2012–13 COMPLETE AKS Gwinnett’s curriculum for grades K–12 is called the The Academic Knowledge and Skills (AKS) were Academic Knowledge and Skills (AKS) and is aligned to developed by our teachers, with input from our parents the state-adopted Common Core Georgia Performance and community, in response to Gwinnett County Public Standards (CCGPS) in Language Arts, Mathematics, and Schools’ mission statement: literacy skills in Science, Social Studies, and Technical The mission of Gwinnett County Public Schools is to Education for middle school students. Gwinnett’s AKS is pursue excellence in academic knowledge, skills, a rigorous curriculum that prepares students for college and behavior for each student resulting in measured and 21st century careers in a globally competitive future. improvement against local, national, and world-class The AKS for each grade level spell out the essential standards. things students are expected to know and be able to do In this booklet, you will find a complete list of in that grade or subject. The AKS offer a solid base on the AKS, by subject and course, for Gwinnett which teachers build rich learning experiences. Teachers School of Mathematics, Science, and use curriculum guides, textbooks, technology, and other Technology. We encourage you to talk to your materials to teach the AKS and to make sure every student student about what he or she is learning. is learning to his or her potential. WELCOME TO THE 2012–13 SCHOOL YEAR! Table of Contents Mathematics 1 Fine Arts 36 Science 12 Foreign Languages 49 Engineering 16 Health and Fitness 53 Humanities 22 About the Academic Knowledge and Skills (AKS) Curriculum The AKS are the standards for academic excellence for all students in Gwinnett County Public Schools (GCPS). In every GCPS classroom, instruction and assessment are tailored so that all students learn the AKS. The alignment of AKS with standardized assessments— such as the SAT and ACT college-admissions tests— ensures that GCPS students are well-prepared for these national measurements of achievement. GCPS’ rigorous AKS curriculum also aligns with the state curriculum, known as the Georgia Performance Standards (GPS).This alignment assures that students are prepared for state tests, including the Georgia High School Writing Test and state-required End of Course Test for designated high school courses. Since its inception in 1996, GCPS’ AKS curriculum has reflected the collective wisdom of thousands of educators and community members who worked together to determine what students need to know and be able to do in order to be successful at the next grade level and in the future. This investment by GCPS’ stakeholders has ensured that the AKS curriculum remains a rigorous and relevant blueprint for student learning in Gwinnett. As part of that ongoing effort, the GEMS Oversight Committee— made up of community and GCPS staff members— meets annually to review proposed additions, deletions, and changes to the AKS that come out of school and community surveys. Following validation by the GEMS committee, recommendations are submitted to the superintendent for approval by the School Board, with implementation the following school year. High School Graduation Requirements All students seeking a regular education diploma in Gwinnett must earn the required course credits set out in state graduation requirements. In addition, students must pass the Georgia High School Graduation Writing Test (GHSWT) and Gwinnett’s High School Gateway Writing Assessment. Students also must demonstrate proficiency in the four core areas— language arts, mathematics, science, and social studies— by either passing one End of Course Test (EOCT) in each of the core content areas or by passing the corresponding subtest of the Georgia High School Graduation Tests (GHSGT). This option is available to students entering high school between July 2008 and June 2011 (for the most part, the graduating classes of 2012, 2013, and 2014). Students starting high school in 2011-12 or after must pass all courses with a required EOCT in order to earn a Georgia diploma. Graduation requirements are specific to each entering freshman class. You can learn more about state requirements in The Choice Book for your student’s class (available on the school system website… www.gwinnett.k12.ga.us) or on the state Department of Education website (http://public.doe.k12.ga.us/). In addition, families will receive a flyer regarding graduation requirements during the fall. Required Testing for High School Georgia High School Writing Test All students seeking a Georgia high school diploma must pass the Georgia High School Writing Test (GHSWT). Students take the graduation writing test in the fall of their junior year. Students produce a composition of no more than two pages on an assigned topic. The two-hour test administration includes 100 minutes of writing and time for planning and editing the paper. This assessment ensures that students who qualify for a Georgia diploma have mastered essential core academic content and skills. Students who do not pass on their first attempt have multiple opportunities to receive extra help, retake the writing test if they didn’t pass, and qualify for graduation before the spring of the 12th grade. Students must pass the writing test to graduate. GCPS High School Gateway Assessment All students must demonstrate knowledge of Gwinnett County Public Schools’ Academic Knowledge and Skills (AKS) curriculum. Students can find the AKS by course on the school system website (at www.gwinnett.k12.ga.us/aks.nsf). Students must pass the school system’s High School Gateway Assessment as a Gwinnett requirement for earning a diploma. The Gateway Assessment measures students’ ability to write effectively about 9th and 10th grade Science and 10th grade Social Studies AKS. Students write two essays— one on a Science topic and one on a Social Studies topic. In writing a response, students must use their own knowledge about the topic and utilize information from documents provided. Students have 125 minutes to write each of the essays, one per day. The assessment is administered in the spring of the 10th grade year. Intervention classes are provided to help students who do not pass this assessment. Students who are not successful on the test the first time have several opportunities to retake the assessment before graduation. Students must pass both sections of the Gateway to graduate. End of Course Tests Students are required to participate in state-mandated End of Course Tests (EOCT) to earn credit for eight designated high school courses. EOCTs— required for two courses in each core subject area— are designed to hold students statewide to the same learning standards. Any student enrolled in and/or receiving credit for a course requiring an EOCT would participate in the assessment at the completion of the course. Results of this multiple-choice test count for 20% of the student’s semester grade in the semester the test is administered. While students are not required to pass the EOCT to pass the course, the EOCT does count 20% of the semester grade so a failing score on an EOCT would have a significant impact on a student’s final grade. The EOCT program includes the following eight content-area assessments: Integrated Algebra I/Accelerated Integrated Algebra I, Integrated Geometry/Accelerated Integrated Geometry, U.S. History, Economics/Business/Free Enterprise, Biology, Physical Science, Freshman Language Arts, and Junior American Literature. Students must take the End of Course Test in order to receive credit for the courses requiring the EOCT. Students starting high school in 2011-12 or after must pass all courses with a required EOCT in order to earn a Georgia diploma. Online Resources… Preparing for Required High School Testing www.usatestprep.com/front/login.php   (Your student can request a user name and password from the school.)  