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 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 Mathematics (208) 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 208 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
116Competencies reviewed
94%Test-aligned
103Covered
12Partially covered
1Gaps
- 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.
Mathematical Practices, Technology, and Disciplinary Literacy (Domain I)Partially covered
SMR I.0001 · Understand mathematical practices.197 questions · 20 materials · 15 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply a variety of strategies (e.g., drawing diagrams, working backward, identifying mathematical structures, recognizing patterns). | M.Selecting Appropriate Solution Strategies; M.Selecting Appropriate Solution Strategies - Look for a Pattern; M.Comparing Fractions | Covered | 59 | 3 | 4 | 1 | Covered by 3 topics (59 questions, 3 materials, 4 cards, 1 videos). |
| b. Generalize the processes used to solve problems and extend them to other problem situations. | M.Prioritizing Relevant and Missing Information; M.Abstract and Quantitative Reasoning; M.Teaching Mathematical Reasoning | Covered | 26 | 3 | 3 | 0 | Covered by 3 topics (26 questions, 3 materials, 3 cards, 0 videos). |
| c. Select appropriate models to analyze and understand situations to improve decision making. | M.Sense Making and Perseverance; M.Using Structure to Analyze Complex Problems; M.Modeling and Evaluating Real-World Situations | Covered | 25 | 3 | 0 | 0 | Covered by 3 topics (25 questions, 3 materials, 0 cards, 0 videos). |
| d. Justify applications of concepts, procedures, and theorems in a given situation. | M.Formal Conclusions from Premises; M.Teaching Mathematical Reasoning for Older Children | Covered | 14 | 2 | 0 | 0 | Covered by 2 topics (14 questions, 2 materials, 0 cards, 0 videos). |
| e. Develop conjectures and evaluate their validity, and critique the reasoning of others. | M.Inductive vs Deductive Reasoning; M.Reasonableness of Results; M.Advanced Abstract and Quantitative Reasoning; M.Indirect Proofs; M.Evaluating Truth of Statements | Covered | 45 | 5 | 8 | 0 | Covered by 5 topics (45 questions, 5 materials, 8 cards, 0 videos). |
| f. Demonstrate knowledge of how to communicate mathematical knowledge using precise mathematical vocabulary, visual representations, and symbols. | M.Alternate Representations of Problems; M.Teaching Mathematical Vocabulary | Covered | 16 | 2 | 1 | 0 | Covered by 2 topics (16 questions, 2 materials, 1 cards, 0 videos). |
| g. Identify and apply connections between mathematical domains (e.g., the distance formula in coordinate geometry and the Pythagorean Theorem, geometric interpretation of the integral, applications of matrices to geometric figures). | M.Mathematical Connections | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| h. Demonstrate knowledge of mathematical connections to other disciplines (e.g., rate of change as applied to business, economics, physics, chemistry, and biology; geometry as applied to carpentry and construction). | M.Interdisciplinary Connections | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR I.0002 · Understand how to select, integrate, and use appropriate technologies in the mathematics classroom.69 questions · 14 materials · 26 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate understanding of the capabilities and benefits of current technologies in the content area of mathematics. | M.Technology and Trigonometric Function Problems | Partially covered | 2 | 1 | 0 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| b. Select appropriate technology (e.g., spreadsheet, graphing calculator, manipulatives) to analyze concepts and solve problems throughout the mathematics curriculum. | M.Manipulatives for Older Children; M.Using Calculators to Check Math; M.Technology and Calculus Problems; M.Spreadsheet Fields | Covered | 10 | 4 | 5 | 0 | Covered by 4 topics (10 questions, 4 materials, 5 cards, 0 videos). |
| c. Demonstrate understanding of how to integrate appropriate technology in mathematics instruction and assessment. | M.Basics of Graphing Calculators; M.Models for Addition and Subtraction; M.Models for Multiplication and Division | Covered | 21 | 3 | 5 | 2 | Covered by 3 topics (21 questions, 3 materials, 5 cards, 2 videos). |
| d. Develop and apply algorithms to analyze concepts and solve problems using technology. | M.Inventive Strategies vs Standard Algorithms; M.Euclidean Algorithm; M.Operational Algorithm Relationships; M.Operation and Algorithm Connections | Covered | 25 | 4 | 14 | 0 | Covered by 4 topics (25 questions, 4 materials, 14 cards, 0 videos). |
| e. Use appropriate technology to individualize and differentiate mathematics instruction and assessment. | M.Diversity and Engagement; M.Diversity and Engagement - ELL | Covered | 11 | 2 | 2 | 2 | Covered by 2 topics (11 questions, 2 materials, 2 cards, 2 videos). |
