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Praxis test alignment

240's Praxis Middle School Mathematics Study Guide Is 89% Test-Aligned

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.

89%test-aligned
103Fully covered
29Partially covered
0Coverage gap

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

Praxis 5164

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.

01

Coverage by content domain

Lessons and questions are organized around the exam’s content areas so your preparation reflects the structure of the assessment.

02

Honest about depth

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.

03

Reviewed as exams change

Alignment records provide a maintainable source of truth when exam frameworks, names, or objectives are updated.

Why Test Alignment Matters for Your Praxis Middle School Mathematics Study Guide

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.

Why 240 is the best choice for the Praxis 5164 study guide

  • Built around the official exam framework
  • Organized by the competencies actually used on the exam
  • Shows exactly what is covered and where depth is partial
  • Includes aligned questions, flashcards, study materials, and videos
  • Helps candidates study what is actually tested instead of broad generic content

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.

How to Read This Alignment Review

6Domains

132Competencies reviewed

89%Test-aligned

103Covered

29Partially covered

0Gaps

  • CoveredCompetency is comprehensively supported by the guide.
  • Partially coveredCore content is covered, but some depth gaps remain.
  • Coverage gap identifiedA content gap has been identified.

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.

Numbers and Operations (Domain I)Partially covered

SMR I.A · Understands operations and properties of the real number system246 questions · 15 materials · 25 cards · 8 videosPartially covered

Official competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Represents and solves word problems involving addition, subtraction, multiplication, and division of real numbersM.Integers in Word Problems; M.Interpreting RemaindersCovered28231Covered 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 NegativesCovered25340Covered by 3 topics (25 questions, 3 materials, 4 cards, 0 videos).
3. Uses the order of operations to simplify computations and solve problemsM.Order of Operations; M.Order of Operations - GroupingCovered42212Covered 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 PropertiesCovered44131Covered by 1 topic (44 questions, 1 materials, 3 cards, 1 videos).
5. Compares and orders real numbers, including absolute values of real numbersM.Order Real Numbers by Magnitude; M.Comparing FractionsCovered69262Covered 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 NumbersCovered192121Covered 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 NumbersPartially covered3100Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content.
8. Performs operations involving integer exponentsM.Scientific Notation OperationsPartially covered7101Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 1 videos); limited supporting content.
9. Approximates the value of a radical expressionM.Square Roots and RadicalsCovered9140Covered by 1 topic (9 questions, 1 materials, 4 cards, 0 videos).
10. Uses scientific notation to represent and compare numbers and to perform calculationsM.Scientific Notation OperationsPartially covered7101Partial 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Converts among fractions, decimals, and percentM.Fraction, Decimal, Percentage ConversionsCovered15171Covered by 1 topic (15 questions, 1 materials, 7 cards, 1 videos).
2. Represents repeating decimals as fractionsM.Fraction, Decimal, Percentage Conversions; M.Fraction Operations - Multiply and DivideCovered332151Covered 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 ProblemsCovered21281Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Uses the language of ratio and rate to describe relationships between two quantitiesM.RatiosCovered12120Covered 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.ProportionsCovered65352Covered 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 PercentsCovered56331Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Chooses and interprets units consistently in formulasM.Units in FormulasPartially covered6110Partial 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 displaysM.Scales in Graphs and ChartsCovered6170Covered 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 RatesCovered43212Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Uses the definitions of prime and composite numbers to solve problemsM.Prime and Composite Numbers; M.Justify and Prove Number RelationshipsCovered32221Covered by 2 topics (32 questions, 2 materials, 2 cards, 1 videos).
2. Solves problems involving factors, multiples, and divisibilityM.Divisibility Rules; M.Factors; M.Prime FactorizationCovered58382Covered by 3 topics (58 questions, 3 materials, 8 cards, 2 videos).

Algebra (Domain II)Partially covered

SMR II.A · Understands how to create, evaluate, and manipulate algebraic expressions, equations, and formulas240 questions · 18 materials · 28 cards · 7 videosCovered

