Coverage by content domain
Lessons and questions are organized around the exam’s content areas so your preparation reflects the structure of the assessment.
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Praxis test alignment
240's Praxis Middle School Mathematics study guide is built around the official exam framework so you can study what is actually tested. This page shows exactly how the guide maps to the real exam — SMR by SMR and competency by competency.
Based on a competency-by-competency review of the official framework and the lessons, practice questions, flashcards, videos, and study materials included in this guide.
Transparent coverage
Our curriculum team begins with the official test framework, identifies the knowledge and skills candidates are expected to demonstrate, and maps instruction and practice to those expectations.
Lessons and questions are organized around the exam’s content areas so your preparation reflects the structure of the assessment.
Every competency is marked covered, partially covered, or a gap, so you can see where the guide is strongest and where to add your own review.
Alignment records provide a maintainable source of truth when exam frameworks, names, or objectives are updated.
Certification test standards are broad, but the exam questions are very specific. Our team of curriculum experts uses the 240 Study Guide Creation Process to ensure the most aligned, specific content for your Praxis Middle School Mathematics (5164) test — so you are not wasting time on broad subject review that may not show up on exam day.
Transparent coverage is a strength. We show where the guide is strong, where depth is partial, and where a gap has been identified so you can make an informed study decision.
6Domains
132Competencies reviewed
89%Test-aligned
103Covered
29Partially covered
0Gaps
This study guide is based on the current official exam framework. We review and update alignment whenever the official framework changes so candidates are always studying current, accurate material.
SMR I.A · Understands operations and properties of the real number system246 questions · 15 materials · 25 cards · 8 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Represents and solves word problems involving addition, subtraction, multiplication, and division of real numbers | M.Integers in Word Problems; M.Interpreting Remainders | Covered | 28 | 2 | 3 | 1 | Covered by 2 topics (28 questions, 2 materials, 3 cards, 1 videos). |
| 2. Represents and identifies the effect that an operation has on a given number (e.g., adding a negative, adding the inverse, dividing by a nonzero fraction) | M.Identities; M.Add and Subtract Negatives; M.Multiply and Divide Negatives | Covered | 25 | 3 | 4 | 0 | Covered by 3 topics (25 questions, 3 materials, 4 cards, 0 videos). |
| 3. Uses the order of operations to simplify computations and solve problems | M.Order of Operations; M.Order of Operations - Grouping | Covered | 42 | 2 | 1 | 2 | Covered by 2 topics (42 questions, 2 materials, 1 cards, 2 videos). |
| 4. Identifies and applies properties of operations on a number system (e.g., commutative, associative, distributive, identity) | M.Operational Properties | Covered | 44 | 1 | 3 | 1 | Covered by 1 topic (44 questions, 1 materials, 3 cards, 1 videos). |
| 5. Compares and orders real numbers, including absolute values of real numbers | M.Order Real Numbers by Magnitude; M.Comparing Fractions | Covered | 69 | 2 | 6 | 2 | Covered by 2 topics (69 questions, 2 materials, 6 cards, 2 videos). |
| 6. Classifies real numbers (e.g., natural, whole, integer, rational, irrational) | M.Structure of Number Systems; M.Characteristics of Rational Numbers | Covered | 19 | 2 | 12 | 1 | Covered by 2 topics (19 questions, 2 materials, 12 cards, 1 videos). |
| 7. Identifies whether the sum or product of rational and/or irrational numbers must be rational, must be irrational, or can be rational or irrational (e.g., the sum of two rational numbers must be rational, the product of two irrational numbers can be rational or irrational) | M.Operations and Rational and Irrational Numbers | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 8. Performs operations involving integer exponents | M.Scientific Notation Operations | Partially covered | 7 | 1 | 0 | 1 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 1 videos); limited supporting content. |
| 9. Approximates the value of a radical expression | M.Square Roots and Radicals | Covered | 9 | 1 | 4 | 0 | Covered by 1 topic (9 questions, 1 materials, 4 cards, 0 videos). |
| 10. Uses scientific notation to represent and compare numbers and to perform calculations | M.Scientific Notation Operations | Partially covered | 7 | 1 | 0 | 1 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 1 videos); limited supporting content. |
SMR I.B · Understands the relationships among fractions, decimals, and percent54 questions · 4 materials · 21 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Converts among fractions, decimals, and percent | M.Fraction, Decimal, Percentage Conversions | Covered | 15 | 1 | 7 | 1 | Covered by 1 topic (15 questions, 1 materials, 7 cards, 1 videos). |