SMR I.0003 · Understand the process of reading, and apply knowledge of strategies for promoting students' reading development in the mathematics classroom.32 questions · 4 materials · 5 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of the reading process (e.g., the construction of meaning through interactions between a reader's prior knowledge, information in the text, and the purpose of the reading situation), and apply knowledge of strategies for integrating language arts into mathematics instruction to support students' reading and concept development (e.g., providing purposeful opportunities for students to read, write about, and discuss content in order to improve their understanding). | M.Interdisciplinary Connections | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| b. Apply knowledge of strategies that foster reading in the mathematics classroom (e.g., incorporating literature for adolescents in the curriculum; encouraging students' independent reading, research, and inquiry related to mathematics). | M.Stimulating Higher Order Thinking | Covered | 14 | 1 | 2 | 0 | Covered by 1 topic (14 questions, 1 materials, 2 cards, 0 videos). |
| c. Demonstrate knowledge of vocabulary's role in supporting students' reading comprehension and concept development, and apply strategies for promoting students' mathematics vocabulary development (e.g., recognizing structural and/or meaning-based relationships between words, using context clues, distinguishing denotative and connotative meanings of words, interpreting idioms and figurative language, consulting specialized reference materials). | M.Interdisciplinary Connections | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| d. Apply knowledge of strategies for preparing students to read text effectively and for teaching and modeling the use of comprehension strategies before, during, and after reading, including strategies that promote close reading (e.g., breaking down complex sentences, monitoring for comprehension to correct confusions and misunderstandings that arise during reading). | M.Conclusions from Premises | Partially covered | 6 | 1 | 0 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| e. Apply knowledge of strategies for developing students' ability to comprehend and critically analyze discipline-specific texts, including recognizing organizational patterns unique to informational texts; using graphic organizers to analyze and recall information from texts; analyzing and summarizing an author's argument, claims, evidence, and point of view; and synthesizing multiple sources of information presented in different media or formats. | M.Interdisciplinary Connections | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| f. Apply knowledge of strategies for evaluating, selecting, modifying, and designing reading materials appropriate to academic tasks and students' reading abilities (e.g., analyzing instructional materials in terms of readability, content, length, format, illustrations). | M.Backward Design | Covered | 9 | 1 | 3 | 1 | Covered by 1 topic (9 questions, 1 materials, 3 cards, 1 videos). |
| g. Apply knowledge of strategies for providing continuous monitoring of students' reading progress through observations, work samples, and various informal assessments and for differentiating mathematics instruction to address students' assessed reading needs. | M.Interdisciplinary Connections | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
Number Systems and Operations (Domain II)Covered
SMR II.0004 · Understand the real number system and its operations.627 questions · 44 materials · 78 cards · 23 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of the structure and properties of the real number system. | M.Structure of Number Systems; M.Characteristics of Rational Numbers; M.Imaginary and Complex Numbers; M.Fraction Composition and Decomposition; M.Place Value; M.Operations and Rational and Irrational Numbers; M.Divisibility Rules; M.Operational Properties; M.Identities | Covered | 142 | 9 | 25 | 4 | Covered by 9 topics (142 questions, 9 materials, 25 cards, 4 videos). |
| b. Solve problems involving prime and composite numbers, least common multiples, greatest common factors, and modular arithmetic. | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization; M.Congruence Classes and Modular Arithmetic; M.Justify and Prove Number Relationships; M.Interpreting Remainders; M.Rounding | Covered | 109 | 7 | 17 | 5 | Covered by 7 topics (109 questions, 7 materials, 17 cards, 5 videos). |
| c. Solve problems involving integers, fractions, decimals, percents, powers, and rational exponents. | M.Fraction, Decimal, Percentage Conversions; M.Representations of Fractions in Word Problems; M.Exponential and Scientific Notation; M.Properties of Exponents; M.Properties of Exponents - Applying Multiple Properties; M.Radicals and Exponents; M.Simplifying Radicals; M.Whole Number Operations on a Number Line; M.Inverse Operations; M.Order of Operations; M.Order of Operations - Grouping; M.Fraction Operations - Multiply and Divide; M.Fraction Operations - Mixed Numbers; M.Fraction Operations - Add and Subtract; M.Operations with Radicals | Covered | 202 | 15 | 29 | 7 | Covered by 15 topics (202 questions, 15 materials, 29 cards, 7 videos). |
