Coverage by content domain
Lessons and questions are organized around the exam’s content areas so your preparation reflects the structure of the assessment.
Why Test Alignment Matters for Your ILTS Middle Grades (5–8) 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 ILTS Middle Grades (5–8) Mathematics (202) 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 ILTS 202 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
97Competencies reviewed
96%Test-aligned
89Covered
8Partially 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.
Core Content (Domain 1)Partially covered
SMR 1.0001 · Understand calculus.299 questions · 36 materials · 72 cards · 2 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of factoring techniques, solving polynomial equations, and performing operations with rational and radical expressions. | M.Square Roots and Radicals; M.Radicals and Exponents; M.Simplifying Radicals; M.Equivalence of Expressions - To Simplify; M.Operations with Radicals; M.Quadratic Expression Evaluation; M.Linear Equations - Rearrange to Slope-Intercept Form; M.Polynomials; M.Advanced Factoring Polynomials; M.Rational Functions; M.Solve for x - Radical | Covered | 90 | 11 | 24 | 2 | Covered by 11 topics (90 questions, 11 materials, 24 cards, 2 videos). |
| b. Demonstrate knowledge of different representations (e.g., tabular, algebraic, graphic) of polynomial, radical, and rational functions and circles; how to find horizontal and vertical asymptotes; and how to find points of intersection of curves. | M.Advanced Quadratic Equation - Real World Problems; M.Exponential Functions - Asymptotes; M.Sketch a Polynomial - From Roots | Covered | 22 | 3 | 2 | 0 | Covered by 3 topics (22 questions, 3 materials, 2 cards, 0 videos). |
| c. Apply the properties of limits to functions and their graphs. | M.Teaching the Concept of Limits in Sequences and Series; M.Limits and Continuity; M.One-Sided Limits; M.Limits That Do Not Exist; M.Diverge or Converge | Covered | 46 | 5 | 7 | 0 | Covered by 5 topics (46 questions, 5 materials, 7 cards, 0 videos). |
| d. Apply the concept of continuity to functions and their graphs. | M.Limits and Continuity; M.Continuity and Differentiability | Covered | 33 | 2 | 8 | 0 | Covered by 2 topics (33 questions, 2 materials, 8 cards, 0 videos). |
| e. Apply the rules of derivatives for finding tangent lines, slopes, rates of change, velocity and acceleration, marginal analysis, and increasing and decreasing functions. | M.Recursion and Iteration; M.Calculus Connections to Formulas; M.Rates of Change - Average vs Instantaneous; M.Derivatives and Slopes; M.Higher Order Derivatives and Slopes; M.Calculus - Velocity and Acceleration | Covered | 62 | 6 | 24 | 0 | Covered by 6 topics (62 questions, 6 materials, 24 cards, 0 videos). |
| f. Apply concepts of differential calculus to model real-world situations. | M.Calculus - Work; M.Calculus - Center of Mass | Partially covered | 4 | 2 | 3 | 0 | Partial coverage by 2 topics (4 questions, 2 materials, 3 cards, 0 videos); limited supporting content. |
| g. Demonstrate knowledge of the properties of exponential and logarithmic functions, graphs, and derivatives. | M.Properties of Logarithms; M.Parent Functions; M.Exponential Functions - Reflections; M.Logarithmic Functions; M.Logarithmic Functions - Change Base | Covered | 43 | 5 | 9 | 0 | Covered by 5 topics (43 questions, 5 materials, 9 cards, 0 videos). |
| h. Demonstrate knowledge of integration and basic antiderivatives and how to interpret integration as the area under a curve. | M.Integration; M.Areas by Integration; M.Distance by Integration | Covered | 23 | 3 | 7 | 0 | Covered by 3 topics (23 questions, 3 materials, 7 cards, 0 videos). |
SMR 1.0002 · Understand college statistics.175 questions · 19 materials · 77 cards · 1 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Construct, identify, or interpret frequency distributions, histograms, box plots, and cumulative frequency tables and associated graphs. | M.Appropriate vs Inappropriate Representations of Data; M.Interpolation of Data; M.Advanced Bivariate Data Analysis; M.Diagrams; M.Chi-Square Test | Covered | 44 | 5 | 20 | 0 | Covered by 5 topics (44 questions, 5 materials, 20 cards, 0 videos). |
| b. Identify, calculate, or interpret measures of central tendency (e.g., mean, median) and dispersion (e.g., interquartile range, standard deviation). | M.Advanced Measures of Center and Range; M.Describing Data Patterns and Outliers; M.Effect of Change in Data on Measures of Center and Range | Covered | 40 | 3 | 16 | 0 | Covered by 3 topics (40 questions, 3 materials, 16 cards, 0 videos). |
| c. Model and solve problems using the concept of expected value. | M.Advanced Bivariate Data Analysis; M.Chi-Square Test | Covered | 18 | 2 | 17 | 0 | Covered by 2 topics (18 questions, 2 materials, 17 cards, 0 videos). |