| 2. Represents repeating decimals as fractions | M.Fraction, Decimal, Percentage Conversions; M.Fraction Operations - Multiply and Divide | Covered | 33 | 2 | 15 | 1 | Covered by 2 topics (33 questions, 2 materials, 15 cards, 1 videos). |
| 3. Represents fractions, decimals, and percepts with models (e.g., area models, base-10 blocks, set models, colored rods) | M.Models for Fractions and Decimals; M.Representations of Fractions in Word Problems | Covered | 21 | 2 | 8 | 1 | Covered by 2 topics (21 questions, 2 materials, 8 cards, 1 videos). |
SMR I.C · Understands how to use ratios and proportional relationships to solve problems133 questions · 7 materials · 7 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Uses the language of ratio and rate to describe relationships between two quantities | M.Ratios | Covered | 12 | 1 | 2 | 0 | Covered by 1 topic (12 questions, 1 materials, 2 cards, 0 videos). |
| 2. Identifies and represents proportional relationships and uses them to solve problems (e.g., unit rates, scale factors, constant of proportionality) | M.Proportional Reasoning - Word Problems; M.Proportional Reasoning - Scale Drawings; M.Proportions | Covered | 65 | 3 | 5 | 2 | Covered by 3 topics (65 questions, 3 materials, 5 cards, 2 videos). |
| 3. Solves percent problems (e.g., expressing a percent as a ratio per 100, discounts, markups, taxes, tips, simple interest, percent error) | M.Percent Change; M.Percent Change - Multiple; M.Ratios and Percents | Covered | 56 | 3 | 3 | 1 | Covered by 3 topics (56 questions, 3 materials, 3 cards, 1 videos). |
SMR I.D · Understands how to reason quantitatively and use units to solve problems55 questions · 4 materials · 9 cards · 2 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Chooses and interprets units consistently in formulas | M.Units in Formulas | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| 2. Chooses and interprets the scale in graphs and data displays | M.Scales in Graphs and Charts | Covered | 6 | 1 | 7 | 0 | Covered by 1 topic (6 questions, 1 materials, 7 cards, 0 videos). |
| 3. Solves problems involving dimensional analysis (e.g., feet per second to miles per hour, feet per second to kilometers per hour) | M.Converting Units - Dimensional Analysis; M.Unit Rates | Covered | 43 | 2 | 1 | 2 | Covered by 2 topics (43 questions, 2 materials, 1 cards, 2 videos). |
SMR I.E · Understands how to use basic concepts of number theory (e.g., divisibility, prime factorization, multiples) to solve problems90 questions · 5 materials · 10 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Uses the definitions of prime and composite numbers to solve problems | M.Prime and Composite Numbers; M.Justify and Prove Number Relationships | Covered | 32 | 2 | 2 | 1 | Covered by 2 topics (32 questions, 2 materials, 2 cards, 1 videos). |
| 2. Solves problems involving factors, multiples, and divisibility | M.Divisibility Rules; M.Factors; M.Prime Factorization | Covered | 58 | 3 | 8 | 2 | Covered by 3 topics (58 questions, 3 materials, 8 cards, 2 videos). |
SMR II.A · Understands how to create, evaluate, and manipulate algebraic expressions, equations, and formulas240 questions · 18 materials · 28 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Adds, subtracts, and multiplies linear and quadratic polynomials, including polynomials with rational coefficients | M.Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Linear Expression Addition and Subtraction; M.Basic Polynomials; M.Polynomials | Covered | 57 | 5 | 15 | 2 | Covered by 5 topics (57 questions, 5 materials, 15 cards, 2 videos). |
| 2. Evaluates, manipulates, and compares algebraic expressions involving rational exponents (e.g., radicals, negative exponents) | M.Properties of Exponents; M.Radicals and Exponents | Covered | 30 | 2 | 2 | 1 | Covered by 2 topics (30 questions, 2 materials, 2 cards, 1 videos). |
| 3. Uses variables to construct and solve equations and inequalities in real-world contexts | M.Linear Equation Word Problems; M.Linear Inequality Word Problems | Covered | 16 | 1 | 0 | 1 | Covered by 2 topics (16 questions, 1 materials, 0 cards, 1 videos). |
| 4. Translates verbal relationships into algebraic equations or expressions | M.Verbal to Symbolic Linear Equations | Covered | 22 | 1 | 5 | 0 | Covered by 1 topic (22 questions, 1 materials, 5 cards, 0 videos). |
| 5. Interprets parts of expressions and equations in terms of a real-world setting | M.Symbolic to Verbal; M.Verbal to Symbolic Expression - Basic | Covered | 53 | 2 | 5 | 2 | Covered by 2 topics (53 questions, 2 materials, 5 cards, 2 videos). |
| 6. Rewrites linear, quadratic, and exponential expressions in equivalent forms to reveal properties of the quantity represented by the expression | M.Advanced Equivalence of Expressions - To Simplify | Covered | 16 | 1 | 1 | 0 | Covered by 1 topic (16 questions, 1 materials, 1 cards, 0 videos). |
| 7. Determines the nature of the solutions of a quadratic equation (e.g., interprets the graph, finds the discriminant, writes the equation in factored form) | M.Quadratic Equations; M.Quadratic Equation - Solve via Graphing; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Complete the Square; M.Advanced Quadratic Equation - Real World Problems | Covered | 37 | 5 | 4 | 1 | Covered by 5 topics (37 questions, 5 materials, 4 cards, 1 videos). |