| d. Apply ratios and proportional reasoning to represent and solve problems. | M.Ratios; M.Unit Rates; M.Direct and Indirect Variation; M.Inversely Proportional vs Directly Proportional; M.Constants of Proportionality; M.Graphs of Proportional Relationships; M.Ratios, Proportions, Percents; M.Proportional Reasoning - Word Problems; M.Percent Change - Multiple; M.Proportional Reasoning - Scale Drawings | Covered | 136 | 10 | 10 | 4 | Covered by 10 topics (136 questions, 10 materials, 10 cards, 4 videos). |
| e. Apply knowledge of dimensional analysis to model and solve problems using appropriate units. | M.Converting Units - Dimensional Analysis with Area; M.Converting Units - Dimensional Analysis with Volume | Covered | 23 | 2 | 0 | 2 | Covered by 2 topics (23 questions, 2 materials, 0 cards, 2 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
SMR II.0005 · Understand the properties of complex numbers and linear algebra.167 questions · 25 materials · 50 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Perform arithmetic operations with complex numbers and their conjugates. | M.Operations with Complex Numbers; M.Operations with Complex Numbers - Division; M.Complex Numbers and Their Conjugates; M.Complex Numbers - Inverses; M.Polynomial Identities - Complex Numbers; M.Complex Numbers - Distance; M.Polar Coordinates - DM Theorem; M.Complex Numbers - Modulus | Covered | 59 | 8 | 17 | 1 | Covered by 8 topics (59 questions, 8 materials, 17 cards, 1 videos). |
| b. Represent complex numbers and their operations in rectangular and polar forms on the complex plane. | M.Complex Numbers and the Complex Plane; M.Different Representations of Complex Numbers | Covered | 13 | 2 | 6 | 0 | Covered by 2 topics (13 questions, 2 materials, 6 cards, 0 videos). |
| c. Apply knowledge of the fundamental theorem of algebra to solve quadratic equations with real coefficients that have complex solutions. | M.Quadratic Equations; M.Quadratic Equations with Complex Roots | Covered | 23 | 2 | 5 | 1 | Covered by 2 topics (23 questions, 2 materials, 5 cards, 1 videos). |
| d. Apply basic properties of vectors and vector arithmetic to model and solve problems. | M.Vectors and Scalars; M.Solving with Vector Representations; M.Vector Multiplication - Cross Product; M.Vector Multiplication - Dot Product; M.Vector Multiplication by a Scalar; M.Vector Addition and Subtraction | Covered | 31 | 6 | 13 | 0 | Covered by 6 topics (31 questions, 6 materials, 13 cards, 0 videos). |
| e. Apply basic properties of matrices and matrix arithmetic to model and solve problems (e.g., solve a system of two linear equations). | M.Matrices and Addition Subtraction; M.Matrices and Multiplication; M.Matrices - Determinant and Inverse; M.Matrices to Solve Systems of Equations; M.Properties of Matrices; M.Advanced Matrices | Covered | 26 | 6 | 8 | 0 | Covered by 6 topics (26 questions, 6 materials, 8 cards, 0 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
Functions and Algebra (Domain III)Partially covered
SMR III.0006 · Understand algebraic techniques.373 questions · 32 materials · 60 cards · 13 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Translate between word situations and algebraic sentences. | M.Symbolic to Verbal; M.Verbal to Symbolic Expression - Basic; M.Verbal to Symbolic Expression - Advanced; M.Verbal to Symbolic Linear Equations | Covered | 81 | 4 | 8 | 3 | Covered by 4 topics (81 questions, 4 materials, 8 cards, 3 videos). |
| b. Identify algebraic expressions or equations that represent mathematical situations (e.g., symbolically, numerically, graphically). | M.Linear Equation Word Problems | Covered | 15 | 1 | 0 | 1 | Covered by 1 topic (15 questions, 1 materials, 0 cards, 1 videos). |
| c. Identify, complete, and extend patterns, sequences, and series and analyze their properties and algebraic representations. | M.Types of Sequences; M.Patterns - Developing an Expression; M.Patterns - Developing a Linear Formula; M.Sequences - Find overlap; M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Mathematical Induction for Creating Formulas; M.Fibonacci Sequences; M.Concepts of Series and Sequence; M.Taylor Polynomial Generation; M.Diverge or Converge; M.Series Convergence Interval; M.Find Sum of Series; M.Find Partial Sum of Series | Covered | 116 | 13 | 25 | 3 | Covered by 13 topics (116 questions, 13 materials, 25 cards, 3 videos). |
| d. Apply properties of real numbers in algebraic contexts to manipulate and simplify algebraic expressions and solve equations. | M.Properties of Equality; M.Equivalence of Expressions - To Simplify; M.Advanced Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Linear Expression Evaluation; M.Quadratic Expression Evaluation; M.Linear Expression Addition and Subtraction; M.Rearranging Formulas; M.Solve for x - Linear; M.Solve for x - Nonlinear; M.Solve for x - Linear with Pictograph | Covered | 123 | 11 | 15 | 4 | Covered by 11 topics (123 questions, 11 materials, 15 cards, 4 videos). |
