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Why Test Alignment Matters for Your TExES CORE Subjects 4-8 (211): 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 TExES CORE Subjects 4-8 (211): Mathematics (211) 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 TExES 211 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
19Domains
136Competencies reviewed
91%Test-aligned
113Covered
21Partially covered
2Gaps
- 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.
Competency 001 (Domain 001)Covered
266 questions · 15 materials · 53 cards · 10 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyzes the structure of numeration systems and the roles of place value and zero in the base ten system. | M.Prime and Composite Numbers | Covered | 20 | 1 | 2 | 1 | Covered by 1 topic (20 questions, 1 materials, 2 cards, 1 videos). |
| B. Understands the relative magnitude of whole numbers, integers, rational numbers, irrational numbers and real numbers. | M.Order Real Numbers by Magnitude | Covered | 28 | 1 | 2 | 1 | Covered by 1 topic (28 questions, 1 materials, 2 cards, 1 videos). |
| C. Demonstrates an understanding of a variety of models for representing numbers (e.g., fraction strips, diagrams, patterns, shaded regions, number lines). | M.Variety of Representations for Older Children | Covered | 3 | 1 | 9 | 0 | Covered by 1 topic (3 questions, 1 materials, 9 cards, 0 videos). |
| D. Demonstrates an understanding of equivalency among different representations of rational numbers. | M.Fraction, Decimal, Percentage Conversions; M.Properties of Exponents; M.Radicals and Exponents; M.Order Real Numbers by Magnitude | Covered | 73 | 4 | 11 | 3 | Covered by 4 topics (73 questions, 4 materials, 11 cards, 3 videos). |
| E. Selects appropriate representations of real numbers (e.g., fractions, decimals, percents, roots, exponents, scientific notation) for particular situations. | M.Fraction, Decimal, Percentage Conversions; M.Representations of Fractions in Word Problems; M.Exponential and Scientific Notation; M.Order Real Numbers by Magnitude; M.Ratios, Proportions, Percents | Covered | 103 | 5 | 13 | 5 | Covered by 5 topics (103 questions, 5 materials, 13 cards, 5 videos). |
| F. Understands the characteristics of the set of whole numbers, integers, rational numbers, real numbers and complex numbers (e.g., commutativity, order, closure, identity elements, inverse elements, density). | M.Structure of Number Systems; M.Characteristics of Rational Numbers; M.Imaginary and Complex Numbers | Covered | 29 | 3 | 18 | 2 | Covered by 3 topics (29 questions, 3 materials, 18 cards, 2 videos). |
| G. Demonstrates an understanding of how some situations that have no solution in one number system (e.g., whole numbers, integers and rational numbers) have solutions in another number system (e.g., real numbers, complex numbers and irrational numbers). | M.Imaginary and Complex Numbers | Covered | 10 | 1 | 10 | 1 | Covered by 1 topic (10 questions, 1 materials, 10 cards, 1 videos). |
| H. Approximates (mentally and with calculators) the value of numbers. | M.Mental Math and Estimation | Covered | 24 | 1 | 7 | 0 | Covered by 1 topic (24 questions, 1 materials, 7 cards, 0 videos). |
| I. Represents fractions and decimals to the tenths or hundredths as distances from zero on a number line. | M.Compare Places on a Number Line; M.Comparing Fractions | Covered | 57 | 2 | 5 | 1 | Covered by 2 topics (57 questions, 2 materials, 5 cards, 1 videos). |
Competency 002 (Domain 002)Partially covered
185 questions · 10 materials · 38 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Works proficiently with real and complex numbers and their operations. | M.Operational Properties; M.Operations with Complex Numbers; M.Operations with Radicals | Covered | 65 | 3 | 7 | 2 | Covered by 3 topics (65 questions, 3 materials, 7 cards, 2 videos). |
| B. Analyzes and describes relationships between number properties, operations and algorithms for the four basic operations involving integers, rational numbers and real numbers. | M.Operational Algorithm Relationships | Covered | 5 | 1 | 13 | 0 | Covered by 1 topic (5 questions, 1 materials, 13 cards, 0 videos). |
| C. Uses a variety of concrete and visual representations to demonstrate the connections between operations and algorithms. | M.Operational Algorithm Relationships | Covered | 5 | 1 | 13 | 0 | Covered by 1 topic (5 questions, 1 materials, 13 cards, 0 videos). |
| D. Justifies procedures used in algorithms for the four basic operations with integers, rational numbers and real numbers and analyzes error patterns that may occur in their application. | M.Operation and Algorithm Connections | Partially covered | 4 | 1 | 0 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| E. Relates operations and algorithms involving numbers to algebraic procedures (e.g., adding fractions to adding rational expressions, division of integers to division of polynomials). | M.Rational Expressions | Covered | 10 | 1 | 2 | 0 | Covered by 1 topic (10 questions, 1 materials, 2 cards, 0 videos). |
| F. Extends and generalizes the operations on rationals and integers to include exponents, their properties and their applications to the real numbers. | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
