Mathematics Department Curriculum Guide

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1 Mathematics Department Curriculum Guide Updated

2 I. PHILOSOPHY AND GOALS PHILOSOPHY: Keenly aware of their responsibility to prepare students for a world immersed in and dependent on technology, the members of the Mathematics Department strive to develop in each student a strong foundation in computational, analytical, and reasoning skills. The department acknowledges the changing complexion of mathematics education, specifically a greater focus on the useful and relevant applications of mathematics and a lesser emphasis on purely computational skills. Motivated by these considerations, a great effort is made by the department to foster and promote an integrated and interdisciplinary curriculum. The members of the department recognize the ever-increasing role of computers and hand held-graphing calculators/computers in facilitating the mathematics education of today s students. Subscribing to the philosophy of Bélen Jesuit Preparatory School, the Mathematics Department believes that in order to effectively teach a student how to learn mathematics, the student must first learn to love, appreciate and respect mathematics. The department considers individual differences among students and strives to offer a diversified college preparatory program which will meet the needs and interests and also be consistent with the abilities of all students. The department also assumes its part in the development of future leaders by emphasizing the importance of quantitative analysis of data in forecasting and decision-making. All members of the Mathematics Department are encouraged to be thoroughly familiar with and strive to meet the Standards of the National Council of Teachers of Mathematics. GOALS AND INSTRUCTIONAL OBJECTIVES: The Mathematics Department of Bélen Jesuit Preparatory School strives: 1. to develop in all students an appreciation and curiosity for mathematics. 2. to provide the students with comprehensive and challenging college prep, honors, and advanced placement classes. 3. to develop in the students analytical, reasoning, and critical thinking skills through problem solving and formal proof. 4. to promote an awareness of the history of mathematics. 5. to facilitate the learning of mathematics by consistently using accepted mathematical terminology and symbols. 2

3 6. to provide a conceptual, theoretical or at least an intuitive basis for mechanical and computational skills. 7. to enable the students to use technology to enhance their learning and understanding of mathematical concepts. 8. to encourage and model independent thinking by presenting, accepting, and encouraging a variety of problem-solving techniques and strategies. 9. to provide opportunities for the students to challenge and assert themselves. 10. to prepare students to think on their feet by presenting new situations in which the students can apply their mathematical knowledge. 11. to afford opportunities for the students to apply mathematical concepts and procedures learned in class to everyday real-life situations. 12. to promote an awareness of the many different careers that utilize mathematics. 13. to provide a solid foundation upon which the students can pursue college-level mathematics and other related courses. 3

4 MTH 3100: MATHEMATICS 6 Grade Level: 6 th Promotion Credit for 6 th Grade Prerequisites: None II. Course Offerings This one-year course of mathematics is designed to develop the student's understanding of basic mathematical concepts, skills and ability to perform arithmetic computations, and facility in working with word problems. The students will be expected to demonstrate proficiency in performing basic mathematical operations with whole numbers, fractions, decimals, and integers as well as a working knowledge of percents, geometrical measures of liquid volume, weight, and linear distance. In addition, the students will be introduced to algebraic expressions and solving basic algebraic equations. MTH 3200: MATHEMATICS 7 Grade Level: 7 th Promotion Credit for 7 th Grade Prerequisites: Successful completion of Mathematics 6 This one-year course of general and pre-algebra mathematics is designed to further develop the student's understanding of mathematical concepts, skills and ability to perform arithmetic computations, and facility in working with word problems. Topics of study include: word problems, algebraic equations and inequalities, basic operations with decimals, estimations, geometric measurements, fractions and percents. MTH 3210: HONORS PRE-ALGEBRA Grade Level: 7 th Promotion Credit for 7 th Grade Prerequisites: A grade of "A+" in Mathematics 6 and a 3.5 GPA This is an entry-level course into the Honor Mathematics Program. It is a comprehensive and accelerated course in pre-algebra mathematics designed for the students who exhibit an aptitude to pursue mathematics at a higher level. Topics of study include: signed number, rational numbers, algebraic equations, geometric figures, ratio, proportion, percent, inequalities, the coordinate plane, areas and volumes, right triangle trigonometry, probability and statistics. 4

