Translate Verbal Relationships into Algebraic Expressions: Which algebraic expression correctly represents a stated relationship, including grouping, repeated quantities, and implied operations? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a - Algebra: Translate Verbal Relationships into Algebraic Expressions: Praxis 5165 I.B.1.a; CCSS 6.EE.A.2, 7.EE.A.1-2, A-SSE.A.1; SMP 1, 2, 4, 6.

Evaluate Algebraic Expressions: Which value results from substituting given values into an expression while respecting grouping, exponents, and domain restrictions? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a - Algebra: Evaluate Algebraic Expressions: Praxis 5165 I.B.1.a; CCSS 6.EE.A.2, 7.EE.A.1, A-SSE.A.1; SMP 1, 2, 6.

Simplify Expressions Using Properties: Which expression is equivalent after correctly using the distributive property, combining like terms, and applying operation properties? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a - Algebra: Simplify Expressions Using Properties: Praxis 5165 I.B.1.a; CCSS 6.EE.A.3-4, 7.EE.A.1-2, A-SSE.A.2; SMP 1, 2, 6, 7.

Factor Out Greatest Common Factors: Which factored form correctly extracts the greatest common monomial or polynomial factor from an expression? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a - Algebra: Factor Out Greatest Common Factors: Praxis 5165 I.B.1.a; CCSS 6.EE.A.3, A-SSE.A.2, A-APR.A.1; SMP 1, 2, 6, 7.

Recognize and Apply Special Product Patterns: Which expansion or factorization correctly uses a difference of squares, perfect-square trinomial, sum or difference of cubes, or binomial pattern? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a-b - Algebra: Recognize and Apply Special Product Patterns: Praxis 5165 I.B.1.a-b; CCSS A-SSE.B.3, A-APR.C.4; SMP 1, 2, 6, 7.

Factor Quadratic Trinomials: Which factored form is equivalent to a quadratic trinomial, including cases with a leading coefficient other than one? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a-b - Algebra: Factor Quadratic Trinomials: Praxis 5165 I.B.1.a-b; CCSS A-SSE.B.3, A-APR.B.2-3; SMP 1, 2, 6, 7.

Complete the Square to Reveal Structure: Which equivalent vertex-form expression results from completing the square, and which feature of the quadratic does that form reveal?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.b, I.B.3.c - Algebra: Complete the Square to Reveal Structure: Praxis 5165 I.B.1.b, I.B.3.c; CCSS A-SSE.B.3, A-REI.B.4, F-IF.C.8; SMP 1, 2, 6, 7.

Rewrite Exponential Expressions and Change Bases: Which equivalent exponential form correctly uses common bases or exponent properties to expose growth factors, rates, or solvable structure? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.a - Algebra: Rewrite Exponential Expressions and Change Bases: Praxis 5165 I.B.1.a; CCSS 8.EE.A.1, A-SSE.B.3, F-LE.A.2; SMP 1, 2, 6, 7.

Rearrange Literal Equations and Formulas: Which algebraic transformation correctly solves a multivariable formula for the specified variable while preserving all restrictions? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.c - Algebra: Rearrange Literal Equations and Formulas: Praxis 5165 I.B.1.c; CCSS A-CED.A.4, N-Q.A.1-3; SMP 1, 2, 6.

Add and Subtract Polynomials: Which polynomial results from correctly combining like terms after addition or subtraction? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.d - Algebra: Add and Subtract Polynomials: Praxis 5165 I.B.1.d; CCSS A-APR.A.1; SMP 1, 2, 6, 7.

Multiply Polynomials: Which expanded polynomial results from correctly multiplying monomials, binomials, or higher-degree polynomials? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.d - Algebra: Multiply Polynomials: Praxis 5165 I.B.1.d; CCSS A-APR.A.1, A-SSE.A.2; SMP 1, 2, 6, 7.

Divide Polynomials: Which quotient and remainder result from polynomial long division or synthetic division, with the divisor restrictions stated correctly? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.d - Algebra: Divide Polynomials: Praxis 5165 I.B.1.d; CCSS A-APR.D.6; SMP 1, 2, 6, 7.

Factor Special Polynomials over the Complex Numbers: Which complete factorization correctly includes complex conjugate factors when a polynomial has nonreal zeros?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.1.e - Algebra: Factor Special Polynomials over the Complex Numbers: Praxis 5165 I.B.1.e; CCSS N-CN.C.8-9, A-APR.B.2-3; SMP 1, 2, 6, 7.

Create One-Variable Equations from Contexts: Which equation in one variable accurately models the quantities and relationships in a verbal, geometric, financial, or scientific situation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.a - Algebra: Create One-Variable Equations from Contexts: Praxis 5165 I.B.2.a; CCSS A-CED.A.1, N-Q.A.1-3; SMP 1, 2, 4, 6.

Create One-Variable Inequalities from Contexts: Which inequality in one variable correctly represents a constraint, threshold, range, or comparison in the stated context? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.a - Algebra: Create One-Variable Inequalities from Contexts: Praxis 5165 I.B.2.a; CCSS 7.EE.B.4, A-CED.A.1, A-REI.B.3; SMP 1, 2, 4, 6.

Create Two-Variable Equations: Which equation in two variables correctly describes the relationship and uses meaningful labels, units, and scales? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.b - Algebra: Create Two-Variable Equations: Praxis 5165 I.B.2.b; CCSS 8.EE.C.8, A-CED.A.2, A-REI.D.10; SMP 1, 2, 4, 6.

Create Two-Variable Inequalities: Which two-variable inequality correctly models the boundary and feasible side of a contextual constraint?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.b - Algebra: Create Two-Variable Inequalities: Praxis 5165 I.B.2.b; CCSS A-CED.A.2-3, A-REI.D.12; SMP 1, 2, 4, 6.

Model Constraints with Systems: Which system of equations or inequalities represents all stated constraints and identifies viable versus nonviable solutions? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.c - Algebra: Model Constraints with Systems: Praxis 5165 I.B.2.c; CCSS A-CED.A.3, A-REI.C-D; SMP 1, 2, 4, 6.

Solve Multistep Linear Equations: Which solution correctly resolves a linear equation involving distribution, fractions, decimals, and variables on one or both sides?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.a - Algebra: Solve Multistep Linear Equations: Praxis 5165 I.B.3.a; CCSS 7.EE.B.4, 8.EE.C.7, A-REI.B.3; SMP 1, 2, 6, 7.

Analyze Linear Equations with Parameters: Which condition on a parameter produces one solution, no solution, or infinitely many solutions in a linear equation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.a - Algebra: Analyze Linear Equations with Parameters: Praxis 5165 I.B.3.a; CCSS 8.EE.C.7, A-REI.A.1, A-REI.B.3; SMP 1, 2, 3, 7.

Solve Linear and Compound Inequalities: Which solution set correctly solves a linear or compound inequality, including reversal of the inequality when required? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.a - Algebra: Solve Linear and Compound Inequalities: Praxis 5165 I.B.3.a; CCSS 7.EE.B.4, A-REI.B.3; SMP 1, 2, 6.

Graph One-Variable Inequality Solutions: Which number-line graph correctly represents an inequality or compound-inequality solution set with appropriate endpoint notation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.a, I.B.3.a - Algebra: Graph One-Variable Inequality Solutions: Praxis 5165 I.B.2.a, I.B.3.a; CCSS 7.EE.B.4, A-REI.B.3; SMP 1, 2, 5, 6.

Solve Absolute-Value Equations and Inequalities: Which solution set correctly handles an absolute-value equation or inequality and distinguishes distance, conjunction, and disjunction cases? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.d, I.B.3.g - Algebra: Solve Absolute-Value Equations and Inequalities: Praxis 5165 I.B.3.d, I.B.3.g; CCSS A-REI.A.1-2, A-CED.A.1; SMP 1, 2, 3, 6.

Solve Quadratic Equations by Factoring: Which real or complex solutions result from factoring a quadratic and applying the zero-product property?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.b, I.B.3.d - Algebra: Solve Quadratic Equations by Factoring: Praxis 5165 I.B.3.b, I.B.3.d; CCSS A-REI.B.4, A-SSE.B.3; SMP 1, 2, 6, 7.

Solve Quadratic Equations by Completing the Square: Which solution correctly transforms a quadratic into square form and accounts for both square-root branches? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.b-c - Algebra: Solve Quadratic Equations by Completing the Square: Praxis 5165 I.B.3.b-c; CCSS A-REI.B.4; SMP 1, 2, 6, 7.

Solve Quadratic Equations with the Quadratic Formula: Which solution set follows from correct substitution into the quadratic formula and accurate simplification of the discriminant? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.b, I.B.3.d - Algebra: Solve Quadratic Equations with the Quadratic Formula: Praxis 5165 I.B.3.b, I.B.3.d; CCSS A-REI.B.4; SMP 1, 2, 6.

Use the Discriminant to Classify Quadratic Roots: Which conclusion correctly identifies the number and type of roots from the discriminant or corresponding graph?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.e - Algebra: Use the Discriminant to Classify Quadratic Roots: Praxis 5165 I.B.3.e; CCSS A-REI.B.4, N-CN.C.7; SMP 1, 2, 3, 7.

Interpret Nonreal Quadratic Solutions: Which pair of complex conjugate solutions correctly solves a quadratic with real coefficients and a negative discriminant? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.b, I.B.3.e - Algebra: Interpret Nonreal Quadratic Solutions: Praxis 5165 I.B.3.b, I.B.3.e; CCSS N-CN.A.1-2, N-CN.C.7, A-REI.B.4; SMP 1, 2, 6.

Justify Equation-Solving Steps: Which explanation correctly names and applies properties that preserve equivalence at each step of an equation solution? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.3.g - Algebra: Justify Equation-Solving Steps: Praxis 5165 I.B.3.g; CCSS A-REI.A.1; SMP 1, 3, 6, 7.

Graph Linear Equations in Two Variables: Which graph represents all ordered-pair solutions of a linear equation and uses correct intercepts, slope, labels, and scale? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.b, I.B.3.f - Algebra: Graph Linear Equations in Two Variables: Praxis 5165 I.B.2.b, I.B.3.f; CCSS 8.EE.B.5-6, A-REI.D.10; SMP 1, 2, 4, 5, 6.

Graph Linear Inequalities in Two Variables: Which half-plane graph correctly represents a linear inequality, including boundary type and a valid test-point check? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.2.b, I.B.3.f - Algebra: Graph Linear Inequalities in Two Variables: Praxis 5165 I.B.2.b, I.B.3.f; CCSS A-REI.D.12; SMP 1, 2, 4, 5, 6.

Solve Linear Systems by Graphing: Which ordered pair or solution classification is supported by the intersection behavior of two graphed linear equations? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.a - Algebra: Solve Linear Systems by Graphing: Praxis 5165 I.B.4.a; CCSS 8.EE.C.8, A-REI.C.6, A-REI.D.10-11; SMP 1, 2, 4, 5.