| G. Compares and orders real numbers with and without a calculator. | M.Order Real Numbers by Magnitude; M.Comparing Fractions | Covered | 69 | 2 | 6 | 2 | Covered by 2 topics (69 questions, 2 materials, 6 cards, 2 videos). |
| H. Uses models, such as concrete objects, pictorial models and number lines, to add, subtract, multiply and divide integers and connect the real-world problems to algorithms, including equivalent ratios and rates. | M.Unit Rates | Covered | 14 | 1 | 0 | 1 | Covered by 1 topic (14 questions, 1 materials, 0 cards, 1 videos). |
| I. Divides whole numbers by unit fractions and unit fractions by whole numbers. | M.Fraction Operations - Multiply and Divide | Covered | 18 | 1 | 10 | 0 | Covered by 1 topic (18 questions, 1 materials, 10 cards, 0 videos). |
Competency 003 (Domain 003)Partially covered
190 questions · 9 materials · 17 cards · 7 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrates an understanding of ideas from number theory (e.g., prime factorization, greatest common divisor) as they apply to whole numbers, integers and rational numbers and uses these ideas in problem situations. | M.Factors; M.Prime Factorization | Covered | 46 | 2 | 8 | 2 | Covered by 2 topics (46 questions, 2 materials, 8 cards, 2 videos). |
| B. ses integers, rational numbers and real numbers to describe and quantify phenomena such as money, length, area, volume and density. | M.United States Money; M.Calculating Elapsed Time | Covered | 31 | 2 | 0 | 1 | Covered by 2 topics (31 questions, 2 materials, 0 cards, 1 videos). |
| C. Applies knowledge of place value and other number properties to develop techniques of mental mathematics and computational estimation. | M.Place Value; M.Rounding | Covered | 39 | 2 | 3 | 2 | Covered by 2 topics (39 questions, 2 materials, 3 cards, 2 videos). |
| D. Applies knowledge of counting techniques such as permutations and combinations to quantify situations and solve problems. | M.Fundamental Counting Principle; M.Combinations and Permutations | Covered | 30 | 2 | 3 | 1 | Covered by 2 topics (30 questions, 2 materials, 3 cards, 1 videos). |
| E. Applies properties of real numbers to solve a variety of theoretical and applied problems. | M.Operational Properties | Covered | 44 | 1 | 3 | 1 | Covered by 1 topic (44 questions, 1 materials, 3 cards, 1 videos). |
| F. Makes connections among various representations of a numerical relationship and generates a different representation of data given another representation of data (such as a table, graph, equation or verbal description). | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
Competency 004 (Domain 004)Covered
300 questions · 17 materials · 37 cards · 10 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Uses inductive reasoning to identify, extend and create patterns using concrete models, figures, numbers, and algebraic expressions. | M.Patterns - Developing a Linear Formula; M.Creating Formulas for Patterns - Arithmetic and Geometric | Covered | 46 | 2 | 4 | 2 | Covered by 2 topics (46 questions, 2 materials, 4 cards, 2 videos). |
| B. Formulates implicit and explicit rules to describe and construct sequences verbally, numerically, graphically and symbolically. | M.Patterns - Developing an Expression; M.Creating Formulas for Patterns - Arithmetic and Geometric | Covered | 48 | 2 | 3 | 2 | Covered by 2 topics (48 questions, 2 materials, 3 cards, 2 videos). |
| C. Makes, tests, validates and uses conjectures about patterns and relationships in data presented in tables, sequences or graphs. | M.Types of Sequences; M.Creating Formulas for Patterns - Arithmetic and Geometric | Covered | 43 | 2 | 6 | 1 | Covered by 2 topics (43 questions, 2 materials, 6 cards, 1 videos). |
| D. Gives appropriate justification of the manipulation of algebraic expressions. | M.Equivalence of Expressions - To Simplify; M.Advanced Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Linear Expression Evaluation | Covered | 52 | 4 | 10 | 2 | Covered by 4 topics (52 questions, 4 materials, 10 cards, 2 videos). |
| E. Illustrates the concept of a function using concrete models, tables, graphs and symbolic and verbal representations. | M.Relation and Function Representations | Covered | 39 | 1 | 4 | 0 | Covered by 1 topic (39 questions, 1 materials, 4 cards, 0 videos). |
| F. Uses transformations to illustrate properties of functions and relations and to solve problems. | M.Parent Functions; M.Functional Transformations - Linear and Quadratic | Covered | 21 | 2 | 6 | 0 | Covered by 2 topics (21 questions, 2 materials, 6 cards, 0 videos). |
| G. Uses graphs, tables and algebraic representations to make predictions and solve problems. | M.Solve for x - Linear | Covered | 20 | 1 | 0 | 1 | Covered by 1 topic (20 questions, 1 materials, 0 cards, 1 videos). |
| H. Uses letters to represent an unknown in an equation. | M.Dependent and Independent Variables; M.Verbal to Symbolic Expression - Advanced; M.Verbal to Symbolic Expression - Basic; M.Verbal to Symbolic Linear Equations | Covered | 79 | 4 | 7 | 3 | Covered by 4 topics (79 questions, 4 materials, 7 cards, 3 videos). |
