Is 240 a good study guide for the TExES Math 4-8 (115)?

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

TExES Math 4-8 (115) Study Guide Alignment

Q: How closely does 240 align to the TExES Math 4-8 (115) exam?

This guide is 92% test-aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.

Q: Does 240 cover every competency?

Coverage is shown transparently across covered, partially covered, and identified gaps: 100 covered, 19 partially covered, and 0 gaps across 119 competencies.

Q: What does "partially covered" mean?

Partially covered means the guide addresses the core parts of a competency, but some depth or subtopics may still be limited.

Why Test Alignment Matters for Your TExES Math 4-8 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 Math 4-8 (115) 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 115 Study Guide

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

Transparent coverage is a strength. We show where the guide is strong, where depth is partial, and where a gap has been identified so you can make an informed study decision.

How to Read This Alignment Review

6 domains · 119 competencies reviewed · 92% test-aligned

Covered— competency is comprehensively supported by the guide

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

Coverage gap identified— a content gap has been identified

✓

This study guide is based on the current official exam framework

We review and update alignment whenever the official framework changes so candidates are always studying current, accurate material.

NUMBER CONCEPTS (DOMAIN I) Partially covered

SMR I.001 The teacher understands the structure of number systems, the development of a sense of quantity and the relationship between quantity and symbolic representations.

201 Qs12 Materials45 Cards10 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 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.Order Real Numbers by Magnitude	Covered	43	2	9	2	Covered by 2 topics (43 questions, 2 materials, 9 cards, 2 videos).
E. Selects appropriate representations of real numbers (e.g., fractions, decimals, percents, roots, exponents, scientific notation) for particular situations.	M.Exponential and Scientific Notation; M.Fraction, Decimal, Percentage Conversions; M.Representations of Fractions in Word Problems; M.Order Real Numbers by Magnitude; M.Radicals and Exponents; M.Comparing Fractions; M.Ratios, Proportions, Percents	Covered	149	7	18	7	Covered by 7 topics (149 questions, 7 materials, 18 cards, 7 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.Imaginary and Complex Numbers; M.Characteristics of Rational Numbers	Covered	29	3	18	2	Covered by 3 topics (29 questions, 3 materials, 18 cards, 2 videos).
G. Demonstrates an understand of how some situations that have no solution in one number system (e.g., whole numbers, integers, rational numbers) have solutions in another number system (e.g., real numbers, complex numbers).	M.Imaginary and Complex Numbers	Covered	10	1	10	1	Covered by 1 topic (10 questions, 1 materials, 10 cards, 1 videos).

SMR I.002 The teacher understands number operations and computational algorithms.

102 Qs7 Materials22 Cards1 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.Operations with Radicals; M.Operational Properties	Covered	51	2	5	1	Covered by 2 topics (51 questions, 2 materials, 5 cards, 1 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; M.Inverse Operations	Covered	12	2	14	0	Covered by 2 topics (12 questions, 2 materials, 14 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.	M.Properties of Exponents	Covered	25	1	1	0	Covered by 1 topic (25 questions, 1 materials, 1 cards, 0 videos).

SMR I.003 The teacher understands ideas of number theory and uses numbers to model and solve problems within and outside of mathematics.

153 Qs8 Materials30 Cards5 VideosCovered

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. Uses integers, rational numbers and real numbers to describe and quantify phenomena such as money, length, area, volume and density.	M.Choosing Appropriate Units	Covered	16	1	2	1	Covered by 1 topic (16 questions, 1 materials, 2 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; M.Mental Math and Estimation	Covered	63	3	10	2	Covered by 3 topics (63 questions, 3 materials, 10 cards, 2 videos).
D. Applies knowledge of counting techniques such as permutations and combinations to quantify situations and solve problems.	M.Combinations and Permutations	Covered	20	1	2	0	Covered by 1 topic (20 questions, 1 materials, 2 cards, 0 videos).
E. Applies properties of the real numbers to solve a variety of theoretical and applied problems.	M.Characteristics of Rational Numbers	Covered	8	1	8	0	Covered by 1 topic (8 questions, 1 materials, 8 cards, 0 videos).

PATTERNS AND ALGEBRA (DOMAIN II) Partially covered

SMR II.004 The teacher understands and uses mathematical reasoning to identify, extend and analyze patterns and understands the relationships among variables, expressions, equations, inequalities, relations and functions.

191 Qs11 Materials28 Cards5 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.Creating Formulas for Patterns - Arithmetic and Geometric; M.Patterns - Developing a Linear Formula	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 Expand; M.Advanced Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Simplify; 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).

SMR II.005 The teacher understands and uses linear functions to model and solve problems.