Solve Linear Systems by Substitution: Which substitution process and ordered-pair solution correctly solve a system of two linear equations? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.a - Algebra: Solve Linear Systems by Substitution: Praxis 5165 I.B.4.a; CCSS 8.EE.C.8, A-REI.C.6; SMP 1, 2, 6.

Solve Linear Systems by Elimination: Which elimination strategy and ordered-pair solution correctly solve a system, including equations that first require scaling?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.a - Algebra: Solve Linear Systems by Elimination: Praxis 5165 I.B.4.a; CCSS 8.EE.C.8, A-REI.C.5-6; SMP 1, 2, 6, 7.

Classify Consistent and Inconsistent Systems: Which conclusion correctly identifies a system as having one, none, or infinitely many solutions from equations, tables, or graphs? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.a - Algebra: Classify Consistent and Inconsistent Systems: Praxis 5165 I.B.4.a; CCSS 8.EE.C.8, A-REI.C.5-6, A-REI.D.10; SMP 1, 2, 3, 7.

Solve Linear-Quadratic Systems: Which intersection points correctly solve a system containing one linear and one quadratic equation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.b - Algebra: Solve Linear-Quadratic Systems: Praxis 5165 I.B.4.b; CCSS A-REI.C.7, A-REI.D.11; SMP 1, 2, 5, 6.

Approximate Intersections of Nonlinear Functions: Which approximate solution to f(x) = g(x) is supported by a graph, table, or numerical technology for the given function types? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.c - Algebra: Approximate Intersections of Nonlinear Functions: Praxis 5165 I.B.4.c; CCSS A-REI.D.11, F-IF.C.7; SMP 1, 2, 4, 5, 6.

Solve Systems of Linear Inequalities: Which graph or set of vertices correctly represents the intersection of multiple linear-inequality constraints? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.4.d - Algebra: Solve Systems of Linear Inequalities: Praxis 5165 I.B.4.d; CCSS A-CED.A.3, A-REI.D.12; SMP 1, 2, 4, 5, 6.

Calculate Average Rate of Change of Nonlinear Functions: Which average rate of change over a specified interval is correct from an equation, table, or graph, with units interpreted in context? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.5.a - Algebra: Calculate Average Rate of Change of Nonlinear Functions: Praxis 5165 I.B.5.a; CCSS 8.F.B.4, F-IF.B.6; SMP 1, 2, 4, 6.

Determine Slope from Multiple Representations: Identify the correct slope for a line shown by two points, an equation, a table, or a graph. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.6.b - Algebra: Determine Slope from Multiple Representations: Praxis 5165 I.B.6.b; CCSS 8.EE.B.5-6, F-IF.B.6; SMP 1, 2, 5, 6.

Interpret Linear Intercepts in Context: Which interpretation correctly explains the meaning and units of x- and y-intercepts in a linear model? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.6.a - Algebra: Interpret Linear Intercepts in Context: Praxis 5165 I.B.6.a; CCSS 8.F.B.4, F-IF.B.4, S-ID.C.7; SMP 1, 2, 4, 6.

Write and Convert Forms of Linear Equations: Which slope-intercept, point-slope, or standard-form equation represents the given line, and which conversion preserves its solution set? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.6 - Algebra: Write and Convert Forms of Linear Equations: Praxis 5165 I.B.6; CCSS 8.EE.B.5-6, A-CED.A.2, A-REI.D.10; SMP 1, 2, 6, 7.

Apply the Remainder and Factor Theorems: Which remainder, factor conclusion, or missing coefficient follows from evaluating or dividing a polynomial? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.7.a - Algebra: Apply the Remainder and Factor Theorems: Praxis 5165 I.B.7.a; CCSS A-APR.B.2-3; SMP 1, 2, 6, 7.

Connect Polynomial Zeros, Factors, and Multiplicity: Which factorization and zero list correctly correspond, including multiplicity and the graph behavior at each intercept? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.7.b-d - Algebra: Connect Polynomial Zeros, Factors, and Multiplicity: Praxis 5165 I.B.7.b-d; CCSS A-APR.B.2-3, F-IF.C.7; SMP 1, 2, 5, 7.

Analyze Polynomial Graphs from Algebraic Structure: Which sketch or feature set is consistent with the degree, leading coefficient, zeros, multiplicities, and end behavior of a polynomial? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.7.c-d - Algebra: Analyze Polynomial Graphs from Algebraic Structure: Praxis 5165 I.B.7.c-d; CCSS A-APR.B.3, F-IF.C.7; SMP 1, 2, 5, 7.

Simplify Rational Expressions and State Restrictions: Which equivalent rational expression is correct after factoring and canceling common factors while retaining excluded values? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.8.a - Algebra: Simplify Rational Expressions and State Restrictions: Praxis 5165 I.B.8.a; CCSS A-APR.D.6-7; SMP 1, 2, 6, 7.

Operate with Rational Expressions: Which sum, difference, product, or quotient of rational expressions is simplified correctly and includes all domain restrictions? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.8.b - Algebra: Operate with Rational Expressions: Praxis 5165 I.B.8.b; CCSS A-APR.D.7; SMP 1, 2, 6, 7.

Solve Rational and Radical Equations with Extraneous-Solution Checks: Which candidate solutions remain valid after solving a rational or radical equation and checking against the original equation and domain? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 I.B.9.a - Algebra: Solve Rational and Radical Equations with Extraneous-Solution Checks: Praxis 5165 I.B.9.a; CCSS A-REI.A.1-2; SMP 1, 2, 3, 6.

Determine Whether a Relation Is a Function: Which relation is a function when presented as ordered pairs, a mapping, a table, a graph, or an equation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.1.a - Functions: Determine Whether a Relation Is a Function: Praxis 5165 II.A.1.a; CCSS 8.F.A.1, F-IF.A.1; SMP 1, 2, 3, 6.

Evaluate and Interpret Function Notation: Which value and contextual interpretation of f(a), f(x) = b, or a related notation statement is correct? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.1.b - Functions: Evaluate and Interpret Function Notation: Praxis 5165 II.A.1.b; CCSS 8.F.A.1-2, F-IF.A.1-2; SMP 1, 2, 4, 6.

Determine Domain and Range from Rules: Which domain and range correctly account for denominator, radical, logarithmic, and contextual restrictions in a function rule? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.1.c - Functions: Determine Domain and Range from Rules: Praxis 5165 II.A.1.c; CCSS F-IF.A.1-2, F-BF.B.4; SMP 1, 2, 6, 7.

Determine Domain and Range from Graphs, Tables, and Sets: Which domain and range accurately describe a function represented by a graph, table, mapping, or set of ordered pairs? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.1.c - Functions: Determine Domain and Range from Graphs, Tables, and Sets: Praxis 5165 II.A.1.c; CCSS 8.F.A.1, F-IF.A.1-2; SMP 1, 2, 5, 6.

Interpret Key Features of Functions in Context: Which interpretation correctly explains intercepts, intervals of increase or decrease, extrema, discontinuities, and end behavior for the modeled quantities? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.a - Functions: Interpret Key Features of Functions in Context: Praxis 5165 II.A.2.a; CCSS F-IF.B.4-6; SMP 1, 2, 4, 6.

Sketch a Function from a Verbal Description: Which graph best matches a verbal description of rates, intervals, turning points, asymptotes, or discrete versus continuous behavior? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.b - Functions: Sketch a Function from a Verbal Description: Praxis 5165 II.A.2.b; CCSS F-IF.B.4-5; SMP 1, 2, 4, 5.

Graph and Analyze Linear and Quadratic Functions: Which graph and feature set correctly represent a linear or quadratic function defined by an expression? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.c - Functions: Graph and Analyze Linear and Quadratic Functions: Praxis 5165 II.A.2.c; CCSS F-IF.C.7a-b, F-LE.A.1-2; SMP 1, 2, 5, 6.

Graph and Analyze Polynomial and Rational Functions: Which graph correctly reflects zeros, multiplicities, end behavior, holes, and asymptotes of a polynomial or rational function?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.c - Functions: Graph and Analyze Polynomial and Rational Functions: Praxis 5165 II.A.2.c; CCSS F-IF.C.7c-d, A-APR.B-D; SMP 1, 2, 5, 7.

Graph and Analyze Radical and Absolute-Value Functions: Which graph correctly represents a radical or absolute-value expression, including domain, range, vertex or endpoint, and transformations?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.c.

Graph and Analyze Piecewise and Step Functions: Which graph correctly represents a piecewise or step function, including endpoint inclusion, discontinuities, and interval-specific rules?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.c - Functions: Graph and Analyze Piecewise and Step Functions: Praxis 5165 II.A.2.c; CCSS F-IF.C.7b, F-IF.B.4-5; SMP 1, 2, 5, 6.

Graph and Analyze Exponential and Logarithmic Functions: Which graph correctly represents an exponential or logarithmic function, including intercepts, asymptotes, domain, range, and growth or decay? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.c, II.A.2.e - Functions: Graph and Analyze Exponential and Logarithmic Functions: Praxis 5165 II.A.2.c, II.A.2.e; CCSS F-IF.C.7e, F-BF.B.5, F-LE.A-B; SMP 1, 2, 5, 6.

Graph and Analyze Trigonometric Functions: Which graph correctly represents a sine, cosine, or tangent function with the stated amplitude, period, phase shift, midline, and asymptotes? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.c, II.A.8.a - Functions: Graph and Analyze Trigonometric Functions: Praxis 5165 II.A.2.c, II.A.8.a; CCSS F-TF.B.5, F-IF.C.7e; SMP 1, 2, 5, 6.

Use Equivalent Function Forms to Reveal Features: Which equivalent form of a function most directly reveals its zeros, vertex, extrema, symmetry, end behavior, or rate parameters?. Aligned to Praxis 5165 II.A.2.d; CCSS F-IF.C.8, A-SSE.B.3; SMP 1, 2, 6, 7.

Interpret Exponential Growth and Decay: Which statement correctly interprets the initial value, growth or decay factor, percent rate, doubling time, or half-life in an exponential model?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.e - Functions: Interpret Exponential Growth and Decay: Praxis 5165 II.A.2.e; CCSS F-IF.C.8b, F-LE.A-B; SMP 1, 2, 4, 6.

Identify Even, Odd, and Neither Functions: Which classification and symmetry statement correctly follow from a function rule, table, or graph?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.f - Functions: Identify Even, Odd, and Neither Functions: Praxis 5165 II.A.2.f; CCSS F-BF.B.3, F-TF.B.5; SMP 1, 2, 3, 7.

Compare Functions Across Representations: Which comparison of rate, intercepts, extrema, growth, domain, or end behavior is supported when two functions are shown in different forms?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.g.