www.GAcollege411.org (Go to the Test Prep resources under the College Planning tab.) Notes about this Booklet • Correlations to the following state-required objectives/assessments/curriculum are indicated for respective Academic Knowledge and Skills: Georgia Performance Standards (GPS) and Character Education (CE) • Academic Knowledge and Skills beginning with “explore” will not be assessed for mastery at that grade level, but are prerequisite for mastery at a higher grade level. • Comprehensive AKS booklets like this one are available by grade level (K–8 and combined grades for high school) and by core academic subject (Language Arts, Mathematics, Science, and Social Studies) on the district website at www.gwinnett.k12.ga.us. These booklets are posted in PDF form. • Parents also can find an online PDF of The Choice Book, which provides an overview of the high school experience, high school and postsecondary planning tools, and a “course catalog.” Rising 9th graders receive a printed copy of The Choice Book. The Choice Book is specific to each entering freshman class. Families may access the appropriate copy of The Choice Book for their student’s class on the school system website. (Click on the “Publications for Students” link on the Parents or Students tabs.) • The AKS numbering system was developed to allow for additions and deletions of AKS without changing the number reference of other AKS. The reference code includes the subject and/or grade level, a letter representing the topic strand, and the year implemented. Character Education The school system supports a mandate from the Georgia General Assembly requiring all schools to teach character education. Society and culture are tied together through common threads that guide the way we live, work, and learn. These common beliefs are taught at home and reinforced by the community, schools, religious institutions, and youth service groups. These basic tenets guide the way Gwinnett County teachers teach and the way the school system conducts the business of teaching and learning. Character education is thoroughly embedded in the AKS curriculum. Traits emphasized in the curriculum include the following: courage respect for self-control generosity respect for creativity patriotism others courtesy punctuality environment sportsmanship citizenship cooperation compassion cleanliness respect for loyalty honesty kindness tolerance cheerfulness creator perseverance fairness self-respect diligence school pride patience virtue Parent Involvement Research shows that when parents are involved in their student’s education at home, their student does better in school. When parents are involved at school, their student’s achievement improves and the schools they attend become even stronger. Be There is a national movement that inspires parents to become more involved in their student’s education and their public schools. Teachable moments are everywhere. You can be your student’s favorite teacher by connecting in meaningful ways as you go through the ordinary routines of the day… driving in the car, preparing a meal, shopping, or doing chores. Below, you will find tips for helping your student have a successful high school experience. Look for more helpful tipsheets and other resources on the school system website and your local school website. Suggestions for Helping Your Student Achieve Academically The school system encourages parents to be an active part of their student’s education. Following are a few ways you can be involved: • Review the AKS for your student’s classes each year. You also can access the AKS on the system’s website (www.gwinnett.k12.ga.us). • Be familiar with important information about required assessments and graduation requirements. You can find this information in your student’s copy of The Choice Book or on the school system website. (The Choice Book is specific to each entering freshman class.) • Ask to see your student’s work and talk about what he or she is learning in school. • Encourage your student to take the most challenging classes in which he or she can be successful. Students who challenge themselves in high school are better prepared for college classes and other postsecondary studies. • Support your student and communicate that his or her academic success is important to you. • Remind your student to edit work when writing and to pay careful attention to appropriate grammar and spelling. • Communicate with your student’s teachers. • Attend curriculum nights, PTA meetings, and other school meetings. • Share these Keys to School Success with your student: • Be prepared each day. Have the needed materials and assignments for each class. • Stay organized. Keep your desk, notebooks, book bag, and home study area neatly arranged. • Use an agenda book or calendar to keep track of assignments and due dates. Check it every