MATHEMATICS COURSES 

GEORGIA PERFORMANCE STANDARDS (GPS) COURSES 

Integrated Advanced Algebra 27.0810000 

Integrated Advanced Algebra is an on-level ninth grade course.  Students must be willing to seek extra help when needed, as the pace is faster than on-level courses in some other disciplines.  Like most math courses, the material builds on itself, so it is important for students to complete homework consistently and to ask for help when needed.  Students will explore the characteristics of basic functions using tables, graphs, and simple algebraic techniques; operate with radical, polynomial, and rational expressions; solve a variety of equations, including quadratic equations with a leading coefficient of one, radical equations, and rational equations; investigate properties of geometric figures in the coordinate plane; use the language of mathematical argument and justification; discover, prove, and apply properties of polygons; utilize counting techniques and determine probability; use summary statistics to compare samples to populations; and explore the variability of data. Students may enroll in Math 1 upon completion of Math 8.   

Students transferring from other states who have not yet completed a Geometry course should be placed in Math 1, where most of the high school Geometry curriculum is taught.  After Math 1, most students go on to Math 2.  A very small number of students who do extremely well in Math 1 take a summer “bridge course” and move into Accelerated Math 2 during their sophomore year. Prerequisite: Math 8 or Math 8 Advanced

Integrated Advanced Algebra Support (Math 1 Support)  27.0810020

Integrated Advanced Algebra Support is an elective course that some students take concurrently with Integrated Advanced Algebra.  Support gives students an extra hour of class time each day to get additional practice and instruction with the material being covered in Math 1.  Some days the Support class focuses on prerequisite skills (e.g., reviewing integer arithmetic to help with factoring); other days it mirrors the Math 1 class more exactly (e.g., giving a set of additional factoring problems like the ones students are doing in Math 1).  There is no homework in Math 1 Support, but class work is collected virtually every day. 

Students who score a “1” on the 8^th grade CRCT (Math) must be enrolled in Math 1 Support.  For other students, placement is based on teacher recommendation.  After Math 1 Support, students may continue with Math 2 Support as a 10^th grade elective, or they may take Math 2 without Math 2 Support.

Students who want to learn the material but need extra time to grasp it are the ideal fit for the Support class.  Students whose struggles are due to lack of effort will not reap the benefits of the Support program. 
 

*Accelerated Integrated Advanced Algebra (Accelerated Math 1)  27.0910040

Accelerated Math 1 is an Honors-level course.  Self-motivated students are best suited for the rigor of this class.  The course builds on itself and on material from previous courses, so students who take good notes and are willing to seek out additional practice or help on difficult topics will be better able to stay on top of the material and not fall behind. Because this is an accelerated course, there is little time for review or re-teaching built into the schedule.  Students are expected to retain information for significant periods of time to ensure that they can apply their knowledge in new situations encountered later in the semester.  Students should be self-motivated to find extra practice or to seek extra help with topics they find difficult.  The work-load is moderate with homework 3 to 4 nights per week.  Good attendance is essential, as in all math courses.  All students in the class are freshmen.

Students may enroll in Accelerated Math 1 upon successful completion of Accelerated Math 8.  Students transferring from other states should be placed in Accelerated Math 1 if they have demonstrated a strong understanding of the topics covered in Accelerated Math 8 (all of Algebra I, parts of Geometry, some Algebra II).  After Accelerated Math 1, students will take Accelerated Math 2 (Accelerated Integrated Geometry), then Accelerated Math 3 (Accelerated Integrated Precalculus), and then either AP Calculus (AB or BC) or AP Statistics.

Students will operate with complex numbers; explore the characteristics of basic functions utilizing tables, graphs, and simple algebraic techniques; operate with radical, polynomial, and rational expressions; solve equations, including quadratic, radical, and rational equations; investigate properties of geometric figures in the coordinate plane; use the language of mathematical argument and justification; discover, prove, and apply properties of polygons, circles and spheres; utilize counting techniques and determine probability; use summary statistics to compare samples to populations; explore variability of data; and fit curves to data and examine the issues related to curve fitting. Prerequisite:  Math 8 or Math 8 Advanced 
 

Integrated Geometry 27.0820000

Integrated Geometry is an on-level tenth grade course.  Students must be willing to seek extra help when needed, as the pace is faster than on-level courses in some other disciplines.  Like most math courses, the material builds on itself, so it is important for students to complete homework consistently and to ask for help when needed. Students may enroll in Math 2 upon completion of Math 1.  Students transferring from other states who have not yet completed an Algebra 2 course should be placed in Math 2, where most of the high school Algebra 2 curriculum is taught.  After Math 2, students will continue to Math 3.  There are no options for moving into the Accelerated Math 3 course following on-level Math 2 because students will have missed so much material in the Accelerated sequence.  Math 2 Support is an elective course that some students may wish to take in conjunction with Math 2 to help them practice and solidify skills.