Extract Features from Quadratic Forms: Identify zeros, vertex, axis of symmetry, opening direction, intercepts, and extrema from quadratic forms. Aligned to ETS Praxis Mathematics (5165) Praxis 5165 II.A.2.h; CCSS F-IF.C.7a, F-IF.C.8a; SMP 1, 2, 6, 7.

Convert among Standard, Vertex, and Factored Quadratic Forms: Which conversion among quadratic forms is algebraically equivalent and best suited to the requested feature or problem?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.2.i.

Write Functions that Relate Two Quantities: Which function rule correctly relates dependent and independent quantities in a verbal, tabular, geometric, or scientific context?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Build Explicit or Recursive Functions from Contexts: Which explicit expression or recursive process correctly generates the values described by a repeated or accumulated situation?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.3.b.

Write Arithmetic Sequences Explicitly and Recursively: Which explicit and recursive formulas represent an arithmetic sequence and correctly model its initial term and common difference? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.3.c; CCSS F-BF.A.1-2, F-LE.A.2; SMP 1, 2, 4, 8.

Write Geometric Sequences Explicitly and Recursively: Which explicit and recursive formulas represent a geometric sequence and correctly model its initial term and common ratio?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.3.c.

Translate Between Recursive and Explicit Sequence Forms: Which explicit formula, recursive rule, or sequence values are equivalent to the given alternate representation?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.3.d.

Apply Vertical and Horizontal Translations: Which equation or graph correctly represents a vertical or horizontal shift of a parent function, including the sign of the shift?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Apply Reflections, Stretches, and Compressions: Which transformation description, equation, or graph correctly represents reflections and vertical or horizontal scaling of a function?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.a - Functions: Apply Reflections, Stretches, and Compressions.

Determine Transformation Parameters from Graphs: Which value of a transformation parameter k is consistent with the relationship between the parent graph and the transformed graph?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Find Inverse-Function Values from Graphs and Tables: Which inverse-function value is correct when the original function is represented by a graph or table? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.b; CCSS F-BF.B.4; SMP 1, 2, 5, 6.

Interpret Inverse Functions in Context: Which statement correctly reverses the input-output relationship and units of an invertible contextual function?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.c - Functions: Interpret Inverse Functions in Context: Praxis 5165 II.A.4.c; CCSS F-BF.B.4, F-IF.B.5; SMP 1, 2, 4, 6.

Restrict Domains to Create Invertible Functions aligned to Praxis 5165 II.A.4.d with CCSS F-BF.B.4 and F-IF.A.1.

Find Inverse Functions Algebraically: Which expression correctly represents the inverse of an invertible function after interchanging variables and solving?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.e - Functions: Find Inverse Functions Algebraically.

Determine Whether an Inverse Relation Is a Function: Which conclusion correctly uses one-to-one behavior, the horizontal-line test, or swapped ordered pairs to determine whether an inverse is a function?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.e.

Use Exponential-Logarithmic Inverse Relationships: Which equivalent exponential or logarithmic statement correctly solves or interprets a problem using inverse functions?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.f.

Combine Functions with Arithmetic Operations: Standards-aligned practice for Praxis 5165 II.A.4.g Praxis 5165 II.A.4.g; CCSS F-BF.A.1; SMP 1, 2, 6, 7 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Determine Domains of Combined Functions: Which domain correctly accounts for all restrictions created by adding, subtracting, multiplying, or dividing functions?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.h.

Compose Functions from Formulas, Tables, and Graphs: Which value or expression correctly evaluates a composition when the component functions are represented algebraically, numerically, or graphically?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.i.

Determine Domains of Composite Functions aligned to Praxis Mathematics 5165 II.A.4.j with CCSS F-BF.A.1, F-IF.A.1 and SMP 1, 2, 6, 7.

Verify Inverse Functions by Composition: Which composition result correctly confirms that two functions are inverses on the stated domains? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.4.k; CCSS F-BF.B.4; SMP 1, 2, 3, 6.

Distinguish Linear, Quadratic, and Exponential Patterns: Which model type is supported by constant first differences, constant second differences, constant ratios, or contextual behavior?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Construct Linear and Exponential Models from Data: Which equation correctly models a relationship from a graph, table, ordered pairs, or verbal description?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Compare Long-Run Growth of Function Families: Which statement correctly compares eventual growth of exponential, linear, quadratic, and higher-degree polynomial functions?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.5.e.

Interpret Parameters in Linear and Exponential Models: Which interpretation correctly explains slope, intercept, initial value, base, continuous rate, or time constant in context? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Apply Logarithm Properties and Change of Base: Standards-aligned practice for Praxis 5165 II.A.6.a, II.A.6.c Praxis 5165 II.A.6.a, II.A.6.c; CCSS F-LE.A.4, F-BF.B.5; SMP 1, 2, 5, 6, 7 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Solve Exponential Equations with Logarithms: Which logarithmic form and numerical solution correctly solve an exponential equation, with the result interpreted in context when applicable?. Aligned to ETS Praxis Mathematics (5165).

Convert Between Degrees and Radians: Which degree-radian conversion or coterminal-angle representation is correct?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.7.a - Functions: Convert Between Degrees and Radians.

Use Reference Angles and Unit-Circle Values: aligned to Praxis 5165 II.A.7.b-c; CCSS F-TF.A.2, F-TF.C.8; SMP 1, 2, 5, 6.

Analyze Trigonometric Symmetry, Periodicity, and Identities: Which statement or equivalent expression correctly uses unit-circle symmetry, periodicity, reciprocal identities, quotient identities, or the Pythagorean identity?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.A.7.d.

Model Periodic Phenomena with Sinusoidal Functions: Choose sine or cosine models matching amplitude, period, midline, phase, and initial conditions. Aligned to ETS Praxis Mathematics (5165) Praxis 5165 II.A.8.a; CCSS F-TF.B.5, F-BF.A.1; SMP 1, 2, 4, 5, 6.

Solve Trigonometric, Logarithmic, and Exponential Equations: aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Estimate Limits from Tables and Graphs: Which limit value is supported by values or graphical behavior as x approaches a specified input?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.b.

Distinguish a Limit from a Function Value: Compare lim f(x) as x approaches a with f(a), including holes, jumps, and redefined points. Aligned to ETS Praxis Mathematics (5165) Praxis 5165 II.B.1.b-c with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Apply Limit Laws and Direct Substitution: Which limit is correctly evaluated using sum, difference, product, quotient, power, root, and constant-multiple laws?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Evaluate Indeterminate Limits by Factoring: Which algebraic simplification and limit value correctly resolve a removable zero-over-zero form by factoring and canceling? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.a.

Evaluate Indeterminate Limits by Rationalization: Which conjugate-based simplification and limit value correctly resolve a radical zero-over-zero form?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.a.

Determine One-Sided Limits and Limit Existence: Which left-hand and right-hand limits are correct, and which conclusion follows about the two-sided limit?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.c.

Analyze Infinite Limits and Vertical Asymptotes: Which sign and infinite behavior correctly describe a function near a vertical asymptote from the left and right?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.d-e.

Evaluate Limits at Infinity and End Behavior: Which finite, infinite, or nonexistent limit correctly describes a function as x approaches positive or negative infinity?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.d - Calculus: Evaluate Limits at Infinity and End Behavior.

Identify Conditions That Make Limits Fail to Exist: Which feature - unequal one-sided limits, unbounded behavior, or oscillation - correctly explains why a limit does not exist?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.1.e.

Use the Limit Definition of the Derivative: Which difference quotient and resulting limit correctly compute the derivative of a function at a point or in general?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.2.a.

Connect Secant Slopes to Tangent Slopes: Which sequence of secant slopes and limiting conclusion correctly represents the tangent slope at a point?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.2.a.

Interpret Derivatives as Instantaneous Rates of Change: Which interpretation correctly states the meaning, sign, and units of a derivative in a contextual model?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.2.a.

Approximate Derivatives from Tables and Graphs: Which numerical or graphical estimate of f prime at a point is supported by nearby values or a tangent-line approximation?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.2.a - Calculus: Approximate Derivatives from Tables and Graphs.

Verify Continuity at a Point: Standards-aligned practice for Praxis 5165 II.B.3.a Praxis 5165 II.B.3.a; CCSS F-IF.B.4-5 (prerequisite); NCTM Functions and Change; SMP 1, 2, 3, 6 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Analyze Discontinuities and Piecewise Continuity aligned to Praxis Mathematics 5165 II.B.3.a.

Distinguish Continuity from Differentiability: Which function is continuous but not differentiable at a point because of a corner, cusp, vertical tangent, or other local behavior? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.3.b.

Differentiate with Constant, Power, Sum, and Difference Rules aligned to Praxis 5165 II.B.4.a.

Differentiate with the Product Rule: Which derivative correctly applies the product rule and simplifies the result without omitting either term?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.4.a.

Differentiate with the Quotient Rule: Which derivative correctly applies the quotient rule and preserves the denominator and subtraction order?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.4.a.

Differentiate Composite Functions with the Chain Rule: identify inner and outer functions and apply the chain rule, including repeated composition. Aligned to ETS Praxis Mathematics (5165) with Praxis 5165 II.B.4.a.

Differentiate Exponential, Logarithmic, and Trigonometric Functions: Which derivative correctly uses standard rules for exponential, logarithmic, sine, cosine, or tangent functions?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.4.a.

Write Tangent and Normal Line Equations: Which equation represents the tangent or normal line to a curve at a specified point using the derivative as slope?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.2.a, II.B.4.a.

Find Antiderivatives and Indefinite Integrals: Which antiderivative family correctly includes the constant of integration and differentiates back to the integrand?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.4.b - Calculus: Find Antiderivatives and Indefinite Integrals.

Interpret Definite Integrals as Signed Accumulation: Which value or interpretation correctly treats a definite integral as net signed area or accumulated change over an interval? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Apply the Fundamental Theorem of Calculus: Which definite-integral value or derivative of an accumulation function correctly applies the Fundamental Theorem of Calculus?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.5.b-c.

Relate Position, Velocity, and Acceleration: Which derivative or integral relationship correctly connects position, velocity, acceleration, displacement, and total distance in a motion context?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.4.c.

Use the First Derivative to Analyze Extrema and Monotonicity: Which intervals of increase or decrease and which local or absolute extrema follow from the sign of the first derivative?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.5.a.

Use the Second Derivative to Analyze Concavity: Which intervals of concavity and points of inflection follow from the sign or zeros of the second derivative?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.5.a - Calculus: Use the Second Derivative to Analyze Concavity: Praxis 5165 II.B.5.a; CCSS F-IF.B.4 (prerequisite); NCTM Functions and Change; SMP 1, 2, 3, 5.

Match Graphs of Functions, Derivatives, and Accumulations: Which graph pairing is consistent with slope, critical-point, concavity, and accumulation relationships among f, f prime, and an integral function?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.5.b.

Compute Areas Under and Between Curves: Which integral setup and value correctly determine geometric area under a curve or between two curves, accounting for intersections and sign?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 II.B.5.c.