| I. Formulates problem situations when given a simple equation and formulates an equation when given a problem situation. | M.Symbolic to Verbal | Covered | 10 | 1 | 5 | 1 | Covered by 1 topic (10 questions, 1 materials, 5 cards, 1 videos). |
Competency 005 (Domain 005)Partially covered
126 questions · 11 materials · 15 cards · 6 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrates an understanding of the concept of linear function using concrete models, tables, graphs and symbolic and verbal representations. | M.Line of Best Fit | Covered | 8 | 1 | 1 | 0 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 0 videos). |
| B. Demonstrates an understanding of the connections among linear functions, proportions and direct variation. | M.Direct and Indirect Variation | Partially covered | 2 | 1 | 2 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| C. Determines the linear function that best models a set of data. | M.Line of Best Fit | Covered | 8 | 1 | 1 | 0 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 0 videos). |
| D. Analyzes the relationship between a linear equation and its graph. | M.Linear Equation Word Problems - More Slope | Partially covered | 4 | 1 | 0 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| E. Uses linear functions, inequalities and systems to model problems. | M.Linear Equation Word Problems; M.Solving Systems of Linear Equations; M.Interpreting Inequalities | Covered | 40 | 3 | 5 | 3 | Covered by 3 topics (40 questions, 3 materials, 5 cards, 3 videos). |
| F. Uses a variety of representations and methods (e.g., numerical methods, tables, graphs, algebraic techniques) to solve systems of linear equations and inequalities. | M.Interpreting Inequalities; M.Compound Inequalities on Number Line; M.Solving Linear Inequalities; M.Solve Linear Inequalities - Graphically | Covered | 30 | 4 | 9 | 3 | Covered by 4 topics (30 questions, 4 materials, 9 cards, 3 videos). |
| G. Demonstrates an understanding of the characteristics of linear models and the advantages and disadvantages of using a linear model in a given situation. | M.Line of Best Fit | Covered | 8 | 1 | 1 | 0 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 0 videos). |
| H. Uses multiplication by a given constant factor (including unit rate) to represent and solve problems involving proportional relationships, including conversions between measurement systems, (e.g., ratio, speed, density, price, recipes, student teacher ratio). | M.Converting Units - Dimensional Analysis | Covered | 29 | 1 | 1 | 1 | Covered by 1 topic (29 questions, 1 materials, 1 cards, 1 videos). |
| I. Identifies proportional or nonproportional linear relationships in problem situations and solves problems. | M.Linear Equation Word Problems; M.Understanding Linear Equations and Their Properties | Covered | 40 | 2 | 2 | 1 | Covered by 2 topics (40 questions, 2 materials, 2 cards, 1 videos). |
Competency 006 (Domain 006)Partially covered
197 questions · 27 materials · 54 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Uses a variety of methods to investigate the roots (real and complex), vertex and symmetry of a quadratic function or relation. | M.Quadratic Equations; M.Quadratic Equation - Solve via Quadratic Formula; M.Advanced Quadratic Equation - Real World Problems; M.Quadratic Equations with Complex Roots | Covered | 35 | 4 | 7 | 1 | Covered by 4 topics (35 questions, 4 materials, 7 cards, 1 videos). |
| B. Demonstrates an understanding of the connections among geometric, graphic, numeric and symbolic representations of quadratic functions. | M.Quadratic Equations; M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form | Covered | 34 | 3 | 5 | 2 | Covered by 3 topics (34 questions, 3 materials, 5 cards, 2 videos). |
| C. Demonstrates an understanding of the connections among proportions, inverse variation and rational functions. | M.Determine the Validity of an Inverse | Partially covered | 3 | 1 | 5 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 5 cards, 0 videos); limited supporting content. |
| D. Understands the effects of transformations such as f ( x ± c ) on the graph of a nonlinear function f(x). | M.Linear Equations - Rearrange to Slope-Intercept Form | Partially covered | 5 | 1 | 0 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| E. Applies properties, graphs and applications of nonlinear functions to analyze, model and solve problems. | M.Polynomials; M.Advanced Factoring Polynomials; M.Exponential Functions; M.Exponential Functions - Real World Problems; M.Logarithmic Functions | Covered | 57 | 5 | 15 | 0 | Covered by 5 topics (57 questions, 5 materials, 15 cards, 0 videos). |
| F. Uses a variety of representations and methods (e.g., numerical methods, tables, graphs, algebraic techniques) to solve systems of quadratic equations and inequalities. | M.Properties of Equality; M.Forms of Equations; M.Solving Systems of Quadratic Equations; M.Solving Systems of Linear Inequalities; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Solving Systems of Quadratic Inequalities; M.Rational Functions; M.Quadratic Equation - Solve via Graphing; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Complete the Square | Covered | 68 | 12 | 22 | 2 | Covered by 12 topics (68 questions, 12 materials, 22 cards, 2 videos). |