| e. Justify algebraic techniques using properties of the real number system. | M.Formal Reasoning Rules | Partially covered | 3 | 1 | 1 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and application. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR III.0007 · Understand functions and the properties of linear relations and functions.307 questions · 33 materials · 58 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply function notation and analyze the properties of relations and functions, including the domain and range of linear, polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric functions. | M.Domain and Range - Discrete; M.Domain and Range - Continuous; M.Advanced Domain and Range of Functions; M.Advanced Domain and Range of Functions - Piecewise; M.Advanced Domain and Range of Functions - Logarithmic; M.Advanced Domain and Range of Functions - Composition; M.Domain and Range - Set Notation; M.Relation and Function Representations | Covered | 55 | 8 | 15 | 0 | Covered by 8 topics (55 questions, 8 materials, 15 cards, 0 videos). |
| b. Build new functions from existing functions (e.g., transformations, inverses, compositions). | M.Function Composition and Inversion; M.Determine the Validity of an Inverse; M.Parent Functions; M.Functional Transformations - Linear and Quadratic; M.Functional Transformations - Absolute Value; M.Functional Transformations - Radical; M.Functional Transformations - Exponential | Covered | 84 | 7 | 13 | 0 | Covered by 7 topics (84 questions, 7 materials, 13 cards, 0 videos). |
| c. Represent linear relations and functions in symbolic, numeric, graphic, and verbal forms. | M.Understanding Linear Functions and Their Properties; M.Linear Equation Word Problems; M.Linear Equation Word Problems - More Slope | Covered | 34 | 3 | 4 | 1 | Covered by 3 topics (34 questions, 3 materials, 4 cards, 1 videos). |
| d. Recognize and apply slopes and intercepts to construct, analyze, interpret, and graph linear equations and inequalities. | M.Line of Best Fit; M.Linear Equations - Rearrange to Slope-Intercept Form; M.Linear Equations - Standard Form; M.Linear Equations - Point-Slope Form; M.Interpreting Inequalities; M.Compound Inequalities on Number Line; M.Solving Linear Inequalities; M.Solving Compound Linear Inequalities; M.Solve Linear Inequalities - Graphically | Covered | 65 | 9 | 12 | 3 | Covered by 9 topics (65 questions, 9 materials, 12 cards, 3 videos). |
| e. Apply linear relations, functions, and systems to model and solve problems. | M.Linear Equation Word Problems; M.Linear Equation Word Problems - More Slope | Covered | 19 | 2 | 0 | 1 | Covered by 2 topics (19 questions, 2 materials, 0 cards, 1 videos). |
| f. Represent and solve systems of linear equations and inequalities both graphically and algebraically (e.g., compare and contrast different solution methods). | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Equations - Scalar Note; M.Solving Systems of Linear Equations - Word Problems; M.Solving Systems of Linear Inequalities | Covered | 34 | 4 | 3 | 1 | Covered by 4 topics (34 questions, 4 materials, 3 cards, 1 videos). |
| g. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR III.0008 · Understand quadratic functions and conic sections.137 questions · 19 materials · 27 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Represent quadratic functions and relations in symbolic, numeric, graphic, and verbal forms. | M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Complete the Square; M.Quadratic Equation - Solve via Quadratic Formula; M.Quadratic Equations - Forms | Covered | 29 | 4 | 6 | 0 | Covered by 4 topics (29 questions, 4 materials, 6 cards, 0 videos). |
| b. Recognize and apply properties of symmetry, roots, intercepts, and vertices to construct, analyze, and interpret quadratic relations and their graphs. | M.Quadratic Equation - Solve via Graphing; M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form | Covered | 20 | 3 | 2 | 1 | Covered by 3 topics (20 questions, 3 materials, 2 cards, 1 videos). |
| c. Solve quadratic equations and inequalities and systems of equations and inequalities both graphically and algebraically. | M.Solving Systems of Quadratic Equations; M.Solving Mixed Systems; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Solving Systems of Quadratic Inequalities | Covered | 29 | 6 | 3 | 0 | Covered by 6 topics (29 questions, 6 materials, 3 cards, 0 videos). |
| d. Apply quadratic relations, functions, and systems to model and find appropriate solution(s) to problems. | M.Advanced Quadratic Equation - Real World Problems | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| e. Recognize and apply the properties of hyperbolas, parabolas, circles, and ellipses to model and solve problems. | M.Conic Sections; M.Conic Sections - Derive Parabola; M.Conic Sections - Derive Ellipses and Hyperbolas | Covered | 21 | 3 | 4 | 0 | Covered by 3 topics (21 questions, 3 materials, 4 cards, 0 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR III.0009 · Understand polynomial, absolute value, radical, and rational functions and inequalities.141 questions · 21 materials · 44 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Represent polynomial, absolute value, radical, and rational functions and relations in symbolic, numeric, graphic, and verbal forms. | M.Rational Expressions; M.Square Roots and Radicals; M.Polynomials; M.Absolute Value Functions | Covered | 34 | 4 | 12 | 0 | Covered by 4 topics (34 questions, 4 materials, 12 cards, 0 videos). |