| 8. Rearranges formulas to solve for a specified variable (e.g., solve for t) | M.Rearranging Formulas | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
SMR II.B · Understands how to recognize and represent linear relationships algebraically57 questions · 5 materials · 6 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Determines the equation of a line from information presented in various forms (e.g., table, graph, description) | M.Understanding Linear Equations and Their Properties; M.Interpreting Graphs of Linear Equations | Covered | 37 | 2 | 4 | 0 | Covered by 2 topics (37 questions, 2 materials, 4 cards, 0 videos). |
| 2. Recognizes and is able to extract information about a linear equation when it is presented in various forms (e.g., slope-intercept, point-slope, standard) | M.Linear Equations - Standard Form; M.Linear Equations - Point-Slope Form | Covered | 15 | 2 | 2 | 0 | Covered by 2 topics (15 questions, 2 materials, 2 cards, 0 videos). |
| 3. Converts among various forms of linear equations (e.g., slope-intercept, point-slope, standard) | M.Linear Equations - Rearrange to Slope-Intercept Form | Partially covered | 5 | 1 | 0 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR II.C · Understands how to solve equations and inequalities76 questions · 10 materials · 16 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves one-variable linear equations and inequalities | M.Solving One-Variable Equations; M.Solving Linear Inequalities; M.Solve for x - Linear | Covered | 36 | 3 | 1 | 1 | Covered by 3 topics (36 questions, 3 materials, 1 cards, 1 videos). |
| 2. Solves one-variable nonlinear equations and inequalities (e.g., absolute value, quadratic) | M.Solve Quadratic Inequalities - Algebraically; M.Absolute Value Inequalities | Partially covered | 5 | 2 | 3 | 0 | Partial coverage by 2 topics (5 questions, 2 materials, 3 cards, 0 videos); limited supporting content. |
| 3. Represents solutions to equations and inequalities (e.g., on a number line, in the xy plane) | M.Solve Linear Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Solve Quadratic Inequalities - Graphically | Covered | 13 | 3 | 3 | 1 | Covered by 3 topics (13 questions, 3 materials, 3 cards, 1 videos). |
| 4. Justifies each step in solving equations and inequalities | M.Properties of Equality; M.Properties of Inequality | Covered | 22 | 2 | 11 | 1 | Covered by 2 topics (22 questions, 2 materials, 11 cards, 1 videos). |
SMR II.D · Understands how to solve systems of equations and inequalities56 questions · 6 materials · 5 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves a system of two linear equations or inequalities in two variables algebraically and graphically | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Inequalities | Covered | 21 | 2 | 1 | 1 | Covered by 2 topics (21 questions, 2 materials, 1 cards, 1 videos). |
| 2. Solves a system consisting of a linear equation and a quadratic equation in two variables graphically | M.Solving Mixed Systems | Covered | 15 | 1 | 1 | 0 | Covered by 1 topic (15 questions, 1 materials, 1 cards, 0 videos). |
| 3. Finds the solutions of f(x) = g(x) approximately (e.g., uses technology to graph the functions); includes cases where f(x) and/or g(x) are linear, quadratic, or exponential functions | M.Estimating Solutions to Systems | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| 4. Graphs the solution set to a system of linear inequalities in two variables in the xy-plane | M.Solving Systems of Linear Inequalities | Covered | 8 | 1 | 0 | 0 | Covered by 1 topic (8 questions, 1 materials, 0 cards, 0 videos). |
| 5. In a modeling context, represents constraints by systems of equations and/or inequalities and interprets solutions as viable or nonviable options | M.Solving Systems of Linear Equations - Word Problems; M.Solving Systems of Linear Inequalities - Word Problems | Covered | 14 | 2 | 2 | 0 | Covered by 2 topics (14 questions, 2 materials, 2 cards, 0 videos). |
SMR III.A · Understands how to identify, define, and evaluate functions48 questions · 2 materials · 6 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Determines whether a relation is a function | M.Relation and Function Representations | Covered | 39 | 1 | 4 | 0 | Covered by 1 topic (39 questions, 1 materials, 4 cards, 0 videos). |
| 2. Given a function (presented as a table of values, algebraically, or graphically), determines if the function is linear, quadratic, or exponential | M.Types of Functions | Partially covered | 0 | 0 | 0 | 0 | Partial coverage by 1 topic (0 questions, 0 materials, 0 cards, 0 videos); limited supporting content. |
| 3. Determines the value of a function for a specified value in its domain | M.Evaluating Functions | Covered | 9 | 1 | 3 | 0 | Covered by 1 topic (9 questions, 1 materials, 3 cards, 0 videos). |
