Chapter 111. Texas Essential Knowledge And Skills For .
High School§111.C.Chapter 111. Texas Essential Knowledge and Skills for MathematicsSubchapter C. High SchoolStatutory Authority: The provisions of this Subchapter C issued under the Texas Education Code, §§7.102(c)(4),28.002, 28.008, and 28.025, unless otherwise noted.§111.38. Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted2012.(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 materialsfunding has been made available to Texas public schools for materials that cover the essential knowledgeand 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 availableunder subsection (b) of this section, §§111.39-111.45 of this subchapter shall be implemented beginningwith 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 madeavailable under subsection (b) of this section, the commissioner shall determine no later than June 30 ofeach subsequent school year whether instructional materials funding has been made available. If thecommissioner determines that instructional materials funding has been made available, the commissionershall notify the State Board of Education and school districts that §§111.39-111.45 of this subchapter shallbe implemented for the following school year.(e)Sections 111.31-111.37 of this subchapter shall be superseded by the implementation of §§111.38-111.45under this section.Source: The provisions of this §111.38 adopted to be effective September 10, 2012, 37 TexReg 7109.§111.39. Algebra I, Adopted 2012 (One Credit).(a)General requirements. Students shall be awarded one credit for successful completion of this course. Thiscourse is recommended for students in Grade 8 or 9. Prerequisite: Mathematics, Grade 8 or its equivalent.(b)Introduction.(1)The desire to achieve educational excellence is the driving force behind the Texas essentialknowledge and skills for mathematics, guided by the college and career readiness standards. Byembedding 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 thechallenges they will face in the 21st century.(2)The process standards describe ways in which students are expected to engage in the content. Theplacement of the process standards at the beginning of the knowledge and skills listed for eachgrade and course is intentional. The process standards weave the other knowledge and skillstogether so that students may be successful problem solvers and use mathematics efficiently andeffectively 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, andthe workplace. Students will use a problem-solving model that incorporates analyzing giveninformation, formulating a plan or strategy, determining a solution, justifying the solution, andevaluating the problem-solving process and the reasonableness of the solution. Students will selectappropriate tools such as real objects, manipulatives, paper and pencil, and technology andtechniques such as mental math, estimation, and number sense to solve problems. Students willeffectively communicate mathematical ideas, reasoning, and their implications using multiplerepresentations such as symbols, diagrams, graphs, and language. Students will use mathematicalrelationships to generate solutions and make connections and predictions. Students will analyzemathematical relationships to connect and communicate mathematical ideas. Students will display,October 2015 UpdatePage 1
§111.C.High Schoolexplain, or justify mathematical ideas and arguments using precise mathematical language inwritten or oral communication.(c)(3)In Algebra I, students will build on the knowledge and skills for mathematics in Grades 6-8, whichprovide a foundation in linear relationships, number and operations, and proportionality. Studentswill study linear, quadratic, and exponential functions and their related transformations, equations,and associated solutions. Students will connect functions and their associated solutions in bothmathematical and real-world situations. Students will use technology to collect and explore dataand analyze statistical relationships. In addition, students will study polynomials of degree one andtwo, radical expressions, sequences, and laws of exponents. Students will generate and solve linearsystems with two equations and two variables and will create new functions throughtransformations.(4)Statements that contain the word "including" reference content that must be mastered, while thosecontaining the phrase "such as" are intended as possible illustrative examples.Knowledge and skills.(1)(2)Page 2Mathematical process standards. The student uses mathematical processes to acquire anddemonstrate mathematical understanding. The student is expected to:(A)apply mathematics to problems arising in everyday life, society, and the workplace;(B)use a problem-solving model that incorporates analyzing given information, formulatinga plan or strategy, determining a solution, justifying the solution, and evaluating theproblem-solving process and the reasonableness of the solution;(C)select tools, including real objects, manipulatives, paper and pencil, and technology asappropriate, and techniques, including mental math, estimation, and number sense asappropriate, to solve problems;(D)communicate mathematical ideas, reasoning, and their implications using multiplerepresentations, including symbols, diagrams, graphs, and language as appropriate;(E)create and use representations to organize, record, and communicate mathematical ideas;(F)analyze mathematical relationships to connect and communicate mathematical ideas; and(G)display, explain, and justify mathematical ideas and arguments using precisemathematical language in written or oral communication.Linear functions, equations, and inequalities. The student applies the mathematical processstandards when using properties of linear functions to write and represent in multiple ways, withand without technology, linear equations, inequalities, and systems of equations. The student isexpected to:(A)determine the domain and range of a linear function in mathematical problems; determinereasonable domain and range values for real-world situations, both continuous anddiscrete; and represent domain and range using inequalities;(B)write linear equations in two variables in various forms, including y mx b, Ax By C, and y - y1 m(x - x1), given one point and the slope and given two points;(C)write linear equations in two variables given a table of values, a graph, and a verbaldescription;(D)write and solve equations involving direct variation;(E)write the equation of a line that contains a given point and is parallel to a given line;(F)write the equation of a line that contains a given point and is perpendicular to a givenline;(G)write an equation of a line that is parallel or perpendicular to the X or Y axis anddetermine whether the slope of the line is zero or undefined;October 2015 Update