| G. Understands how to use properties, graphs and applications of nonlinear relations including polynomial, rational, radical, absolute value, exponential, logarithmic, trigonometric and piecewise functions and relations to analyze, model and solve problems. | M.Binomial Expansion; M.Exponential Functions; M.Logarithmic Functions; M.Logarithmic Phenomena | Covered | 30 | 4 | 12 | 0 | Covered by 4 topics (30 questions, 4 materials, 12 cards, 0 videos). |
Competency 007 (Domain 007)Partially covered
25 questions · 3 materials · 4 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Relates topics in middle school mathematics to the concept of limit in sequences and series. | M.Teaching the Concept of Limits in Sequences and Series | Partially covered | 7 | 1 | 0 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| B. Relates the concept of average rate of change to the slope of the line and the concept of instantaneous rate of change as a slope of the line. | M.Rates of Change - Average vs Instantaneous | Covered | 11 | 1 | 4 | 0 | Covered by 1 topic (11 questions, 1 materials, 4 cards, 0 videos). |
| C. Demonstrates an understanding of the use of calculus concepts to answer questions about rates of change, areas, volumes and properties of functions and their graphs. | M.Calculus Connections to Formulas | Partially covered | 7 | 1 | 0 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
Competency 008 (Domain 008)Covered
108 questions · 6 materials · 22 cards · 4 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Selects and uses appropriate units of measurement (e.g., temperature, money, mass, weight, area, capacity, density, percents, speed, acceleration) to quantify, compare and communicate information. | M.Choosing Appropriate Units | Covered | 16 | 1 | 2 | 1 | Covered by 1 topic (16 questions, 1 materials, 2 cards, 1 videos). |
| B. Develops, justifies and uses conversions within measurement systems. | M.Converting Units - Proportional Reasoning | Covered | 20 | 1 | 1 | 1 | Covered by 1 topic (20 questions, 1 materials, 1 cards, 1 videos). |
| C. Applies dimensional analysis to derive units and formulas in a variety of situations (e.g., rates of change of one variable with respect to another) and to find and evaluate solutions to problems. | M.Converting Units - Dimensional Analysis | Covered | 29 | 1 | 1 | 1 | Covered by 1 topic (29 questions, 1 materials, 1 cards, 1 videos). |
| D. Describes the precision of measurement and the effects of error on measurement. | M.Advanced Measurement Principles | Covered | 9 | 1 | 6 | 0 | Covered by 1 topic (9 questions, 1 materials, 6 cards, 0 videos). |
| E. Applies the Pythagorean Theorem, proportional reasoning and right triangle trigonometry to solve measurement problems. | M.Pythagorean Theorem; M.Apply Triangle Properties | Covered | 34 | 2 | 12 | 1 | Covered by 2 topics (34 questions, 2 materials, 12 cards, 1 videos). |
Competency 009 (Domain 009)Partially covered
97 questions · 7 materials · 58 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands concepts and properties of points, lines, planes, angles, lengths and distances. | M.Points, Lines, Planes, Angles | Covered | 13 | 1 | 13 | 1 | Covered by 1 topic (13 questions, 1 materials, 13 cards, 1 videos). |
| B. Analyzes and applies the properties of parallel and perpendicular lines. | M.Solving with Points, Lines, Planes, Angles | Covered | 27 | 1 | 6 | 1 | Covered by 1 topic (27 questions, 1 materials, 6 cards, 1 videos). |
| C. Uses the properties of congruent triangles to explore geometric relationships and prove theorems. | M.Proportional Reasoning - 2D Shapes; M.Advanced Similar Shapes | Covered | 24 | 2 | 10 | 1 | Covered by 2 topics (24 questions, 2 materials, 10 cards, 1 videos). |
| D. Describes and justifies geometric constructions. | M.Geometric Constructions | Partially covered | 4 | 1 | 2 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| E. Applies knowledge of right angles to identify acute, right and obtuse triangles. | M.Attributes of Polygons - Advanced | Covered | 11 | 1 | 23 | 0 | Covered by 1 topic (11 questions, 1 materials, 23 cards, 0 videos). |
| F. Measures angles correctly using a protractor. | M.Measurement Tools | Covered | 18 | 1 | 8 | 1 | Covered by 1 topic (18 questions, 1 materials, 8 cards, 1 videos). |
Competency 010 (Domain 010)Partially covered
279 questions · 17 materials · 66 cards · 7 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Uses and understands the development of formulas to find lengths, perimeters, areas and volumes of basic geometric figures. | M.Area and Perimeter of Polygons; M.Surface Area in 3D; M.Volume in 3D; M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 120 | 5 | 7 | 3 | Covered by 5 topics (120 questions, 5 materials, 7 cards, 3 videos). |
| B. Applies relationships among similar figures, scale and proportion and analyzes how changes in scale affect area and volume measurements. | M.Dimensional Changes Affecting Area and Volume | Covered | 23 | 1 | 0 | 0 | Covered by 1 topic (23 questions, 1 materials, 0 cards, 0 videos). |