| b. Recognize and apply symmetry, roots, intercepts, critical points, asymptotes, and vertices to construct, analyze, and interpret polynomial, absolute value, radical, and rational functions and inequalities and their graphs. | M.Absolute Value Inequalities; M.Polynomials; M.Piecewise Functions; M.Solving Piecewise Functions; M.Sketch a Polynomial - From Roots | Covered | 31 | 5 | 9 | 0 | Covered by 5 topics (31 questions, 5 materials, 9 cards, 0 videos). |
| c. Recognize and apply the properties of polynomial, absolute value, radical, and rational functions and equations to solve problems. | M.Remainder Theorem; M.Solve for x - Radical | Covered | 16 | 2 | 1 | 0 | Covered by 2 topics (16 questions, 2 materials, 1 cards, 0 videos). |
| d. Solve polynomial, absolute value, radical, and rational equations and inequalities and systems of equations and inequalities graphically, algebraically, and numerically. | M.Rational Functions; M.Recursion and Iteration; M.Recursion vs Closed - Form | Covered | 10 | 3 | 7 | 0 | Covered by 3 topics (10 questions, 3 materials, 7 cards, 0 videos). |
| e. Apply polynomial, absolute value, radical, and rational relations, functions, and systems to model and solve problems. | M.Binomial Expansion; M.Extraneous Solutions; M.Absolute Value Functions; M.Solve for x - Radical | Covered | 17 | 4 | 6 | 0 | Covered by 4 topics (17 questions, 4 materials, 6 cards, 0 videos). |
| f. Recognize and apply the algebraic properties of polynomial and rational functions (e.g., factoring, partial fractions). | M.Advanced Factoring Polynomials; M.Factor Theorem; M.Rational Root Theorem; M.Conjugate Root Theorem | Covered | 22 | 4 | 6 | 0 | Covered by 4 topics (22 questions, 4 materials, 6 cards, 0 videos). |
| g. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR III.0010 · Understand exponential and logarithmic functions.104 questions · 11 materials · 24 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Recognize the relationship between exponential and logarithmic functions. | M.Logarithmic Functions | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
| b. Represent exponential and logarithmic functions in symbolic, numeric, graphic, and verbal forms. | M.Exponential Functions; M.Logarithmic Functions | Covered | 20 | 2 | 6 | 0 | Covered by 2 topics (20 questions, 2 materials, 6 cards, 0 videos). |
| c. Recognize and apply properties of symmetry, roots, intercepts, critical points, and asymptotes to construct, analyze, and interpret exponential and logarithmic functions and inequalities and their graphs. | M.Exponential Functions - Asymptotes; M.Exponential Functions - Reflections; M.Logarithmic Functions - Graph | Covered | 11 | 3 | 2 | 0 | Covered by 3 topics (11 questions, 3 materials, 2 cards, 0 videos). |
| d. Apply the equations of exponential and logarithmic functions and systems to make predictions and model and solve problems (e.g., compound interest, exponential growth and decay, logistics). | M.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound Interest; M.Exponential Functions - Real World Problems - Annuities | Covered | 32 | 3 | 8 | 0 | Covered by 3 topics (32 questions, 3 materials, 8 cards, 0 videos). |
| e. Solve exponential and logarithmic equations and inequalities and systems of equations and inequalities both graphically and algebraically. | M.Exponential Functions; M.Exponential Functions - Real World Problems; M.Logarithmic Functions - Change Base | Covered | 35 | 3 | 5 | 0 | Covered by 3 topics (35 questions, 3 materials, 5 cards, 0 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR III.0011 · Understand trigonometric functions.134 questions · 13 materials · 18 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply trigonometric functions to solve problems involving the unit circle. | M.The Unit Circle; M.Trigonometric Ratios | Covered | 21 | 2 | 0 | 1 | Covered by 2 topics (21 questions, 2 materials, 0 cards, 1 videos). |
| b. Analyze relationships between trigonometric functions and their graphs. | M.Trigonometric Ratio Graphs; M.Trigonometric Ratio Graphs - Real Word Problems | Covered | 26 | 2 | 3 | 0 | Covered by 2 topics (26 questions, 2 materials, 3 cards, 0 videos). |
| c. Use trigonometric functions to model periodic phenomena. | M.Trigonometric Ratio Graphs - Real Word Problems; M.Analyze and Solve Trigonometric Functions | Covered | 18 | 2 | 0 | 0 | Covered by 2 topics (18 questions, 2 materials, 0 cards, 0 videos). |
| d. Manipulate trigonometric expressions and solve equations. | M.Laws of Sines and Cosines; M.Inverse Trigonometric Ratios | Covered | 19 | 2 | 2 | 0 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 0 videos). |
| e. Identify or verify trigonometric identities using algebraic techniques. | M.Advanced Trigonometric Identities - Special Triangles; M.Advanced Trigonometric Identities - Quotient and Reciprocal; M.Advanced Trigonometric Identities - Pythagorean Identities; M.Advanced Trigonometric Identities - More | Covered | 22 | 4 | 0 | 0 | Covered by 4 topics (22 questions, 4 materials, 0 cards, 0 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
Differential and Integral Calculus (Domain IV)Covered
