# STAAR STANDARDS ALGEBRA I ALGEBRA II GEOMETRY

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1 STANDARDS ALGEBRA I ALGEBRA II GEOMETRY

2 STANDARDS ALGEBRA I

3 TEKS Snapshot Algebra I (New TEKS ) Mathematical Process Standards A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. Tools to Know Ways to Show A.1(A) A.1(B) A.1(C) A.1(D) A.1(E) A.1(F) A.1(G) apply mathematics to arising in everyday life, society, and the workplace 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 select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate create and use representations to organize, record, and communicate mathematical ideas analyze mathematical relationships to connect and communicate mathematical ideas display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Knowledge and Skills Statements A.2 Linear 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 without technology, linear equations, inequalities, and systems of equations. A.3 Linear 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 multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. A.4 Linear 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.5 Linear 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.6 Quadratic 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.7 Quadratic 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 and determine, with and without technology, the solutions to equations. A.8 Quadratic 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. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. A.9 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 in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. A.10 Number 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.11 Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. A.12 Number 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 Agency Resources REV May 2015

4 Rptg Cat Readiness Standards Supporting Standards TEKS Snapshot Algebra I (New TEKS ) 1 Number and Algebraic Methods 11 A.10(E) factor, if possible, trinomials with real factors in the form ax 2 + bx + c, including perfect square trinomials of degree two A.11(B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents A.10(A) add and subtract polynomials of degree one and degree two A.10(B) multiply polynomials of degree one and degree two A.10(C) determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend A.10(D) rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property A.10(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 A.11(A) simplify numerical radical expressions involving square roots A.12(A) decide whether relations represented verbally, tabularly, graphically, and symbolically define a function A.12(B) evaluate functions, expressed in function notation, given one or more elements in their domains A.12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes A.12(D) write a formula for the n th term of arithmetic and geometric sequences, given the value of several of their terms A.12(E) solve mathematic and scientific formulas, and other literal equations, for a specified variable 2 Describing and Graphing Linear Functions, Equations, and Inequalities 12 A.3(B) A.3(C) A.3(D) calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world graph the solution set of linear inequalities in two variables on the coordinate plane A.3(A) determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y y 1 = m(x x 1) A.3(E) 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 d A.3(F) graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist A.3(G) estimate graphically the solutions to systems of two linear equations with two variables in real-world A.3(H) graph the solution set of systems of two linear inequalities in two variables on the coordinate plane A.4(A) calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association A.4(B) compare and contrast association and causation in real-world A.4(C) write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world Source: Texas Education Agency Resources REV May 2015

6 STANDARDS ALGEBRA II

7 TEKS Snapshot Algebra II (New TEKS ) Mathematical Process Standards 2A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. Tools to Know Ways to Show 2A.1(A) 2A.1(B) 2A.1(C) 2A.1(D) 2A.1(E) 2A.1(F) 2A.1(G) apply mathematics to arising in everyday life, society, and the workplace 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 select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate create and use representations to organize, record, and communicate mathematical ideas analyze mathematical relationships to connect and communicate mathematical ideas display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Knowledge and Skills Statements 2A.2 Attributes 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 its inverse. 2A.3 Systems 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 of solutions. 2A.4 Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve, and make predictions. 2A.5 Exponential 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. 2A.6 Cubic, 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, and make predictions. 2A.7 Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. 2A.8 Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. Rptg Cat Readiness Standards Supporting Standards 1 Number and Algebraic Methods 9 2A.7(E) determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping 2A.7(F) determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two 2A.7(H) solve equations involving rational exponents 2A.7(A) add, subtract, and multiply complex numbers 2A.7(B) add, subtract, and multiply polynomials 2A.7(C) determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two 2A.7(D) determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods 2A.7(G) rewrite radical expressions that contain variables to equivalent forms 2A.7(I) write the domain and range of a function in interval notation, inequalities, and set notation Source: Texas Education Agency Resources REV May 2015

9 STANDARDS GEOMETRY

10 TEKS Snapshot Geometry (New TEKS ) Mathematical Process Standards G.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. Tools to Know Ways to Show G.1(A) G.1(B) G.1(C) G.1(D) G.1(E) G.1(F) G.1(G) apply mathematics to arising in everyday life, society, and the workplace 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 select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate create and use representations to organize, record, and communicate mathematical ideas analyze mathematical relationships to connect and communicate mathematical ideas display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Knowledge and Skills Statements G.2 Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures. G.3 Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). G.4 Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. G.5 Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. G.6 Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. G.7 Similarity, proof, and trigonometry. The student uses the process skills in applying similarity to solve. G.8 Similarity, proof, and trigonometry. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. G.9 Similarity, proof, and trigonometry. The student uses the process skills to understand and apply relationships in right triangles Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. G.12 Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. G.13 Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. Source: Texas Education Agency Resources REV May 2015