High School(3)(4)(5)(6)§111.C.(H)write linear inequalities in two variables given a table of values, a graph, and a verbaldescription; and(I)write systems of two linear equations given a table of values, a graph, and a verbaldescription.Linear functions, equations, and inequalities. The student applies the mathematical processstandards when using graphs of linear functions, key features, and related transformations torepresent in multiple ways and solve, with and without technology, equations, inequalities, andsystems of equations. The student is expected to:(A)determine the slope of a line given a table of values, a graph, two points on the line, andan equation written in various forms, including y mx b, Ax By C, and y - y1 m(x - x1);(B)calculate the rate of change of a linear function represented tabularly, graphically, oralgebraically in context of mathematical and real-world problems;(C)graph linear functions on the coordinate plane and identify key features, including xintercept, y-intercept, zeros, and slope, in mathematical and real-world problems;(D)graph the solution set of linear inequalities in two variables on the coordinate plane;(E)determine the effects on the graph of the parent function f(x) x when f(x) is replaced byaf(x), f(x) d, f(x - c), f(bx) for specific values of a, b, c, and d;(F)graph systems of two linear equations in two variables on the coordinate plane anddetermine the solutions if they exist;(G)estimate graphically the solutions to systems of two linear equations with two variables inreal-world problems; and(H)graph the solution set of systems of two linear inequalities in two variables on thecoordinate plane.Linear functions, equations, and inequalities. The student applies the mathematical processstandards to formulate statistical relationships and evaluate their reasonableness based on realworld data. The student is expected to:(A)calculate, using technology, the correlation coefficient between two quantitative variablesand interpret this quantity as a measure of the strength of the linear association;(B)compare and contrast association and causation in real-world problems; and(C)write, with and without technology, linear functions that provide a reasonable fit to datato estimate solutions and make predictions for real-world problems.Linear functions, equations, and inequalities. The student applies the mathematical processstandards to solve, with and without technology, linear equations and evaluate the reasonablenessof their solutions. The student is expected to:(A)solve linear equations in one variable, including those for which the application of thedistributive property is necessary and for which variables are included on both sides;(B)solve linear inequalities in one variable, including those for which the application of thedistributive property is necessary and for which variables are included on both sides; and(C)solve systems of two linear equations with two variables for mathematical and real-worldproblems.Quadratic functions and equations. The student applies the mathematical process standards whenusing properties of quadratic functions to write and represent in multiple ways, with and withouttechnology, quadratic equations. The student is expected to:October 2015 UpdatePage 3
§111.C.High School(7)(8)(9)(10)Page 4(A)determine the domain and range of quadratic functions and represent the domain andrange using inequalities;(B)write equations of quadratic functions given the vertex and another point on the graph,write the equation in vertex form (f(x) a(x - h)2 k), and rewrite the equation fromvertex form to standard form (f(x) ax2 bx c); and(C)write quadratic functions when given real solutions and graphs of their related equations.Quadratic functions and equations. The student applies the mathematical process standards whenusing graphs of quadratic functions and their related transformations to represent in multiple waysand determine, with and without technology, the solutions to equations. The student is expected to:(A)graph quadratic functions on the coordinate plane and use the graph to identify keyattributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimumvalues, vertex, and the equation of the axis of symmetry;(B)describe the relationship between the linear factors of quadratic expressions and the zerosof their associated quadratic functions; and(C)determine the effects on the graph of the parent function f(x) x2 when f(x) is replacedby af(x), f(x) d, f(x - c), f(bx) for specific values of a, b, c, and d.Quadratic functions and equations. The student applies the mathematical process standards tosolve, with and without technology, quadratic equations and evaluate the reasonableness of theirsolutions. The student formulates statistical relationships and evaluates their reasonableness basedon real-world data. The student is expected to:(A)solve quadratic equations having real solutions by factoring, taking square roots,completing the square, and applying the quadratic formula; and(B)write, using technology, quadratic functions that provide a reasonable fit to data toestimate solutions and make predictions for real-world problems.Exponential functions and equations. The student applies the mathematical process standardswhen using properties of exponential functions and their related transformations to write, graph,and represent in multiple ways exponential equations and evaluate, with and without technology,the reasonableness of their solutions. The student formulates statistical relationships and evaluatestheir reasonableness based on real-world data. The student is expected to:(A)determine the domain and range of exponential functions of the form f(x) abx andrepresent the domain and range using inequalities;(B)interpret the meaning of the values of a and b in exponential functions of the form f(x) abx in real-world problems;(C)write exponential functions in the form f(x) abx (where b is a rational number) todescribe problems arising from mathematical and real-world situations, including growthand decay;(D)graph exponential functions that model growth and decay and identify key features,including y-intercept and asymptote, in mathematical and real-world problems; and(E)write, using technology, exponential functions that provide a reasonable fit to data andmake predictions for real-world problems.Number and algebraic methods. The student applies the mathematical process standards andalgebraic methods to rewrite in equivalent forms and perform operations on polynomialexpressions. The student is expected to:(A)add and subtract polynomials of degree one and degree two;(B)multiply polynomials of degree one and degree two;October 2015 Update