SMR III.B · Knows how to determine and interpret the domain and the range of a function presented as a table of values, algebraically, or graphically10 questions · 2 materials · 5 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Determines the domain and range of a function | M.Domain and Range - Continuous | Partially covered | 4 | 1 | 5 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 5 cards, 0 videos); limited supporting content. |
| 2. Interprets domain and range in real-world settings | M.Domain and Range - Applications | Partially covered | 6 | 1 | 2 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
SMR III.C · Understands basic characteristics of linear functions (e.g., intercepts, slope)34 questions · 3 materials · 7 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Calculates the intercepts of a line and interprets them in a modeling context | M.Interpreting Slopes and Intercepts of Linear Equations | Covered | 13 | 1 | 0 | 0 | Covered by 1 topic (13 questions, 1 materials, 0 cards, 0 videos). |
| 2. Calculates the slope of a line presented as a table of values, algebraically, or graphically and interprets it in a modeling context | M.Understanding Linear Functions and Their Properties | Covered | 15 | 1 | 4 | 0 | Covered by 1 topic (15 questions, 1 materials, 4 cards, 0 videos). |
| 3. Interprets what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (l, r) where r is the unit rate | M.Directly and Inversely Proportional Relationships - Basic | Partially covered | 6 | 1 | 3 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
SMR III.D · Understands the relationships among functions, tables, and graphs74 questions · 8 materials · 14 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Determines an equation to represent a linear or quadratic function presented graphically | M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form; M.Sketch a Polynomial - From Roots | Covered | 29 | 3 | 2 | 1 | Covered by 3 topics (29 questions, 3 materials, 2 cards, 1 videos). |
| 2. Determines the type of equation that best represents a given graph | M.Parent Functions | Partially covered | 7 | 1 | 1 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| 3. Sketches a graph, given an equation of a function (e.g., square root, absolute value) | M.Absolute Value Functions; M.Exponential Functions | Covered | 14 | 2 | 4 | 0 | Covered by 2 topics (14 questions, 2 materials, 4 cards, 0 videos). |
| 4. Compares properties (e.g., intercepts, slope, maximum) of two functions presented as tables of values, algebraically, graphically, or by verbal descriptions | M.Comparing Functions | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| 5. Identifies the symbolic representation of a linear function that is created when a graph is translated horizontally or vertically or reflected across the x-axis | M.Functional Transformations - Linear and Quadratic | Covered | 14 | 1 | 6 | 0 | Covered by 1 topic (14 questions, 1 materials, 6 cards, 0 videos). |
SMR III.E · Knows how to analyze and represent functions (i.e., linear, quadratic, exponential) that model given information55 questions · 5 materials · 11 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Interprets statements that use function notation in terms of a context | M.Linear Function Word Problems | Covered | 18 | 1 | 0 | 0 | Covered by 1 topic (18 questions, 1 materials, 0 cards, 0 videos). |
| 2. Interprets the parameters in a linear or exponential function in terms of a context | M.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound Interest | Covered | 28 | 2 | 7 | 0 | Covered by 2 topics (28 questions, 2 materials, 7 cards, 0 videos). |
| 3. Calculates the rate of change of a function over a given interval and interprets it in a context | M.Rates of Change of Functions | Partially covered | 6 | 1 | 4 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| 4. Determines and interprets the x- and y-intercepts of quadratic functions | M.Advanced Quadratic Equation - Real World Problems | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 5. Develops a function—represented by a graph, equation, or table—to model a given set of conditions | M.Linear Function Word Problems | Covered | 18 | 1 | 0 | 0 | Covered by 1 topic (18 questions, 1 materials, 0 cards, 0 videos). |
| 6. Evaluates whether a particular mathematical model (e.g., graph, equation, table) can be used to describe a given set of conditions | M.Linear Function Word Problems | Covered | 18 | 1 | 0 | 0 | Covered by 1 topic (18 questions, 1 materials, 0 cards, 0 videos). |
| 7. Interprets a particular mathematical model (e.g., graph, equation, table) in a given context | M.Conjectures from Graphs | Partially covered | 0 | 0 | 0 | 0 | Partial coverage by 1 topic (0 questions, 0 materials, 0 cards, 0 videos); limited supporting content. |
SMR III.F · Understands differences between linear, quadratic, and exponential models, including how their equations are created and used to solve problems16 questions · 2 materials · 6 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identifies situations in which one quantity changes at a constant rate per unit interval relative to another | M.Rates of Change of Functions | Partially covered | 6 | 1 | 4 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| 2. Identifies situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another | M.Rates of Change of Functions | Partially covered | 6 | 1 | 4 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| 3. Observes that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratic ally | M.Comparing Functions | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
