Source: http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html
Timestamp: 2019-04-24 18:25:58+00:00

Document:
(a) The provisions of §§111.39-111.45 of this subchapter shall be implemented by school districts.
(b) No later than June 30, 2015, the commissioner of education shall determine whether instructional materials funding has been made available to Texas public schools for materials that cover the essential knowledge and skills for mathematics as adopted in §§111.39-111.45 of this subchapter.
(c) If the commissioner makes the determination that instructional materials funding has been made available under subsection (b) of this section, §§111.39-111.45 of this subchapter shall be implemented beginning with the 2015-2016 school year and apply to the 2015-2016 and subsequent school years.
(d) If the commissioner does not make the determination that instructional materials funding has been made available under subsection (b) of this section, the commissioner shall determine no later than June 30 of each subsequent school year whether instructional materials funding has been made available. If the commissioner determines that instructional materials funding has been made available, the commissioner shall notify the State Board of Education and school districts that §§111.39-111.45 of this subchapter shall be implemented for the following school year.
(e) Sections 111.31-111.37 of this subchapter shall be superseded by the implementation of §§111.38-111.45 under this section.
Source: The provisions of this §111.38 adopted to be effective September 10, 2012, 37 TexReg 7109.
(a) General requirements. Students shall be awarded one credit for successful completion of this course. This course is recommended for students in Grade 8 or 9. Prerequisite: Mathematics, Grade 8 or its equivalent.
(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.
(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
(3) In Algebra I, students will build on the knowledge and skills for mathematics in Grades 6-8, which provide a foundation in linear relationships, number and operations, and proportionality. Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions. Students will connect functions and their associated solutions in both mathematical and real-world situations. Students will use technology to collect and explore data and analyze statistical relationships. In addition, students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents. Students will generate and solve linear systems with two equations and two variables and will create new functions through transformations.
(I) write systems of two linear equations given a table of values, a graph, and a verbal description.
(H) graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
(C) write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
(C) solve systems of two linear equations with two variables for mathematical and real-world problems.
(C) write quadratic functions when given real solutions and graphs of their related equations.
(C) determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
(B) write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
(E) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.
(F) decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.
(B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
(E) solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Source: The provisions of this §111.39 adopted to be effective September 10, 2012, 37 TexReg 7109.
(a) General requirements. Students shall be awarded one-half to one credit for successful completion of this course. Prerequisite: Algebra I.
(3) In Algebra II, students will build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I. Students will broaden their knowledge of quadratic functions, exponential functions, and systems of equations. Students will study logarithmic, square root, cubic, cube root, absolute value, rational functions, and their related equations. Students will connect functions to their inverses and associated equations and solutions in both mathematical and real-world situations. In addition, students will extend their knowledge of data analysis and numeric and algebraic methods.
(G) display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
(D) use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.
(G) determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.
(E) determine the reasonableness of a solution to a logarithmic equation.
(L) formulate and solve equations involving inverse variation.
(C) predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
Source: The provisions of this §111.40 adopted to be effective September 10, 2012, 37 TexReg 7109.
(a) General requirements. Students shall be awarded one credit for successful completion of this course. Prerequisite: Algebra I.
(3) In Geometry, students will build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I to strengthen their mathematical reasoning skills in geometric contexts. Within the course, students will begin to focus on more precise terminology, symbolic representations, and the development of proofs. Students will explore concepts covering coordinate and transformational geometry; logical argument and constructions; proof and congruence; similarity, proof, and trigonometry; two- and three-dimensional figures; circles; and probability. Students will connect previous knowledge from Algebra I to Geometry through the coordinate and transformational geometry strand. In the logical arguments and constructions strand, students are expected to create formal constructions using a straight edge and compass. Though this course is primarily Euclidean geometry, students should complete the course with an understanding that non-Euclidean geometries exist. In proof and congruence, students will use deductive reasoning to justify, prove and apply theorems about geometric figures. Throughout the standards, the term "prove" means a formal proof to be shown in a paragraph, a flow chart, or two-column formats. Proportionality is the unifying component of the similarity, proof, and trigonometry strand. Students will use their proportional reasoning skills to prove and apply theorems and solve problems in this strand. The two- and three-dimensional figure strand focuses on the application of formulas in multi-step situations since students have developed background knowledge in two- and three-dimensional figures. Using patterns to identify geometric properties, students will apply theorems about circles to determine relationships between special segments and angles in circles. Due to the emphasis of probability and statistics in the college and career readiness standards, standards dealing with probability have been added to the geometry curriculum to ensure students have proper exposure to these topics before pursuing their post-secondary education.