| d. Demonstrate knowledge of the probability distributions (e.g., normal, uniform, binomial) that random variables generate. | M.Probability Distributions; M.Using Distributions; M.Uniform Distributions; M.Describing Data Patterns and Outliers | Covered | 34 | 4 | 25 | 0 | Covered by 4 topics (34 questions, 4 materials, 25 cards, 0 videos). |
| e. Demonstrate knowledge of the sampling distribution of sample means and sample proportions. | M.Central Limit Theorem and Large Numbers; M.Fundamental Counting Principle; M.Observations, Conclusions, and Relationships; M.Sampling Methods | Covered | 35 | 4 | 17 | 1 | Covered by 4 topics (35 questions, 4 materials, 17 cards, 1 videos). |
| f. Demonstrate knowledge of confidence intervals and hypothesis testing for single population means and proportions. | M.Level of Confidence; M.Hypothesis Testing | Covered | 18 | 2 | 9 | 0 | Covered by 2 topics (18 questions, 2 materials, 9 cards, 0 videos). |
| g. Identify, calculate, or interpret correlation coefficients and regression equations. | M.Advanced Bivariate Data Analysis; M.Calculating Linear Regression; M.Linear Regression with Non-Linear Data | Covered | 21 | 3 | 16 | 0 | Covered by 3 topics (21 questions, 3 materials, 16 cards, 0 videos). |
Fractions, Ratios, and the Number System (Domain 2)Covered
SMR 2.0003 · Understand ratios and proportional relationships.285 questions · 17 materials · 58 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Represent fractions and arithmetic operations on fractions using a variety of models (e.g., number lines, area models, diagrams). | M.Fraction, Decimal, Percentage Conversions; M.Compare Places on a Number Line; M.Comparing Fractions | Covered | 72 | 3 | 12 | 2 | Covered by 3 topics (72 questions, 3 materials, 12 cards, 2 videos). |
| b. Apply properties of number operations to perform operational procedures with fractions, including the use of equivalent fractions. | M.Fraction Composition and Decomposition; M.Fraction Operations - Multiply and Divide; M.Fraction Operations - Mixed Numbers | Covered | 43 | 3 | 16 | 0 | Covered by 3 topics (43 questions, 3 materials, 16 cards, 0 videos). |
| c. Solve problems using fractions, ratios, rates, and proportional relationships. | M.Representations of Fractions in Word Problems; M.Unit Rates; M.Fraction Operations - Add and Subtract; M.Ratios, Proportions, Percents; M.Proportional Reasoning - Word Problems | Covered | 116 | 5 | 7 | 4 | Covered by 5 topics (116 questions, 5 materials, 7 cards, 4 videos). |
| d. Represent how quantities vary together in a proportional relationship, using tables, double number lines, and tape diagrams. | M.Ratios; M.Inversely Proportional vs Directly Proportional | Covered | 15 | 2 | 4 | 0 | Covered by 2 topics (15 questions, 2 materials, 4 cards, 0 videos). |
| e. Analyze the relationships between fractions, terminating decimals, and nonterminating decimals. | M.Characteristics of Rational Numbers | Covered | 17 | 1 | 8 | 0 | Covered by 1 topic (17 questions, 1 materials, 8 cards, 0 videos). |
| f. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Multimodal Teaching - Math; M.Variety of Representations; M.Integrating Digital Technology | Covered | 22 | 3 | 23 | 1 | Covered by 3 topics (22 questions, 3 materials, 23 cards, 1 videos). |
SMR 2.0004 · Understand the structure and properties of the real number system.399 questions · 25 materials · 70 cards · 14 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of the place value system to represent and perform operations on real numbers in a variety of ways (e.g., numerical expressions, diagrams, objects). | M.Place Value; M.Composition and Decomposition of Multi-Digit Numbers; M.Whole Number Operations on a Number Line; M.Order Real Numbers by Magnitude; M.Counting Techniques | Covered | 92 | 5 | 6 | 3 | Covered by 5 topics (92 questions, 5 materials, 6 cards, 3 videos). |
| b. Apply knowledge of number properties to solve problems using various representations of numbers (e.g., integers, exponents, scientific notation). | M.Exponential and Scientific Notation; M.Rational Expressions; M.Operational Properties; M.Identities; M.Order of Operations; M.Order of Operations - Grouping; M.Inverse Operations; M.Connecting Situations with Operations | Covered | 135 | 8 | 13 | 4 | Covered by 8 topics (135 questions, 8 materials, 13 cards, 4 videos). |
| c. Analyze and justify a variety of algorithms and computational strategies, including mental math approaches and techniques. | M.Rounding; M.Mental Math and Estimation; M.Operational Algorithm Relationships; M.Operation and Algorithm Connections | Covered | 39 | 4 | 21 | 1 | Covered by 4 topics (39 questions, 4 materials, 21 cards, 1 videos). |