day. • Give your best effort to both homework and in-class assignments. Complete assignments and turn them in on time. • Review your work from each class every evening, even if you don’t have a homework assignment due the next day. • Study for every test and quiz. • Ask your teacher questions if you do not understand a lesson or an assignment. • Get involved in at least one extracurricular activity. Mathematics Mathematics - Advanced Algebra II with Trigonometry and Data Analysis A - Process Skills  use appropriate technology to solve mathematical problems (GPS) (GSAA_A2008-1)  build new mathematical knowledge through problem-solving (GPS) (GSAA_A2008-2)  solve problems that arise in mathematics and in other areas (GPS) (GSAA_A2008-3)  apply and adapt a variety of appropriate strategies to solve problems (GPS) (GSAA_A2008-4)  monitor and reflect on the process of mathematical problem-solving (GPS) (GSAA_A2008-5)  recognize reasoning and proof (evidence) as fundamental aspects of mathematics (GPS) (GSAA_A2008-6)  make and investigate mathematical conjectures (GPS) (GSAA_A2008-7)  investigate, develop, and evaluate mathematical arguments and proofs (GPS) (GSAA_A2008-8)  select and use various types of reasoning and methods of proof (GPS) (GSAA_A2008-9)  organize and consolidate mathematical thinking (GPS) (GSAA_A2008-10)  communicate mathematical thinking coherently to peers, teachers, and others (GPS) (GSAA_A2008-11)  analyze and evaluate the mathematical thinking and strategies of others (GPS) (GSAA_A2008-12)  use the terminology and language of mathematics to express mathematical ideas precisely (GPS) (GSAA_A2008-13)  recognize and use connections among mathematical ideas (GPS) (GSAA_A2008-14)  explain how mathematical ideas interconnect and build on one another to produce a coherent whole (GPS) (GSAA_A2008-15)  recognize and apply mathematics in contexts outside of mathematics (GPS) (GSAA_A2008-16)  create and use pictures, manipulatives, models, and symbols to organize, record, and communicate mathematical ideas (GPS) (GSAA_A2008-17)  select, apply, and translate among mathematical representations to solve problems (GPS) (GSAA_A2008-18)  use representations to model and interpret physical, social, and mathematical phenomena (GPS) (GSAA_A2008-19) B - Numbers and Operations  write square roots of negative numbers in imaginary form (GPS) (GSAA_B2008-20)  write complex numbers in the form a + bi (GPS) (GSAA_B2008-21)  add, subtract, multiply, and divide complex numbers (GPS) (GSAA_B2008-22)  simplify expressions involving complex numbers (GPS) (GSAA_B2008-23)  extend properties of exponents to include rational exponents (GPS) (GSAA_B2008-24) C - Algebra  represent functions using function notation (GPS) (GSAA_C2008-25)  explore functions, solve equations, and operate with radical, polynomial, and rational expressions (GPS) (GSAA_C2008-26)  graph the basic functions f(x)=xn, where n=1 to 3, f(x)=√x, f(x)=│x│, and f(x)=1/x (GPS) (GSAA_C2008-27)  compare and contrast linear, quadratic, exponential, logarithmic, and power functions (GPS) (GSAA_C2008-28)  graph transformations of basic functions including vertical shifts, stretches and shrinks, as well as reflections across the x- and y- axes (GPS) (GSAA_C2008-29)  investigate and explain the characteristics of different types of functions including polynomial functions such as quadratics: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, rates of change, and end behavior (GPS) (GSAA_C2008-30)  solve polynomial equations using the following theorems: remainder, factor, rational root, and fundamental theorem of algebra (GPS) (GSAA_C2008-31)  apply Pascal's Triangle and its properties to binomial expansions and experiments (GPS) (GSAA_C2008-32)  use the Binomial Theorem to expand and simplify expressions (GPS) (GSAA_C2008-33)  describe the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros (GPS) (GSAA_C2008-34) Page 1 Mathematics C – Algebra (continued)  analyze the characteristics of a function in a given context, and use graphs and tables to investigate its behavior (GPS) (GSAA_C2008-35)  determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither (GPS) (GSAA_C2008-36)  determine whether a polynomial function has symmetry and whether it is even, odd, or