Official competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Adds, subtracts, and multiplies linear and quadratic polynomials, including polynomials with rational coefficientsM.Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Linear Expression Addition and Subtraction; M.Basic Polynomials; M.PolynomialsCovered575152Covered 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 ExponentsCovered30221Covered by 2 topics (30 questions, 2 materials, 2 cards, 1 videos).
3. Uses variables to construct and solve equations and inequalities in real-world contextsM.Linear Equation Word Problems; M.Linear Inequality Word ProblemsCovered16101Covered by 2 topics (16 questions, 1 materials, 0 cards, 1 videos).
4. Translates verbal relationships into algebraic equations or expressionsM.Verbal to Symbolic Linear EquationsCovered22150Covered by 1 topic (22 questions, 1 materials, 5 cards, 0 videos).
5. Interprets parts of expressions and equations in terms of a real-world settingM.Symbolic to Verbal; M.Verbal to Symbolic Expression - BasicCovered53252Covered 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 expressionM.Advanced Equivalence of Expressions - To SimplifyCovered16110Covered 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 ProblemsCovered37541Covered 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 FormulasCovered9100Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
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 EquationsCovered37240Covered 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 FormCovered15220Covered 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 FormPartially covered5100Partial 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves one-variable linear equations and inequalitiesM.Solving One-Variable Equations; M.Solving Linear Inequalities; M.Solve for x - LinearCovered36311Covered 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 InequalitiesPartially covered5230Partial 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 - GraphicallyCovered13331Covered by 3 topics (13 questions, 3 materials, 3 cards, 1 videos).
4. Justifies each step in solving equations and inequalitiesM.Properties of Equality; M.Properties of InequalityCovered222111Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves a system of two linear equations or inequalities in two variables algebraically and graphicallyM.Solving Systems of Linear Equations; M.Solving Systems of Linear InequalitiesCovered21211Covered 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 graphicallyM.Solving Mixed SystemsCovered15110Covered 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 functionsM.Estimating Solutions to SystemsPartially covered6110Partial 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-planeM.Solving Systems of Linear InequalitiesCovered8100Covered 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 optionsM.Solving Systems of Linear Equations - Word Problems; M.Solving Systems of Linear Inequalities - Word ProblemsCovered14220Covered by 2 topics (14 questions, 2 materials, 2 cards, 0 videos).

Functions (Domain III)Partially covered

SMR III.A · Understands how to identify, define, and evaluate functions48 questions · 2 materials · 6 cards · 0 videosPartially covered

Official competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Determines whether a relation is a functionM.Relation and Function RepresentationsCovered39140Covered 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 exponentialM.Types of FunctionsPartially covered0000Partial 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 domainM.Evaluating FunctionsCovered9130Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Determines the domain and range of a functionM.Domain and Range - ContinuousPartially covered4150Partial coverage by 1 topic (4 questions, 1 materials, 5 cards, 0 videos); limited supporting content.
2. Interprets domain and range in real-world settingsM.Domain and Range - ApplicationsPartially covered6120Partial 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Calculates the intercepts of a line and interprets them in a modeling contextM.Interpreting Slopes and Intercepts of Linear EquationsCovered13100Covered 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 contextM.Understanding Linear Functions and Their PropertiesCovered15140Covered 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 rateM.Directly and Inversely Proportional Relationships - BasicPartially covered6130Partial 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Determines an equation to represent a linear or quadratic function presented graphicallyM.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form; M.Sketch a Polynomial - From RootsCovered29321Covered by 3 topics (29 questions, 3 materials, 2 cards, 1 videos).
2. Determines the type of equation that best represents a given graphM.Parent FunctionsPartially covered7110Partial 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 FunctionsCovered14240Covered 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 descriptionsM.Comparing FunctionsCovered10130Covered 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-axisM.Functional Transformations - Linear and QuadraticCovered14160Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Interprets statements that use function notation in terms of a contextM.Linear Function Word ProblemsCovered18100Covered 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 contextM.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound InterestCovered28270Covered 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 contextM.Rates of Change of FunctionsPartially covered6140Partial 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 functionsM.Advanced Quadratic Equation - Real World ProblemsPartially covered3100Partial 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 conditionsM.Linear Function Word ProblemsCovered18100Covered 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 conditionsM.Linear Function Word ProblemsCovered18100Covered 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 contextM.Conjectures from GraphsPartially covered0000Partial 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Identifies situations in which one quantity changes at a constant rate per unit interval relative to anotherM.Rates of Change of FunctionsPartially covered6140Partial 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 anotherM.Rates of Change of FunctionsPartially covered6140Partial 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 allyM.Comparing FunctionsCovered10130Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Writes arithmetic sequences both recursively and with an explicit formula and uses them to model situationsM.Types of Sequences; M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Patterns - Developing a Linear FormulaCovered60382Covered by 3 topics (60 questions, 3 materials, 8 cards, 2 videos).