SMR IV.0012 · Understand principles of differential calculus.209 questions · 24 materials · 60 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply the concept of a limit to analyze properties of functions (e.g., continuity, asymptotes) and series. | M.Teaching the Concept of Limits in Sequences and Series; M.Limits and Continuity; M.Limits and Continuity - Asymptote Equations; M.One-Sided Limits; M.Limits That Do Not Exist; M.Advanced Limits with Trig; M.Intermediate Value Theorem; M.Operation Rules for Limits | Covered | 62 | 8 | 13 | 0 | Covered by 8 topics (62 questions, 8 materials, 13 cards, 0 videos). |
| b. Demonstrate conceptual knowledge of the derivative and its role in the historical development of calculus. | M.Calculus Connections to Formulas; M.Rates of Change - Average vs Instantaneous; M.Derivatives and Slopes; M.Derivatives by Newton's Method; M.Continuity and Differentiability; M.Calculus - Velocity and Acceleration | Covered | 51 | 6 | 14 | 0 | Covered by 6 topics (51 questions, 6 materials, 14 cards, 0 videos). |
| c. Find the derivative of a function and interpret its meaning. | M.Derivatives and Slopes; M.Mean Value Theorem; M.Derivatives and Trig Functions; M.Derivatives and Exponential Functions; M.Derivatives and Logarithmic Functions | Covered | 29 | 5 | 10 | 0 | Covered by 5 topics (29 questions, 5 materials, 10 cards, 0 videos). |
| d. Apply differentiation to analyze the graph of a function (e.g., maxima, concavity). | M.Higher Order Derivatives and Slopes | Covered | 20 | 1 | 13 | 0 | Covered by 1 topic (20 questions, 1 materials, 13 cards, 0 videos). |
| e. Apply principles of differential calculus to model and solve problems (e.g., rates of change, optimization, analyzing functions, related rates). | M.Differential Equations; M.Calculus - Rates; M.Differential Equations - Word Problems | Covered | 27 | 3 | 5 | 0 | Covered by 3 topics (27 questions, 3 materials, 5 cards, 0 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR IV.0013 · Understand principles of integral calculus.117 questions · 16 materials · 35 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate conceptual knowledge of the integral. | M.Riemann Sums; M.Approximating Area; M.Riemann Sum - Integral Calculations | Covered | 14 | 3 | 4 | 0 | Covered by 3 topics (14 questions, 3 materials, 4 cards, 0 videos). |
| b. Calculate the integrals of functions. | M.Integration; M.Integration by Parts; M.Integrating Exponentials; M.Integrating Trigonometric Functions; M.Integrals Yielding Logarithms | Covered | 31 | 5 | 8 | 0 | Covered by 5 topics (31 questions, 5 materials, 8 cards, 0 videos). |
| c. Apply the fundamental theorem of calculus to model and solve problems. | M.Foundational Theorems of Calculus | Covered | 8 | 1 | 5 | 0 | Covered by 1 topic (8 questions, 1 materials, 5 cards, 0 videos). |
| d. Apply principles of integral calculus to solve problems (e.g., finding areas and volumes, describing the motion of an object). | M.Accumulations; M.Areas by Integration; M.Volumes by Integration; M.Distance by Integration; M.Calculus - Work | Covered | 29 | 5 | 7 | 0 | Covered by 5 topics (29 questions, 5 materials, 7 cards, 0 videos). |
| e. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
Measurement and Geometry (Domain V)Partially covered
SMR V.0014 · Understand principles and applications of measurement.321 questions · 16 materials · 54 cards · 8 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Convert measurements within various systems of measurement (e.g., English, metric). | M.Metric System; M.Metric System Estimations; M.Converting Units - Proportional Reasoning; M.Converting Units - Dimensional Analysis | Covered | 85 | 4 | 6 | 3 | Covered by 4 topics (85 questions, 4 materials, 6 cards, 3 videos). |
| b. Solve problems involving time, temperature, degree and radian measures of angles, weight, and mass. | M.Choosing Appropriate Units; M.Calculating Elapsed Time; M.Angles and Measurements in Polygons | Covered | 58 | 3 | 22 | 2 | Covered by 3 topics (58 questions, 3 materials, 22 cards, 2 videos). |
| c. Use nonlinear measuring scales (e.g., Richter, decibel, pH) to solve practical problems. | M.Logarithmic Phenomena | Partially covered | 4 | 1 | 2 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| d. Explain how changing one measure of a multidimensional object may affect other measures. | M.Dimensional Changes Affecting Area and Volume | Covered | 23 | 1 | 0 | 0 | Covered by 1 topic (23 questions, 1 materials, 0 cards, 0 videos). |
| e. Apply measurement formulas (e.g., length, area, volume) to regular and irregular shapes, regions, and solids. | M.Area and Perimeter of Polygons; M.Area and Perimeter of Polygons - Irregular Shapes; M.Volume in 3D; M.Convert Between Surface Area and Volume | Covered | 105 | 4 | 3 | 1 | Covered by 4 topics (105 questions, 4 materials, 3 cards, 1 videos). |
| f. Solve problems involving indirect measurement (e.g., trigonometric ratios, proportional reasoning). | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
| g. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction; M.Measurement Principles | Covered | 46 | 3 | 22 | 2 | Covered by 3 topics (46 questions, 3 materials, 22 cards, 2 videos). |
