining their algebra skills. Students learn to read mathematical exposition and analyze and solve problems that are geometric in nature, and realize the importance of course concepts in their everyday lives. Students become familiar with all basic terms, definitions, useful language and symbolism in relation to the coursework, which are of value in later mathematics courses and applications. Among the many topics covered in this fastpaced course are elements of geometry, angles and perpendicular lines, congruent and right triangles, similarity, circles, areas and volumes, coordinate geometry and a number of proofs. Trigonometry Grades Course Open To: Credit: 0.5 Prerequisite: Successful completion of, or current enrollment in, Geometry Description: This course is designed for students who intend to pursue mathematics beyond the Algebra II level, or for those who are interested in careers involving engineering, mathematics, physics, architecture or drafting. It includes a thorough introduction to trigonometry concepts that are necessary for further study of mathematics and physics at the college level, and is highly recommended for all collegebound students. Students work to master a number of trig concepts, including right triangle trig, trig functions, trig equations, trig identities, the unit circle, area of a triangle, law of sines and cosines, graphing functions, and numerous applications. Accelerated Trigonometry Honors Grades Course Open To: Credit: Honors credit Prerequisite: Grade of B or better in Accelerated Algebra II Honors; concurrent enrollment in Accelerated Geometry Honors Fees: $10 course fee Description: This advancedlevel course covers trigonometry material in greater depth, and also introduces students to additional topics related to trigonometric concepts. Students study values of trigonometric functions, solving trigonometric equations, right triangle trigonometry, trigonometric identities and laws, applications and graphing trigonometric functions. This course is required for students who intend to take Accelerated PreCalculus Honors or AP Calculus BC at the high school level. 42 Lemont High School Program of Studies
5 PreCalculus Grades Course Open To: Credit: 1.0 Prerequisite: Successful completion of Geometry and successful completion of, or current enrollment in, Trigonometry Description: This course is designed to prepare students for AP Calculus AB, helping them obtain a deeper mathematical comprehension of the material. It is a collaboration of material from previous courses, of which students should have a solid foundation, and new concepts. A variety of functions are studied, including linear, polynomial, rational, exponential, logarithmic, inverse and piecewise. Additionally, the course correlates algebraic concepts with graphical representations of the material. The language of functions is used extensively. Course material also includes the study of series and sequences, conics and limits. Accelerated PreCalculus Honors Grades Course Open To: Credit: Honors credit Prerequisite: Grades of B or better in Accelerated Algebra II Honors, Accelerated Geometry Honors and Accelerated Trigonometry Honors Description: This course is a continuation of the accelerated mathematics sequence, introduces students to advanced mathematical concepts, and serves as a preparatory course for AP Calculus BC. The curriculum is based on materials developed for the Mathematics Investigations course offered by the Illinois Math & Science Academy (IMSA), and concentrates on the study of matrices, functions (linear, polynomial, rational, logarithmic, exponential, parametric and piecewise), series and sequences, theory of equations and analytic geometry, and also provides an introduction to combinatorics. Students enrolled in this course must have a good grasp of algebraic, geometric and trigonometric concepts. AP Calculus AB Grades Course Open To: Credit: weighted for AP Prerequisite: Grade of C or better in PreCalculus Fees: AP Calculus AB exam (paid at fall registration) Description: This is one of the toplevel courses offered by the mathematics department, and can be the equivalent of one semester of calculus coursework at the college level. Students must demonstrate mastery of concepts and skills learned in previous courses. The course content is comprised of linear, polynomial, logarithmic and exponential functions. Students develop all basic concepts of differential and integral calculus of functions in one variable. A thorough discussion of the concept of limits and its application to advanced mathematics is included. Other major topics covered are the nature and applications of the integral, techniques of integration, and elementary differential equations. Only those students who intend to take collegelevel mathematics courses and who have shown a high degree of aptitude in previous mathematics courses should enroll. The course meets daily in the first semester, and every other day in the second semester. Note: All students enrolled in this course must take the AP Calculus AB exam in the spring. Lemont High School Program of Studies 43
6 AP Calculus BC Grades Course Open To: Credit: weighted for AP Prerequisite: Grade of C or better in Accelerated PreCalculus Honors Fees: AP Calculus BC exam (paid at fall registration) Description: This is one of the toplevel courses offered by the mathematics department, and can be the equivalent of two semesters of calculus courses offered at the college level. Students must demonstrate mastery of concepts and skills learned in previous courses. The course content is comprised of linear, polynomial, logarithmic, exponential, polar and vector functions, and introduces and develops all basic concepts of limits and their application to advanced mathematics. Fundamental integration, as well as advanced integration techniques, are examined. Other topics include: solving differential equations, infinite series, and power series for elementary functions. Only those students who intend to take collegelevel mathematics courses and who have shown a high degree of aptitude in previous mathematics courses should enroll. The course meets daily in the first semester, and every other day in the second semester. Note: All students enrolled in this course must take the AP Calculus BC exam in the spring. AP Statistics Grades Course Open To: Credit: weighted for AP Prerequisite: Grade of B or better in Accelerated Algebra II Honors and Accelerated Geometry Honors; or grade of B or better in Algebra II or grade of B or better in PreCalculus Fees: AP Statistics exam (paid at fall registration); $5 course fee Description: This advancedlevel 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, anticipating patterns, and statistical inferences. Among the many topics discussed are: interpreting graphical displays of distribution, summarizing and comparing distributions, exploring bivariate and categorical data, methods of data collection, planning and conducting surveys and experiments, generalizability of results from observations and experiments, probability as relative frequency, combining independent random variables, confidence intervals, tests of significance, and special cases of normally distributed data. Students who are successful in this course may receive advanced placement, college credit or both for a onesemester introductory college statistics course. Note: All students enrolled in this course must take the AP Statistics exam in the spring. Advanced Calculus Grades Course Open To: Credit: Honors credit Prerequisite: Score of 4 or 5 on the AP Calculus BC Exam Fees: $225 (may change at the discretion of the University of Illinois, UrbanaChampaign) Description: The most advanced mathematics course offered by the department, this is the third course in calculus and analytic geometry, and is the equivalent of a one semester course offered at the college level. This course uses the software program Mathematica as a teaching device to cover threedimensional space, functions of several variables, partial derivatives and multiple integrals. Major units of study include parametric plotting, vectors, perpendicularity, 2D integration, gradients, trajectories, 2D and 3D measurements, sources and sinks, transforming 2D and 3D integrals, spherical coordinates and 3D flow. Only those students who intend to take collegelevel mathematics courses and have shown a high degree of aptitude in previous mathematics courses should enroll. Four hours of college credit is given upon successful completion of the course and credit payment to University of Illinois, Urbana Champaign. 44 Lemont High School Program of Studies
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