Geometry and Measurement (Domain IV)Partially covered

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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves problems involving parallel, perpendicular, and intersecting linesM.Parallel and Perpendicular Lines and FormulasCovered19131Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos).
2. Applies angle relationships (e.g., supplementary, vertical, alternate interior) to solve problemsM.Points, Lines, Planes, Angles; M.Solving with Points, Lines, Planes, AnglesCovered402182Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves problems involving the Pythagorean theorem in two dimensionsM.Pythagorean TheoremCovered15131Covered 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 problemsM.Apply Triangle PropertiesCovered19190Covered 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 anglesM.Apply Triangle InequalitiesPartially covered6110Partial 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 triangleM.Apply Triangle InequalitiesPartially covered6110Partial 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Identifies the relationships among various quadrilaterals (e.g., parallelogram, rectangle, rhombus)M.Attributes of Polygons - AdvancedCovered111230Covered by 1 topic (11 questions, 1 materials, 23 cards, 0 videos).
2. Solves problems involving sides and angles of polygonsM.Angles and Measurements in PolygonsCovered181200Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
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 TransformationsCovered16140Covered 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 TransformationsPartially covered6140Partial 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 imageM.Multiple TransformationsCovered18120Covered 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 symmetryM.Multiple TransformationsCovered18120Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos).
5. For a given transformation, determines the coordinates of a point on an imageM.Multiple TransformationsCovered18120Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Determines whether two figures are congruent or similarM.Attributes of Polygons - Similar vs CongruentCovered10120Covered 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 figuresM.Proportional Reasoning - 2D ShapesCovered13121Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves problems involving circles (e.g., circumference, area)M.Measurements in CirclesCovered18131Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
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 GeometryCovered11110Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos).
2. Determines the distance between two pointsM.Slope, Midpoint, and DistanceCovered16101Covered by 1 topic (16 questions, 1 materials, 0 cards, 1 videos).
3. Determines the midpoint of a segmentM.Slope, Midpoint, and DistanceCovered16101Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Calculates and interprets perimeter and area of polygons that can be composed of triangles and quadrilaterals, including in real-world situationsM.Area and Perimeter of Polygons; M.Solving with Shapes - Quadrilaterals; M.Area and Perimeter of Polygons - Irregular ShapesCovered77320Covered by 3 topics (77 questions, 3 materials, 2 cards, 0 videos).
2. Calculates changes in perimeter and area as the dimensions of a polygon changeM.Dimensional Changes Affecting Area and VolumeCovered23100Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Calculates and interprets surface area and volume of solids (e.g., prisms, pyramids, cylinders, spheres) and composite solids, including in real-world situationsM.Attributes of Three Dimensional Figures; M.Surface Area in 3D; M.Volume in 3DCovered653113Covered 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 changeM.Proportional Reasoning - 3D FiguresCovered8120Covered 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 problemsM.NetsCovered17110Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves measurement, estimation, and conversion problems involving time, length, temperature, volume, and mass in standard measurement systemsM.Measurement Principles; M.Metric System Estimations; M.Converting Units - Proportional Reasoning; M.Calculating Elapsed TimeCovered724102Covered by 4 topics (72 questions, 4 materials, 10 cards, 2 videos).
2. Uses appropriate units of measurement in a given contextM.Choosing Appropriate UnitsCovered16121Covered by 1 topic (16 questions, 1 materials, 2 cards, 1 videos).

Statistics and Probability (Domain V)Partially covered

SMR V.A · Understands statistical processes and how to evaluate them44 questions · 4 materials · 9 cards · 0 videosCovered

Official competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Recognizes a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answersM.Statistical QuestionsCovered11110Covered 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 populationM.Statistical ExperimentsCovered11110Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos).
3. Distinguishes between random and biased samplingM.Surveys; M.Sampling MethodsCovered22270Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
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 PlotsCovered32191Covered 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 variablesM.Data Analysis - FrequencyCovered81100Covered 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 AnalysisCovered23291Covered 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 CausationPartially covered7121Partial 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 PlotCovered15191Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Solves for the mean and weighted average of given sets of dataM.Measures of Center and RangeCovered56141Covered 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 problemsM.Advanced Measures of Center and RangeCovered19190Covered by 1 topic (19 questions, 1 materials, 9 cards, 0 videos).
3. Summarizes a given numerical data set in relation to its contextM.Statistics of One-Variable Data; M.Observations, Conclusions, and RelationshipsCovered212100Covered by 2 topics (21 questions, 2 materials, 10 cards, 0 videos).
4. Describes the distribution of a set of data by its center and spreadM.Describing Data Patterns and Outliers; M.Data Analysis and InterpretationCovered332131Covered 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 setsM.Using Distributions; M.Normal DistributionCovered29260Covered 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 outliersM.Effect of Change in Data on Measures of Center and RangeCovered16130Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Uses counting techniques (e.g., the counting principle, tree diagrams) to answer questions involving a finite sample spaceM.Diagrams; M.Fundamental Counting PrincipleCovered26231Covered by 2 topics (26 questions, 2 materials, 3 cards, 1 videos).
2. Solves probability problems involving simple eventsM.Probability; M.Simple and Compound EventsCovered58282Covered by 2 topics (58 questions, 2 materials, 8 cards, 2 videos).
3. Solves probability problems involving compound eventsM.Compound Probabilities (OR)Partially covered4120Partial 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 eventsM.Probability ModelsCovered11110Covered 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 goodM.Observations, Conclusions, and RelationshipsCovered111100Covered by 1 topic (11 questions, 1 materials, 10 cards, 0 videos).
6. Interprets a uniform probability model and uses it to determine probabilities of eventsM.Comparing to Probability Distribution; M.Probability DistributionsCovered162100Covered by 2 topics (16 questions, 2 materials, 10 cards, 0 videos).

