STAAR Standards Snapshot Math REV STAAR M Oct 2011

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TEKSSNAPSHOTAlgebra I. 2Algebra II. 6Geometry. 9

T EK SSNAPSHOTALGEBRA I

TEKS Snapshot – Algebra IMathematical Process StandardsA.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.Tools to KnowA.1(A)apply mathematics toproblems arising ineveryday life, society, andthe workplaceA.1(B)use a problem-solvingmodel that incorporatesanalyzing given information,formulating a plan orstrategy, determining asolution, justifying thesolution, and evaluating theproblem-solving processand the reasonableness ofthe solutionWays to ShowA.1(C)select tools, including realobjects, manipulatives,paper and pencil, andtechnology as appropriate,and techniques, includingmental math, estimation,and number sense asappropriate, to solveproblemsA.1(D)A.1(E)communicate mathematicalideas, reasoning, and theirimplications using multiplerepresentations, includingsymbols, diagrams, graphs,and language asappropriatecreate and userepresentations to organize,record, and communicatemathematical ideasA.1(F)analyze mathematicalrelationships to connectand communicatemathematical ideasA.1(G)display, explain, and justifymathematical ideas andarguments using precisemathematical language inwritten or oralcommunicationKnowledge and Skills StatementsA.2Linear functions, equations, and inequalities. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and withouttechnology, linear equations, inequalities, and systems of equations.A.3Linear functions, equations, and inequalities. The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multipleways and solve, with and without technology, equations, inequalities, and systems of equations.A.4Linear functions, equations, and inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.A.5Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.A.6Quadratic functions and equations. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology,quadratic equations.A.7Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways anddetermine, with and without technology, the solutions to equations.A.8A.9Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. Thestudent formulates statistical relationships and evaluates their reasonableness based on real-world data.Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent inmultiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness basedon real-world data.A.10Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.A.11Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.A.12Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.Source: Texas Education Agencyv. 9.16.16

TEKS Snapshot – Algebra I2Describing and Graphing Linear Functions,Equations, and Inequalities1Number and Algebraic MethodsRptg CatReadiness StandardsSupporting StandardsA.10(E) factor, if possible, trinomials with real factors in theform ax2 bx c, including perfect square trinomials ofdegree twoA.11(B) simplify numeric and algebraic expressions using thelaws of exponents, including integral and rationalexponentsA.10(A) add and subtract polynomials of degree one and degree twoA.10(B) multiply polynomials of degree one and degree twoA.10(C) determine the quotient of a polynomial of degree one and polynomial of degree two when divided by apolynomial of degree one and polynomial of degree two when the degree of the divisor does not exceedthe degree of the dividendA.10(D) rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributivepropertyA.10(F) decide if a binomial can be written as the difference of two squares and, if possible, use the structure of adifference of two squares to rewrite the binomialA.11(A) simplify numerical radical expressions involving square rootsA.12(A) decide whether relations represented verbally, tabularly, graphically, and symbolically define a functionA.12(B) evaluate functions, expressed in function notation, given one or more elements in their domainsA.12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function formusing recursive processesA.12(D) write a formula for the nth term of arithmetic and geometric sequences, given the value of several of theirtermsA.12(E) solve mathematic and scientific formulas, and other literal equations, for a specified variableA.3(B)A.3(A)STAAR11A.3(C)12Source: Texas Education AgencyA.3(D)calculate the rate of change of a linear functionrepresented tabularly, graphically, or algebraically incontext of mathematical and real-world problemsgraph linear functions on the coordinate plane andidentify key features, including x-intercept, y-intercept,zeros, and slope, in mathematical and real-worldproblemsgraph the solution set of linear inequalities in twovariables on the coordinate ermine the slope of a line given a table of values, a graph, two points on the line, and an equationwritten in various forms, including y mx b, Ax By C, and y – y1 m(x – x1)determine the effects on the graph of the parent function f(x) x when f(x) is replaced by af(x), f(x) d,f(x – c), f(bx) for specific values o f a, b, c, and dgraph systems of two linear equations in two variables on the coordinate plane and determine thesolutions if they existestimate graphically the solutions to systems of two linear equations with two variables in real-worldproblemsgraph the solution set of systems of two linear inequalities in two variables on the coordinate planecalculate, using technology, the correlation coefficient between two quantitative variables and interpretthis quantity as a measure of the strength of the linear associationcompare and contrast association and causation in real-world problemswrite, with and without technology, linear functions that provide a reasonable fit to data to estimatesolutions and make predictions for real-world problemsv. 9.16.16