| C. Uses a variety of representations (e.g., numeric, verbal, graphic, symbolic) to analyze and solve problems involving two- and three-dimensional figures such as circles, triangles, polygons, cylinders, prisms and spheres. | M.Angles in Triangles; M.Measurements in Circles; M.Measurements in Circles Advanced; M.Angles and Measurements in Polygons; M.Generating Formulas for Shapes; M.Coordinate Geometry | Covered | 86 | 6 | 27 | 2 | Covered by 6 topics (86 questions, 6 materials, 27 cards, 2 videos). |
| D. Analyzes the relationship among three-dimensional figures and related two-dimensional representations (e.g., projections, cross-sections, nets) and uses these representations to solve problems. | M.Nets | Covered | 17 | 1 | 1 | 0 | Covered by 1 topic (17 questions, 1 materials, 1 cards, 0 videos). |
| E. Generates formulas involving perimeter, area, circumference, volume and scaling. | M.Generating Formulas for Shapes | Partially covered | 5 | 1 | 0 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| F. Estimates measurements and solves application problems involving length (including perimeter and circumference) and area of polygons and other shapes. | M.Measurement Principles; M.Area and Perimeter of Polygons; M.Angles in Triangles; M.Measurements in Circles; M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 110 | 6 | 14 | 3 | Covered by 6 topics (110 questions, 6 materials, 14 cards, 3 videos). |
| G. Knows the various types of triangles (e.g., scalene, obtuse, acute) and how to calculate angle degrees. | M.Angles in Triangles; M.Attributes of Polygons - Advanced | Covered | 23 | 2 | 23 | 1 | Covered by 2 topics (23 questions, 2 materials, 23 cards, 1 videos). |
| H. Uses geometry and spatial reasoning, compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. | M.Nets; M.Pyramids and Prisms; M.Types of Prisms; M.Coordinate Geometry; M.Attributes of Polygons - Advanced | Covered | 50 | 5 | 33 | 2 | Covered by 5 topics (50 questions, 5 materials, 33 cards, 2 videos). |
Competency 011 (Domain 011)Partially covered
162 questions · 12 materials · 29 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Describes and justifies geometric constructions made using a reflection device and other appropriate technologies. | M.Geometric Constructions | Partially covered | 4 | 1 | 2 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| B. Uses translations, reflections, glide-reflections and rotations to demonstrate congruence and to explore the symmetries of figures. | M.Multiple Transformations | Covered | 18 | 1 | 2 | 0 | Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos). |
| C. Uses dilations (expansions and contractions) to illustrate similar figures and proportionality. | M.Non-Rigid Transformations | Partially covered | 6 | 1 | 4 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| D. Uses symmetry to describe tessellations and shows how they can be used to illustrate geometric concepts, properties and relationships. | M.Tessellations | Partially covered | 4 | 1 | 1 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| E. Applies concepts and properties of slope, midpoint, parallelism and distance in the coordinate plane to explore properties of geometric figures and solve problems. | M.Parallel and Perpendicular Lines and Formulas; M.Coordinate Geometry; M.Solving with Points, Lines, Planes, Angles; M.Slope, Midpoint, and Distance | Covered | 73 | 4 | 10 | 3 | Covered by 4 topics (73 questions, 4 materials, 10 cards, 3 videos). |
| F. Applies transformations in the coordinate plane. | M.Rigid Transformations | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| G. Uses geometry to model and describe the physical world. | M.Proportional Reasoning - Scale Drawings; M.Polar Coordinates | Covered | 23 | 2 | 2 | 1 | Covered by 2 topics (23 questions, 2 materials, 2 cards, 1 videos). |
| H. Identifies, locates and names points on a coordinate plane using ordered pairs of real numbers in all quadrants | M.The Coordinate Plane | Covered | 18 | 1 | 4 | 1 | Covered by 1 topic (18 questions, 1 materials, 4 cards, 1 videos). |
| I. Graphs in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table. | M.The Coordinate Plane | Covered | 18 | 1 | 4 | 1 | Covered by 1 topic (18 questions, 1 materials, 4 cards, 1 videos). |
| J. Graphs reflections across the horizontal or vertical axis and graph translations on a coordinate plane. | M.Rigid Transformations | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
Competency 012 (Domain 012)Covered
185 questions · 9 materials · 31 cards · 4 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Organizes and displays data in a variety of formats (e.g., tables, frequency distributions, stem-and-leaf plots, box-and-whisker plots, histograms, pie charts). | M.Graphs and Plots; M.Boxplots; M.Choosing a Graph or Plot | Covered | 58 | 3 | 17 | 2 | Covered by 3 topics (58 questions, 3 materials, 17 cards, 2 videos). |
| B. Applies concepts of center, spread, shape and skewness to describe a data distribution. | M.Describing Data Patterns and Outliers | Covered | 5 | 1 | 11 | 0 | Covered by 1 topic (5 questions, 1 materials, 11 cards, 0 videos). |
| C. Supports arguments, makes predictions and draws conclusions using summary statistics and graphs to analyze and interpret one-variable data. | M.Data Analysis and Interpretation; M.Appropriate vs Inappropriate Representations of Data; M.Statistics of One-Variable Data | Covered | 47 | 3 | 2 | 1 | Covered by 3 topics (47 questions, 3 materials, 2 cards, 1 videos). |