Tasks of Teaching (Domain VI)Partially covered

SMR VI.A · Mathematical explanations, justifications, and definitions9 questions · 1 materials · 1 cards · 0 videosCovered

Official competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Identifies valid explanations of mathematical concepts (e.g., explaining why a mathematical idea is considered to be true), procedures, representations, or modelsM.Justifications, Explanations, and Definitions (ToT)Covered9110Covered 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 justificationsM.Justifications, Explanations, and Definitions (ToT)Covered9110Covered 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 justificationM.Justifications, Explanations, and Definitions (ToT)Covered9110Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos).
4. Evaluates whether counterarguments address a critique of a given justificationM.Justifications, Explanations, and Definitions (ToT)Covered9110Covered 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 ideasM.Justifications, Explanations, and Definitions (ToT)Covered9110Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Identifies problems or tasks that fit a particular structure, address the same concept, demonstrate desired characteristics, or elicit particular student thinkingM.Problems, Tasks, Examples, and Procedures (ToT)Covered13130Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos).
2. Identifies two or more problems that systematically vary in difficulty or complexityM.Problems, Tasks, Examples, and Procedures (ToT)Covered13130Covered 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 practiceM.Problems, Tasks, Examples, and Procedures (ToT)Covered13130Covered 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 contentM.Problems, Tasks, Examples, and Procedures (ToT)Covered13130Covered 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 incorrectM.Problems, Tasks, Examples, and Procedures (ToT)Covered13130Covered 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 robustnessM.Problems, Tasks, Examples, and Procedures (ToT)Covered13130Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
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 representedM.Representations, Models, and Technology (ToT); M.Manipulatives for Older ChildrenCovered11290Covered 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 strategiesM.Representations, Models, and Technology (ToT)Covered8150Covered 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 ideasM.Representations, Models, and Technology (ToT)Covered8150Covered 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 competencyMatching 240 topicsAlignmentQsMatsCardsVidsNotes
1. Identifies likely misconceptions about or partial understanding of particular mathematics content and practicesM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial 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 errorsM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial 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 precisionM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial 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 strategyM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial 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 problemsM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial 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 reasoningM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial 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 thinkingM.Student Reasoning and Misconceptions (ToT)Partially covered6100Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content.

How 240 Creates The Praxis Middle School Mathematics (5164) Study Guide

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.

1

Review the official exam framework

We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.

2

Map the tested categories

We map every major area the exam is designed to cover so the guide reflects the real structure of the test.

3

Build lessons around tested content

We create study materials to support the official blueprint, not broad filler content.

4

Cross-check practice against exam expectations

We review practice content against the framework and real exam patterns so preparation stays targeted.

5

Review and update as standards change

When official frameworks change, we review guides and update alignment as needed.

Reviewed by subject-matter experts and maintained to reflect current standards.

Why 240 Is Better Than Other Generic Study Guides

Not all study guides are built the same way. Here is what separates a test-aligned guide from a generic one — and why it matters when you are preparing for the Praxis Middle School Mathematics.

Generic prep

  • Covers broad subject areas without structure
  • No clear connection to the official exam framework
  • Practice questions may not reflect the real test format
  • May not update when official standards change
  • Can be helpful for quick, broad review

240 test-aligned Praxis 5164 prep

  • Every lesson maps to an official domain or competency
  • Built directly from the official exam framework
  • Practice questions aligned to what the exam actually measures
  • A clear study path by tested category
  • Study smarter and enter test day more prepared

FAQs About the Praxis Middle School Mathematics Study Guide

The questions teacher candidates ask us most often about the Praxis Middle School Mathematics study guide.

Is 240 a good study guide for Praxis Middle School Mathematics?

240 is a strong option because the guide is built around the official exam framework and shows detailed alignment by SMR and competency.

How closely does 240 align to the Praxis 5164 exam?

This guide is 89% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.

Does 240 cover every competency?

This page shows coverage transparently across covered, partially covered, and identified gaps so candidates can see exactly how the guide maps to the exam.

What does “partially covered” mean?

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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