| d. Apply knowledge of prime numbers, factors, and divisibility to model and solve problems. | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization; M.Divisibility Rules; M.Models for Multiplication and Division | Covered | 86 | 5 | 13 | 4 | Covered by 5 topics (86 questions, 5 materials, 13 cards, 4 videos). |
| e. Apply knowledge of greatest common factors and least common multiples to model number theory concepts and solve mathematical and real-world problems. | M.Factors; M.Euclidean Algorithm | Covered | 49 | 2 | 7 | 1 | Covered by 2 topics (49 questions, 2 materials, 7 cards, 1 videos). |
| f. Apply knowledge of the structure of the real number system, integer and rational exponents, irrational numbers, and radicals to model and solve problems. | M.Structure of Number Systems | Covered | 11 | 1 | 5 | 1 | Covered by 1 topic (11 questions, 1 materials, 5 cards, 1 videos). |
| g. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Types of Assessment - Math | Covered | 20 | 1 | 13 | 1 | Covered by 1 topic (20 questions, 1 materials, 13 cards, 1 videos). |
Relations, Functions, and Algebra (Domain 3)Partially covered
SMR 3.0005 · Understand expressions and equations.128 questions · 8 materials · 19 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Identify one- and two-variable equations and inequalities that represent a variety of situations or representations. | M.Forms of Equations; M.Dependent and Independent Variables; M.Symbolic to Verbal | Covered | 25 | 3 | 12 | 3 | Covered by 3 topics (25 questions, 3 materials, 12 cards, 3 videos). |
| b. Identify equivalent forms of mathematical expressions or equations that result from application of a variety of algebraic techniques (e.g., simplifying, factoring, solving for a different variable). | M.Advanced Equivalence of Expressions - To Simplify; M.Properties of Equality | Covered | 32 | 2 | 5 | 1 | Covered by 2 topics (32 questions, 2 materials, 5 cards, 1 videos). |
| c. Justify algebraic techniques using the properties of the real numbers. | M.Properties of Equality; M.Understanding Linear Equations and Their Properties | Covered | 41 | 2 | 6 | 1 | Covered by 2 topics (41 questions, 2 materials, 6 cards, 1 videos). |
| d. Evaluate the validity of proposed solutions to inequalities, equations, or systems of equations. | M.Evaluate Student Solutions | Covered | 40 | 1 | 0 | 1 | Covered by 1 topic (40 questions, 1 materials, 0 cards, 1 videos). |
| e. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Authentic Assessment | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
SMR 3.0006 · Understand relations and functions.169 questions · 12 materials · 30 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Distinguish between relations and functions using a variety of representations. | M.Relation and Function Representations | Covered | 39 | 1 | 4 | 0 | Covered by 1 topic (39 questions, 1 materials, 4 cards, 0 videos). |
| b. Analyze various representations (e.g., tabular, algebraic, graphic) of functions with respect to their characteristics (e.g., domain, intercepts, maxima and minima). | M.Domain and Range - Discrete; M.Domain and Range - Continuous; M.Advanced Domain and Range of Functions | Covered | 13 | 3 | 10 | 0 | Covered by 3 topics (13 questions, 3 materials, 10 cards, 0 videos). |
| c. Translate between representations of graphs, tables, and real-world situations or equations. | M.Absolute Value Functions | Partially covered | 2 | 1 | 1 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| d. Identify the effects of transformations such as f(x + k), f(x) + k, and k(f(x)) on the graph of a function. | M.Functional Transformations - Linear and Quadratic; M.Functional Transformations - Absolute Value | Covered | 33 | 2 | 6 | 0 | Covered by 2 topics (33 questions, 2 materials, 6 cards, 0 videos). |
| e. Identify patterns of change in proportional, linear, inversely proportional, quadratic, and exponential functions and the types of real-world relationships that these functions can model. | M.Linear Equation Word Problems - More Slope; M.Exponential Functions - Real World Problems - Compound Interest | Covered | 15 | 2 | 4 | 0 | Covered by 2 topics (15 questions, 2 materials, 4 cards, 0 videos). |
| f. Identify expressions, equations, or functions that model specific situations. | M.Verbal to Symbolic Linear Equations; M.Linear Equation Word Problems - More Slope; M.Verbal to Symbolic Expression - Basic | Covered | 69 | 3 | 5 | 1 | Covered by 3 topics (69 questions, 3 materials, 5 cards, 1 videos). |