| D. Demonstrates an understanding of measures of central tendency (e.g., mean, median, mode) and dispersion (e.g., range, interquartile range, variance, standard deviation). | M.Measures of Center and Range; M.Advanced Measures of Center and Range | Covered | 75 | 2 | 12 | 1 | Covered by 2 topics (75 questions, 2 materials, 12 cards, 1 videos). |
| E. Analyzes connections among concepts of center and spread, data clusters and gaps, data outliers and measures of central tendency and dispersion. | M.Advanced Measures of Center and Range | Covered | 19 | 1 | 9 | 0 | Covered by 1 topic (19 questions, 1 materials, 9 cards, 0 videos). |
| F. Calculates and interprets percentiles and quartiles. | M.Measures of Center and Range | Covered | 56 | 1 | 4 | 1 | Covered by 1 topic (56 questions, 1 materials, 4 cards, 1 videos). |
Competency 013 (Domain 013)Partially covered
112 questions · 8 materials · 18 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Explores concepts of experimental and theoretical probability through data collection, experiments and simulations. | 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. |
| B. Uses the concepts and principles of probability to describe the outcome of simple and compound events, including independent and dependent events. | M.Probability; M.Simple and Compound Events | Covered | 58 | 2 | 8 | 2 | Covered by 2 topics (58 questions, 2 materials, 8 cards, 2 videos). |
| C. Generates, simulates and uses probability models to represent a situation. | M.Probability Models | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| D. Determines probabilities by constructing sample spaces to model situations. | M.Sample Spaces to Determine Probabilities | Partially covered | 4 | 1 | 1 | 1 | Partial coverage by 1 topic (4 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
| E. Solves a variety of probability problems using combinations, permutations and geometric probability (i.e., probability as the ratio of two areas). | 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. |
| F. Uses the binomial, geometric and normal distributions to solve problems. | M.Normal Distribution; M.Using Distributions | Covered | 29 | 2 | 6 | 0 | Covered by 2 topics (29 questions, 2 materials, 6 cards, 0 videos). |
Competency 014 (Domain 014)Covered
91 questions · 7 materials · 35 cards · 1 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Applies knowledge of designing, conducting, analyzing and interpreting statistical experiments to investigate real-world problems. | M.Statistical Experiments | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| B. Demonstrates an understanding of random samples, sample statistics and the relationship between sample size and confidence intervals. | M.Sampling Methods; M.Level of Confidence | Covered | 27 | 2 | 9 | 0 | Covered by 2 topics (27 questions, 2 materials, 9 cards, 0 videos). |
| C. Applies knowledge of the use of probability to make observations and draw conclusions from single variable data and to describe the level of confidence in the conclusion. | M.Observations, Conclusions, and Relationships; M.Level of Confidence | Covered | 26 | 2 | 13 | 0 | Covered by 2 topics (26 questions, 2 materials, 13 cards, 0 videos). |
| D. Makes inferences about a population using binomial, normal and geometric distributions. | M.Using Distributions | Covered | 13 | 1 | 4 | 0 | Covered by 1 topic (13 questions, 1 materials, 4 cards, 0 videos). |
| E. Demonstrates an understanding of the use of techniques such as scatter plots, regression lines, correlation coefficients and residual analysis to explore bivariate data and to make and evaluate predictions. | M.Bivariate Data Analysis; M.Advanced Bivariate Data Analysis | Covered | 29 | 2 | 13 | 1 | Covered by 2 topics (29 questions, 2 materials, 13 cards, 1 videos). |
Competency 015 (Domain 015)Partially covered
72 questions · 7 materials · 9 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrates an understanding of proof, including indirect proof, in mathematics. | M.Proofs | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
| B. Applies correct mathematical reasoning to derive valid conclusions from a set of premises. | 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. |
| C. Demonstrates an understanding of the use of inductive reasoning to make conjectures and deductive methods to evaluate the validity of conjectures. | M.Inductive vs Deductive Reasoning | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| D. Applies knowledge of the use of formal and informal reasoning to explore, investigate and justify mathematical ideas. | M.Formal vs Informal Reasoning | Partially covered | 3 | 1 | 3 | 1 | Partial coverage by 1 topic (3 questions, 1 materials, 3 cards, 1 videos); limited supporting content. |
| E. Recognizes that a mathematical problem can be solved in a variety of ways and selects an appropriate strategy for a given problem. | M.Selecting Appropriate Solution Strategies | Covered | 13 | 1 | 0 | 0 | Covered by 1 topic (13 questions, 1 materials, 0 cards, 0 videos). |