Students will use numerical, graphical, and algebraic techniques to explore quadratic, exponential, and piecewise functions and to solve quadratic, exponential and absolute value equations and inequalities; use algebraic models to represent and explore real phenomena; explore inverses of functions; use right triangle trigonometry to formulate and solve problems; discover, justify and apply properties of circles and spheres; use sample data to make informal inferences about population means and standard deviations; and fit curves to data and examine the issues related to curve fitting. Prerequisite: Integrated Advanced Algebra  

Integrated Geometry Support (Math 2 Support)  27.0450000

Integrated Geometry Support is an elective course that some students take concurrently with Integrated Geometry.  Support gives students an extra hour of class time each day to get additional practice and instruction with the material being covered in Math 2.  Some days the Support class focuses on prerequisite skills (e.g., reviewing topics from Math 1); other days it mirrors the Math 2 class more exactly (e.g., giving a set of additional graphing problems like the ones students are doing in Math 2).  There is no homework in Math 2 Support, but class work is collected virtually every day.  Students enroll in Integrated Geometry Support concurrently with Integrated Geometry. Students generally personally elect to take Integrated Geometry Support, but other students are placed based on teacher recommendation.  Students who want to learn the material but need extra time to grasp it are the ideal fit for the Support class.  Students whose struggles are due to lack of effort will not reap the benefits of the Support program.

*Accelerated Integrated Geometry (Accelerated Math 2)  27.0920040

Accelerated Math 2 is a Honors-level course.  Self-motivated students are best suited for the rigor of this class.  The course builds on itself and on material from previous courses, so students who are willing to seek out additional practice or help on difficult topics will be better able to stay on top of the material and not fall behind.  Because this is an accelerated course, there is little time for review or re-teaching built into the schedule.  Students are expected to retain information for significant periods of time to ensure that they can apply their knowledge in new situations encountered later in the semester.  Students should be self-motivated to find extra practice or to seek extra help with topics they find difficult.  The work-load is moderate with homework 3 to 4 nights per week.  Good attendance is essential, as in all math courses.  Students in the class are freshmen and sophomores.

Students may enroll in Accelerated Math 2 upon successful completion of Accelerated Math 1 OR on-level Math 1 with the summer bridge course.  Even for students who were successful in Math 1 and the bridge course sometimes have an “adjustment period” at the beginning of Accelerated Math 2 to acclimate themselves to the rigor of the new class.  Students transferring from other states should be placed in Accelerated Math 2 if they have demonstrated a strong understanding of the topics covered in Accelerated Math 1 (most of Geometry, large portions of what used to be called Algebra II, some probability / statistics).  After Accelerated Math 2, students will take Accelerated Math 3 (Accelerated Integrated Precalculus), followed the next year by either AP Calculus (AB or BC) or AP Statistics. Topics include exploration of the characteristics of exponential, logarithmic, and higher degree polynomial functions using tables, graphs, and algebraic techniques; explore inverses of functions; use algebraic models to represent and explore real phenomena; solve a variety of equations and inequalities using numerical, graphical, and algebraic techniques with appropriate technology; use matrices to formulate and solve problems; use linear programming to solve problems; use matrices to represent and solve problems involving vertex-edge; use right triangle trigonometry to formulate and solve problems; investigate the relationships between lines and circles; recognize, analyze, and graph the equations of conic sections; investigate planes and spheres; use sample data to make informal inferences about population means and standard deviations; solve problems by interpreting a normal distribution as a probability distribution; and design and conduct experimental and observational studies. Prerequisite: Accelerated Integrated Advanced Algebra H

Student Comments:

“You have to be willing to put in a lot of time for this course.  If you miss one topic, you’re going to be confused for the rest of the unit.”

“Whenever I fall behind I go see [my teacher] for extra help.  I know I can’t just ignore it if I don’t understand it.”

Integrated Geometry Honors 27.0820040 

Represent and operate with complex numbers; use numerical, graphical, and algebraic techniques to explore quadratic, exponential, and piecewise functions and to solve quadratic, exponential and absolute value equations and inequalities; use algebraic models to represent and explore real phenomena; explore inverses of functions; use right triangle trigonometry to formulate and solve problems; discover, justify and apply properties of circles and spheres; use sample data to make informal inferences about population means and standard deviations; and fit curves to data and examine the issues related to curve fitting. Additional topics from Accelerated Integrated Geometry Honors; (individual projects.) Prerequisite: Integrated Advanced Algebra Honors  