SMR V.0015 · Understand Euclidean geometry.418 questions · 41 materials · 121 cards · 12 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate understanding of points, lines, angles, planes, and space and their geometric applications. | M.Attributes of Three Dimensional Figures; M.Points, Lines, Planes, Angles; M.Solving with Points, Lines, Planes, Angles | Covered | 54 | 3 | 24 | 3 | Covered by 3 topics (54 questions, 3 materials, 24 cards, 3 videos). |
| b. Apply definitions, axioms, principles, and theorems of Euclidean geometry to develop or analyze different types of proofs (e.g., direct, indirect, flow, paragraph). | M.Derivation of Geometric Equations; M.Derivation of Geometric Equations - Triangle Formulas; M.Generating Formulas for Shapes; M.Proofs; M.Prove Theorems - Lines and Angles; M.Prove Theorems - Parallelograms; M.Prove Properties - Quadrilateral Inscribed in a Circle; M.Prove Theorems - Similar Shapes; M.Prove Slope Criteria | Covered | 55 | 9 | 24 | 0 | Covered by 9 topics (55 questions, 9 materials, 24 cards, 0 videos). |
| c. Solve problems in Euclidean geometry (e.g., justify geometric constructions). | M.Pythagorean Theorem; M.Geometric Constructions; M.Advanced Geometric Constructions - Angles; M.Advanced Geometric Constructions - Lines; M.Advanced Geometric Constructions - Triangles; M.Advanced Geometric Constructions - Shapes; M.Advanced Geometric Constructions - Tangent Line; M.Combine and Dissect 2D Figures | Covered | 73 | 8 | 5 | 1 | Covered by 8 topics (73 questions, 8 materials, 5 cards, 1 videos). |
| d. Apply properties of circles and other two- and three-dimensional figures to solve mathematical and real-world problems. | M.Angles in Triangles; M.Measurements in Circles; M.Measurements in Circles Advanced; M.Solving with Shapes - Quadrilaterals; M.Nets; M.Types of Prisms; M.Surface Area in 3D; M.Coordinate Geometry | Covered | 114 | 8 | 22 | 4 | Covered by 8 topics (114 questions, 8 materials, 22 cards, 4 videos). |
| e. Apply concepts of similarity and congruence to analyze the properties and compare the measures (e.g., perimeter, area, volume) of two- and three-dimensional figures. | M.Attributes of Polygons - Irregular Shapes; M.Attributes of Polygons - Symmetry; M.Attributes of Polygons - Lines of Symmetry; M.Attributes of Polygons - Similar vs Congruent; M.Proportional Reasoning - 2D Shapes; M.Apply Triangle Properties; M.Apply Triangle Inequalities; M.Measurements Inside Triangles; M.Attributes of Polygons - Advanced | Covered | 74 | 9 | 46 | 1 | Covered by 9 topics (74 questions, 9 materials, 46 cards, 1 videos). |
| f. Translate between two- and three-dimensional representations of geometric figures (e.g., cross sections, nets, projections, perspective drawings). | M.Nets; M.Pyramids and Prisms; M.Rotating 3D Objects | Covered | 30 | 3 | 8 | 1 | Covered by 3 topics (30 questions, 3 materials, 8 cards, 1 videos). |
| g. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
SMR V.0016 · Understand coordinate and transformational geometry.169 questions · 13 materials · 43 cards · 5 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Use coordinate geometry methods (e.g., distance formula, slope) to prove theorems and analyze geometric figures. | M.The Coordinate Plane; M.Slope, Midpoint, and Distance | Covered | 34 | 2 | 4 | 2 | Covered by 2 topics (34 questions, 2 materials, 4 cards, 2 videos). |
| b. Use the slope criteria for parallel and perpendicular lines to find the equations of lines and solve geometric problems. | M.Parallel and Perpendicular Lines and Formulas | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
| c. Demonstrate knowledge of congruence, similarity (including scale and size changes), and symmetry from the perspective of any geometric transformation. | M.Advanced Similar Shapes; M.Prove Theorems - Triangles; M.Non-Rigid Transformations; M.Rigid Transformations | Covered | 41 | 4 | 19 | 0 | Covered by 4 topics (41 questions, 4 materials, 19 cards, 0 videos). |
| d. Analyze transformations (i.e., reflections, rotations, translations, dilations) in the coordinate plane. | M.Tessellations; M.Non-Rigid Transformations; M.Multiple Transformations; M.Rigid Transformations | Covered | 44 | 4 | 11 | 0 | Covered by 4 topics (44 questions, 4 materials, 11 cards, 0 videos). |
| e. Use two- and three-dimensional coordinate systems to represent and analyze geometric figures. | M.Solving with Matrix Transformations; M.Polar Coordinates | Covered | 18 | 2 | 1 | 0 | Covered by 2 topics (18 questions, 2 materials, 1 cards, 0 videos). |
| f. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
Statistics, Probability, and Discrete Mathematics (Domain VI)Partially covered
SMR VI.0017 · Understand the process of collecting, organizing, and representing data.407 questions · 32 materials · 104 cards · 9 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of appropriate sampling techniques that collect representative data and avoid bias. | M.Surveys; M.Linear Data Transformations; M.Sampling Methods; M.Statistical Questions | Covered | 35 | 4 | 9 | 0 | Covered by 4 topics (35 questions, 4 materials, 9 cards, 0 videos). |