(4) These standards are meant to provide clarity and specificity in regards to the content covered in the high school geometry course. These standards are not meant to limit the methodologies used to convey this knowledge to students. Though the standards are written in a particular order, they are not necessarily meant to be taught in the given order. In the standards, the phrase "to solve problems" includes both contextual and non-contextual problems unless specifically stated.
(C) determine an equation of a line parallel or perpendicular to a given line that passes through a given point.
(D) identify and distinguish between reflectional and rotational symmetry in a plane figure.
(D) compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.
(D) verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.
(E) prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.
(B) apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.
(B) identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.
(B) apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.
(B) determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change.
(D) apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
(E) show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)2 + (y - k)2 =r2.
(E) apply independence in contextual problems.
Source: The provisions of this §111.41 adopted to be effective September 10, 2012, 37 TexReg 7109.
(a) General requirements. Students shall be awarded one-half to one credit for successful completion of this course. Prerequisites: Algebra I, Geometry, and Algebra II.
(3) Precalculus is the preparation for calculus. The course approaches topics from a function point of view, where appropriate, and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. The study of Precalculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems.
(P) determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.
(I) use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k).
(K) apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems.
(N) generate and solve trigonometric equations in mathematical and real-world problems.
Source: The provisions of this §111.42 adopted to be effective September 10, 2012, 37 TexReg 7109.
(a) General requirements. Students can be awarded one credit for successful completion of this course. Prerequisite: Algebra I.
(3) Mathematical Models with Applications is designed to build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I. This mathematics course provides a path for students to succeed in Algebra II and prepares them for various post-secondary choices. Students learn to apply mathematics through experiences in personal finance, science, engineering, fine arts, and social sciences. Students use algebraic, graphical, and geometric reasoning to recognize patterns and structure, model information, solve problems, and communicate solutions. Students will select from tools such as physical objects; manipulatives; technology, including graphing calculators, data collection devices, and computers; and paper and pencil and from methods such as algebraic techniques, geometric reasoning, patterns, and mental math to solve problems.
(E) report: report on the conclusions and the reasoning behind the conclusions.
(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees.
(D) use technology to create amortization models to investigate automobile financing and compare buying a vehicle to leasing a vehicle.
(C) analyze types of savings options involving simple and compound interest and compare relative advantages of these options.
(C) use quadratic functions to model motion.
(D) use trigonometric ratios to calculate distances and angle measures as applied to fields.
(D) use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields.
(C) use experiments to determine the reasonableness of a theoretical model such as binomial or geometric.
(F) use regression methods available through technology to model linear and exponential functions, interpret correlations, and make predictions.
(B) communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation.
Statutory Authority: The provisions of this §111.43 issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025.
Source: The provisions of this §111.43 adopted to be effective September 10, 2012, 37 TexReg 7109; amended to be effective August 24, 2015, 40 TexReg 5330.
(a) General requirements. Students shall be awarded one-half to one credit for successful completion of this course. Prerequisites: Geometry and Algebra II.
(3) In Advanced Quantitative Reasoning, students will develop and apply skills necessary for college, careers, and life. Course content consists primarily of applications of high school mathematics concepts to prepare students to become well-educated and highly informed 21st century citizens. Students will develop and apply reasoning, planning, and communication to make decisions and solve problems in applied situations involving numerical reasoning, probability, statistical analysis, finance, mathematical selection, and modeling with algebra, geometry, trigonometry, and discrete mathematics.
(H) select and apply an algorithm of interest to solve real-life problems such as problems using recursion or iteration involving population growth or decline, fractals, and compound interest; the validity in recorded and transmitted data using checksums and hashing; sports rankings, weighted class rankings, and search engine rankings; and problems involving scheduling or routing situations using vertex-edge graphs, critical paths, Euler paths, and minimal spanning trees and communicate to peers the application of the algorithm in precise mathematical and nontechnical language.
(H) create, represent, and analyze mathematical models and appropriate representations, including formulas and amortization tables, for various types of loans and investments to determine the best option for a given situation.
(T) communicate statistical results in oral and written formats using appropriate statistical and nontechnical language.
Source: The provisions of this §111.44 adopted to be effective September 10, 2012, 37 TexReg 7109.
(1) Students shall be awarded one-half to one credit for successful completion of this course. Prerequisites: Geometry and Algebra II.