SMR III.G · Is familiar with how to represent arithmetic sequences as functions60 questions · 3 materials · 8 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Writes arithmetic sequences both recursively and with an explicit formula and uses them to model situations | M.Types of Sequences; M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Patterns - Developing a Linear Formula | Covered | 60 | 3 | 8 | 2 | Covered by 3 topics (60 questions, 3 materials, 8 cards, 2 videos). |
SMR IV.A · Knows the properties of types of lines (e.g., parallel, perpendicular, intersecting) and angles59 questions · 3 materials · 21 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves problems involving parallel, perpendicular, and intersecting lines | M.Parallel and Perpendicular Lines and Formulas | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
| 2. Applies angle relationships (e.g., supplementary, vertical, alternate interior) to solve problems | M.Points, Lines, Planes, Angles; M.Solving with Points, Lines, Planes, Angles | Covered | 40 | 2 | 18 | 2 | Covered by 2 topics (40 questions, 2 materials, 18 cards, 2 videos). |
SMR IV.B · Understands the properties of triangles40 questions · 3 materials · 13 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves problems involving the Pythagorean theorem in two dimensions | M.Pythagorean Theorem | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| 2. Identifies characteristics of special triangles (e.g., equilateral, isosceles, right) and uses them to solve problems | M.Apply Triangle Properties | Covered | 19 | 1 | 9 | 0 | Covered by 1 topic (19 questions, 1 materials, 9 cards, 0 videos). |
| 3. Determines whether given side lengths or angle measures would produce a triangle (e.g., triangle inequality theorem) and classifies triangles by their sides or angles | M.Apply Triangle Inequalities | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| 4. Determines whether given conditions would produce a unique triangle, no triangle, or more than one triangle | M.Apply Triangle Inequalities | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
SMR IV.C · Knows the properties of quadrilaterals and other polygons29 questions · 2 materials · 35 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identifies the relationships among various quadrilaterals (e.g., parallelogram, rectangle, rhombus) | M.Attributes of Polygons - Advanced | Covered | 11 | 1 | 23 | 0 | Covered by 1 topic (11 questions, 1 materials, 23 cards, 0 videos). |
| 2. Solves problems involving sides and angles of polygons | M.Angles and Measurements in Polygons | Covered | 18 | 1 | 20 | 0 | Covered by 1 topic (18 questions, 1 materials, 20 cards, 0 videos). |
SMR IV.D · Knows the concepts of transformations (i.e., translations, reflections, rotations, dilations)40 questions · 3 materials · 10 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Applies properties of translations, reflections, and rotations (e.g., line segments are taken to congruent line segments, angles are taken to congruent angles, parallel lines are taken to parallel lines) | M.Rigid Transformations | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| 2. Applies properties of dilations (e.g., angles are taken to congruent angles, parallel lines are taken to parallel lines) | M.Non-Rigid Transformations | Partially covered | 6 | 1 | 4 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| 3. Identifies a sequence of transformations that maps a preimage onto an image | M.Multiple Transformations | Covered | 18 | 1 | 2 | 0 | Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos). |
| 4. Given a figure, describes the transformations that map the figure onto itself, including reflection over a line of symmetry | M.Multiple Transformations | Covered | 18 | 1 | 2 | 0 | Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos). |
| 5. For a given transformation, determines the coordinates of a point on an image | M.Multiple Transformations | Covered | 18 | 1 | 2 | 0 | Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos). |
SMR IV.E · Understands the concepts of congruence and similarity23 questions · 2 materials · 2 cards · 1 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Determines whether two figures are congruent or similar | M.Attributes of Polygons - Similar vs Congruent | Covered | 10 | 1 | 2 | 0 | Covered by 1 topic (10 questions, 1 materials, 2 cards, 0 videos). |
| 2. Uses congruence and similarity to solve problems with two-dimensional and three-dimensional figures | M.Proportional Reasoning - 2D Shapes | Covered | 13 | 1 | 2 | 1 | Covered by 1 topic (13 questions, 1 materials, 2 cards, 1 videos). |
SMR IV.F · Understands the properties of circles18 questions · 1 materials · 3 cards · 1 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves problems involving circles (e.g., circumference, area) | M.Measurements in Circles | Covered | 18 | 1 | 3 | 1 | Covered by 1 topic (18 questions, 1 materials, 3 cards, 1 videos). |