Use Definitions of Points, Lines, Segments, Rays, and Planes: Which notation or statement correctly describes collinearity, betweenness, intersection, distance, midpoint, or another foundational geometric relationship? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.1.a - Geometry: Use Definitions of Points, Lines, Segments, Rays, and Planes.

Solve Problems with Parallel, Perpendicular, and Intersecting Lines: Which angle, distance, slope, or logical conclusion follows from stated relationships among parallel, perpendicular, and intersecting lines?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.1.a - Geometry: Solve Problems with Parallel, Perpendicular, and Intersecting Lines.

Apply Complementary, Supplementary, Vertical, and Adjacent Angle Relationships: Which angle measure or relationship is correct using linear pairs, vertical angles, angle addition, or complementary and supplementary definitions?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.1.b.

Apply Transversal Angle Relationships: Which corresponding, alternate interior, alternate exterior, or same-side interior angle conclusion is valid when a transversal crosses parallel lines?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.1.b.

Solve Algebraic Angle-Measure Problems: Which value of the variable and resulting angle measures satisfy the geometric relationships shown in a diagram? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.1.b.

Classify Triangles by Sides and Angles: Which classification correctly identifies a triangle as scalene, isosceles, equilateral, acute, right, or obtuse from given measures or coordinates?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.2.a.

Apply the Triangle Inequality Theorem: Which set of lengths can form a triangle, or which range correctly describes a possible missing side length?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.2.a.

Use Triangle Angle-Sum and Exterior-Angle Theorems: Standards-aligned practice for Praxis 5165 III.A.2.b, III.A.5.b Praxis 5165 III.A.2.b, III.A.5.b; CCSS 8.G.A.5, G-CO.C.10; SMP 1, 2, 3, 6 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Use Isosceles and Equilateral Triangle Properties: Which side or angle conclusion correctly uses base-angle, converse, or equilateral-triangle properties? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.2.b, III.A.5.b.

Apply the Pythagorean Theorem and Its Converse aligned to ETS Praxis Mathematics 5165 standards.

Solve Special Right Triangles: Which exact side length is correct for a 45-45-90 or 30-60-90 triangle using its fixed side ratios?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Use Medians, Midpoints, Midsegments, and the Centroid: Which length, coordinate, or ratio follows from triangle medians, midpoint definitions, the midsegment theorem, or centroid division?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Use Altitudes, Bisectors, and Triangle Centers: identify points, distances, and geometric properties associated with triangle constructions. Aligned to ETS Praxis Mathematics (5165) Praxis 5165 III.A.2.c, III.A.5.a-b; CCSS G-CO.C.9-10; SMP 1, 2, 3, 5.

Classify Quadrilaterals in a Property Hierarchy: Which most specific quadrilateral classification follows from given side, angle, diagonal, or symmetry properties?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.2.d.

Apply Parallelogram Properties and Converses: Which side, angle, diagonal, or coordinate conclusion follows from parallelogram properties or a valid converse?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.2.d, III.A.5.c.

Apply Rectangle, Rhombus, and Square Properties: Which conclusion correctly uses distinctive diagonal, side, angle, or symmetry properties of rectangles, rhombi, and squares? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Apply Trapezoid and Kite Properties: Standards-aligned practice for Praxis 5165 III.A.2.d-e Praxis 5165 III.A.2.d-e; CCSS G-CO.A.1, G-CO.C.11; SMP 1, 2, 3, 6 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Find Interior and Exterior Angle Sums of Polygons aligned to Praxis 5165 III.A.2.e.

Analyze Regular Polygons and Diagonals: Which side, central angle, interior angle, exterior angle, symmetry, or diagonal count is correct for a regular polygon?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.2.e.

Represent Translations with Coordinates and Vectors: Which coordinate rule or vector correctly translates a figure and identifies the image of each point?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.a, III.A.3.g.

Represent Reflections in the Coordinate Plane: Which reflected image or coordinate rule is correct for a reflection across a line, axis, or specified mirror line?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.a.

Represent Rotations in the Coordinate Plane: Which rotated image or coordinate rule is correct for a rotation about the origin or another center?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.a.

Compose Rigid Motions: Which sequence of translations, rotations, and reflections maps a preimage onto the stated image?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.a, III.A.3.e.

Apply Invariants of Rigid Motions: Which distance, angle, parallelism, collinearity, or orientation property is preserved or changed by a rigid motion?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.c.

Represent Dilations and Determine Scale Factors: Which image, coordinate rule, center, or scale factor correctly describes a dilation?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.b.

Analyze the Effects of Dilations: Which statement correctly describes how a dilation affects angle measure, length, perimeter, area, slope, and parallel lines?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.d.

Identify Transformation Sequences Mapping Figures: Which sequence of rigid motions and dilations maps one figure onto another exactly?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.e.

Analyze Line and Rotational Symmetry: Which transformation maps a figure onto itself, and which line or angle correctly represents its symmetry? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.3.f.

Establish Congruence through Rigid Motions: Which rigid-motion sequence or invariant evidence demonstrates that two figures are congruent?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.4.c - Geometry: Establish Congruence through Rigid Motions: Praxis 5165 III.A.4.c; CCSS 8.G.A.2, G-CO.B.6-8; SMP 1, 2, 3, 5.

Apply Triangle Congruence Criteria: Which criterion - SSS, SAS, ASA, AAS, or HL - proves two triangles congruent from the given information?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.4.a.

Use Congruent Parts to Solve Problems: Which unknown side or angle follows after establishing triangle congruence and matching corresponding parts correctly? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Establish Similarity through Transformations: Which sequence of dilations and rigid motions demonstrates that two figures are similar?. Aligned to ETS Praxis Mathematics (5165) Praxis 5165 III.A.4.d; CCSS 8.G.A.4, G-SRT.A.2-3; SMP 1, 2, 3, 5.

Apply Triangle Similarity Criteria: Which criterion - AA, SAS similarity, or SSS similarity - proves two triangles similar from the given information?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.4.b; CCSS G-SRT.B.4-5; SMP 1, 2, 3, 6.

Use Proportionality Theorems in Triangles: Which length or proportion follows from similar triangles, parallel lines dividing sides proportionally, or the triangle midsegment theorem?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.4.b-e, III.A.5.b - Geometry: Use Proportionality Theorems in Triangles.

Use Congruence and Similarity in Two- and Three-Dimensional Figures: Which missing measure, scale relationship, or structural conclusion follows from congruent or similar plane and solid figures? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.4.e.

Analyze Proofs about Lines and Angles: Which step, reason, or conclusion makes a proof about vertical angles, parallel lines, transversals, or perpendicular bisectors valid?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.5.a - Geometry: Analyze Proofs about Lines and Angles.

Analyze Proofs about Triangles aligned to ETS Praxis Mathematics (5165), CCSS Mathematics, SMP, and NCTM crosswalks.

Analyze Proofs about Parallelograms: Which step, reason, or conclusion makes a proof about opposite sides, opposite angles, diagonals, or rectangle properties valid? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Evaluate Geometric Proof Logic: Which proof is valid, which assumption is unjustified, or which counterexample disproves a converse or overgeneralized claim? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.5.d - Geometry: Evaluate Geometric Proof Logic: Praxis 5165 III.A.5.d; CCSS G-CO.C.9-11; SMP 1, 3, 6, 7.

Use Sine-Cosine Relationships for Complementary Angles: Which identity or value correctly relates the sine of an acute angle to the cosine of its complement?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.6.a - Geometry: Use Sine-Cosine Relationships for Complementary Angles: Praxis 5165 III.A.6.a; CCSS G-SRT.C.7; SMP 1, 2, 6, 7.

Solve Right Triangles with Trigonometric Ratios aligned to Praxis Mathematics 5165 III.A.6.b.

Use Exact Trigonometric Values of Special Angles: Standards-aligned practice for Praxis 5165 III.A.6.c Praxis 5165 III.A.6.c; CCSS F-TF.A.3, G-SRT.C.6-8; SMP 1, 2, 6 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Apply the Law of Sines: Which missing side or angle is correctly found using the Law of Sines in an oblique triangle?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.6.d.

Apply the Law of Cosines: Which missing side or angle is correctly found using the Law of Cosines in an oblique triangle?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.6.d.

Select an Appropriate Triangle-Solving Method aligned to Praxis 5165 III.A.6.b-d; CCSS G-SRT.C-D; SMP 1,2,4,5.

Calculate Circle Circumference and Area: Which exact or approximate circumference or area is correct for a circle or composite figure?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.7.a.

Calculate Arc Length and Sector Area aligned to ETS Praxis Mathematics 5165 III.A.7.b.

Relate Central Angles, Inscribed Angles, and Arcs: Which angle or arc measure correctly applies central-angle and inscribed-angle theorems?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.7.c.

Solve Circle Angle Problems with Chords, Secants, and Tangents: Which interior or exterior angle measure correctly follows from intersecting chords, secants, tangents, and intercepted arcs?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.7.c-d - Geometry: Solve Circle Angle Problems with Chords, Secants, and Tangents.

Use Chord, Radius, Tangent, and Secant Length Properties: aligned to Praxis 5165 III.A.7.d; CCSS G-C.A.2-4; SMP 1,2,3,6.

Write Equations of Circles from Center and Radius: Which equation represents the locus of points a fixed distance from a center with the stated radius? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Find Circle Centers and Radii from Equations: Which center and radius are correct after interpreting standard form or completing the square in a general-form circle equation?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.7.g.

Classify Geometric Shapes with Coordinates: Which classification is supported by coordinate evidence involving slopes, distances, midpoints, and diagonal properties? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Use the Distance Formula: Which distance between two points is correct and how does it connect to the Pythagorean theorem? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Use the Midpoint Formula and Find Missing Endpoints: Which midpoint or missing endpoint is correct for a segment in the coordinate plane? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Partition a Directed Segment in a Given Ratio: Which coordinate point divides a directed segment in the stated ratio, including internal weighted-average reasoning?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.8.c.

Use Slope Criteria in Coordinate Geometry: Which conclusion or equation correctly uses slopes to establish parallelism, perpendicularity, or collinearity? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.8.d; CCSS G-GPE.B.5; SMP 1, 2, 3, 6.

Compute Perimeter and Area Using Coordinates: Which perimeter or area is correct for a polygon represented by coordinates, including decompositions and the distance formula?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.8.a, III.A.9.a - Geometry: Compute Perimeter and Area Using Coordinates.

Solve Composite Perimeter and Area Problems: Which decomposition, formula combination, and result correctly determine perimeter or area of a polygonal or mixed-shape region? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.9.a.

Analyze Changes in Perimeter and Area under Scaling: Which multiplicative change in perimeter or area follows when one or more dimensions of a polygon are scaled?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.9.b.