11 Rptg Cat Readiness Standards Supporting Standards TEKS Snapshot Geometry (New TEKS ) 1 Logical Argument and Constructions G.4(C) G.5(A) verify that a conjecture is false using a counterexample investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools G.4(A) G.4(B) G.4(D) G.5(B) G.5(C) G.5(D) distinguish between undefined terms, definitions, postulates, conjectures, and theorems identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships verify the Triangle Inequality theorem using constructions and apply the theorem to solve 2 Coordinate and Transformational Geometry G.2(B) G.2(C) G.3(B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines determine an equation of a line parallel or perpendicular to a given line that passes through a given point determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane G.2(A) G.3(A) G.3(C) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint describe and perform transformations of figures in a plane using coordinate notation identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane G.3(D) identify and distinguish between reflectional and rotational symmetry in a plane figure G.12(E) show that the equation of a circle with center at the origin and radius r is x 2 + y 2 = r 2 and determine the equation for the graph of a circle with radius r and center (h, k), (x h) 2 + (y k) 2 = r 2 3 Proof and Congruence G.6(A) G.6(B) verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve prove two triangles are congruent by applying the Side-Angle-Side, Angle- Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions G.6(C) G.6(D) G.6(E) apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve 4 Similarity and Trigonometry G.7(B) G.9(A) apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve G.9(B) apply the relationships in special right triangles and and the Pythagorean theorem, including Pythagorean triples, to solve G.7(A) G.8(A) G.8(B) apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve 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 NOTE: The classification of standards on this snapshot represents the reviewed and synthesized input of a sample of Texas high school mathematics teachers. This snapshot DOES NOT represent a publication of the Texas Education Agency. District curriculum may reflect other classifications. Source: Texas Education Agency Resources REV May 2015

12 Rptg Cat Readiness Standards Supporting Standards TEKS Snapshot Geometry (New TEKS ) 5 Two- and Three-dimensional Figures G.10(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 G.11(B) determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve using appropriate units of measure G.11(C) apply the formulas for the total and lateral surface area of threedimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve using appropriate units of measure G.11(D) apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve using appropriate units of measure G.10(A) identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes G.11(A) apply the formula for the area of regular polygons to solve using appropriate units of measure G.12(A) apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual G.12(B) apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve G.12(C) apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve G.12(D) describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle 6 Probability G.13(C) identify whether two events are independent and compute the probability of the two events occurring together with or without replacement G.13(A) develop strategies to use permutations and combinations to solve contextual G.13(B) determine probabilities based on area to solve contextual G.13(D) apply conditional probability in contextual G.13(E) apply independence in contextual NOTE: The classification of standards on this snapshot represents the reviewed and synthesized input of a sample of Texas high school mathematics teachers. This snapshot DOES NOT represent a publication of the Texas Education Agency. District curriculum may reflect other classifications. Source: Texas Education Agency Resources REV May 2015

13 OLD STANDARDS ALGEBRA I

14 Standards Snapshot Algebra I Rptg Cat 1 Functional Relationships Modified Readiness Standards Supporting Standards A.1.D represent relationships among quantities A.1.A describe independent and dependent quantities in functional using concrete models, tables, graphs, relationships diagrams, verbal descriptions, equations, and A.1.B gather and record data and use data sets to determine 8 6 inequalities functional relationships between quantities A.1.E interpret and make decisions, predictions, and A.1.C describe functional relationships for given problem situations critical judgments from functional and write equations or inequalities to answer questions arising relationships from the situations 2 Properties and Attributes of Functions A.2.B A.2.D A.4.A identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations A.2.A A.2.C A.3.A A.3.B A.4.B A.4.C identify and sketch the general forms of linear (y = x) and quadratic (y = x 2 ) parent functions interpret situations in terms of given graphs or creates situations that fit given graphs use symbols to represent unknowns and variables look for patterns and represent generalizations algebraically use the commutative, associative, and distributive properties to simplify algebraic expressions connect equation notation with function notation, such as y = x + 1 and f(x) = x Linear Functions A.5.C A.6.B A.6.C A.6.F use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b interpret and predict the effects of changing slope and y intercept in applied situations A.5.A A.5.B A.6.A A.6.D A.6.E A.6.G determine whether or not given situations can be represented by linear functions determine the domain and range for linear functions in given situations develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y intercept determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations relate direct variation to linear functions and solve involving proportional change 4 Linear Equations and Inequalities 10 8 A.7.B A.8.B investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities solve systems of linear equations using concrete models, graphs, tables, and algebraic methods A.7.A A.7.C A.8.A A.8.C analyze situations involving linear functions and formulate linear equations or inequalities to solve interpret and determine the reasonableness of solutions to linear equations and inequalities analyze situations and formulate systems of linear equations in two unknowns to solve interpret and determine the reasonableness of solutions to systems of linear equations 5 Quadratics and Other Nonlinear Functions 9 7 A.9.D A.10.A analyze graphs of quadratic functions and draw conclusions solve quadratic equations using concrete models, tables, graphs, and algebraic methods A.9.A determine the domain and range for quadratic functions in given situations A.9.B investigate, describe, and predict the effects of changes in a on the graph of y = ax 2 + c A.9.C investigate, describe, and predict the effects of changes in c on the graph of y = ax 2 + c A.10.B make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x intercepts) of the graph of the function A.11.A use patterns to generate the laws of exponents and apply them in problem solving situations A.11.B analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods A.11.C analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods 54 (5 Grid) questions from Readiness Standards questions from Supporting Standards Modified 42 (1 Grid) questions from Readiness Standards questions from Supporting Standards Source: Texas Education Agency Resources REV Oct 2011

15 OLD STANDARDS ALGEBRA II

17 OLD STANDARDS GEOMETRY

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