SMR IV.G · Knows how to interpret relationships between geometric objects in the (e.g., distance, midpoint)27 questions · 2 materials · 1 cards · 1 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Uses coordinate geometry to represent and identify the properties of geometric shapes and to solve problems (e.g., Pythagorean theorem, perimeter, area) | M.Coordinate Geometry | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| 2. Determines the distance between two points | M.Slope, Midpoint, and Distance | Covered | 16 | 1 | 0 | 1 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 1 videos). |
| 3. Determines the midpoint of a segment | M.Slope, Midpoint, and Distance | Covered | 16 | 1 | 0 | 1 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 1 videos). |
SMR IV.H · Understands how to solve problems involving perimeter and area of polygons100 questions · 4 materials · 2 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Calculates and interprets perimeter and area of polygons that can be composed of triangles and quadrilaterals, including in real-world situations | M.Area and Perimeter of Polygons; M.Solving with Shapes - Quadrilaterals; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 77 | 3 | 2 | 0 | Covered by 3 topics (77 questions, 3 materials, 2 cards, 0 videos). |
| 2. Calculates changes in perimeter and area as the dimensions of a polygon change | M.Dimensional Changes Affecting Area and Volume | Covered | 23 | 1 | 0 | 0 | Covered by 1 topic (23 questions, 1 materials, 0 cards, 0 videos). |
SMR IV.I · Knows how to solve problems involving solids90 questions · 5 materials · 13 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Calculates and interprets surface area and volume of solids (e.g., prisms, pyramids, cylinders, spheres) and composite solids, including in real-world situations | M.Attributes of Three Dimensional Figures; M.Surface Area in 3D; M.Volume in 3D | Covered | 65 | 3 | 11 | 3 | Covered by 3 topics (65 questions, 3 materials, 11 cards, 3 videos). |
| 2. Calculates changes in surface area and volume as the dimensions of a solid change | M.Proportional Reasoning - 3D Figures | Covered | 8 | 1 | 2 | 0 | Covered by 1 topic (8 questions, 1 materials, 2 cards, 0 videos). |
| 3. Uses two-dimensional representations (e.g., nets) of three-dimensional objects to visualize and solve problems | M.Nets | Covered | 17 | 1 | 1 | 0 | Covered by 1 topic (17 questions, 1 materials, 1 cards, 0 videos). |
SMR IV.J · Understands systems of measurement (i.e., metric, United States customary)88 questions · 5 materials · 12 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves measurement, estimation, and conversion problems involving time, length, temperature, volume, and mass in standard measurement systems | M.Measurement Principles; M.Metric System Estimations; M.Converting Units - Proportional Reasoning; M.Calculating Elapsed Time | Covered | 72 | 4 | 10 | 2 | Covered by 4 topics (72 questions, 4 materials, 10 cards, 2 videos). |
| 2. Uses appropriate units of measurement in a given context | M.Choosing Appropriate Units | Covered | 16 | 1 | 2 | 1 | Covered by 1 topic (16 questions, 1 materials, 2 cards, 1 videos). |
SMR V.A · Understands statistical processes and how to evaluate them44 questions · 4 materials · 9 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Recognizes a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers | M.Statistical Questions | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| 2. Uses statistics to make inferences about population parameters based on a sample from that population | M.Statistical Experiments | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| 3. Distinguishes between random and biased sampling | M.Surveys; M.Sampling Methods | Covered | 22 | 2 | 7 | 0 | Covered by 2 topics (22 questions, 2 materials, 7 cards, 0 videos). |
SMR V.B · Understands how to interpret, analyze, and represent data presented in a variety of displays85 questions · 6 materials · 30 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Represents and analyzes data in various displays (e.g., bar graphs, line graphs, circle graphs, boxplots, histograms, scatterplots, stem-and-leaf plots, two-way tables) | M.Graphs and Plots | Covered | 32 | 1 | 9 | 1 | Covered by 1 topic (32 questions, 1 materials, 9 cards, 1 videos). |
| 2. Calculates relative frequencies for rows or columns in two-way tables and uses the calculations to describe possible associations between the two variables | M.Data Analysis - Frequency | Covered | 8 | 1 | 10 | 0 | Covered by 1 topic (8 questions, 1 materials, 10 cards, 0 videos). |
| 3. Uses the equation of a linear model to solve problems in the context of bivariate measurement data (e.g., interpreting the slope and intercept, interpolation) | M.Calculating Linear Regression; M.Bivariate Data Analysis | Covered | 23 | 2 | 9 | 1 | Covered by 2 topics (23 questions, 2 materials, 9 cards, 1 videos). |