neither (GPS) (GSAA_C2008-37)  analyze any equation in x that can be interpreted as the equation f(x)=g(x), and then interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x) (GPS) (GSAA_C2008-38)  add, subtract, multiply, and divide polynomials (GPS) (GSAA_C2008-39)  add, subtract, multiply, and divide rational expressions (GPS) (GSAA_C2008-40)  factor expressions by greatest common factor, grouping, trial and error, and special products limited to the following formulas: (x + y)² = x² + 2xy + y²; (x - y)² = x² - 2xy + y²; (x + y)(x - y) = x² - y²; (x + a)(x + b) = x² + (a + b)x + ab; (x + y)³= x³ + 3x²y + 3xy² + y³; (x – y)³ = x³ – 3x²y + 3xy² – y³ (GPS) (GSAA_C2008-41)  solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1 (GPS) (GSAA_C2008-42)  analyze quadratic functions in the forms f(x) = ax² + bx + c and f(x) = a(x-h)² + k (GPS) (GSAA_C2008-43)  find real and complex solutions of quadratic equations by factoring, taking square roots, and applying the quadratic formula (GPS) (GSAA_C2008-44)  analyze the nature of roots using technology and the discriminant (GPS) (GSAA_C2008-45)  solve quadratic equations in one variable algebraically and graphically (GPS) (GSAA_C2008-46)  solve quadratic inequalities both graphically and algebraically and describe the solutions using linear inequalities (GPS) (GSAA_C2008-47)  use area and volume models for polynomial arithmetic (GPS) (GSAA_C2008-48)  explore rates of change, comparing constant rates of change (e.g., slope) versus variable rates of change and compare rates of change of linear, quadratic, square root, and other function families (GPS) (GSAA_C2008-49)  simplify algebraic and numeric expressions involving square root (GPS) (GSAA_C2008-50)  solve equations involving radicals such as √x + b = c (GPS) (GSAA_C2008-51)  investigate step and piecewise functions, including greatest integer and absolute value functions (GPS) (GSAA_C2008-52)  write absolute value functions as piecewise functions (GPS) (GSAA_C2008-53)  investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change (GPS) (GSAA_C2008-54)  solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology (GPS) (GSAA_C2008-55) D - Data Analysis and Probability  apply the addition and multiplication principles of counting (GPS) (GSAA_D2008-56)  calculate and use simple permutations and combinations (GPS) (GSAA_D2008-57)  find the probabilities of mutually exclusive events (GPS) (GSAA_D2008-58)  find the probabilities of dependent and independent events (GPS) (GSAA_D2008-59)  calculate conditional probabilities (GPS) (GSAA_D2008-60)  use expected value to predict outcomes (GPS) (GSAA_D2008-61)  compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions (GPS) (GSAA_D2008-62)  compare the averages of the summary statistics from a large number of samples to the corresponding population parameters (GPS) (GSAA_D2008-63)  explain how a random sample is used to improve the chance of selecting a representative sample (GPS) (GSAA_D2008-64)  explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations) (GPS) (GSAA_D2008-65) Page 2 Mathematics D – Data Analysis and Probability (continued)  determine an algebraic model to quantify the association between two quantitative variables (GPS) (GSAA_D2008-66)  gather and plot data that can be modeled with linear and quadratic functions (GPS) (GSAA_D2008-67)  examine the issues of curve-fitting by finding good linear fits to data using simple methods such as the median-median line and "eyeballing" (GPS) (GSAA_D2008-68)  apply the processes of linear and quadratic regression for curve-fitting using appropriate technology (GPS) (GSAA_D2008-69)  determine the effect that large changes in data have on lines of best fit (e.g., regression, median-median) (GPS) (GSAA_D2008-70)  model exponential, logarithmic, and sinusoidal situations (GPS) (GSAA_D2008-71) E - Trigonometry  graph and model circular functions (GPS) (GSAA_E2008-72)  convert measures of angles between radians and degrees (GPS) (GSAA_E2008-73)  develop, graph, and apply the six trigonometric functions (GPS) (GSAA_E2008-74)  apply the six trigonometric functions as functions of general angles in standard position (GPS) (GSAA_E2008-75)  determine characteristics of the graphs of the six basic trigonometric