5 MTH 3300: PRE-ALGEBRA Grade Level: 8 th Promotion Credit for 8 th Grade Prerequisites: Successful completion of Mathematics 7 This eighth grade mathematics course is designed to review previously learned mathematical skills and provide the students with a pre-algebra background as well as a strong introduction to Algebra I (MTH 3400). The new areas of study include integers, problem solving, equations, graphs, measurements, and statistical probability. MTH 3310: HONORS ALGEBRA I Grade Level: 8 th Promotion Credit for 8 th Grade Prerequisites: A grade of B in Honors Pre-Algebra or an A+ in Mathematics 7 and a 3.5 GPA This eighth grade mathematics course is an accelerated course in algebra. The course will help the students organize their thoughts in solving mathematical problems that are met in everyday life. Topics of study include: variables and equations, real numbers and operations with real numbers, factoring of polynomials, algebraic fractions, ratios and proportions, solving equations, linear functions and their properties, inequalities in one and two variables, rational and irrational numbers, radicals and quadratic functions. This course will also prepare the students to continue their studies in advanced mathematics courses. MTH 3400: ALGEBRA I Grade Level: 9 th Prerequisites: Successful completion of Pre-Algebra This ninth grade mathematics course is designed to teach Algebra. The course will help the students organize their thoughts in solving mathematical problems that are met in everyday life. The course will also prepare the student to continue studies in mathematics and the sciences. Topics of study include: variables and equations, real numbers and operations with real numbers, factoring of polynomials, algebraic fractions, ratios and proportions, solving equations, linear functions and their properties, inequalities in one and two variables, rational and irrational numbers, radicals and quadratic functions. 5

6 MTH 3410: HONORS GEOMETRY Grade Level: 9 th Prerequisites: A grade of "B" or better in Honors Algebra I and/or departmental approval This ninth grade mathematics course is an accelerated course in geometry. The course also covers deductive and inductive reasoning, indirect proofs, plane geometry, coordinate geometry, constructions and loci, trigonometry and transformations. The course is structured to teach the theory of geometry and its applications. Therefore, students will learn geometric theorems and their applications. MTH 3411: HONORS ALGEBRA 1/GEOMETRY A Grade Level: 9 th Prerequisites: A grade of A+ in Pre-Algebra and a 3.5 GPA or placement exam with department approval This ninth grade mathematics course is an accelerated course in algebra. The course will help the students organize their thoughts in solving mathematical problems that are met in everyday life. Topics of study include: variables and equations, real numbers and operations with real numbers, factoring of polynomials, algebraic fractions, ratios and proportions, solving equations, linear functions and their properties, inequalities in one and two variables, rational and irrational numbers, radicals and quadratic functions. This course will also prepare the students to continue their studies in honor mathematics courses. It is part of a two year program designed to accelerate students one year in mathematics. MTH 3500: GEOMETRY Grade Level: 10 th Prerequisites: Successful completion of Pre-Algebra This tenth grade mathematics course is a complete course in geometry. The course covers formal proofs, deductive and inductive reasoning, indirect proofs, plane geometry, coordinate geometry, constructions and loci, trigonometry and transformations. The course is structured to teach the theory of geometry and its applications. Therefore, students will learn geometric theorems and their applications. 6