| g. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Basics of Graphing Calculators | Partially covered | 2 | 1 | 0 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR 3.0007 · Understand linear functions and relations.157 questions · 19 materials · 26 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the relationship between the equation of a line and its graph in mathematical and real-world contexts. | M.Parallel and Perpendicular Lines and Formulas; M.Line of Best Fit; M.Linear Equations - Point-Slope Form | Covered | 37 | 3 | 5 | 1 | Covered by 3 topics (37 questions, 3 materials, 5 cards, 1 videos). |
| b. Determine the equation of a line using different types of information (e.g., two points, slope and one point). | M.Linear Equations - Standard Form; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph | Covered | 11 | 3 | 2 | 0 | Covered by 3 topics (11 questions, 3 materials, 2 cards, 0 videos). |
| c. Identify the connection between proportional and linear relationships. | M.Constants of Proportionality; M.Solve Quadratic Inequalities - Algebraically; M.Solving Systems of Quadratic Inequalities | Covered | 10 | 3 | 2 | 0 | Covered by 3 topics (10 questions, 3 materials, 2 cards, 0 videos). |
| d. Model and solve problems using different representations of linear equations and inequalities, and systems of linear equations and inequalities. | M.Linear Equation Word Problems; M.Solve for x - Linear; M.Solving Systems of Linear Equations; M.Interpreting Inequalities; M.Solve Linear Inequalities - Graphically; M.Solving Linear Inequalities; M.Compound Inequalities on Number Line; M.Solving Systems of Linear Inequalities | Covered | 94 | 8 | 10 | 6 | Covered by 8 topics (94 questions, 8 materials, 10 cards, 6 videos). |
| e. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Variety of Representations for Older Children; M.Basics of Graphing Calculators | Covered | 5 | 2 | 9 | 0 | Covered by 2 topics (5 questions, 2 materials, 9 cards, 0 videos). |
SMR 3.0008 · Understand nonlinear functions.104 questions · 11 materials · 20 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Distinguish between linear and nonlinear relationships in a variety of situations (e.g., tables, real world). | 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. |
| b. Translate between different representations (e.g., tabular, algebraic, graphic) of quadratic and exponential functions. | M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form | Covered | 19 | 2 | 2 | 1 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 1 videos). |
| c. Model and solve problems involving quadratic equations and inequalities using a variety of techniques (e.g., completing the square, factoring, graphing, quadratic formula). | M.Solving Systems of Quadratic Equations; M.Quadratic Equations; M.Quadratic Equation - Solve via Graphing; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Complete the Square; M.Quadratic Equation - Solve via Quadratic Formula | Covered | 49 | 6 | 7 | 1 | Covered by 6 topics (49 questions, 6 materials, 7 cards, 1 videos). |
| d. Model and solve problems involving exponential equations. | M.Exponential Functions; M.Exponential Functions - Real World Problems | Covered | 29 | 2 | 5 | 0 | Covered by 2 topics (29 questions, 2 materials, 5 cards, 0 videos). |
| e. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Fair Assessment | Covered | 7 | 1 | 6 | 1 | Covered by 1 topic (7 questions, 1 materials, 6 cards, 1 videos). |
Measurement and Geometry (Domain 4)Covered
SMR 4.0009 · Understand the principles of two- and three-dimensional geometry.422 questions · 26 materials · 78 cards · 14 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of quantities and units to convert measurements within and between various measurement systems. | M.Measurement Principles; M.Advanced Measurement Principles; M.Metric System; M.Choosing Appropriate Units; M.Converting Units - Proportional Reasoning; M.Converting Units - Dimensional Analysis | Covered | 104 | 6 | 21 | 4 | Covered by 6 topics (104 questions, 6 materials, 21 cards, 4 videos). |
| b. Apply formulas to find measures (e.g., angle, area, volume) of a variety of two- and three-dimensional figures in mathematical and real-world problems. | M.Measurement Tools; M.Area and Perimeter of Polygons; M.Measurements in Circles; M.Surface Area in 3D; M.Volume in 3D; M.Dimensional Changes Affecting Area and Volume; M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 179 | 8 | 18 | 5 | Covered by 8 topics (179 questions, 8 materials, 18 cards, 5 videos). |
| c. Apply the Pythagorean theorem and its converse to solve mathematical and real-world problems. | M.Pythagorean Theorem | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| d. Use the properties of lines (e.g., parallel, perpendicular) and angles (e.g., supplementary, vertical) to characterize geometric relationships and solve problems. | M.Angles in Triangles | Covered | 12 | 1 | 0 | 1 | Covered by 1 topic (12 questions, 1 materials, 0 cards, 1 videos). |
