Is 240 a good study guide for the Praxis Middle School Mathematics (5164)?

Yes. The 240 study guide is built around the official exam framework and this page shows detailed alignment domain by domain and competency by competency.

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

Q: How closely does 240 align to the Praxis Middle School Mathematics (5164) exam?

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

Q: Does 240 cover every competency?

Coverage is shown transparently across covered, partially covered, and identified gaps: 103 covered, 29 partially covered, and 0 gaps across 132 competencies.

Q: 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.

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 — so you can see where coverage is strongest, where some depth gaps remain, and how each part of the guide supports your prep.

Start Studying for Praxis 5164 See Full Alignment Details

89%

test-aligned

103

Fully covered

Partially covered

Coverage 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.

2250

Practice Questions

353

Flashcards

158

Study Materials

Videos

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

6 domains · 132 competencies reviewed · 89% test-aligned

Covered— competency is comprehensively supported by the guide

Partially covered— core content is covered, but some depth gaps remain

Coverage gap identified— a 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 system

246 Qs15 Materials25 Cards8 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 percent

54 Qs4 Materials21 Cards2 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 problems

128 Qs7 Materials7 Cards3 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	51	3	3	1	Covered by 3 topics (51 questions, 3 materials, 3 cards, 1 videos).

SMR I.D Understands how to reason quantitatively and use units to solve problems

55 Qs4 Materials9 Cards2 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 problems

90 Qs5 Materials10 Cards3 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).

ALGEBRA (DOMAIN II) Partially covered

SMR II.A Understands how to create, evaluate, and manipulate algebraic expressions, equations, and formulas

240 Qs18 Materials28 Cards7 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 algebraically

57 Qs5 Materials6 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	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 inequalities

76 Qs10 Materials16 Cards3 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 inequalities

56 Qs6 Materials5 Cards1 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).

FUNCTIONS (DOMAIN III) Partially covered

SMR III.A Understands how to identify, define, and evaluate functions

48 Qs2 Materials6 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	Notes
1. Determines whether a relation is a function	M.Relation and Function Representations	Covered	39	1	4	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	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	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 graphically

10 Qs2 Materials5 Cards0 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 Qs3 Materials7 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	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 graphs

74 Qs8 Materials14 Cards1 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 information

55 Qs5 Materials11 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	Notes
1. Interprets statements that use function notation in terms of a context	M.Linear Function Word Problems	Covered	18	1	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	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	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	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	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	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	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 problems

16 Qs2 Materials6 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos).

SMR III.G Is familiar with how to represent arithmetic sequences as functions

60 Qs3 Materials8 Cards2 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).

GEOMETRY AND MEASUREMENT (DOMAIN IV) Partially covered

SMR IV.A Knows the properties of types of lines (e.g., parallel, perpendicular, intersecting) and angles

59 Qs3 Materials21 Cards3 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 triangles

40 Qs3 Materials13 Cards1 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 polygons

29 Qs2 Materials35 Cards0 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 Qs3 Materials10 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	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	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	Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos).

SMR IV.E Understands the concepts of congruence and similarity

23 Qs2 Materials2 Cards1 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 circles

18 Qs1 Materials3 Cards1 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 Qs2 Materials1 Cards1 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 polygons

100 Qs4 Materials2 Cards0 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 solids

90 Qs5 Materials13 Cards3 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 Qs5 Materials12 Cards3 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).

STATISTICS AND PROBABILITY (DOMAIN V) Partially covered

SMR V.A Understands statistical processes and how to evaluate them

44 Qs4 Materials9 Cards0 VideosCovered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	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 displays

85 Qs6 Materials30 Cards4 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 dispersion

174 Qs9 Materials31 Cards2 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 models

126 Qs9 Materials34 Cards3 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).

TASKS OF TEACHING (DOMAIN VI) Partially covered

SMR VI.A Mathematical explanations, justifications, and definitions

9 Qs1 Materials1 Cards0 VideosCovered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	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	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	Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos).

SMR VI.B Mathematical problems, tasks, examples, and procedures

13 Qs1 Materials3 Cards0 VideosCovered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	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	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	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	Covered by 1 topic (13 questions, 1 materials, 3 cards, 0 videos).

SMR VI.C Mathematical representations, models, manipulatives, and technology

11 Qs2 Materials9 Cards0 VideosCovered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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	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	Covered by 1 topic (8 questions, 1 materials, 5 cards, 0 videos).

SMR VI.D Students' mathematical reasoning

6 Qs1 Materials0 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	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	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	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	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	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	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	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	Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content.

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