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Mathematics Department

MATHEMATICS DEPARTMENT

                                                                                 
                      




PHILOSOPHY, GOALS AND OBJECTIVES

OF THE MATHEMATICS DEPARTMENT


In accordance with the philosophy of Cardinal O'Hara High School, the Mathematics Department "professes its mission to be one of preparing students for a fullness of life" by encouraging the student "to bring to maturity his gifts and talents" with a special emphasis on the development of his reasoning capabilities.


The goals and instructional objectives of the Math Department are such that, through the math program and student's experiences in the math classroom, the student


  1. will learn to value mathematics


  1. will become confident in his own ability


  1. will become a mathematical problem solver


  1. will learn to communicate mathematically


  1. will grow to appreciate, respect and value his own gifts and talents and those of others

  2. will become a truth seeker and, consequently, a seeker of God Who is Ultimate Truth.


INTRODUCTION


A solid four year, college prep math program is available for all students. All students are required to take three years of math; all are encouraged to take four years of math.


Mathematics courses are taught on levels reflecting the differences in ability and learning rate of students.  Ninth grade students are placed in track levels by means of a selection formula which includes seventh and eighth grade marks and standardized test scores. Eighth grade teachers review the student's placement and may recommend a change of track.  O'Hara math teachers will request a track change for a student who seems to be mistracked.


The Mathematics Department reserves the right to deny admission to a course when the applicant has not met the published prerequisites.  The department also reserves the right to cancel a course if an insufficient number of students have enrolled.

 

If a student and/or parents have requested a change to a lower track, the student and/or parents may not request placement in a higher track for the following school year.


An eighth-grade student who has completed a full year of Algebra I in a Diocesan Honors Program or in a public/private school may be considered for enrollment in Course 331.  Recommendation of Algebra I teacher as well as an outstanding proficiency on an Algebra Placement test are required.


Because of the sequential nature of mathematics, a student must achieve a degree of proficiency in a course before taking the next course.  Teacher recommendation is the most important factor considered when placing a student in the next course.  Approval by the Department Chair is required when a student requests a track that the present Teacher has not recommended.


Track 1

This is a challenging program meant for highly motivated students.  The courses are geared to prepare students to major in mathematics and related fields.


Track 2

This is a college preparatory program for above average and motivated students.  The mathematics courses are geared to prepare students for college programs requiring the study of mathematics.

 

Track 3

This program offers the student a fundamental high school mathematics sequence from algebra through trigonometry.  Students successfully completing the program are prepared to study college algebra or a similar course.


Track 5

This is an advanced placement course for superior students.  It is a challenging program preparing students to be successful in an AP examination.


* A graphics calculator is required for all mathematics courses.*


* Most courses require the purchase of a Mathematics Workbook. *




        RECOMMENDED SEQUENCE OF MATHEMATICS COURSES


    9th Grade    10th Grade    11th Grade    12th Grade


Track 5 (AP)        AP Prep:    AP Calculus AB

            Pre-Calculus


Track 1    Algebra 1    Geometry    Algebra 2    Pre-Calculus


Track 2    Algebra 1    Geometry    Algebra 2    Pre-Calculus


Track 3    Algebra 1    Geometry    Algebra 2    Algebra 3/Trig




Electives


Calculus

AP Statistics, Statistics

AP Calculus BC   



311 Algebra 1       6 ppc  1.00 cr.  Tr. 1   Gr. 9



Based on the Common Core Standards, students enrolled in Algebra 1 will examine structure in equations, and will create equations that describe numbers or relationships.  Students will reason with equations and inequalities abstractly and quantitatively, will solve systems of equations and will represent and solve equations and inequalities graphically.  Students will construct viable arguments for their reasoning and critique the reasoning of others.

 The top students in this class will be invited to take 321 and 331 concurrently.


2 semesters


312 Algebra 1      6 ppc     1.00 cr. Tr. 2     Gr. 9



This course covers the outline as named above.  The pace and depth of content depend on track level.


2 semesters



313 Algebra 1        6 ppc     1.00 cr. Tr. 3     Gr. 9


This course covers the outline as named above.  The pace and depth of content depend on track level.


2 semesters


321 Geometry      6 ppc     1.00 cr. Tr. 1  Gr. 10


Based on the Common core Standards, students enrolled in Geometry will experiment with transformations in the plane, will prove geometric theorems and will make geometric constructions.  Students will understand similarity, right triangles and trigonometric rations.  Students will understand and apply theorems about circles, will express geometric properties with equations, and will use geometric measurement and dimension to solve problems.  Students will reason abstractly and quantitatively and will construct viable arguments and critique the reasoning of others.