Integrated Algebra II 

Analyze polynomial functions of higher degree; explore logarithmic functions as inverses of exponential functions; solve a variety of equations and inequalities numerically, algebraically, and graphically; use matrices and linear programming to represent and solve problems; use matrices to represent and solve problems involving vertex-edge graphs; investigate the relationships between lines and circles; recognize, analyze, and graph the equations of conic sections; investigate planes and spheres; solve problems by interpreting a normal distribution as a probability distribution; and design and conduct experimental and observational studies. Prerequisite: Integrated Geometry  
 

Integrated Algebra II Honors  

Students will analyze polynomial functions of higher degree; explore logarithmic functions as inverses of exponential functions; solve a variety of equations and inequalities numerically, algebraically, and graphically; use matrices and linear programming to represent and solve problems; use matrices to represent and solve problems involving vertex-edge graphs; investigate the relationships between lines and circles; recognize, analyze, and graph the equations of conic sections; investigate planes and spheres; solve problems by interpreting a normal distribution as a probability distribution; and design and conduct experimental and observational studies ; Additional topics from Accelerated Integrated Pre-Calculus Honors; (individual projects). Prerequisite: Integrated Geometry Honors 

Integrated Trigonometry (Pre-Calculus)  

Students will investigate and use rational functions; analyze and use trigonometric functions, their graphs, and their inverses; use trigonometric identities to solve problems and verify equivalence statements; solve trigonometric equations analytically and with technology; find areas of triangles using trigonometric relationships; use sequences and series; understand and use vectors; investigate the Central Limit theorem; and use margins of error and confidence intervals to make inferences from data Prerequisite: Integrated Algebra II 

Integrated Trigonometry Honors (Pre-Calculus)  

Students will investigate and use rational functions; analyze and use trigonometric functions, their graphs, and their inverses; use trigonometric identities to solve problems and verify equivalence statements; solve trigonometric equations analytically and with technology; find areas of triangles using trigonometric relationships; use sequences and series; understand and use vectors; investigate the Central Limit theorem; and use margins of error and confidence intervals to make inferences from data; Additional topics from Calculus; (individual projects) Prerequisite: Integrated Algebra II Honors 

*Accelerated Integrated Pre-Calculus Honors 27.2670040 

Students will investigate and use rational functions; analyze and use trigonometric functions, their graphs, and their inverses; find areas of triangles using trigonometric relationships; use trigonometric identities to solve problems and verify equivalence statements; solve trigonometric equations analytically and with technology; use complex numbers in trigonometric form; understand and use vectors; use sequences and series; explore parametric representations of plane curves; explore polar equations; investigate the Central Limit theorem; and use margins of error and confidence intervals to make inferences from data.  Prerequisite: Accelerated Integrated Geometry H 

*Students will complete work equivalent to a year and a half in one year.

QUALITY CORE CURRICULUM (QCC)

Algebra III   27.0661000

During the first half of the first semester Algebra III covers many of the same topics as Algebra II at a greater depth.  As the year progresses, the topics presented will include polynomial functions, rational functions, exponential and logarithmic functions.  It includes a brief introduction to Trigonometry.  Additional topics include systems of equations, matrices, arithmetic and geometric sequences and probability.  The work-load is light to moderate with homework assignments most nights.   Good attendance is essential, as in all math courses.   There is no grade criteria for this class, but students should have passed Algebra II.  Most of the students in the class will be juniors and seniors. The prerequisite for this course is Algebra II.  This will be the only class available to take as a follow-up to Algebra II for the year 2010/2011. 

Problem solving, reasoning, estimation, language of algebra, real number system, patterns and models, graphing, measurement, linear equations and systems, literal equations, linear equations and inequalities and their graphs, quadratic equations, functions and graphs; variation, measurement and geometry, trigonometry, statistics, probability, matrices  

Advanced Algebra/ Trigonometry  27.065000

A self-motivated student with a strong work ethic will be most successful in Advanced Algebra and Trigonometry.  The work-load is moderate to heavy, with homework essentially every night.   Good attendance is essential, as in all math courses.   To be successful in the class, students should have achieved a minimum of an 82 in both semesters of on-level Algebra II.  This minimum grade average not only demonstrates mastery of the material but an adequate work ethic.   Most students who take the class are juniors, although it is not unusual to have sophomores and seniors as well.  The prerequisite courses are Geometry (honors or on-level) and Algebra II (honors or on-level).  High achieving students from Advanced Algebra and Trigonometry should take AP Calculus AB.   The collaboration team strongly urges the on-level Calculus class be offered, as this gives the weaker Advanced Algebra and Trigonometry students an introduction to Calculus, which will prepare them well for college Calculus.   Currently, many midrange students have chosen to go to AP Statistics, while weaker students have opted for Discrete / Statistics.    It is the opinion of the collaboration team that Calculus would serve these college bound students far better.         

Topics include problem solving, reasoning & estimation, exponential & logarithmic functions, trigonometry, complex numbers, vectors, matrices, analytical geometry/conic sections, sequences & series, probability & statistics.