| 4. Describes how two quantitative variables are related (e.g., fit a function to data, association, correlation) | M.Correlation vs Causation | Partially covered | 7 | 1 | 2 | 1 | Partial coverage by 1 topic (7 questions, 1 materials, 2 cards, 1 videos); limited supporting content. |
| 5. Chooses appropriate graphs based on data type (e.g., numerical, categorical) | M.Choosing a Graph or Plot | Covered | 15 | 1 | 9 | 1 | Covered by 1 topic (15 questions, 1 materials, 9 cards, 1 videos). |
SMR V.C · Understands concepts associated with measures of central tendency and dispersion174 questions · 9 materials · 31 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Solves for the mean and weighted average of given sets of data | M.Measures of Center and Range | Covered | 56 | 1 | 4 | 1 | Covered by 1 topic (56 questions, 1 materials, 4 cards, 1 videos). |
| 2. Determines and interprets measures of center (e.g., mean, median, mode) and spread (e.g., range, interquartile range) in a variety of problems | M.Advanced Measures of Center and Range | Covered | 19 | 1 | 9 | 0 | Covered by 1 topic (19 questions, 1 materials, 9 cards, 0 videos). |
| 3. Summarizes a given numerical data set in relation to its context | M.Statistics of One-Variable Data; M.Observations, Conclusions, and Relationships | Covered | 21 | 2 | 10 | 0 | Covered by 2 topics (21 questions, 2 materials, 10 cards, 0 videos). |
| 4. Describes the distribution of a set of data by its center and spread | M.Describing Data Patterns and Outliers; M.Data Analysis and Interpretation | Covered | 33 | 2 | 13 | 1 | Covered by 2 topics (33 questions, 2 materials, 13 cards, 1 videos). |
| 5. Uses statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets | M.Using Distributions; M.Normal Distribution | Covered | 29 | 2 | 6 | 0 | Covered by 2 topics (29 questions, 2 materials, 6 cards, 0 videos). |
| 6. Interprets differences in center and spread in the context of the data sets, accounting for possible effects of outliers | M.Effect of Change in Data on Measures of Center and Range | Covered | 16 | 1 | 3 | 0 | Covered by 1 topic (16 questions, 1 materials, 3 cards, 0 videos). |
SMR V.D · Knows how to use and evaluate probability models126 questions · 9 materials · 34 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Uses counting techniques (e.g., the counting principle, tree diagrams) to answer questions involving a finite sample space | M.Diagrams; M.Fundamental Counting Principle | Covered | 26 | 2 | 3 | 1 | Covered by 2 topics (26 questions, 2 materials, 3 cards, 1 videos). |
| 2. Solves probability problems involving simple events | M.Probability; M.Simple and Compound Events | Covered | 58 | 2 | 8 | 2 | Covered by 2 topics (58 questions, 2 materials, 8 cards, 2 videos). |
| 3. Solves probability problems involving compound events | M.Compound Probabilities (OR) | Partially covered | 4 | 1 | 2 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| 4. Interprets a probability model and uses it to find probabilities of events | M.Probability Models | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| 5. Compares probabilities from a model to observed frequencies and identifies possible sources of the discrepancy if the agreement is not good | M.Observations, Conclusions, and Relationships | Covered | 11 | 1 | 10 | 0 | Covered by 1 topic (11 questions, 1 materials, 10 cards, 0 videos). |
| 6. Interprets a uniform probability model and uses it to determine probabilities of events | M.Comparing to Probability Distribution; M.Probability Distributions | Covered | 16 | 2 | 10 | 0 | Covered by 2 topics (16 questions, 2 materials, 10 cards, 0 videos). |
SMR VI.A · Mathematical explanations, justifications, and definitions9 questions · 1 materials · 1 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identifies valid explanations of mathematical concepts (e.g., explaining why a mathematical idea is considered to be true), procedures, representations, or models | M.Justifications, Explanations, and Definitions (ToT) | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| 2. Evaluates or compares explanations and justifications for their validity, generalizability, coherence, or precision, including identifying flaws in explanations and justifications | M.Justifications, Explanations, and Definitions (ToT) | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| 3. Determines the changes that would improve the validity, generalizability, coherence, and/or precision of an explanation or justification | M.Justifications, Explanations, and Definitions (ToT) | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| 4. Evaluates whether counterarguments address a critique of a given justification | M.Justifications, Explanations, and Definitions (ToT) | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| 5. Evaluates definitions or other mathematical language for validity, generalizability, precision, usefulness in a particular context, or support of key ideas | M.Justifications, Explanations, and Definitions (ToT) | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