Calculate Surface Area of Solids: Which surface-area formula and result correctly apply to prisms, pyramids, cylinders, cones, spheres, or composite solids?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Calculate Volume of Solids: Which volume formula and result correctly apply to prisms, pyramids, cylinders, cones, spheres, or composite solids?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.10.a.

Identify Cross Sections and Solids of Revolution: Which two-dimensional cross section results from slicing a solid, or which three-dimensional solid results from rotating a plane figure?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.10.c - Geometry: Identify Cross Sections and Solids of Revolution: Praxis 5165 III.A.10.c; CCSS G-GMD.B.4; SMP 1, 2, 5, 7.

Use Nets and Analyze Scaling of Solids: Which net correctly represents a solid, and which change in surface area or volume follows when its dimensions are scaled? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 III.A.10.b,d.

Distinguish Populations, Samples, Parameters, and Statistics: Which term correctly identifies the population, sample, parameter, or statistic in a study description?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.a; CCSS 7.SP.A.1-2, S-IC.A.1; SMP 1, 2, 4, 6.

Evaluate Representative Samples and Sources of Bias: Which sampling method is most representative, or which selection, nonresponse, wording, or convenience bias threatens an inference? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.a-b - Statistics & Probability.

Design Random Samples and Sample Surveys: Which sampling plan correctly uses random selection and appropriate survey methods to estimate a population characteristic? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.b-c.

Distinguish Surveys, Observational Studies, and Experiments: Which study type is described, and which conclusions can validly follow from that design? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.b.

Distinguish Random Sampling from Random Assignment: Which conclusion about generalization or causation follows from the presence or absence of random sampling and random assignment?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.b-d; CCSS S-IC.B.3-5; SMP 1, 2, 3, 4.

Identify Controls, Confounding, Placebos, and Blinding: Which design feature reduces confounding or bias and strengthens a comparison in an experiment? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.b,d.

Estimate a Population Mean from a Sample: Which sample mean, interval estimate, or repeated-sampling conclusion is appropriate for estimating a population mean?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.1.a,c - Statistics & Probability: Estimate a Population Mean from a Sample: Praxis 5165 IV.A.1.a,c; CCSS 7.SP.A.2, S-IC.A.1-2, S-IC.B.4; SMP 1, 2, 4, 5, 6.

Estimate a Population Proportion from a Sample aligned to Praxis 5165 IV.A.1.a,c.

Compare Treatments in Randomized Experiments: aligned to ETS Praxis Mathematics (5165) Praxis 5165 IV.A.1.d; CCSS S-IC.B.5; SMP 1, 2, 3, 4, 5.

State Valid Scope and Limitations of Statistical Conclusions: Standards-aligned practice for Praxis 5165 IV.A.1 Praxis 5165 IV.A.1; CCSS S-IC.B.3-6; SMP 1, 2, 3, 4, 6 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM crosswalks.

Choose Appropriate Displays for One-Variable Data: Standards-aligned practice for Praxis 5165 IV.A.2.a Praxis 5165 IV.A.2.a; CCSS 6.SP.B.4, S-ID.A.1; SMP 1, 2, 4, 5 Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Construct and Interpret Dot Plots: Which dot plot or interpretation correctly represents frequency, clusters, gaps, center, and spread in a quantitative data set?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.a - Statistics & Probability: Construct and Interpret Dot Plots.

Construct and Interpret Histograms: Which histogram correctly uses class intervals and frequencies, and which shape or distribution statement is supported?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.a.

Construct and Interpret Boxplots aligned to Praxis Mathematics 5165 IV.A.2.a with CCSS Mathematics, SMP, and NCTM crosswalks.

Construct and Interpret Stem-and-Leaf and Time-Series Displays: aligned to Praxis Mathematics 5165 Statistics & Probability standards.

Compute and Interpret Mean, Median, and Mode aligned to Praxis 5165 IV.A.2.b.

Compute Quartiles, Five-Number Summaries, and IQR: Which quartile, five-number summary, or interquartile range is correct under the stated convention?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.b; CCSS 6.SP.B.5, S-ID.A.2; SMP 1, 2, 6.

Compute and Interpret Variance and Standard Deviation: Which variance or standard deviation is correct, and which interpretation accurately describes typical distance from the mean?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.b - Statistics & Probability: Compute and Interpret Variance and Standard Deviation: Praxis 5165 IV.A.2.b; CCSS S-ID.A.2; SMP 1, 2, 5, 6.

Describe Distribution Shape: Which description correctly identifies symmetry, skewness, modality, clusters, gaps, tails, or uniformity in a distribution?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.c-d.

Identify and Analyze Outliers: Which value is an outlier by a stated rule, and which effect on center, spread, or model fit is most plausible? Aligned to Praxis 5165 IV.A.2.d; CCSS 6.SP.B.5, S-ID.A.3; SMP 1, 2, 3, 5.

Choose Appropriate Measures of Center and Spread aligned to Praxis 5165 IV.A.2.c-d; CCSS S-ID.A.2-3; SMP 1, 2, 3, 6.

Compare Two or More One-Variable Distributions: Which comparison accurately addresses shape, center, spread, overlap, and unusual values in context? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.c-d; CCSS 7.SP.B.3-4, S-ID.A.2-3; SMP 1, 2, 3, 5, 6.

Analyze Effects of Transforming Data: Which change in mean, median, range, IQR, variance, or standard deviation follows when a constant is added or all values are multiplied by a factor?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.2.b-d - Statistics & Probability: Analyze Effects of Transforming Data: Praxis 5165 IV.A.2.b-d; CCSS S-ID.A.2-3; SMP 1, 2, 3, 7.

Construct Two-Way Frequency Tables: Which two-way table correctly organizes counts for two categorical variables and includes accurate totals?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.3.a.

Compute Joint and Marginal Relative Frequencies: Which joint or marginal relative frequency is correct and uses the appropriate denominator?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.3.a - Statistics & Probability: Compute Joint and Marginal Relative Frequencies: Praxis 5165 IV.A.3.a; CCSS 8.SP.A.4, S-ID.B.5; SMP 1, 2, 6.

Compute and Interpret Conditional Relative Frequencies: Which conditional relative frequency is correct and which group comparison does it support?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.3.a; CCSS 8.SP.A.4, S-ID.B.5; SMP 1, 2, 4, 6.

Identify Associations in Categorical Data: Which conclusion about association or independence is supported by conditional distributions in a two-way table? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.3.b.

Construct and Interpret Scatterplots: Which scatterplot correctly represents paired quantitative data, and which overall relationship is visible?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.3.c - Statistics & Probability: Construct and Interpret Scatterplots.

Describe Bivariate Direction, Form, Strength, and Outliers: Which description correctly characterizes a scatterplot as positive, negative, or absent in direction; linear or nonlinear in form; and weak or strong in association?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.3.b-c - Statistics & Probability.

Analyze Trends in Time-Series Data: Which trend, seasonal pattern, cycle, abrupt change, or forecast is supported by a time-series display?. Aligned to ETS Praxis Mathematics (5165) Praxis 5165 IV.A.3.b; CCSS S-ID.B.6, F-IF.B.4; SMP 1, 2, 4, 5.

Fit Linear Regression Models with Technology: Which regression equation and correlation coefficient are supported by the data and correct technology output?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.a - Statistics & Probability.

Use Regression Models for Contextual Predictions: Which predicted value is obtained from a fitted model and interpreted with correct units and practical meaning?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.b - Statistics & Probability: Use Regression Models for Contextual Predictions: Praxis 5165 IV.A.4.b; CCSS 8.SP.A.2-3, S-ID.B.6, S-ID.C.7; SMP 1, 2, 4, 5, 6.

Distinguish Interpolation from Extrapolation: Which prediction is interpolation or extrapolation, and which reliability concern is appropriate for the prediction range? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.b.

Calculate and Interpret Residuals: Which residual is correct using observed minus predicted value, and what does its sign mean in context?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.c - Statistics & Probability: Calculate and Interpret Residuals: Praxis 5165 IV.A.4.c; CCSS S-ID.B.6; SMP 1, 2, 4, 6.

Use Residual Plots to Assess Model Fit: Which residual pattern supports a linear model, and which pattern indicates curvature, changing variance, or an outlier? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.c - Statistics & Probability.

Interpret Regression Slope and Intercept: Which contextual interpretation correctly explains the slope and intercept of a regression line, including when the intercept is not meaningful?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks.

Interpret the Linear Correlation Coefficient: Which statement correctly interprets the sign, magnitude, and limitations of a correlation coefficient?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.e - Statistics & Probability: Interpret the Linear Correlation Coefficient: Praxis 5165 IV.A.4.e; CCSS S-ID.C.8; SMP 1, 2, 3, 6.

Distinguish Correlation from Causation: Which conclusion correctly avoids claiming causation from association and identifies possible confounding, reverse causation, or coincidence? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.4.f - Statistics & Probability: Distinguish Correlation from Causation: Praxis 5165 IV.A.4.f; CCSS S-ID.C.9, S-IC.B.3; SMP 1, 2, 3, 4.

Represent Sample Spaces and Events: Which list, table, tree, Venn diagram, or set notation correctly represents the sample space and specified events? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.a - Statistics & Probability: Represent Sample Spaces and Events: Praxis 5165 IV.A.5.a; CCSS 7.SP.C.8, S-CP.A.1; SMP 1, 2, 5, 6.

Use Unions, Intersections, and Complements: Which event description, set expression, or Venn-diagram region correctly represents a union, intersection, complement, or relative complement?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.a - Statistics & Probability: Use Unions, Intersections, and Complements: Praxis 5165 IV.A.5.a; CCSS S-CP.A.1, S-CP.B.7; SMP 1, 2, 5, 6.

Compute Theoretical and Empirical Probabilities: Which probability is correct from equally likely outcomes, relative frequency, or a simulation, and which interpretation matches the result? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.d - Statistics & Probability: Compute Theoretical and Empirical Probabilities: Praxis 5165 IV.A.5.d; CCSS 7.SP.C.5-8, S-CP.A.1; SMP 1, 2, 4, 5, 6.

Compute Compound Probabilities with Organized Models: Which probability is correct for a multistage event represented by a table, list, area model, or tree diagram?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.d - Statistics & Probability: Compute Compound Probabilities with Organized Models: Praxis 5165 IV.A.5.d; CCSS 7.SP.C.8, S-CP.A.1; SMP 1, 2, 4, 5, 6.

Apply the Addition Rule: Which probability correctly applies the general addition rule and subtracts overlap when events are not mutually exclusive? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.f - Statistics & Probability: Apply the Addition Rule: Praxis 5165 IV.A.5.f; CCSS S-CP.B.7; SMP 1, 2, 6, 7.

Compute and Interpret Conditional Probability: Which conditional probability is correct and which statement accurately interprets the conditioning event? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.c,e - Statistics & Probability: Compute and Interpret Conditional Probability: Praxis 5165 IV.A.5.c,e; CCSS S-CP.A.3, S-CP.B.6; SMP 1, 2, 4, 6.