| e. Apply the principles of congruence, similarity, and proportional and spatial reasoning (e.g., scale drawings) to solve mathematical and real-world problems. | M.Spatial Reasoning; M.Proportional Reasoning - 2D Shapes; M.Advanced Similar Shapes; M.Proportional Reasoning - Scale Drawings; M.Apply Triangle Properties; M.Measurements Inside Triangles; M.Proportional Reasoning - 3D Figures | Covered | 85 | 7 | 30 | 2 | Covered by 7 topics (85 questions, 7 materials, 30 cards, 2 videos). |
| f. Analyze proofs of geometric theorems. | M.Derivation of Geometric Equations; M.Proofs | Covered | 12 | 2 | 3 | 0 | Covered by 2 topics (12 questions, 2 materials, 3 cards, 0 videos). |
| g. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
SMR 4.0010 · Understand the principles of coordinate and transformational geometries.201 questions · 15 materials · 65 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply connections between geometric and algebraic properties (e.g., distance formula, midpoint formula, slope) to model and solve mathematical and real-world problems. | M.Coordinate Geometry; M.Slope, Midpoint, and Distance | Covered | 27 | 2 | 1 | 1 | Covered by 2 topics (27 questions, 2 materials, 1 cards, 1 videos). |
| b. Use two- and three-dimensional coordinate systems to represent and analyze the characteristics of various geometric figures. | M.The Coordinate Plane; M.Points, Lines, Planes, Angles; M.Solving with Points, Lines, Planes, Angles; M.Direction and Structure | Covered | 73 | 4 | 22 | 3 | Covered by 4 topics (73 questions, 4 materials, 22 cards, 3 videos). |
| c. Analyze geometric transformations (e.g., translations, reflections, dilations, rotations) in a coordinate plane and their effects on congruence and similarity. | M.Non-Rigid Transformations; M.Rigid Transformations | Covered | 27 | 2 | 8 | 0 | Covered by 2 topics (27 questions, 2 materials, 8 cards, 0 videos). |
| d. Apply the properties of polygons (e.g., numbers and lengths of sides, measures of angles) to analyze and solve problems. | M.Attributes of Three Dimensional Figures; M.Pyramids and Prisms; M.Types of Prisms; M.Combine and Dissect 2D Figures; M.Solving with Shapes - Quadrilaterals; M.Attributes of Polygons - Advanced | Covered | 58 | 6 | 33 | 3 | Covered by 6 topics (58 questions, 6 materials, 33 cards, 3 videos). |
| e. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Manipulatives for Young Children | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
Probability and Statistics (Domain 5)Partially covered
SMR 5.0011 · Understand the principles and techniques of probability.136 questions · 10 materials · 21 cards · 7 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply methods of counting, including the difference between combinations and permutations, to represent and solve problems. | M.Combinations and Permutations | Covered | 20 | 1 | 2 | 0 | Covered by 1 topic (20 questions, 1 materials, 2 cards, 0 videos). |
| b. Identify theoretical or experimental probabilities of simple, compound, independent, and conditional events using a variety of approaches (e.g., addition and multiplication rules). | M.Probability; M.Simple and Compound Events | Covered | 58 | 2 | 8 | 2 | Covered by 2 topics (58 questions, 2 materials, 8 cards, 2 videos). |
| c. Apply the concept of sample space and its role in determining probabilities. | M.Probability Models; M.Sample Spaces to Determine Probabilities | Covered | 15 | 2 | 2 | 1 | Covered by 2 topics (15 questions, 2 materials, 2 cards, 1 videos). |
| d. Use and interpret a variety of representations of probabilities (e.g., Venn diagrams, tree diagrams). | M.Geometric Probability | Partially covered | 3 | 1 | 1 | 1 | Partial coverage by 1 topic (3 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
| e. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Learning Progressions in Math; M.Planning for Group Experiences; M.Diversity and Engagement - ELL; M.Spreadsheet Fields | Covered | 40 | 4 | 8 | 3 | Covered by 4 topics (40 questions, 4 materials, 8 cards, 3 videos). |
SMR 5.0012 · Understand the principles and techniques of statistics.241 questions · 15 materials · 49 cards · 6 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply random sampling techniques to collect representative data. | M.Surveys; M.Probability Simulations; M.Statistical Questions; M.Statistical Experiments | Covered | 39 | 4 | 8 | 0 | Covered by 4 topics (39 questions, 4 materials, 8 cards, 0 videos). |
| b. Select appropriate data displays for a given situation (e.g., table, scatter plot). | M.Graphs and Plots; M.Expressing Probabilities; M.Choosing Graphs and Plots | Covered | 50 | 3 | 12 | 2 | Covered by 3 topics (50 questions, 3 materials, 12 cards, 2 videos). |