135 Qs11 Materials16 Cards6 VideosCovered

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.Proportional Reasoning - Word Problems; M.Direct and Indirect Variation	Covered	39	2	3	1	Covered by 2 topics (39 questions, 2 materials, 3 cards, 1 videos).
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 Equations - Standard Form; M.Understanding Linear Equations and Their Properties	Covered	30	2	3	0	Covered by 2 topics (30 questions, 2 materials, 3 cards, 0 videos).
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.Solving Linear Inequalities; M.Solve Linear Inequalities - Graphically; M.Compound Inequalities on Number Line	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).

SMR II.006 The teacher understands and uses nonlinear functions and relations to model and solve problems.

126 Qs16 Materials28 Cards3 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 with Complex Roots; M.Quadratic Equations; M.Quadratic Equation - Solve via Quadratic Formula; M.Advanced Quadratic Equation - Real World Problems	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.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form; M.Quadratic Equations	Covered	34	3	5	2	Covered by 3 topics (34 questions, 3 materials, 5 cards, 2 videos).
C. Analyzes data and represents and solves problems involving exponential growth and decay.	M.Exponential Functions - Real World Problems - Compound Interest; M.Exponential Functions	Covered	23	2	5	0	Covered by 2 topics (23 questions, 2 materials, 5 cards, 0 videos).
D. 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.
E. Understands the effects of transformations such as fx c ( ) ± on the graph of a nonlinear function f x( ) .	M.Functional Transformations - Linear and Quadratic	Covered	14	1	6	0	Covered by 1 topic (14 questions, 1 materials, 6 cards, 0 videos).
F. Applies properties, graphs and applications of nonlinear functions to analyze, model and solve problems.	M.Basic Polynomials; M.Advanced Factoring Polynomials; M.Exponential Functions	Covered	28	3	4	1	Covered by 3 topics (28 questions, 3 materials, 4 cards, 1 videos).
G. Uses a variety of representations and methods (e.g., numerical methods, tables, graphs, algebraic techniques) to solve systems of quadratic equations and inequalities.	M.Solve Quadratic Inequalities - Algebraically; M.Advanced Factoring Polynomials; M.Quadratic Equations; M.Solving Systems of Quadratic Equations; M.Solving Systems of Linear Inequalities; M.Solving Systems of Quadratic Inequalities	Covered	38	6	6	1	Covered by 6 topics (38 questions, 6 materials, 6 cards, 1 videos).
H. 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.Advanced Factoring Polynomials	Partially covered	7	1	1	0	Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content.

SMR II.007 The teacher uses and understands the conceptual foundations of calculus related to topics in middle school mathematics.

25 Qs3 Materials4 Cards0 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	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	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 secant line and instantaneous rate of change to the slope of the tangent line.	M.Rates of Change - Average vs Instantaneous	Covered	11	1	4	Covered by 1 topic (11 questions, 1 materials, 4 cards, 0 videos).
C. Relates topics in middle school mathematics to the area under a curve.	M.Rates of Change - Average vs Instantaneous	Covered	11	1	4	Covered by 1 topic (11 questions, 1 materials, 4 cards, 0 videos).
D. 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	Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 0 videos); limited supporting content.

GEOMETRY AND MEASUREMENT (DOMAIN III) Partially covered

SMR III.008 The teacher understands measurement as a process.

126 Qs8 Materials23 Cards5 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; M.Apply Triangle Inequalities; M.Trigonometric Ratios	Covered	52	4	13	2	Covered by 4 topics (52 questions, 4 materials, 13 cards, 2 videos).

SMR III.009 The teacher understands the geometric relationships and axiomatic structure of Euclidean geometry.

49 Qs5 Materials28 Cards2 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.Points, Lines, Planes, Angles	Covered	13	1	13	1	Covered by 1 topic (13 questions, 1 materials, 13 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 made using a compass and straight edge 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.
E. Applies knowledge of the axiomatic structure of Euclidean geometry to justify and prove theorems.	M.Proofs	Covered	8	1	3	0	Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos).

SMR III.010 The teacher analyzes the properties of two- and threedimensional figures.

280 Qs16 Materials49 Cards5 VideosCovered

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.Volume in 3D; M.Surface Area in 3D; M.Area and Perimeter of Polygons; 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; M.Solving with Shapes - Quadrilaterals; M.Attributes of Polygons - Advanced	Covered	111	8	42	2	Covered by 8 topics (111 questions, 8 materials, 42 cards, 2 videos).
D. Analyzes the relationship among three-dimensional figures and related twodimensional representations (e.g., projections, cross-sections, nets) and uses these representations to solve problems.	M.2D of 3D shape; M.Nets	Covered	26	2	1	0	Covered by 2 topics (26 questions, 2 materials, 1 cards, 0 videos).

SMR III.011 The teacher understands transformational geometry and relates algebra to geometry and trigonometry using the Cartesian coordinate system.