Determine Whether Events Are Independent: Which equality, table comparison, or contextual conclusion correctly establishes whether two events are independent? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.b-c,e - Statistics & Probability: Determine Whether Events Are Independent: Praxis 5165 IV.A.5.b-c,e; CCSS S-CP.A.2-5; SMP 1, 2, 3, 6.

Apply the General Multiplication Rule: Which probability correctly uses P(A and B) = P(A)P(B given A) or an equivalent conditional form? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.g - Statistics & Probability: Apply the General Multiplication Rule: Praxis 5165 IV.A.5.g; CCSS S-CP.B.8; SMP 1, 2, 6, 7.

Use Two-Way Tables as Probability Sample Spaces: Which simple, joint, conditional, or independence probability is correct when a two-way table serves as the sample space? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.5.e - Statistics & Probability: Use Two-Way Tables as Probability Sample Spaces: Praxis 5165 IV.A.5.e; CCSS S-CP.A.4-5, S-CP.B.6; SMP 1, 2, 4, 5, 6.

Use Probability Simulations and Finite Sample Spaces: Which simulation design, outcome count, or long-run relative-frequency interpretation appropriately models a finite probability situation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.6.a - Statistics & Probability: Use Probability Simulations and Finite Sample Spaces: Praxis 5165 IV.A.6.a; CCSS 7.SP.C.6-8, S-IC.A.2; SMP 1, 2, 4, 5.

Apply the Fundamental Counting Principle: Which product of stage counts correctly determines the number of outcomes in a multistep process? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.6.a - Statistics & Probability: Apply the Fundamental Counting Principle: Praxis 5165 IV.A.6.a; CCSS 7.SP.C.8, S-CP.B.9; SMP 1, 2, 6, 7.

Count Arrangements with Permutations: Which permutation count correctly handles order, repeated objects, restrictions, or selections without replacement? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.6.b - Statistics & Probability: Count Arrangements with Permutations: Praxis 5165 IV.A.6.b; CCSS S-CP.B.9; SMP 1, 2, 6, 7.

Count Selections with Combinations: Which combination count correctly handles unordered selections and distinguishes combinations from permutations? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.6.b - Statistics & Probability: Count Selections with Combinations: Praxis 5165 IV.A.6.b; CCSS S-CP.B.9; SMP 1, 2, 6, 7.

Compute Probabilities with Counting Techniques: Which probability correctly divides favorable permutation or combination counts by the total number of equally likely outcomes? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.6.a-b - Statistics & Probability: Compute Probabilities with Counting Techniques: Praxis 5165 IV.A.6.a-b; CCSS S-CP.B.9; SMP 1, 2, 6, 7.

Construct and Interpret Discrete Probability Distributions: Which table or graph is a valid probability distribution for a discrete random variable and which event probability follows from it? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.7.a-b - Statistics & Probability: Construct and Interpret Discrete Probability Distributions: Praxis 5165 IV.A.7.a-b; CCSS S-MD.A.1-4; SMP 1, 2, 5, 6.

Calculate and Use Expected Value: Which expected value is correct for a theoretical or empirical distribution, and which decision is favored when gains, losses, risks, or fairness are considered? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.7.a-c - Statistics & Probability: Calculate and Use Expected Value: Praxis 5165 IV.A.7.a-c; CCSS S-MD.A.2-4, S-MD.B.5-7; SMP 1, 2, 3, 4, 6.

Recognize and Standardize Normal Distributions: Which data set is plausibly normal, or which z-score, empirical-rule percentage, or standardized interpretation is correct? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.8.a-b - Statistics & Probability: Recognize and Standardize Normal Distributions: Praxis 5165 IV.A.8.a-b; CCSS S-ID.A.4; SMP 1, 2, 5, 6.

Estimate Normal-Curve Areas, Percentiles, and Cut Scores: Which population percentage, percentile, interval, or cutoff is supported by the mean and standard deviation of a normal distribution? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 IV.A.8.b-c - Statistics & Probability: Estimate Normal-Curve Areas, Percentiles, and Cut Scores: Praxis 5165 IV.A.8.b-c; CCSS S-ID.A.4; SMP 1, 2, 4, 5, 6.

Identify Mathematically Valid Explanations: Which explanation correctly communicates why a mathematical concept, procedure, representation, or model is valid rather than merely stating a rule?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 1 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Identify Mathematically Valid Explanations: Praxis 5165 Task of Teaching 1; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 1, 3, 6.

Compare Explanations for Validity and Generalizability: Which comparison correctly identifies whether two explanations are valid, generalizable beyond the example, coherent, and mathematically precise? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 2 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Compare Explanations for Validity and Generalizability: Praxis 5165 Task of Teaching 2; NCTM 2020 Secondary Standards 1, 2, 4, 5; CCSS SMP 1, 3, 6, 7.

Identify Flaws in Explanations and Justifications: Which step contains an invalid assumption, unsupported inference, hidden domain restriction, circular argument, or overgeneralization?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 2 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Identify Flaws in Explanations and Justifications: Praxis 5165 Task of Teaching 2; NCTM 2020 Secondary Standards 1, 2, 4, 5; CCSS SMP 1, 3, 6, 7.

Improve Explanations and Justifications: Which revision most improves the validity, generalizability, coherence, or precision of a mathematical explanation or justification?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 3 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Improve Explanations and Justifications: Praxis 5165 Task of Teaching 3; NCTM 2020 Secondary Standards 2, 4, 5; CCSS SMP 1, 3, 6.

Evaluate Counterarguments: Which counterargument directly addresses the stated critique, and which response fails to engage the mathematical issue?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 4 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Evaluate Counterarguments: Praxis 5165 Task of Teaching 4; NCTM 2020 Secondary Standards 2, 4; CCSS SMP 1, 3, 6.

Evaluate Mathematical Definitions: Which definition is necessary and sufficient, uses precise language, avoids circularity, and fits the intended mathematical context? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 5 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Evaluate Mathematical Definitions: Praxis 5165 Task of Teaching 5; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 3, 6, 7.

Distinguish Examples, Nonexamples, and Counterexamples: Which example confirms a definition, which nonexample clarifies a boundary, or which counterexample disproves a universal claim? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 1, 5, 10 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Distinguish Examples, Nonexamples, and Counterexamples: Praxis 5165 Task of Teaching 1, 5, 10; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 1, 3, 7.

Select Explanations That Connect Representations: Which explanation most clearly connects symbolic, graphical, numerical, verbal, and geometric representations of the same idea? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 1-3, 13 - Tasks of Teaching Mathematics - Mathematical Explanations, Justifications, and Definitions: Select Explanations That Connect Representations: Praxis 5165 Task of Teaching 1-3, 13; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 2, 3, 4, 5.

Select Problems with a Target Mathematical Structure: Which problem or task has the requested mathematical structure, addresses the same underlying concept, or satisfies specified content constraints?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 6 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Select Problems with a Target Mathematical Structure: Praxis 5165 Task of Teaching 6; NCTM 2020 Secondary Standards 1, 3, 4; CCSS SMP 1, 4, 7.

Select Tasks That Elicit Particular Student Thinking: Which task is most likely to reveal a target strategy, misconception, conceptual connection, or level of reasoning?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 6 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Select Tasks That Elicit Particular Student Thinking: Praxis 5165 Task of Teaching 6; NCTM 2020 Secondary Standards 3, 4, 5; CCSS SMP 1, 3, 4.

Sequence Problems by Difficulty and Complexity: Which ordering systematically varies one feature at a time and progresses from accessible cases to more complex or generalized cases? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 7 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Sequence Problems by Difficulty and Complexity: Praxis 5165 Task of Teaching 7; NCTM 2020 Secondary Standards 3, 4; CCSS SMP 1, 7, 8.

Evaluate Introductory Examples: Which example best introduces a concept without hiding essential structure, creating a false generalization, or adding unnecessary cognitive load? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 8 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Evaluate Introductory Examples: Praxis 5165 Task of Teaching 8; NCTM 2020 Secondary Standards 3, 4; CCSS SMP 1, 4, 7.

Evaluate Examples for Illustrating Strategies: Which example most effectively demonstrates a strategy, procedure, or mathematical practice and makes the key decision points visible? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks; Praxis 5165 Task of Teaching 8 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Evaluate Examples for Illustrating Strategies; Praxis 5165 Task of Teaching 8; NCTM 2020 Secondary Standards 3, 4; CCSS SMP 1, 4, 7.

Choose Examples That Address Misconceptions: Which example directly challenges a specified misconception or content obstacle while preserving an appropriate level of mathematical demand? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 9 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Choose Examples That Address Misconceptions: Praxis 5165 Task of Teaching 9; NCTM 2020 Secondary Standards 3, 4, 5; CCSS SMP 1, 3, 4.

Choose Nonexamples and Counterexamples for Instruction: Which nonexample or counterexample most clearly highlights a mathematical distinction or shows why a conjecture is false or only partly true? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 10 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Choose Nonexamples and Counterexamples for Instruction: Praxis 5165 Task of Teaching 10; NCTM 2020 Secondary Standards 2, 3, 4; CCSS SMP 1, 3, 7.

Evaluate the Validity of Procedures: Which procedure is mathematically valid for all stated cases, and which procedure depends on an unjustified step or a missing condition? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 11 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Evaluate the Validity of Procedures: Praxis 5165 Task of Teaching 11; NCTM 2020 Secondary Standards 1, 2, 4, 5; CCSS SMP 1, 3, 6, 7.

Identify Special Cases and Procedure Limitations: Which input, boundary case, denominator restriction, degeneracy, or representation makes a generally useful procedure fail or require modification?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 11 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Identify Special Cases and Procedure Limitations: Praxis 5165 Task of Teaching 11; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 1, 3, 7.

Compare Procedures for Efficiency and Robustness: Which procedure is most efficient, transparent, or robust for the given problem while remaining mathematically valid and generalizable? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks; Praxis 5165 Task of Teaching 11 - Tasks of Teaching Mathematics - Mathematical Problems, Tasks, Examples, and Procedures: Compare Procedures for Efficiency and Robustness: Praxis 5165 Task of Teaching 11; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 1, 3, 5, 7.

Select Representations That Fit a Concept: Which concrete, pictorial, graphical, tabular, symbolic, or verbal representation best supports the target concept and learner goal?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 12 - Tasks of Teaching Mathematics - Mathematical Representations, Models, Manipulatives, and Technology: Select Representations That Fit a Concept: Praxis 5165 Task of Teaching 12; NCTM 2020 Secondary Standards 2, 3, 4; CCSS SMP 2, 4, 5.

Evaluate Models for Validity and Generalizability: Which model accurately represents the mathematical relationship, and which limitation affects how far its conclusions can be generalized? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 12 - Tasks of Teaching Mathematics - Mathematical Representations, Models, Manipulatives, and Technology: Evaluate Models for Validity and Generalizability: Praxis 5165 Task of Teaching 12; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 1, 2, 4, 5.