functions (GPS) (GSAA_E2008-76)  use the coordinates of a point on the terminal side of an angle to express x as r cos θ and y as r sin θ (GPS) (GSAA_E2008-77)  verify and apply the trigonometric formula to find the area of a triangle (GPS) (GSAA_E2008-78)  find values of trigonometric functions using points on the terminal sides of angles in the standard position (GPS) (GSAA_E2008-79)  apply the six trigonometric functions as functions of arc length on the unit circle (GPS) (GSAA_E2008-80)  find values of trigonometric functions using the unit circle (GPS) (GSAA_E2008-81)  apply the six basic trigonometric functions as functions of real numbers (GPS) (GSAA_E2008-82)  graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift (GPS) (GSAA_E2008-83)  apply laws of sines and cosines and determine area of any triangle (GPS) (GSAA_E2008-84)  perform vector operations algebraically and geometrically (GPS) (GSAA_E2008-85)  graph and perform two- and three-dimensional vector problems (GPS) (GSAA_E2008-86) F - Reading Across the Curriculum  read mathematical materials to establish context for subject matter, develop vocabulary, and to be aware of current research (GPS) (GSAA_F2008-87) Mathematics - Advanced Geometry with Discrete Topics A - Process Skills  use appropriate technology to solve mathematical problems (GPS) (GSAG_A2008-1)  build new mathematical knowledge through problem-solving (GPS) (GSAG_A2008-2)  solve problems that arise in mathematics and in other areas (GPS) (GSAG_A2008-3)  apply and adapt a variety of appropriate strategies to solve problems (GPS) (GSAG_A2008-4)  monitor and reflect on the process of mathematical problem-solving (GPS) (GSAG_A2008-5)  recognize reasoning and proof (evidence) as fundamental aspects of mathematics (GPS) (GSAG_A2008-6)  make and investigate mathematical conjectures (GPS) (GSAG_A2008-7)  investigate, develop, and evaluate mathematical arguments and proofs (GPS) (GSAG_A2008-8)  select and use various types of reasoning and methods of proof (GPS) (GSAG_A2008-9)  organize and consolidate mathematical thinking (GPS) (GSAG_A2008-10)  communicate mathematical thinking coherently to peers, teachers, and others (GPS) (GSAG_A2008-11)  analyze and evaluate the mathematical thinking and strategies of others (GPS) (GSAG_A2008-12)  use the terminology and language of mathematics to express mathematical ideas precisely (GPS) (GSAG_A2008-13) Page 3 Mathematics A - Process Skills (continued)  recognize and use connections among mathematical ideas (GPS) (GSAG_A2008-14)  explain how mathematical ideas interconnect and build on one another to produce a coherent whole (GPS) (GSAG_A2008-15)  recognize and apply mathematics in contexts outside of mathematics (GPS) (GSAG_A2008-16)  create and use pictures, manipulatives, models, and symbols to organize, record, and communicate mathematical ideas (GPS) (GSAG_A2008-17)  select, apply, and translate among mathematical representations to solve problems (GPS) (GSAG_A2008-18)  use representations to model and interpret physical, social, and mathematical phenomena (GPS) (GSAG_A2008-19) B - Coordinate Geometry  determine the distance between two points in 2-space and 3-space (GPS) (GSAG_B2008-20)  use the coordinate plane to investigate properties of and verify conjectures related to triangles, quadrilaterals, and other geometric figures (GPS) (GSAG_B2008-21)  determine the midpoint of a segment (GPS) (GSAG_B2008-22)  determine the distance between a point and a line (GPS) (GSAG_B2008-23)  plot the point (x, y, z) and understand it as a vertex of a rectangular prism (GPS) (GSAG_B2008-24)  analyze effects of reflections, rotations, translations, dilations, and symmetry of geometric figures in the coordinate plane (GPS) (GSAG_B2008-25)  investigate and apply transformation vectors and scale changes to find the image of figures on the coordinate plane (GPS) (GSAG_B2008-26)  create composites of transformations (GPS) (GSAG_B2008-27)  determine the image, pre-image, or inverse of a given mapping, and the composite of two mappings using matrices (GPS) (GSAG_B2008-28)  apply properties of vectors to solve problems (GPS) (GSAG_B2008-29)  represent addition of vectors and multiplication of a vector by a scalar both symbolically and pictorially (GPS) (GSAG_B2008-30) C - Classic Geometry - Area, Volume, Similarity, Locus, Cross Section  compare areas of similar polygons to solve problems and justify the reasonableness of results (GPS) (GSAG_C2008-31)  optimize perimeter, area, and volume of geometric figures and solids (GPS) (GSAG_C2008-32)  find the exact or approximate volume and surface area of solids composed of prisms, pyramids, cylinders, cones, and/or spheres (GPS) (GSAG_C2008-33)  compare the volume of similar solids to solve problems and justify the reasonableness of results (GPS) (GSAG_C2008-34)  apply indirect measurement and similarity theorems to solve problems (GPS) (GSAG_C2008-35)  apply and prove congruence and similarity properties of solids (GPS) (GSAG_C2008-36)  use and apply surface area and volume of a sphere (GPS) (GSAG_C2008-37)  determine the effect on surface area and volume of changing the radius or diameter of a sphere (GPS) (GSAG_C2008-38)  use data to analyze properties of geometric solids and figures (GPS) (GSAG_C2008-39)  analyze and interpret three-dimensional geometric figures using such topics as projections, cross-sections, and locus problems (GPS) (GSAG_C2008-40)  analyze, interpret, and measure dihedral and solid angles (GPS) (GSAG_C2008-41) D - Classic Geometry - Logic & Discrete  use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate (GPS) (GSAG_D2008-42)  apply and use the relationships among a statement and its converse, inverse, and contrapositive (GPS) (GSAG_D2008-43)  determine the equivalence and validity of truth tables including sentences involving conditional statements, conjunctions, disjunctions, and negations (GPS) (GSAG_D2008-44)  determine truth tables for sentences and use Venn Diagrams to illustrate the relationship represented by truth tables (GPS) (GSAG_D2008-45) Page 4 Mathematics E - Classic Geometry - Plane Geometry - Triangles & Quadrilaterals  find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid (GPS) (GSAG_E2008-46)  determine the sum of interior and exterior angles in a polygon (GPS) (GSAG_E2008-47)  use congruence postulates and theorems for triangles (GPS) (GSAG_E2008-48)  discover, prove, and apply properties of triangles, quadrilaterals, and other polygons (GPS) (GSAG_E2008-49)  use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite (GPS) (GSAG_E2008-50)  use and explain triangle inequality, side-angle inequality, and exterior-angle inequality (GPS) (GSAG_E2008-51) F - Classic Geometry - Trigonometry Foundations  define and apply sine, cosine, and tangent ratios to right triangles (GPS) (GSAG_F2008-52)  determine the lengths of sides of 30° - 60º - 90° triangles (GPS) (GSAG_F2008-53)  determine the lengths of sides of 45° - 45° - 90° triangles (GPS) (GSAG_F2008-54)  use and apply the relationship of the trigonometric ratios for similar and special right triangles (GPS) (GSAG_F2008-55) G - Classic Geometry - Circles  apply properties of chords, tangents, and secants as an application of triangle similarity (GPS) (GSAG_G2008-56)  apply properties of central, inscribed, and related angles (GPS) (GSAG_G2008-57)  use the properties of circles to solve problems involving the length of an arc and the area of a sector (GPS) (GSAG_G2008-58)  justify measurements and relationships in circles using geometric and algebraic properties (GPS) (GSAG_G2008-59) H - Non Euclidean Geometry  investigate spherical and hyperbolic geometry (GPS) (GSAG_H2008-60) I - Discrete Topics  discover the basic properties of fractals, including self-similarity and iteration (GPS) (GSAG_I2008-61)  build fractal designs by using iterative steps (GPS) (GSAG_I2008-62)  investigate applications of the Fibonacci sequence (GPS) (GSAG_I2008-63)  investigate the relationship known as the Golden Ratio (GPS) (GSAG_I2008-64)  solve problems using the Golden Ratio (GPS) (GSAG_I2008-65) J - Reading Across the Curriculum  read mathematical materials to establish context for subject matter, develop vocabulary, and to be aware of current research (GPS) (GSAG_J2008-66) Mathematics - Advanced Pre-Calculus with Discrete Mathematics and Data Analysis A - Process Skills  use appropriate technology to solve mathematical problems (GPS) (GSAP_A2008-1)  build new mathematical knowledge through problem-solving (GPS) (GSAP_A2008-2)  solve problems