SMR VI.B · Mathematical problems, tasks, examples, and procedures13 questions · 1 materials · 3 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identifies problems or tasks that fit a particular structure, address the same concept, demonstrate desired characteristics, or elicit particular student thinking | M.Problems, Tasks, Examples, and Procedures (ToT) | Covered | 13 | 1 | 3 | 0 | Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos). |
| 2. Identifies two or more problems that systematically vary in difficulty or complexity | M.Problems, Tasks, Examples, and Procedures (ToT) | Covered | 13 | 1 | 3 | 0 | Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos). |
| 3. Evaluates the usefulness of examples for introducing a concept, illustrating an idea, or demonstrating a strategy, procedure, or practice | M.Problems, Tasks, Examples, and Procedures (ToT) | Covered | 13 | 1 | 3 | 0 | Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos). |
| 4. Identifies examples that support particular strategies or address particular student questions, misconceptions, or challenges with content | M.Problems, Tasks, Examples, and Procedures (ToT) | Covered | 13 | 1 | 3 | 0 | Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos). |
| 5. Identifies nonexamples or counterexamples that highlight a mathematical distinction or demonstrate why a student conjecture is incorrect or partially incorrect | M.Problems, Tasks, Examples, and Procedures (ToT) | Covered | 13 | 1 | 3 | 0 | Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos). |
| 6. Evaluates procedures for working with mathematics content to identify special cases in which the procedure might be problematic or for validity, appropriateness, or robustness | M.Problems, Tasks, Examples, and Procedures (ToT) | Covered | 13 | 1 | 3 | 0 | Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos). |
SMR VI.C · Mathematical representations, models, manipulatives, and technology11 questions · 2 materials · 9 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Evaluates representations and models (e.g., concrete, pictorial) in terms of validity, generalizability, usefulness for supporting students’ understanding, or fit to the concept, calculation, etc. to be represented | M.Representations, Models, and Technology (ToT); M.Manipulatives for Older Children | Covered | 11 | 2 | 9 | 0 | Covered by 2 topics (11 questions, 2 materials, 9 cards, 0 videos). |
| 2. Evaluates how representations and models (e.g., concrete, pictorial) have been used to show particular ideas, relationships between ideas, processes, or strategies | M.Representations, Models, and Technology (ToT) | Covered | 8 | 1 | 5 | 0 | Covered by 1 topic (8 questions, 1 materials, 5 cards, 0 videos). |
| 3. Evaluates the use of technology (e.g., graphing tools, software) for its appropriateness or its support of key ideas | M.Representations, Models, and Technology (ToT) | Covered | 8 | 1 | 5 | 0 | Covered by 1 topic (8 questions, 1 materials, 5 cards, 0 videos). |
SMR VI.D · Students' mathematical reasoning6 questions · 1 materials · 0 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identifies likely misconceptions about or partial understanding of particular mathematics content and practices | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 2. Identifies how new mathematics content and practices can build on or connect to students’ prior knowledge, including misconceptions and errors | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 3. Evaluates or compares student work (e.g., solutions, explanations, justifications, representations) in terms of validity, generalizability, coherence, and/or precision | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 4. Evaluates student work to identify the use of a particular concept, idea, or strategy | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 5. Identifies how a student’s reasoning would replicate across similar problems | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 6. Identifies different pieces of student work that demonstrate the same reasoning | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 7. Identifies situations in which student work that seems valid might mask incorrect thinking | M.Student Reasoning and Misconceptions (ToT) | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
Every 240 study guide starts with the official exam framework. From there, we organize lessons, practice, and study tools around the categories the exam uses to measure candidate knowledge.
We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.
We map every major area the exam is designed to cover so the guide reflects the real structure of the test.
We create study materials to support the official blueprint, not broad filler content.
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Reviewed by subject-matter experts and maintained to reflect current standards.
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240 is a strong option because the guide is built around the official exam framework and shows detailed alignment by SMR and competency.
This guide is 89% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.
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Partially covered means the guide addresses the core parts of a competency, but some depth or subtopics may still be limited.
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