7 MTH 3510: HONORS ALGEBRA II and TRIGONOMETRY Grade Level: 10 th Prerequisites: A grade of B or better in Honors Geometry and/or departmental approval This tenth grade mathematics course is an accelerated second-year algebra course. It includes a review of skills from Algebra I and all the essential topics of Algebra II. The emphasis is on equation solving and its application to solutions of world problems. Topics of study include: practice in fundamental operations of arithmetic, properties of real numbers, concepts of equations, inequalities, polynomials and functions, graphs, trigonometry, problem solving and algebraic language. MTH 3511: HONORS GEOMETRY B/ALGEBRA II Grade Level: 10 th Prerequisites: A grade of B or better in Honors Algebra/Geometry A and/or departmental approval This tenth grade mathematics course is an accelerated two-semester course, which is a general survey of geometry with an emphasis on Algebra 2. This course is designed to prepare students for Pre-Calculus. The topics covered include triangles, quadrilaterals, circles, transformations, similarity, area, and volume. Additional topics include linear, rational, circular, trigonometric, exponential, and logarithmic functions, composition of functions, inverse functions, sequences and series, and limits. MTH 3600: ALGEBRA II and TRIGONOMETRY Grade Level: 11 th Prerequisites: Successful completion of Geometry This mathematics course is a second-year algebra course in a college preparatory curriculum. It includes a review of skills from Algebra I and all the essential topics of Algebra II. The emphasis is on equation solving and its application to solutions of word problems. Topics of study include: practice in fundamental operations of arithmetic, properties of real numbers, concepts of equations, inequalities, polynomials and functions, graphs, problem solving and algebraic language. 7

8 MTH 3610/3611: HONORS PRECALCULUS Grade Level: 11 th Prerequisites: A grade of B or better in Honors Algebra 2 or Honors Geometry/Algebra 2 and/or departmental approval Honors Pre-Calculus is a two-semester course, which is a general survey of pre-calculus mathematics with an introduction to calculus. This course is designed to prepare students for AP Calculus AB or BC. The topics covered include polynomial, rational, circular, trigonometric, exponential, and logarithmic functions, composition of functions, inverse functions, polar coordinates and graphs, analytic geometry, sequences and series, and limits MTH 3700: MATHEMATICAL ANALYSIS Grade Level: 12 th Prerequisites: Successful completion of Algebra II and Trigonometry Mathematical Analysis is a two-semester course which is a general survey of Precalculus mathematics with an introduction to calculus. The topics that are covered include polynomial, rational, circular and trigonometric, exponential, and logarithmic functions, composition of functions, inverse functions, analytical geometry, sequences and series, and limits. HONORS CALCULUS (3710) / 1 additional quality point Grade Level: 12 th Prerequisites: Successful completion of Honors Pre-Calculus or an A in Math Analysis and/or departmental approval A two-semester course designed to provide a foundation for the study of college-level Calculus. The course will be taught at an AP level without the requirement of taking the AP exam. Topics include: properties of functions, limits, differential and integral calculus. This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, geometry, trigonometry, and analytic geometry. 8

9 MTH 3750/3755: A.P. CALCULUS AB/BC / 2 additional quality points Grade Level: 12 th Prerequisites: A grade of B or better in Honors Pre-Calculus and/or departmental approval A year long advanced placement course designed to qualify the student for one to two semesters of college credit in calculus. Credit and/or placement varies with the college or university and depends upon the performance on the AB/BC Calculus test administered by the College Board in May. Topics include: properties of functions, limits, and differential and integral calculus. This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry (rectangular and polar coordinates, equations, graphs and lines). MTH 3757: AP STATISTICS / 2 additional quality points Grade Level: 11 th - 12 th Prerequisites: A grade of A or higher in Algebra II or Math Analysis and a 3.5 GPA or successful completion of Honors Pre-Calculus Advanced Placement Statistics is designed to prepare students for the Advanced Placement Examination. It is a two-semester, non-calculus based, course in the formal study of the basic principles of statistical thinking and scientific investigation. An emphasis will be made in the following four areas: Exploring Data; Planning a Study; Anticipating Patterns; and Statistical Inferences. Topics include: data collection and organization, central tendencies, probability theory, binomial probability distribution, normal distributions, sampling distributions, confidence intervals, estimation, hypothesis testing, regression, correlation, chi-square, and t- distributions. 9

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in