| c. Interpret data in a variety of graphic formats (e.g., circle graphs, box plots, histograms). | M.Boxplots; M.Data Analysis and Interpretation | Covered | 39 | 2 | 9 | 1 | Covered by 2 topics (39 questions, 2 materials, 9 cards, 1 videos). |
| d. Analyze patterns in bivariate data and two-way frequency tables. | M.Bivariate Data Analysis; M.Statistics of One-Variable Data | Covered | 27 | 2 | 7 | 1 | Covered by 2 topics (27 questions, 2 materials, 7 cards, 1 videos). |
| e. Apply knowledge of measures of central tendency (e.g., mean, median), dispersion (e.g., interquartile range, standard deviation), and shapes of data distributions. | M.Normal Distribution; M.Measures of Center and Range | Covered | 72 | 2 | 6 | 1 | Covered by 2 topics (72 questions, 2 materials, 6 cards, 1 videos). |
| f. Select or analyze instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and allow students to develop understanding of mathematical practices, concepts, and skills. | M.Backward Design; M.Multimodal Teaching - Math | Covered | 14 | 2 | 8 | 1 | Covered by 2 topics (14 questions, 2 materials, 8 cards, 1 videos). |
Disciplinary Literacy in Mathematics (Domain 6)Partially covered
SMR 6.0013 · Apply knowledge of foundations of research-based disciplinary literacy instruction and assessment.66 questions · 7 materials · 18 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of appropriate research to identify and implement instructional practices and strategies that are effective in supporting the disciplinary literacy development of all students. | M.Major Math Instructional Theories | Covered | 5 | 1 | 5 | 1 | Covered by 1 topic (5 questions, 1 materials, 5 cards, 1 videos). |
| b. Apply knowledge of the developmental sequence of language and literacy skills for adolescent learners, and analyze the role of systematic and explicit instruction in the development of disciplinary literacy skills. | M.Major Math Instructional Theories; M.Learning Progressions in Math | Covered | 24 | 2 | 8 | 2 | Covered by 2 topics (24 questions, 2 materials, 8 cards, 2 videos). |
| c. Analyze the nature and communicative role of various features of language (e.g., semantics, syntax, discourse) in disciplinary literacy development. | M.Teaching Mathematical Reasoning | Partially covered | 7 | 1 | 1 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| d. Apply knowledge of the use of a wide range of high-quality informational texts to support the development of disciplinary literacy (e.g., selecting appropriate, high interest, and culturally responsive texts; using a variety of media). | ELA.Measures of Text Complexity - Three-Part Model (Cross-Curricular) | Partially covered | 4 | 1 | 3 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| e. Apply knowledge of the use of assessment to monitor students' development of disciplinary literacy (e.g., using continuous monitoring of student progress to plan and evaluate disciplinary literacy instruction, providing feedback to students on their work to help them understand their own progress and how to improve performance, engaging students in self-assessment of their development in disciplinary literacy). | M.Using Assessment to Adjust Instruction; M.Sense Making and Perseverance | Covered | 19 | 2 | 3 | 1 | Covered by 2 topics (19 questions, 2 materials, 3 cards, 1 videos). |
| f. Analyze strategies and routines that contribute to the development of a supportive language and literacy environment in the mathematics classroom (e.g., promoting self-direction that leads to independence and ownership, building collaborative classroom communities). | M.Planning for Group Experiences | Covered | 12 | 1 | 3 | 1 | Covered by 1 topic (12 questions, 1 materials, 3 cards, 1 videos). |
SMR 6.0014 · Apply knowledge of academic-language and vocabulary development to support students' disciplinary literacy development in the mathematics classroom.17 questions · 2 materials · 13 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the role of language structures, mathematical symbols, and vocabulary in supporting students' understanding of mathematical concepts, content, skills, and processes. | ELA.Cross-Curricular Applications - Academic Vocabulary (Math) | Covered | 6 | 1 | 12 | 0 | Covered by 1 topic (6 questions, 1 materials, 12 cards, 0 videos). |
| b. Apply knowledge of criteria for selecting vocabulary for explicit word study in the mathematics classroom (e.g., words central to a unit of study and/or the meaning of a text and likely to be unfamiliar to students). | ELA.Cross-Curricular Applications - Academic Vocabulary (Math); M.Teaching Mathematical Vocabulary | Covered | 17 | 2 | 13 | 0 | Covered by 2 topics (17 questions, 2 materials, 13 cards, 0 videos). |