| b. Calculate and interpret measures of central tendency (e.g., mean, median, mode) and variation (e.g., range, standard deviation) to characterize a given set of data. | M.Normal Distribution; M.Uniform Distributions; M.Measures of Center and Range; M.Statistics of One-Variable Data; M.Advanced Measures of Center and Range | Covered | 106 | 5 | 15 | 1 | Covered by 5 topics (106 questions, 5 materials, 15 cards, 1 videos). |
| c. Select and justify an appropriate measure of central tendency from given data. | M.Choosing Measures of Center; M.Describing Data Patterns and Outliers; M.Effect of Change in Data on Measures of Center and Range | Covered | 29 | 3 | 13 | 1 | Covered by 3 topics (29 questions, 3 materials, 13 cards, 1 videos). |
| d. Select appropriate representations and interpretations of data using a variety of graphs (e.g., bar graphs, scatterplots, box plots, stem-and-leaf diagrams, histograms). | M.Graphs and Plots; M.Boxplots; M.Choosing a Graph or Plot; M.Data Analysis and Interpretation; M.Appropriate vs Inappropriate Representations of Data; M.Interpolation of Data; M.Bivariate Data Analysis | Covered | 113 | 7 | 25 | 4 | Covered by 7 topics (113 questions, 7 materials, 25 cards, 4 videos). |
| e. Estimate population percentages in normal distributions, given the mean and standard deviation. | M.Normal Distribution; M.Using Distributions | Covered | 29 | 2 | 6 | 0 | Covered by 2 topics (29 questions, 2 materials, 6 cards, 0 videos). |
| f. Analyze data presented in a two-way frequency table or scatterplot (e.g., draw conclusions, interpret a correlation coefficient, identify a line of best fit). | M.Bivariate Data Analysis; M.Advanced Bivariate Data Analysis; M.Calculating Linear Regression; M.Linear Regression with Non-Linear Data | Covered | 38 | 4 | 19 | 1 | Covered by 4 topics (38 questions, 4 materials, 19 cards, 1 videos). |
| g. Evaluate inferences and claims based on sample data. | M.Central Limit Theorem and Large Numbers; M.Observations, Conclusions, and Relationships; M.Correlation vs Causation; M.Level of Confidence; M.Chi-Square Test; M.Hypothesis Testing | Covered | 44 | 6 | 27 | 1 | Covered by 6 topics (44 questions, 6 materials, 27 cards, 1 videos). |
| h. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction; M.Statistical Experiments | Covered | 46 | 3 | 14 | 2 | Covered by 3 topics (46 questions, 3 materials, 14 cards, 2 videos). |
SMR VI.0018 · Understand probability and discrete mathematics.205 questions · 22 materials · 49 cards · 7 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of basic set theory (e.g., unions, intersections) and logic (e.g., if/then, if and only if). | M.Diagrams - Venn Symbols | Partially covered | 0 | 1 | 2 | 0 | Partial coverage by 1 topic (0 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| b. Apply various counting strategies (e.g., combinations, permutations) to represent and solve problems, including those involving probability. | M.Combinations and Permutations; M.Tables to Determine Independence | Covered | 28 | 2 | 4 | 0 | Covered by 2 topics (28 questions, 2 materials, 4 cards, 0 videos). |
| c. Find probabilities using a variety of probability techniques (e.g., addition and multiplication rules, determining sample spaces) for different kinds of events (e.g., independent, conditional). | M.Probability; M.Simple and Compound Events; M.Compound Probabilities (OR); M.Probability Models; M.Probability-Based Algebra; M.Sample Spaces to Determine Probabilities; M.Fundamental Counting Principle; M.Geometric Probability | Covered | 95 | 7 | 14 | 5 | Covered by 8 topics (95 questions, 7 materials, 14 cards, 5 videos). |
| d. Apply knowledge of expected value to analyze problem situations (e.g., fairness of games, lotteries) and determine the probability of events. | M.Probability vs Odds; M.Probability Distributions; M.Comparing to Probability Distribution; M.Probability Distributions - Expected Value; M.Payoff; M.Fairness; M.Probability Distributions - From Simulation | Covered | 21 | 7 | 16 | 0 | Covered by 7 topics (21 questions, 7 materials, 16 cards, 0 videos). |
| e. Use a variety of graphic representations to represent situations and determine probabilities (e.g., Venn diagrams, trees). | M.Diagrams; M.Diagrams - Venn Symbols; M.Expressing Probabilities | Covered | 19 | 3 | 6 | 0 | Covered by 3 topics (19 questions, 3 materials, 6 cards, 0 videos). |
| f. Select or analyze simulations that model simple theoretical and experimental probabilities. | M.Probability Simulations | Partially covered | 7 | 1 | 3 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| g. Demonstrate understanding of instructional and assessment activities, methods, or strategies that use appropriate instructional materials or technology and enable students to develop understanding of mathematical practices, concepts, skills, and applications. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
How 240 Creates The ILTS Mathematics (208) 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 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 208 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 Mathematics Study Guide
The questions teacher candidates ask us most often about the ILTS Mathematics study guide.
Is 240 a good study guide for ILTS 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 208 exam?
This guide is 94% 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.