Prerequisite:  Successful completion of Algebra I, recommendation of teacher, and approval of the department chair.


2 semesters


322 Geometry      6 ppc     1.00 cr. Tr. 2     Gr. 10


This course covers the outline as named above.  The pace and depth of content depend on track level


2 semesters


323 Geometry      6 ppc     1.00 cr. Tr. 3     Gr. 10


This course covers the outline as named above.  The pace and depth of content depend on track level.


2 semesters


331 Algebra 2       6 ppc    1.00 cr.   Tr. 1         Gr. 11


Based on the Common Core Standards, students enrolled in Algebra II will interpret and build functions, will perform arithmetic with polynomials and rational functions, will analyze functions using various representations and will construct and compare linear and exponential models and solve problems.  Students will reason abstractly and quantitatively, will construct viable arguments and critique reasoning of others and will use appropriate tools of mathematics.

Prerequisite:  Successful completion of Geometry 321 with an average of 93+, recommendation of teacher, and approval of the department chair.

2 semesters


332 Algebra 2      6 ppc     1.00 cr. Tr. 2     Gr. 11


This course covers the outline as named above.  The pace and depth of content depend on track level.


2 semesters



333 Algebra 2          6 ppc     1.00 cr. Tr. 3     Gr. 11-12


This course covers the outline as named above.  The pace and depth of content depend on track level


2 semesters


341 Pre-Calculus        6 ppc 1.00 cr. Tr. 1 Gr. 12


Students will reason abstractly and quantitatively about the interdependence of logarithmic, exponential and trigonometric graphs and functions, and discrete mathematics and the underpinnings of calculus.  Students will be able to apply said functions to real world applications, and construct viable arguments and critique the reasoning of others.

Prerequisite:  To be admitted to this course, students must have completed Geometry and Algebra II at least at the track 2 level, maintained an average of at least 90, and have the approval of the department chair.

2 semesters


342 Pre-Calculus      6 ppc     1.00 cr. Tr. 2     Gr. 12


This course covers the outline as named above.  The pace and depth of content depend on track level


2 semesters


343 Algebra 3/Trigonometry      6 ppc 1.00 cr. Tr. 3     Gr. 12



This course is designed for students who have learned the basic skills of Algebra I and II and who know the basic concepts of Geometry.  This course is designed to build on this knowledge from previous courses.  This course covers the following topics:  relations and functions, radical expressions, linear systems, topics of analytic geometry and coordinate geometry, if possible logarithmic and exponential equations, right triangles, oblique triangles, trigonometric and circular functions, identities and equations.


Prerequisite:  75 in 333 or approval by Department Head and Teacher.


2 semesters


346 Calculus          6 ppc     1.00 cr. Tr. 1   Gr. 11-12

This course includes the study of:  functions, the derivative and its application, integration, applications of the definite integral, and a study of plane and analytic geometry using calculus.  


Prerequisite:  Approval by Department Head and Teacher.

                                             2 semesters



345 A.P. Calculus AB      6 ppc 1.00 cr. Tr. 5     Gr. 11-12


This course includes the study of functions and limits, the derivative and its application, integration, applications of the definite integral, transcendental functions, methods of integration, and a study of plane and analytic geometry using calculus.  Students achieving success in this course will have mastered the entire AB syllabus for advanced placement in college.  All A.P. Calculus AB students MUST take the Advanced Placement Examination in May.


Students should expect to meet with the instructor one extra period per week for a LAB activity.


Prerequisite:   approval by Department Chair and Teacher.


2 semesters


385 A.P. Calculus BC        6 ppc     1.00 cr.  Tr. 5   Gr. 12


This course covers:  a review of limits, differentiation and applications, integration and applications, differential equations, logarithmic and exponential functions, Trigonometric and Inverse Trigonometric functions, integration techniques, infinite series, parametric and polar equations.  All A.P. Calculus BC students MUST take the Advanced Placement Examination in May.


Prerequisite:  Approval by Department Head and Teacher.


2 semesters


395 A.P. Statistics      6 ppc     1.00 cr. Tr. 5   Gr. 11-12
396 Statistics          6 ppc     1.00 cr. Tr. 1   Gr. 12



The topics include:  exploratory analysis, planning a study, probability, and statistical inference.  All A.P. Statistics students MUST take the Advanced Placement Examination in May.  Students in course 396 DO NOT take the AP examination.


Prerequisites:  88 in present Math Course and recommendation of present Math teacher and approval by Department Chair.