(2) Students may repeat this course with different course content for up to three credits.
(3) The requirements for each course must be approved by the local district before the course begins.
(4) If this course is being used to satisfy requirements for the Distinguished Achievement Program, student research/products must be presented before a panel of professionals or approved by the student's mentor.
(3) In Independent Study in Mathematics, students will extend their mathematical understanding beyond the Algebra II level in a specific area or areas of mathematics such as theory of equations, number theory, non-Euclidean geometry, linear algebra, advanced survey of mathematics, or history of mathematics.
(7) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Source: The provisions of this §111.45 adopted to be effective September 10, 2012, 37 TexReg 7109.
(a) General requirements. Students shall be awarded one-half to one credit for successful completion of this course. Prerequisite: Algebra II.
(3) In Discrete Mathematics for Problem Solving, students are introduced to the improved efficiency of mathematical analysis and quantitative techniques over trial-and-error approaches to management problems involving organization, scheduling, project planning, strategy, and decision making. Students will learn how mathematical topics such as graph theory, planning and scheduling, group decision making, fair division, game theory, and theory of moves can be applied to management and decision making. Students will research mathematicians of the past whose work is relevant to these topics today and read articles about current mathematicians who either teach and conduct research at major universities or work in business and industry solving real-world logistical problems. Through the study of the applications of mathematics to society's problems today, students will become better prepared for and gain an appreciation for the value of a career in mathematics.
(L) explain the difference between a graph and a directed graph.
(G) explain the relationship between scheduling problems and bin packing problems.
(J) compute the Banzhaf power index and explain its significance.
(K) identify fair division procedures that exhibit envy-freeness.
(K) determine when a pair of strategies for two players is in equilibrium.
(G) model a conflict from literature or from a real-life situation as a two-by-two strict ordinal game and compare the results predicted by game theory and by TOM.
Statutory Authority: The provisions of this §111.46 issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025, as that section existed before amendment by House Bill 5, 83rd Texas Legislature, Regular Session, 2013.
Source: The provisions of this §111.46 adopted to be effective August 25, 2014, 38 TexReg 9027.
(3) In Statistics, students will build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I. Students will broaden their knowledge of variability and statistical processes. Students will study sampling and experimentation, categorical and quantitative data, probability and random variables, inference, and bivariate data. Students will connect data and statistical processes to real-world situations. In addition, students will extend their knowledge of data analysis.
(G) critically analyze published findings for appropriateness of study design implemented, sampling methods used, or the statistics applied.
(D) describe and model variability using population and sampling distributions.
(F) analyze categorical data, including determining marginal and conditional distributions, using two-way tables.
(D) compare statistical measures such as sample mean and standard deviation from a technology-simulated sampling distribution to the theoretical sampling distribution.
(J) describe the potential impact of Type I and Type II Errors.
(F) identify and interpret the reasonableness of attributes of lines of best fit within the context, including slope and y-intercept.
Statutory Authority: The provisions of this §111.47 issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025.
Source: The provisions of this §111.47 adopted to be effective March 18, 2015, 40 TexReg 1371.
(3) In Algebraic Reasoning, students will build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I, continue with the development of mathematical reasoning related to algebraic understandings and processes, and deepen a foundation for studies in subsequent mathematics courses. Students will broaden their knowledge of functions and relationships, including linear, quadratic, square root, rational, cubic, cube root, exponential, absolute value, and logarithmic functions. Students will study these functions through analysis and application that includes explorations of patterns and structure, number and algebraic methods, and modeling from data using tools that build to workforce and college readiness such as probes, measurement tools, and software tools, including spreadsheets.
(D) determine a function that models real-world data and mathematical contexts using finite differences such as the age of a tree and its circumference, figurative numbers, average velocity, and average acceleration.
(F) compare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically such as a quadratic function that results from multiplying two linear functions.
(D) determine the linear factors of a polynomial function of degree two and of degree three when represented symbolically and tabularly and graphically where appropriate.
(E) represent and solve systems of three linear equations arising from mathematical and real-world situations using matrices and technology.
(C) approximate solutions to equations arising from questions asked about exponential, logarithmic, square root, and cubic functions that model real-world applications tabularly and graphically.
(E) determine if a given linear function is a reasonable model for a set of data arising from a real-world situation.
Statutory Authority: The provisions of this §111.48 issued under the Texas Education Code, §§7.102(c)(4), 28.002, and 28.025.
Source: The provisions of this §111.48 adopted to be effective May 31, 2015, 40 TexReg 3146.

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