Discrete Mathematics   27.0690000

This is a course for students who have completed Algebra I, Geometry, and Algebra II.  Discrete Statistics covers the meaning and computations of statistical analysis.    In addition to mathematical computations, students will be required to write and analyze the meanings of statistical information.   The work-load is light to moderate with homework and reading assignments 2 to 4 nights per week.   Good attendance is essential, as in all math courses.   There is no grade criteria for this class, but students should have fulfilled their core math requirements before taking this class.  Almost all students in the class are seniors.

Discrete Mathematics may be taken before, in place of, concurrently with, or after Advanced Algebra and Trigonometry.  The course allows students to explore unique problem situations that are not directly approachable through writing an equation or applying a common formula.  Students are often required to visualize the situation through developing a model or another form of representation.  Other settings call for analyzing special cases or developing a solution by considering a simpler problem involving fewer cases. Recommended grade: 12

Calculus (non-AP) 27.0710000

The content standards for Calculus include many of the topics taught in Advanced Placement Calculus.  Both the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) recommend that the calculus course offered in the twelfth grade be treated as a college-level course and follow four years of strong mathematical preparation, beginning with Algebra. Prerequisites: Advanced Algebra and Trigonometry 
 
College Calculus II and III 27.0750405 and 27.0750406

In cooperation with Fulton County Schools, Georgia Tech offers these advanced calculus courses by distance learning. Our students sit in our distance learning lab and interact with a class going on at the Georgia Tech campus, taught by a Georgia Tech professor. Prerequisites: AP Calculus BC with a 3,4, or 5 on AP test; or calculus AB with a 4, or 5 on AP test

AP Calculus AB 27.0720010

This course consists of a review of real numbers and the Cartesian plane; review of functions; limits and their properties; derivatives and differentiation applications; anti-derivatives and indefinite integration; area and definite integrals; integration by substitution; the trapezoidal rule; logarithmic, exponential and other transcendental functions; applications and methods of integration; miscellaneous topics in Calculus BC. Prerequisites: Precalculus or Advanced Algebra/Trig  
 
AP Calculus BC 27.0730010

This course is for students who have completed pre-cal with an 85 or higher and have shown an extreme interest in math and diligence in past math courses.  Since calculus I and II are covered in this course only students with high work ethics, good attendance and a willingness to work should enroll. Topics include all topics of AP Calculus AB, additional topics are applications of integration involving work and arc length; parametric equations; analysis of acceleration and velocity vectors; applications of slope fields to differential equations; analysis of geometric, harmonic, p-series and alternating series; and approximations of polynomials with Taylor and Maclaurin series.  Prerequisites: students must have completed Precalculus with an 85 or higher.  After this course, students will likely take Georgia Tech distance learning calculus.

This is an advanced placement course.  Self-motivated students are best suited for the rigor of this class.  Most of the course builds on itself so students who are willing to seek out additional practice or help on difficult topics will be better able to stay abreast of the material and not fall behind.  Students need to have a good work ethic and the motivation to seek help when they do not understand a topic.  Prerequisites: Pre Calculus  
Student Comment: “You have to enjoy math, be organized, and diligent so you will be willing to put forth the effort.”

AP Statistics 27.0740010 Students should expect to do homework daily, have good work/study habits, and must attend class daily.  This course is fairly rigorous and should be taken by students who desire to learn about other branches of mathematics.  Topics include introduction to statistics; descriptive statistics; probability; probability distributions; normal probability distributions; estimates and sample size; hypotheses testing; inferences from two samples; correlation and regression; multinomial experiments; analysis of variance; statistical process control; nonparametric statistics; design and sampling. Prerequisites: QCC--Algebra II, GPS--Accelerated Integrated Geometry. Students are required to do a fair amount of reading and are expected to use the text book as a primary source of information. Prerequisites: students must have completed Algebra II or higher (QCC) OR Math 3 or higher (GPS). This is an advanced placement course.  Self-motivated students are best suited for the rigor of this class.  Most of the course builds on itself so students who are willing to seek out additional practice or help on difficult topics will be better able to stay abreast of the material and not fall behind.  There is a major emphasis on writing, so students do not have to be extremely strong math students.  However, they do need to have a good work ethic and the motivation to seek help when they do not understand a topic.

Student Comments:

“AP Stats isn’t as easy as a lot of people thought it was going to be.  Be sure to do your homework because it will help you prepare for the tests.  The class never takes breaks so be prepared to work hard.” 

“It is a fun class.  It isn’t easy but you won’t be stressing out every night over AP Stat.  I like it because you learn things that are actually useful in life.” 

“The class is fast-paced and requires a lot of analysis and writing but few calculations and little algebra.  Be prepared to do a lot of writing.  It is unlike any other math class that I have taken before.”