TEKS Snapshot – Algebra IRptg CatReadiness StandardsSTAAR3Writing and Solving Linear Functions,Equations, and ential Functions andEquations4Quadratic Functions and EquationsA.6(A)# ItemsA.7(A)11A.7(C)A.8(A)A.9(C)654(5 Griddable)Source: Texas Education AgencyA.9(D)Supporting Standardsdetermine the domain and range of a linear function inmathematical problems; determine reasonable domainand range values for real-world situations, bothcontinuous and discrete; and represent domain andrange using inequalitieswrite linear equations in two variables given a table ofvalues, a graph, and a verbal descriptionwrite systems of two linear equations given a table ofvalues, a graph, and a verbal descriptionsolve linear equations in one variable, including thosefor which the application of the distributive property isnecessary and for which variables are included on bothsidessolve systems of two linear equations with twovariables for mathematical and real-world problemsA.2(B)determine the domain and range of quadratic functionsand represent the domain and range using inequalitiesgraph quadratic functions on the coordinate plane anduse the graph to identify key attributes, if possible,including x-intercept, y-intercept, zeros, maximumvalue, minimum values, vertex, and the equation of theaxis of symmetrydetermine the effects on the graph of the parentfunction f(x) x2 when f(x) is replaced by af(x), f(x) d,f(x – c), f(bx) for specific values o f a, b, c, and dsolve quadratic equations having real solutions byfactoring, taking square roots, completing the square,and applying the quadratic formulaA.6(B)write exponential functions in the form f(x) abx(where b is a rational number) to describe problemsarising from mathematical and real-world situations,including growth and decaygraph exponential functions that model growth anddecay and identify key features, including y-interceptand asymptote, in mathematical and real-worldproblemsA.9(A)32-35 questions from Readiness )A.7(B)A.8(B)A.9(B)A.9(E)write linear equations in two variables in various forms, including y mx b, Ax By C, andy – y1 m(x – x1), given one point and the slope and given two pointswrite and solve equations involving direct variationwrite the equation of a line that contains a given point and is parallel to a given linewrite the equation of a line that contains a given point and is perpendicular to a given linewrite an equation of a line that is parallel or perpendicular to the x- or y-axis and determine whether theslope of the line is zero or undefinedwrite linear inequalities in two variables given a table of values, a graph, and a verbal descriptionsolve linear inequalities in one variable, including those for which the application of the distributiveproperty is necessary and for which variables are included on both sideswrite equations of quadratic functions given the vertex and another point on the graph, write theequation in vertex form (f(x) a(x – h)2 k), and rewrite the equation from vertex form to standard form(f(x) ax2 bx c)write quadratic functions when given real solutions and graphs of their related equationsdescribe the relationship between the linear factors of quadratic expressions and the zeros of theirassociated quadratic functionswrite, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions andmake predictions for real-world problemsdetermine the domain and range of exponential functions of the form f(x) abx and represent the domainand range using inequalitiesinterpret the meaning of the values of a and b in exponential functions of the form f(x) abx in real-worldproblemswrite, using technology, exponential functions that provide a reasonable fit to data and make predictionsfor real-world problems19-22 questions from Supporting Standardsv. 9.16.16

T EK SSNAPSHOTALGEBRA II

TEKS Snapshot – Algebra IIMathematical Process Standards2A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.Tools to Know2A.1(A)Ways to Show2A.1(B)apply mathematics toproblems arising ineveryday life, society, andthe workplace2A.1(C)use a problem-solvingmodel that incorporatesanalyzing given information,formulating a plan orstrategy, determining asolution, justifying thesolution, and evaluating theproblem-solving processand the reasonableness ofthe solutionselect tools, including realobjects, manipulatives,paper and pencil, andtechnology as appropriate,and techniques, includingmental math, estimation,and number sense asappropriate, to solveproblems2A.1(D)2A.1(E)2A.1(F)communicate mathematicalideas, reasoning, and theirimplications using multiplerepresentations, includingsymbols, diagrams, graphs,and language asappropriatecreate and userepresentations to organize,record, and communicatemathematical ideasanalyze mathematicalrelationships to connectand communicatemathematical ideas2A.1(G)display, explain, and justifymathematical ideas andarguments using precisemathematical language inwritten or oralcommunicationKnowledge and Skills Statements2A.2Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and itsinverse.2A.3Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness ofsolutions.2A.4Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities canbe used to model situations, solve problems, and make predictions.2A.5Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.2A.6Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions,equations, and inequalities can be used to model situations, solve problems, and make predictions.2A.7Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.2A.8Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.1Number andAlgebraic MethodsRptg CatSTAAR9Source: Texas Education AgencyReadiness Standards2A.7(E) determine linear and quadratic factors of a polynomial expressionof degree three and of degree four, including factoring the sumand difference of two cubes and factoring by grouping2A.7(F) determine the sum, difference, product, and quotient of rationalexpressions with integral exponents of degree one and of degreetwo2A.7(H) solve equations involving rational exponentsSupporting Standards2A.7(A) add, subtract, and multiply complex numbers2A.7(B) add, subtract, and multiply polynomials2A.7(C) determine the quotient of a polynomial of degree three and of degree four when divided by apolynomial of degree one and of degree two2A.7(D) determine the linear factors of a polynomial function of degree three and of degree four usingalgebraic methods2A.7(G) rewrite radical expressions that contain variables to equivalent forms2A.7(I) write the domain and range of a function in interval notation, inequalities, and set notationv. 9.16.16