| c. Apply knowledge of a wide variety of strategies for developing and expanding students' depth of understanding and retention of new mathematics vocabulary. | ELA.Cross-Curricular Applications - Academic Vocabulary (Math) | Covered | 6 | 1 | 12 | 0 | Covered by 1 topic (6 questions, 1 materials, 12 cards, 0 videos). |
| d. Apply knowledge of strategies for promoting students' understanding of and ability to use various forms (e.g., sentence structures, text structures) and functions (e.g., interpreting, classifying, justifying) of language to develop and express content understanding in the mathematics classroom. | ELA.Cross-Curricular Applications - Academic Vocabulary (Math) | Covered | 6 | 1 | 12 | 0 | Covered by 1 topic (6 questions, 1 materials, 12 cards, 0 videos). |
| e. Apply knowledge of strategies for promoting students' ability to analyze, interpret, and use conventions of Standard American English grammar and usage to support their listening comprehension, speaking, reading comprehension, and writing in the mathematics classroom. | ELA.Cross-Curricular Applications - Academic Vocabulary (Math) | Covered | 6 | 1 | 12 | 0 | Covered by 1 topic (6 questions, 1 materials, 12 cards, 0 videos). |
| f. Apply knowledge of differentiated instruction and appropriate assessment strategies in mathematical language and vocabulary development that are responsive to the diverse strengths and needs of all students. | ELA.Cross-Curricular Applications - Academic Vocabulary (Math) | Covered | 6 | 1 | 12 | 0 | Covered by 1 topic (6 questions, 1 materials, 12 cards, 0 videos). |
SMR 6.0015 · Apply knowledge of reading comprehension to support students' disciplinary literacy development in the mathematics classroom.46 questions · 5 materials · 16 cards · 0 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of the organizational structures, rhetorical features, text features, and graphics commonly used in texts in the mathematics classroom, including the characteristics of various forms of informational texts and the role, perspective, and purpose of various texts. | ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 8 | 1 | 15 | 0 | Covered by 1 topic (8 questions, 1 materials, 15 cards, 0 videos). |
| b. Analyze text features that may impede students' reading comprehension (e.g., use of vocabulary, complexity of sentences, use of data). | ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 8 | 1 | 15 | 0 | Covered by 1 topic (8 questions, 1 materials, 15 cards, 0 videos). |
| c. Apply fundamental principles for instruction to enable students to understand and learn from challenging text, using various reading strategies to improve comprehension (e.g., visualizing, questioning, synthesizing, evaluating) and providing explicit instruction in note-taking and text annotation. | ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 8 | 1 | 15 | 0 | Covered by 1 topic (8 questions, 1 materials, 15 cards, 0 videos). |
| d. Apply knowledge of strategies for promoting students' ability to trace and evaluate the argument and specific claims in texts and to distinguish claims that are supported by reasons and evidence from claims that are not supported. | M.Conclusions from Premises; M.Reasonableness of Results; M.Prioritizing Relevant and Missing Information; ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 41 | 4 | 16 | 0 | Covered by 4 topics (41 questions, 4 materials, 16 cards, 0 videos). |
| e. Apply knowledge of strategies for promoting students' ability to interpret graphic features of texts (e.g., tables, charts, illustrations, captions, headings) and determine their relationship to the text (e.g., how well information in a graphic feature aligns with informational text). | M.Alternate Representations of Problems; ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 13 | 2 | 15 | 0 | Covered by 2 topics (13 questions, 2 materials, 15 cards, 0 videos). |
| f. Apply knowledge of strategies for promoting students' ability to analyze texts (e.g., chronological, sequential, cause/effect, compare/contrast) and recognize features of text common to mathematics. | ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 8 | 1 | 15 | 0 | Covered by 1 topic (8 questions, 1 materials, 15 cards, 0 videos). |
| g. Apply knowledge of differentiated instruction and appropriate assessment strategies in reading comprehension that are responsive to the diverse strengths and needs of all students. | ELA.Cross-Curricular Applications - Reading Comprehension (Math) | Covered | 8 | 1 | 15 | 0 | Covered by 1 topic (8 questions, 1 materials, 15 cards, 0 videos). |