High School(11)(12)§111.C.(C)determine the quotient of a polynomial of degree one and polynomial of degree two whendivided by a polynomial of degree one and polynomial of degree two when the degree ofthe divisor does not exceed the degree of the dividend;(D)rewrite polynomial expressions of degree one and degree two in equivalent forms usingthe distributive property;(E)factor, if possible, trinomials with real factors in the form ax2 bx c, including perfectsquare trinomials of degree two; and(F)decide if a binomial can be written as the difference of two squares and, if possible, usethe structure of a difference of two squares to rewrite the binomial.Number and algebraic methods. The student applies the mathematical process standards andalgebraic methods to rewrite algebraic expressions into equivalent forms. The student is expectedto:(A)simplify numerical radical expressions involving square roots; and(B)simplify numeric and algebraic expressions using the laws of exponents, includingintegral and rational exponents.Number and algebraic methods. The student applies the mathematical process standards andalgebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. Thestudent is expected to:(A)decide whether relations represented verbally, tabularly, graphically, and symbolicallydefine a function;(B)evaluate functions, expressed in function notation, given one or more elements in theirdomains;(C)identify terms of arithmetic and geometric sequences when the sequences are given infunction form using recursive processes;(D)write a formula for the nth term of arithmetic and geometric sequences, given the value ofseveral of their terms; and(E)solve mathematic and scientific formulas, and other literal equations, for a specifiedvariable.Source: The provisions of this §111.39 adopted to be effective September 10, 2012, 37 TexReg 7109.§111.40. Algebra II, Adopted 2012 (One-Half to One Credit).(a)General requirements. Students shall be awarded one-half to one credit for successful completion of thiscourse. Prerequisite: Algebra I.(b)Introduction.(1)The desire to achieve educational excellence is the driving force behind the Texas essentialknowledge and skills for mathematics, guided by the college and career readiness standards. Byembedding 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 thechallenges they will face in the 21st century.(2)The process standards describe ways in which students are expected to engage in the content. Theplacement of the process standards at the beginning of the knowledge and skills listed for eachgrade and course is intentional. The process standards weave the other knowledge and skillstogether so that students may be successful problem solvers and use mathematics efficiently andeffectively 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, andthe workplace. Students will use a problem-solving model that incorporates analyzing giveninformation, formulating a plan or strategy, determining a solution, justifying the solution, andOctober 2015 UpdatePage 5
§111.C.High Schoolevaluating the problem-solving process and the reasonableness of the solution. Students will selectappropriate tools such as real objects, manipulatives, paper and pencil, and technology andtechniques such as mental math, estimation, and number sense to solve problems. Students willeffectively communicate mathematical ideas, reasoning, and their implications using multiplerepresentations such as symbols, diagrams, graphs, and language. Students will use mathematicalrelationships to generate solutions and make connections and predictions. Students will analyzemathematical relationships to connect and communicate mathematical ideas. Students will display,explain, or justify mathematical ideas and arguments using precise mathematical language inwritten or oral communication.(c)(3)In Algebra II, students will build on the knowledge and skills for mathematics in KindergartenGrade 8 and Algebra I. Students will broaden their knowledge of quadratic functions, exponentialfunctions, 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 totheir inverses and associated equations and solutions in both mathematical and real-worldsituations. In addition, students will extend their knowledge of data analysis and numeric andalgebraic methods.(4)Statements that contain the word "including" reference content that must be mastered, while thosecontaining the phrase "such as" are intended as possible illustrative examples.Knowledge and skills.(1)(2)Page 6Mathematical process standards. The student uses mathematical processes to acquire anddemonstrate mathematical understanding. The student is expected to:(A)apply mathematics to problems arising in everyday life, society, and the workplace;(B)use a problem-solving model that incorporates analyzing given information, formulatinga plan or strategy, determining a solution, justifying the solution, and evaluating theproblem-solving process and the reasonableness of the solution;(C)select tools, including real objects, manipulatives, paper and pencil, and technology asappropriate, and techniques, including mental math, estimation, and number sense asappropriate, to solve problems;(D)communicate mathematical ideas, reasoning, and their implications using multiplerepresentations, incl
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
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
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