Evaluate How Representations Show Relationships: Which interpretation correctly explains how a representation displays structure, equivalence, covariation, transformation, or a process? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 13 - Tasks of Teaching Mathematics - Mathematical Representations, Models, Manipulatives, and Technology: Evaluate How Representations Show Relationships: Praxis 5165 Task of Teaching 13; NCTM 2020 Secondary Standards 1, 2, 4; CCSS SMP 2, 3, 5, 7.

Evaluate Manipulatives and Visual Models: Which use of a manipulative or visual model preserves the mathematics, supports abstraction, and avoids a misleading feature?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 12-13 - Tasks of Teaching Mathematics - Mathematical Representations, Models, Manipulatives, and Technology: Evaluate Manipulatives and Visual Models: Praxis 5165 Task of Teaching 12-13; NCTM 2020 Secondary Standards 2, 3, 4; CCSS SMP 2, 4, 5.

Evaluate Strategic Use of Technology: Which use of graphing, dynamic geometry, simulation, spreadsheet, computer algebra, or calculator technology is appropriate and supports rather than replaces the key idea? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 14 - Tasks of Teaching Mathematics - Mathematical Representations, Models, Manipulatives, and Technology: Evaluate Strategic Use of Technology: Praxis 5165 Task of Teaching 14; NCTM 2020 Secondary Standards 2, 4; CCSS SMP 1, 4, 5, 6.

Diagnose Likely Student Misconceptions: Which misconception or partial understanding most plausibly explains a student error pattern, representation, or verbal explanation?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 15 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Diagnose Likely Student Misconceptions: Praxis 5165 Task of Teaching 15; NCTM 2020 Secondary Standards 3, 4, 5; CCSS SMP 1, 3, 7.

Connect New Content to Prior Knowledge: Which prior concept, representation, or known procedure provides the strongest foundation for the new mathematical idea, including productive use of an error?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 16 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Connect New Content to Prior Knowledge: Praxis 5165 Task of Teaching 16; NCTM 2020 Secondary Standards 3, 4; CCSS SMP 1, 4, 7, 8.

Evaluate Student Work for Mathematical Quality: Which evaluation accurately addresses the validity, generalizability, coherence, and precision of a student solution, explanation, proof, or representation? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 17 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Evaluate Student Work for Mathematical Quality: Praxis 5165 Task of Teaching 17; NCTM 2020 Secondary Standards 2, 4, 5; CCSS SMP 1, 3, 6.

Identify Concepts and Strategies in Student Work: Which mathematical concept, representation, theorem, heuristic, or strategy is the student using, whether or not the final answer is correct?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 18 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Identify Concepts and Strategies in Student Work: Praxis 5165 Task of Teaching 18; NCTM 2020 Secondary Standards 2, 3, 4, 5; CCSS SMP 1, 2, 3, 7.

Predict How Student Reasoning Generalizes: Which result is most likely when a student repeats the same reasoning on a structurally similar problem with changed numbers or representations? Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 19 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Predict How Student Reasoning Generalizes: Praxis 5165 Task of Teaching 19; NCTM 2020 Secondary Standards 3, 4, 5; CCSS SMP 1, 3, 7, 8.

Match Student Work Showing the Same Reasoning: Which two student responses use the same underlying reasoning despite differences in notation, representation, efficiency, or correctness?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 20 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Match Student Work Showing the Same Reasoning: Praxis 5165 Task of Teaching 20; NCTM 2020 Secondary Standards 2, 3, 4, 5; CCSS SMP 2, 3, 5, 7.

Detect Correct Answers That Mask Incorrect Thinking: Which student response arrives at a correct answer through reasoning that will fail in other cases, and which follow-up item would expose the misconception?. Aligned to ETS Praxis Mathematics (5165) with CCSS Mathematics, SMP, and NCTM 2020 crosswalks Praxis 5165 Task of Teaching 21 - Tasks of Teaching Mathematics - Students' Mathematical Reasoning: Detect Correct Answers That Mask Incorrect Thinking: Praxis 5165 Task of Teaching 21; NCTM 2020 Secondary Standards 3, 4, 5; CCSS SMP 1, 3, 4, 7.

Passage-First Evidence Rule: Select the answer that is supported by what the passage states or clearly implies, even when outside knowledge suggests a different answer. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Select the answer that is supported by what the passage states or clearly implies, even when outside knowledge suggests a different answer. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Stimulus and Passage-Set Recognition: Identify whether a task uses a brief statement, short passage, long passage, paired passages, or a text-plus-visual stimulus, and choose the reading approach that best fits the set. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy; Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10; Praxis Reading Foundations and Selected-Response Method.

Purposeful First Read: Choose the most effective first-read focus for locating the topic, central point, organizational path, and overall tone without becoming trapped in minor details. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Choose the most effective first-read focus for locating the topic, central point, organizational path, and overall tone without becoming trapped in minor details. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Question-Stem Classification: Determine which reading skill a stem is testing - main idea, detail, inference, vocabulary, structure, tone, visual interpretation, argument evaluation, or passage comparison - before evaluating choices. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Determine which reading skill a stem is testing - main idea, detail, inference, vocabulary, structure, tone, visual interpretation, argument evaluation, or passage comparison - before evaluating choices. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Evidence-Based Answer Verification: Select the choice that can be verified by a specific word, sentence, relationship, or data point in the stimulus rather than by plausibility alone. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Select the choice that can be verified by a specific word, sentence, relationship, or data point in the stimulus rather than by plausibility alone. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Distractor Analysis and Elimination: Eliminate answer choices that reverse the passage, exaggerate or weaken its claim, introduce outside information, answer a different question, or state something true but irrelevant. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Eliminate answer choices that reverse the passage, exaggerate or weaken its claim, introduce outside information, answer a different question, or state something true but irrelevant. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Scope, Strength, and Qualification Control: Choose an answer whose breadth and certainty match the passage, giving careful attention to words such as some, most, often, may, must, only, and always. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Choose an answer whose breadth and certainty match the passage, giving careful attention to words such as some, most, often, may, must, only, and always. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Passage-Set Pacing and Strategic Rechecking: Select a pacing and review plan that preserves enough time for every passage set while reserving deeper rechecking for questions with competing text-based choices. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10 - Praxis Reading Foundations and Selected-Response Method: Select a pacing and review plan that preserves enough time for every passage set while reserving deeper rechecking for questions with competing text-based choices. Aligned to Praxis 5713 Test Format and Content Topics I-III; CCSS CCRA.R.1, CCRA.R.10.

Topic versus Main Idea: Select the choice that distinguishes the broad subject of a passage from the specific point the author makes about that subject. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Select the choice that distinguishes the broad subject of a passage from the specific point the author makes about that subject. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Explicit Main Idea: Identify the sentence or answer choice that most accurately restates a directly stated central idea. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Identify the sentence or answer choice that most accurately restates a directly stated central idea. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Implied Main Idea: Infer the central idea when it is developed across details but never stated in a single sentence. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Infer the central idea when it is developed across details but never stated in a single sentence. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Paragraph Main Idea: Choose the best statement of what one paragraph chiefly contributes, rather than a detail that appears only within it. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Choose the best statement of what one paragraph chiefly contributes, rather than a detail that appears only within it. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Whole-Passage Central Idea: Select the central idea that accounts for the passage as a whole, including its beginning, development, and conclusion. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Select the central idea that accounts for the passage as a whole, including its beginning, development, and conclusion.

Multiple Central Ideas: Identify two or more coordinated central ideas and the relationship that unifies them in a complex passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Identify two or more coordinated central ideas and the relationship that unifies them in a complex passage. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Central Idea in Informational and Explanatory Text: Choose the statement that best captures the core explanation, finding, process, or concept developed in an informational passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Choose the statement that best captures the core explanation, finding, process, or concept developed in an informational passage. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Central Focus in Narrative and Reflective Text: Identify the main experience, conflict, realization, or reflection that gives a narrative or personal passage its central focus. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Identify the main experience, conflict, realization, or reflection that gives a narrative or personal passage its central focus.

Primary Purpose: Select the option that best states what the author is mainly trying to accomplish, such as explain, describe, compare, persuade, question, illustrate, or reflect. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Select the option that best states what the author is mainly trying to accomplish, such as explain, describe, compare, persuade, question, illustrate, or reflect. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Dominant Purpose in a Mixed-Purpose Passage: Determine the primary purpose when a passage both informs and persuades, narrates and reflects, or combines several rhetorical aims. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Determine the primary purpose when a passage both informs and persuades, narrates and reflects, or combines several rhetorical aims. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Accurate Main-Idea Paraphrase: Choose a restatement that preserves the meaning, emphasis, and qualifications of the original central idea without copying its wording. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Choose a restatement that preserves the meaning, emphasis, and qualifications of the original central idea without copying its wording. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Objective Summary: Select the concise summary that includes the central idea and essential support while excluding opinion, interpretation, and minor examples. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Select the concise summary that includes the central idea and essential support while excluding opinion, interpretation, and minor examples. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Summary Scope and Completeness: Distinguish a complete summary from choices that are too broad, too narrow, distorted, repetitive, or unsupported. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy; Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Distinguish a complete summary from choices that are too broad, too narrow, distorted, repetitive, or unsupported. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Best Title for Main Idea or Purpose: Choose the title that most accurately reflects the passage's central idea and purpose rather than a vivid but secondary detail. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2 - Key Ideas and Details - Main Idea and Primary Purpose: Choose the title that most accurately reflects the passage's central idea and purpose rather than a vivid but secondary detail. Aligned to Praxis 5713 I.A.1; CCSS CCRA.R.2; RI.11-12.2; RL.11-12.2.

Explicit Detail Retrieval: Locate the answer choice that accurately reports a fact, action, statement, or description directly provided in the passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Locate the answer choice that accurately reports a fact, action, statement, or description directly provided in the passage. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Detail Paraphrase: Select a choice that restates a specific detail in new language without changing its meaning or level of certainty. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Select a choice that restates a specific detail in new language without changing its meaning or level of certainty. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Major versus Minor Support: Distinguish details that materially develop the central idea from incidental examples, background, or descriptive flourishes. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Distinguish details that materially develop the central idea from incidental examples, background, or descriptive flourishes.

Claim-to-Evidence Match: Identify which sentence, fact, example, or observation most directly supports a stated claim or subclaim. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Identify which sentence, fact, example, or observation most directly supports a stated claim or subclaim. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Examples and Illustrations: Determine what general idea a particular example, case, anecdote, or illustration is intended to clarify or support. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Determine what general idea a particular example, case, anecdote, or illustration is intended to clarify or support.