| F. Evaluates the reasonableness of a solution to a given problem. | M.Reasonableness of Results | Covered | 16 | 1 | 0 | 0 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 0 videos). |
| G. Applies content knowledge to develop a mathematical model of a real-world situation and analyzes and evaluates how well the model represents the situation. | M.Modeling and Evaluating Real-World Situations | Covered | 16 | 1 | 0 | 0 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 0 videos). |
| H. Demonstrates an understanding of estimation and evaluates its appropriate uses. | M.Reasonableness of Results | Covered | 16 | 1 | 0 | 0 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 0 videos). |
Competency 016 (Domain 016)Partially covered
68 questions · 9 materials · 28 cards · 1 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Recognizes and uses multiple representations of a mathematical concept (e.g., a point and its coordinates, the area of circle as a quadratic function in r, probability as the ratio of two areas). | M.Variety of Representations for Older Children | Covered | 3 | 1 | 9 | 0 | Covered by 1 topic (3 questions, 1 materials, 9 cards, 0 videos). |
| B. Uses mathematics to model and solve problems in other disciplines, such as art, music, science, social science and business. | M.Interdisciplinary Connections; M.Exponential Functions - Real World Problems - Compound Interest | Covered | 14 | 2 | 4 | 0 | Covered by 2 topics (14 questions, 2 materials, 4 cards, 0 videos). |
| C. Expresses mathematical statements using developmentally appropriate language, Standard English, mathematical language and symbolic mathematics. | M.Diversity and Engagement - ELL; M.Teaching Mathematical Vocabulary | Covered | 19 | 2 | 2 | 1 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 1 videos). |
| D. Communicates mathematical ideas using a variety of representations (e.g., numeric, verbal, graphic, pictorial, symbolic, concrete). | M.Variety of Representations | Covered | 10 | 1 | 10 | 0 | Covered by 1 topic (10 questions, 1 materials, 10 cards, 0 videos). |
| E. Demonstrates an understanding of the use of visual media such as graphs, tables, diagrams and animations to communicate mathematical information. | 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. |
| F. Uses the language of mathematics as a precise means of expressing mathematical ideas. | M.Teaching Mathematical Vocabulary | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| G. Understands the structural properties common to the mathematical disciplines. | M.Mathematical Connections | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| H. Explores and applies concepts of financial literacy as it relates to teaching students (e.g., describes the basic purpose of financial institutions, distinguishes the difference between gross income and net income, identifies various savings options, defines different types of taxes, identifies the advantages and disadvantages of different methods of payments). | M.Financial Literacy | Covered | 11 | 1 | 9 | 0 | Covered by 1 topic (11 questions, 1 materials, 9 cards, 0 videos). |
| I. Applies mathematics to model and solve problems to manage financial resources effectively for lifetime financial security as it relates to teaching students (e.g., distinguish between fixed and variable expenses, calculate profit in a given situation, develop a system for keeping and using financial records, describe actions that might be taken to balance a budget when expenses exceed income and balance a simple budget.) | M.Financial Literacy | Covered | 11 | 1 | 9 | 0 | Covered by 1 topic (11 questions, 1 materials, 9 cards, 0 videos). |
Competency 017 (Domain 017)Covered
118 questions · 8 materials · 26 cards · 6 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Applies theories and principles of learning mathematics to plan appropriate instructional activities for all students. | M.Major Math Instructional Theories; M.Evaluate Student Solutions | Covered | 45 | 2 | 5 | 2 | Covered by 2 topics (45 questions, 2 materials, 5 cards, 2 videos). |
| B. Understands how students differ in their approaches to learning mathematics with regards to diversity. | M.Diversity and Engagement - ELL | Covered | 8 | 1 | 1 | 1 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 1 videos). |
| C. Uses students’ prior mathematical knowledge to build conceptual links to new knowledge and plans instruction that builds on students’ strengths and addresses students’ needs. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| D. Understands how learning may be assisted through the use of mathematics manipulatives and technological tools. | M.Manipulatives for Young Children; M.Variety of Representations for Older Children | Covered | 19 | 2 | 12 | 0 | Covered by 2 topics (19 questions, 2 materials, 12 cards, 0 videos). |
| E. Understands how to motivate students and actively engage them in the learning process by using a variety of interesting, challenging and worthwhile mathematical tasks in individual, small-group and large-group settings. | M.Planning for Group Experiences; M.Diversity and Engagement - ELL | Covered | 20 | 2 | 4 | 2 | Covered by 2 topics (20 questions, 2 materials, 4 cards, 2 videos). |