SMR 6.0016 · Apply knowledge of the development of writing, listening, and speaking skills to support students' disciplinary literacy development in the mathematics classroom.45 questions · 7 materials · 15 cards · 1 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply fundamental principles for instruction in writing, listening, and speaking in the mathematics classroom, including providing instructional support and opportunities for students to write, listen, and speak routinely for authentic purposes; providing feedback on written work and oral presentations to guide students' revisions; engaging students in writing and oral language activities to develop their understanding of mathematics concepts and skills (e.g., participating in collaborative writing and discussions about mathematics, asking mathematics and text-based questions, reporting on a topic, recounting experiences related to mathematics learning); and engaging students in using technology to produce and publish mathematics writing and to interact and collaborate with others about mathematics. | M.Teaching Mathematical Reasoning for Older Children; ELA.Cross-Curricular Applications - Writing (Math); ELA.Cross-Curricular Applications - Listening and Speaking (Math) | Covered | 13 | 3 | 8 | 0 | Covered by 3 topics (13 questions, 3 materials, 8 cards, 0 videos). |
| b. Apply knowledge of strategies for promoting students' ability to present ideas and information effectively in the mathematics classroom and to produce coherent and clear writing and oral presentations that reflect organization, development, substance (e.g., relevant facts and details), transitional devices, style, and use of technology (e.g., presentation software, media and visual displays) appropriate to the task, purpose, and audience. | ELA.Cross-Curricular Applications - Writing (Math); ELA.Cross-Curricular Applications - Listening and Speaking (Math) | Covered | 9 | 2 | 8 | 0 | Covered by 2 topics (9 questions, 2 materials, 8 cards, 0 videos). |
| c. Apply knowledge of strategies for promoting students' ability to develop arguments and claims that are supported by valid reasoning and sufficient, relevant evidence; and knowledge of narrative texts that use description and organize a sequence of events. | M.Formal vs Informal Reasoning; M.Inductive vs Deductive Reasoning; M.Evaluating Truth of Statements; ELA.Cross-Curricular Applications - Writing (Math); ELA.Cross-Curricular Applications - Listening and Speaking (Math) | Covered | 25 | 5 | 15 | 1 | Covered by 5 topics (25 questions, 5 materials, 15 cards, 1 videos). |
| d. Apply knowledge of strategies for promoting students' ability to conduct mathematics research projects, including selecting and developing topics; gathering information from a variety of sources; assessing the credibility and accuracy of sources; synthesizing information; and avoiding plagiarism through the use of appropriate paraphrasing and summarizing and by quoting or citing sources following a standard format for citations. | M.Modeling and Evaluating Real-World Situations; ELA.Cross-Curricular Applications - Writing (Math); ELA.Cross-Curricular Applications - Listening and Speaking (Math) | Covered | 25 | 3 | 8 | 0 | Covered by 3 topics (25 questions, 3 materials, 8 cards, 0 videos). |
| e. Apply knowledge of differentiated instruction and appropriate assessment strategies in writing, listening, and speaking that are responsive to the diverse strengths and needs of all students. | ELA.Cross-Curricular Applications - Writing (Math); ELA.Cross-Curricular Applications - Listening and Speaking (Math) | Covered | 9 | 2 | 8 | 0 | Covered by 2 topics (9 questions, 2 materials, 8 cards, 0 videos). |
How 240 Creates The ILTS Middle Grades (5–8) Mathematics (202) 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.
Review the official exam framework
We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.
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.
Build lessons around tested content
We create study materials to support the official blueprint, not broad filler content.
Cross-check practice against exam expectations
We review practice content against the framework and real exam patterns so preparation stays targeted.
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 ILTS Middle Grades (5–8) 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 ILTS 202 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 ILTS Middle Grades (5–8) Mathematics Study Guide
The questions teacher candidates ask us most often about the ILTS Middle Grades (5–8) Mathematics study guide.
Is 240 a good study guide for ILTS Middle Grades (5–8) 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 ILTS 202 exam?
This guide is 96% 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.