Definitions and Explanations: Choose the detail that defines a term, explains a process, or clarifies an unfamiliar concept within the passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Choose the detail that defines a term, explains a process, or clarifies an unfamiliar concept within the passage. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Statistical and Quantitative Details: Interpret numerical information in prose and select the statement that accurately represents the amount, rate, proportion, ranking, or change described. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Interpret numerical information in prose and select the statement that accurately represents the amount, rate, proportion, ranking, or change described. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Sequence and Chronology: Identify the correct order of events, steps, discoveries, or stages when the passage presents a temporal or procedural sequence. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Identify the correct order of events, steps, discoveries, or stages when the passage presents a temporal or procedural sequence. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Cause-and-Effect Details: Match a stated cause with its stated effect, or identify the detail that explains why an event or outcome occurred. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Match a stated cause with its stated effect, or identify the detail that explains why an event or outcome occurred. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Compare-and-Contrast Details: Select the choice that accurately states a similarity, difference, or point of comparison developed between people, ideas, methods, or events. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Select the choice that accurately states a similarity, difference, or point of comparison developed between people, ideas, methods, or events. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Conditions, Exceptions, and Qualifications: Identify limitations, exceptions, prerequisites, and qualifying details that restrict when a statement is true. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Identify limitations, exceptions, prerequisites, and qualifying details that restrict when a statement is true. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Reference and Pronoun Tracking: Determine the word, phrase, person, event, or idea to which a pronoun or other referring expression points. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Determine the word, phrase, person, event, or idea to which a pronoun or other referring expression points. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Synthesizing Details across Paragraphs: Combine information from separated parts of a passage to answer a question that no single sentence resolves by itself. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Combine information from separated parts of a passage to answer a question that no single sentence resolves by itself. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

EXCEPT, NOT, and Unsupported-Detail Questions: Choose the one option that is not stated, not supported, or inconsistent with the passage while verifying every remaining choice. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1 - Key Ideas and Details - Supporting Ideas and Specific Details: Choose the one option that is not stated, not supported, or inconsistent with the passage while verifying every remaining choice. Aligned to Praxis 5713 I.B.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3; RH.11-12.1; RST.11-12.1.

Directly Supported Inference: Select the conclusion that follows most naturally from explicit evidence even though the conclusion is not stated word for word. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Select the conclusion that follows most naturally from explicit evidence even though the conclusion is not stated word for word. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Inference versus Speculation: Distinguish a reasonable text-based inference from an answer that depends on imagination, stereotypes, outside knowledge, or unsupported assumptions. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Distinguish a reasonable text-based inference from an answer that depends on imagination, stereotypes, outside knowledge, or unsupported assumptions. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Implied Cause: Infer the most likely cause of a stated event, behavior, or condition from contextual evidence in the passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Infer the most likely cause of a stated event, behavior, or condition from contextual evidence in the passage. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Implied Effect: Infer the most likely consequence of a stated action, decision, trend, or condition without extending beyond the passage's logic. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Infer the most likely consequence of a stated action, decision, trend, or condition without extending beyond the passage's logic. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Motivation and Intention: Choose the inference that best explains why a speaker, character, researcher, institution, or author acts or speaks as described. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Choose the inference that best explains why a speaker, character, researcher, institution, or author acts or speaks as described.

Implied Relationships among People or Ideas: Infer a relationship such as support, tension, dependence, contrast, hierarchy, or influence from the details provided. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Infer a relationship such as support, tension, dependence, contrast, hierarchy, or influence from the details provided. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Prediction from Textual Evidence: Select the most likely next event or future outcome when the passage supplies a clear pattern, condition, or causal direction. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Select the most likely next event or future outcome when the passage supplies a clear pattern, condition, or causal direction.

Generalization from Examples: Infer the broader principle or pattern that is reasonably supported by several examples without overgeneralizing beyond them. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy - Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Infer the broader principle or pattern that is reasonably supported by several examples without overgeneralizing beyond them. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Inference from Comparison or Contrast: Use stated similarities and differences to infer an additional relationship that the author implies. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Use stated similarities and differences to infer an additional relationship that the author implies. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Inference from Quantitative Information: Draw a supported inference from numbers, proportions, rankings, or trends embedded in prose. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Draw a supported inference from numbers, proportions, rankings, or trends embedded in prose.

Likely Agreement or Disagreement: Determine which statement an author, speaker, or person described in the passage would most likely accept or reject. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Determine which statement an author, speaker, or person described in the passage would most likely accept or reject. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Resolving Ambiguity through Context: Use surrounding sentences to infer the intended meaning of an ambiguous reference, action, or statement. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Use surrounding sentences to infer the intended meaning of an ambiguous reference, action, or statement. Aligned to Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3.

Least-Supported or Negative Inference: Identify the choice that cannot reasonably be inferred while the other choices follow from the passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy - Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications.

Multi-Step Inference: Combine two or more stated facts or relationships to reach the strongest supported implication without adding an unstated premise. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 I.C.1; CCSS CCRA.R.1, CCRA.R.3; RI.11-12.1, RI.11-12.3; RL.11-12.1, RL.11-12.3 - Key Ideas and Details - Inferences and Implications: Combine two or more stated facts or relationships to reach the strongest supported implication without adding an unstated premise.

Tone from Diction: Select the tone word best supported by the author's vocabulary, descriptive choices, and level of emotional intensity. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy; Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6; Craft, Structure, and Language Skills - Attitude, Tone, and Point of View.

Author Attitude toward the Subject: Identify whether the author is approving, critical, skeptical, concerned, amused, enthusiastic, detached, or otherwise positioned toward the main topic. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Identify whether the author is approving, critical, skeptical, concerned, amused, enthusiastic, detached, or otherwise positioned toward the main topic.

Attitude toward a Person, Group, Idea, or Source: Determine the author's stance toward a specific person, institution, claim, method, or source discussed within the passage. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Determine the author's stance toward a specific person, institution, claim, method, or source discussed within the passage. Aligned to Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6.

Tone versus Subject Matter: Choose the tone based on how the author presents the subject, not merely on whether the subject itself is serious, humorous, tragic, or controversial. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Choose the tone based on how the author presents the subject, not merely on whether the subject itself is serious, humorous, tragic, or controversial. Aligned to Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6.

Tone Shift: Identify where and how the tone changes, and select the explanation that best connects the shift to a change in topic, evidence, or purpose. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Identify where and how the tone changes, and select the explanation that best connects the shift to a change in topic, evidence, or purpose.

Objective, Neutral, and Subjective Tone: Distinguish detached reporting from language that signals judgment, advocacy, emotion, or personal involvement. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Distinguish detached reporting from language that signals judgment, advocacy, emotion, or personal involvement. Aligned to Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6.

Formal and Informal Register: Determine the level of formality created by sentence structure, vocabulary, contractions, colloquialisms, and direct address. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Determine the level of formality created by sentence structure, vocabulary, contractions, colloquialisms, and direct address. Aligned to Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6.

Irony and Sarcasm: Recognize when the intended attitude differs from the literal wording and select the interpretation best supported by context. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Recognize when the intended attitude differs from the literal wording and select the interpretation best supported by context. Aligned to Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6.

Connotation and Emotional Coloring: Identify how positive, negative, or neutral associations in word choice shape the author's attitude. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy; Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6; Craft, Structure, and Language Skills - Attitude, Tone, and Point of View.

Perspective, Viewpoint, and Bias: Select the description that best explains the perspective from which the passage is presented and how that perspective may shape emphasis or omission. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6 - Craft, Structure, and Language Skills - Attitude, Tone, and Point of View: Select the description that best explains the perspective from which the passage is presented and how that perspective may shape emphasis or omission. Aligned to Praxis 5713 II.A.1; CCSS CCRA.R.4, CCRA.R.6; RI.11-12.4, RI.11-12.6; RL.11-12.4, RL.11-12.6.

Transitions of Addition and Example: Identify words and phrases that add information or introduce examples, and determine the relationship they signal between ideas. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.1; CCSS CCRA.R.5; RI.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Identify words and phrases that add information or introduce examples, and determine the relationship they signal between ideas.

Transitions of Contrast and Concession: Interpret transitions such as however, although, nevertheless, instead, and on the other hand as signals of contrast, qualification, or concession. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.1; CCSS CCRA.R.5; RI.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Interpret transitions such as however, although, nevertheless, instead, and on the other hand as signals of contrast, qualification, or concession.

Transitions of Cause, Effect, and Result: Determine how words such as because, therefore, consequently, and thus connect reasons, causes, results, and conclusions. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.1; CCSS CCRA.R.5; RI.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Determine how words such as because, therefore, consequently, and thus connect reasons, causes, results, and conclusions.

Transitions of Sequence, Time, and Conclusion: Identify transitions that order events or steps, mark time, summarize, or signal a final conclusion. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.1; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Identify transitions that order events or steps, mark time, summarize, or signal a final conclusion. Aligned to Praxis 5713 II.B.1; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.

Cause-and-Effect Structure: Select the description that best explains how a passage organizes causes, contributing factors, immediate effects, and long-term consequences. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Select the description that best explains how a passage organizes causes, contributing factors, immediate effects, and long-term consequences. Aligned to Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.

Compare-and-Contrast Structure: Identify how a passage arranges similarities and differences, including point-by-point and subject-by-subject patterns. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Identify how a passage arranges similarities and differences, including point-by-point and subject-by-subject patterns. Aligned to Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.

Problem-and-Solution Structure: Determine how a passage defines a problem, explains its causes or stakes, proposes solutions, and evaluates their feasibility. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Determine how a passage defines a problem, explains its causes or stakes, proposes solutions, and evaluates their feasibility.

Chronological and Process Structure: Recognize organization by time, historical development, sequence of events, or ordered steps in a process. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Recognize organization by time, historical development, sequence of events, or ordered steps in a process. Aligned to Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.

Classification and Division Structure: Identify how a broad subject is divided into categories, types, components, or stages and how those groups are related. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Identify how a broad subject is divided into categories, types, components, or stages and how those groups are related. Aligned to Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.

Definition and Example Structure: Determine how an author introduces a concept, defines its features, and clarifies it with illustrations or cases. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Determine how an author introduces a concept, defines its features, and clarifies it with illustrations or cases.

General-to-Specific and Specific-to-General Structure: Identify whether a passage begins with a broad claim and narrows to evidence or builds from examples toward a general conclusion. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Identify whether a passage begins with a broad claim and narrows to evidence or builds from examples toward a general conclusion. Aligned to Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.

Claim, Counterclaim, and Rebuttal Structure: Recognize how an argumentative passage presents a position, acknowledges an opposing view, and responds to that opposition. Aligned to ETS Praxis Core Academic Skills for Educators: Reading (5713) and CCSS ELA/Literacy Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5 - Craft, Structure, and Language Skills - Organization, Structure, and Function: Recognize how an argumentative passage presents a position, acknowledges an opposing view, and responds to that opposition. Aligned to Praxis 5713 II.B.2; CCSS CCRA.R.5; RI.11-12.5; RL.11-12.5.