| F. Understands how to provide instruction along a continuum from concrete to abstract. | M.Learning Progressions in Math | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
| G. Recognizes the implications of current trends and research in mathematics and mathematics education. | M.Major Math Instructional Theories | Covered | 5 | 1 | 5 | 1 | Covered by 1 topic (5 questions, 1 materials, 5 cards, 1 videos). |
Competency 018 (Domain 018)Partially covered
110 questions · 12 materials · 17 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrates an understanding of a variety of instructional methods, tools and tasks that promote students’ ability to do mathematics described in the TEKS. | M.Diversity and Engagement | Partially covered | 3 | 1 | 1 | 1 | Partial coverage by 1 topic (3 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
| B. Understands planning strategies for developing mathematical instruction as a discipline of interconnected concepts and procedures. | M.Mathematical Connections | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| C. Develops clear learning goals to plan, deliver, assess and reevaluate instruction based on the TEKS. | M.Planning from TEKS | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| D. Understands procedures for developing instruction that establishes transitions between concrete, symbolic and abstract representations of mathematical knowledge. | M.Learning Progressions in Math | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
| E. Applies knowledge of a variety of instructional delivery methods, such as individual, structured small-group and large-group formats. | M.Planning for Group Experiences | Covered | 12 | 1 | 3 | 1 | Covered by 1 topic (12 questions, 1 materials, 3 cards, 1 videos). |
| F. Understands how to create a learning environment that provides all students, including English-language learners, with opportunities to develop and improve mathematical skills and procedures. | M.Diversity and Engagement - ELL | Covered | 8 | 1 | 1 | 1 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 1 videos). |
| G. Demonstrates an understanding of a variety of questioning strategies to encourage mathematical discourse and to help students analyze and evaluate their mathematical thinking. | M.Teaching Mathematical Reasoning; M.Stimulating Higher Order Thinking | Covered | 21 | 2 | 3 | 0 | Covered by 2 topics (21 questions, 2 materials, 3 cards, 0 videos). |
| H. Understands how technological tools and manipulatives can be used appropriately to assist students in developing, comprehending and applying mathematical concepts. | M.Manipulatives for Young Children; M.Using Calculators to Check Math | Covered | 21 | 2 | 5 | 0 | Covered by 2 topics (21 questions, 2 materials, 5 cards, 0 videos). |
| I. Understands how to relate mathematics to students’ lives and a variety of careers and professions. | M.Careers; M.Historical Events and Contributions | Covered | 11 | 2 | 0 | 0 | Covered by 2 topics (11 questions, 2 materials, 0 cards, 0 videos). |
Competency 019 (Domain 019)Partially covered
57 questions · 5 materials · 23 cards · 4 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrates an understanding of the purpose, characteristics and uses of various assessments in mathematics, including formative and summative assessments. | M.Types of Assessment - Math | Covered | 20 | 1 | 13 | 1 | Covered by 1 topic (20 questions, 1 materials, 13 cards, 1 videos). |
| B. Understands how to select and develop assessments that are consistent with what is taught and how it is taught. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| C. Demonstrates an understanding of how to develop a variety of assessments and scoring procedures consisting of worthwhile tasks that assess mathematical understanding, common misconceptions and error patterns. | 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. |
| D. Understands how to evaluate a variety of assessment methods and materials for reliability, validity, absence of bias, clarity of language and appropriate-ness of mathematical level. | M.Fair Assessment | Covered | 7 | 1 | 6 | 1 | Covered by 1 topic (7 questions, 1 materials, 6 cards, 1 videos). |
| E. Understands the relationship between assessment and instruction and knows how to evaluate assessment results to design, monitor and modify instruction to improve mathematical learning for all students, including English-language learners | M.Backward Design; M.Using Assessment to Adjust Instruction | Covered | 24 | 2 | 6 | 2 | Covered by 2 topics (24 questions, 2 materials, 6 cards, 2 videos). |
How 240 Creates The TExES CORE Subjects 4-8 (211): Mathematics (211) 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 TExES CORE Subjects 4-8 (211): 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 TExES 211 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 TExES CORE Subjects 4-8 (211): Mathematics Study Guide
The questions teacher candidates ask us most often about the TExES CORE Subjects 4-8 (211): Mathematics study guide.
Is 240 a good study guide for TExES CORE Subjects 4-8 (211): 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 TExES 211 exam?
This guide is 91% 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.