TEKS Snapshot – Algebra IIRptg CatSTAARReadiness StandardsSupporting Standards2A.2(A) graph the functions f(x) 𝑋𝑋 , f(x) 1/x, f(x) x ,f(x) 3 𝑥𝑥 , f(x) bx , f(x) x , and f(x) logb (x) where b is 2, 10,and e, and, when applicable, analyze the key attributes such asdomain, range, intercepts, symmetries, asymptotic behavior, andmaximum and minimum given an interval2A.2(C) describe and analyze the relationship between a function and itsinverse (quadratic and square root, logarithmic and exponential),including the restriction(s) on domain, which will restrict its range2A.8(C) predict and make decisions and critical judgments from a givenset of data using linear, quadratic, and exponential models2A.2(B) graph and write the inverse of a function using notation such as f –1(x)2A.2(D) use the composition of two functions, including the necessary restrictions on the domain, todetermine if the functions are inverses of each other2A.8(A) analyze data to select the appropriate model from among linear, quadratic, and exponentialmodels2A.8(B) use regression methods available through technology to write a linear function, a quadraticfunction, and an exponential function from a given set of data2A.3(A) formulate systems of equations, including systems consisting ofthree linear equations in three variables and systems consisting oftwo equations, the first linear and the second quadratic2A.3(B) solve systems of three linear equations in three variables by usingGaussian elimination, technology with matrices, and substitution2A.3(C) solve, algebraically, systems of two equations in two variables consisting of a linear equationand a quadratic equation2A.3(D) determine the reasonableness of solutions to systems of a linear equation and a quadraticequation in two variables2A.3(E) formulate systems of at least two linear inequalities in two variables2A.3(F) solve systems of two or more linear inequalities in two variables2A.3(G) determine possible solutions in the solution set of systems of two or more linear inequalities intwo variables102A.4(B) write the equation of a parabola using given attributes, includingvertex, focus, directrix, axis of symmetry, and direction of opening2A.4(C) determine the effect on the graph of f(x) 𝑥𝑥 when f(x) isreplaced by af(x), f(x) d, f(bx), and f(x – c) for specific positiveand negative values of a, b, c, and d2A.4(F) solve quadratic and square root equations2A.4(A) write the quadratic function given three specified points in the plane2A.4(D) transform a quadratic function f(x) ax2 bx c to the form f(x) a(x – h)2 k to identify thedifferent attributes of f(x)2A.4(E) formulate quadratic and square root equations using technology given a table of data2A.4(G) identify extraneous solutions of square root equations2A.4(H) solve quadratic inequalities62A.5(A) determine the effects on the key attributes on the graphs off(x) bx and f(x) logb (x) where b is 2, 10, and e when f(x) isreplaced by af(x), f(x) d, and f(x – c) for specific positive andnegative real values o f a, c, and d2A.5(D) solve exponential equations of the form y abx where a is anonzero real number and b is greater than zero and not equal toone and single logarithmic equations having real solutions2A.5(B) formulate exponential and logarithmic equations that model real-world situations, includingexponential relationships written in recursive notation2A.5(C) rewrite exponential equations as their corresponding logarithmic equations and logarithmicequations as their corresponding exponential equations2A.5(E) determine the reasonableness of a solution to a logarithmic equation2A.6(E) solve absolute value linear equations2A.6(I) solve rational equations that have real solutions2A.6(L) formulate and solve equations involving inverse variation2A.6(A) analyze the effect on the graphs of f(x) x3 and f(x) 3 𝑥𝑥 when f(x) is replaced by af(x),f(bx), f(x – c), and f(x) d for specific positive and negative real values of a, b, c, and d2A.6(B) solve cube root equations that have real roots2A.6(C) analyze the effect on the graphs of f(x) x when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) d for specific positive and negative real values of a, b, c, and d2A.6(D) formulate absolute value linear equations2A.6(F) solve absolute value linear inequalities2A.6(G) analyze the effect on the graphs of f(x) 1/x when f(x) is replaced by af(x), f(bx), f(x – c), andf(x) d for specific positive and negative real values of a, b, c, and d2A.6(H) formulate rational equations that model real-world situations2A.6(J) determine the reasonableness of a solution to a rational equation2A.6(K) determine the asymptotic

Source: Texas Education Agency v. 9.16.16 Rptg Cat STAAR Readiness Standards Supporting Standards 1 Number and Algebraic Methods 11 A.10(E) factor, if possible, trinomials with real factors in the form ax2 bx c, including perfect square trinomials of degree two A.11(B) simplify numeric and algebraic expressions using the

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