that arise in mathematics and in other areas (GPS) (GSAP_A2008-3)  apply and adapt a variety of appropriate strategies to solve problems (GPS) (GSAP_A2008-4)  monitor and reflect on the process of mathematical problem-solving (GPS) (GSAP_A2008-5)  recognize reasoning and proof (evidence) as fundamental aspects of mathematics (GPS) (GSAP_A2008-6)  make and investigate mathematical conjectures (GPS) (GSAP_A2008-7)  investigate, develop, and evaluate mathematical arguments and proofs (GPS) (GSAP_A2008-8)  select and use various types of reasoning and methods of proof (GPS) (GSAP_A2008-9)  organize and consolidate mathematical thinking (GPS) (GSAP_A2008-10) Page 5 Mathematics A – Process Skills (continued)  communicate mathematical thinking coherently to peers, teachers, and others (GPS) (GSAP_A2008-11)  analyze and evaluate the mathematical thinking and strategies of others (GPS) (GSAP_A2008-12)  use the terminology and language of mathematics to express mathematical ideas precisely (GPS) (GSAP_A2008-13)  recognize and use connections among mathematical ideas (GPS) (GSAP_A2008-14)  explain how mathematical ideas interconnect and build on one another to produce a coherent whole (GPS) (GSAP_A2008-15)  recognize and apply mathematics in contexts outside of mathematics (GPS) (GSAP_A2008-16)  create and use pictures, manipulatives, models, and symbols to organize, record, and communicate mathematical ideas (GPS) (GSAP_A2008-17)  select, apply, and translate among mathematical representations to solve problems (GPS) (GSAP_A2008-18)  use representations to model and interpret physical, social, and mathematical phenomena (GPS) (GSAP_A2008-19) B - Algebra  investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior (GPS) (GSAP_B2008-20)  find inverses of rational functions discussing domain, range, symmetry, and function composition (GPS) (GSAP_B2008-21)  solve rational equations and inequalities analytically, graphically, and by using appropriate technology (GPS) (GSAP_B2008-22)  apply graphs of trigonometric functions in realistic contexts involving periodic phenomena (GPS) (GSAP_B2008-23)  compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise (GPS) (GSAP_B2008-24)  investigate transformations of functions (GPS) (GSAP_B2008-25)  investigate characteristics of functions built through sum, difference, product, quotient, and composition (GPS) (GSAP_B2008-26)  apply the definitions and properties of logarithms (GSAP_B2008-27)  recognize the inverse relationship of logarithms and exponential functions and graph each function (GSAP_B2008-28)  define logarithmic functions as inverses of exponential functions (GPS) (GSAP_B2008-29)  apply properties of logarithms by extending laws of exponents (GPS) (GSAP_B2008-30)  determine values of common and natural logarithms and antilogarithms and apply the change of base rule (GSAP_B2008-31)  solve exponential and logarithmic equations (GPS) (GSAP_B2008-32)  investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change (GPS) (GSAP_B2008-33)  graph functions as transformations of f(x) = ax, f(x) = log ax, f(x) = ex, f(x) = In x (GPS) (GSAP_B2008-34)  explore real phenomena related to exponential and logarithmic functions including half-life and doubling time (GPS) (GSAP_B2008-35)  find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates (GPS) (GSAP_B2008-36)  solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology (GPS) (GSAP_B2008-37)  solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology and represent solution sets of inequalities using interval notation (GPS) (GSAP_B2008-38)  extend properties of exponents to include all integer exponents (GPS) (GSAP_B2008-39)  explain the relationship between the trigonometric ratios of complementary angles (GPS) (GSAP_B2008-40)  solve application problems using the trigonometric ratios (GPS) (GSAP_B2008-41)  establish and utilize trigonometric identities to simplify expressions and verify equivalence statements (GPS) (GSAP_B2008-42)  solve trigonometric equations both graphically and algebraically over a variety of domains using technology as appropriate (GPS) (GSAP_B2008-43)  find values of the inverse sine, inverse cosine, and inverse tangent functions using technology as appropriate (GPS) (GSAP_B2008-44) Page 6