111 Qs9 Materials20 Cards2 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.Coordinate Geometry; M.Solving with Points, Lines, Planes, Angles; M.Slope, Midpoint, and Distance	Covered	54	3	7	2	Covered by 3 topics (54 questions, 3 materials, 7 cards, 2 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 the unit circle in the coordinate plane to explore properties of trigonometric functions.	M.The Unit Circle	Covered	9	1	0	0	Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos).

PROBABILITY AND STATISTICS (DOMAIN IV) Partially covered

SMR IV.012 The teacher understands how to use graphical and numerical techniques to explore data, characterize patterns and describe departures from patterns.

161 Qs7 Materials31 Cards3 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	Covered	43	2	17	1	Covered by 2 topics (43 questions, 2 materials, 17 cards, 1 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.Statistics of One-Variable Data	Covered	38	2	2	1	Covered by 2 topics (38 questions, 2 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.Advanced Measures of Center and Range	Covered	19	1	9	0	Covered by 1 topic (19 questions, 1 materials, 9 cards, 0 videos).

SMR IV.013 The teacher understands the theory of probability.

132 Qs9 Materials20 Cards4 VideosPartially covered

Official Competency	Matching 240 Topics	Alignment	Qs	Mats	Cards	Vids	Notes
A. Explores concepts of 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.	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.Combinations and Permutations; M.Geometric Probability	Covered	23	2	3	1	Covered by 2 topics (23 questions, 2 materials, 3 cards, 1 videos).
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).

SMR IV.014 The teacher understands the relationship among probability theory, sampling and statistical inference and how statistical inference is used in making and evaluating predictions.

91 Qs7 Materials35 Cards1 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	Covered	11	1	10	0	Covered by 1 topic (11 questions, 1 materials, 10 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).

MATHEMATICAL PROCESSES AND PERSPECTIVES (DOMAIN V) Partially covered

SMR V.015 The teacher understands mathematical reasoning and problem solving.

72 Qs7 Materials9 Cards1 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).

SMR V.016 The teacher understands mathematical connections within and outside of mathematics and how to communicate mathematical ideas and concepts.

102 Qs9 Materials30 Cards3 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	Partially covered	3	1	0	0	Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content.
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.Graphs and Plots; M.Choosing a Graph or Plot	Covered	47	2	9	2	Covered by 2 topics (47 questions, 2 materials, 9 cards, 2 videos).
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., describe the basic purpose of financial institutions, distinguish the difference between gross income and net income, identify various savings options, define different types of taxes, identify 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).

MATHEMATICAL LEARNING, INSTRUCTION AND ASSESSMENT (DOMAIN VI) Partially covered

SMR VI.017 The teacher understands how children learn and develop mathematical skills, procedures and concepts.

92 Qs9 Materials34 Cards6 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	Covered	5	1	5	1	Covered by 1 topic (5 questions, 1 materials, 5 cards, 1 videos).
B. Understands how students differ in their approaches to learning mathematics with regard 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; M.Backward Design	Covered	24	2	6	2	Covered by 2 topics (24 questions, 2 materials, 6 cards, 2 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.Multimodal Teaching - Math; M.Diversity and Engagement - ELL	Covered	25	3	9	2	Covered by 3 topics (25 questions, 3 materials, 9 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).

SMR VI.018 The teacher understands how to plan, organize and implement instruction using knowledge of students, subject matter and statewide curriculum (Texas Essential Knowledge and Skills [TEKS]) to teach all students to use mathematics.

96 Qs11 Materials21 Cards3 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.Multimodal Teaching - Math	Partially covered	5	1	5	0	Partial coverage by 1 topic (5 questions, 1 materials, 5 cards, 0 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; M.Multimodal Teaching - Math	Covered	17	2	8	1	Covered by 2 topics (17 questions, 2 materials, 8 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	Partially covered	7	1	1	0	Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content.
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; M.Manipulatives for Older Children	Covered	24	3	7	0	Covered by 3 topics (24 questions, 3 materials, 7 cards, 0 videos).
I. Understands how to relate mathematics to students’ lives and a variety of careers and professions.	M.Careers	Partially covered	6	1	0	0	Partial coverage by 1 topic (6 questions, 1 materials, 0 cards, 0 videos); limited supporting content.

SMR VI.019 The teacher understands assessment and uses a variety of formal and informal assessment techniques to monitor and guide mathematics instruction and to evaluate student progress.

48 Qs4 Materials20 Cards3 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 appropriateness 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.Using Assessment to Adjust Instruction	Covered	15	1	3	1	Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos).

How 240 Creates The TExES Math 4-8 (115) Study Guide

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Every 240 study guide starts with the official exam framework. From there, we organize lessons, practice, and study tools around the categories the exam uses to measure candidate knowledge.

1

Review the official exam framework

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

2

Map the tested categories

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

3

Build lessons around tested content

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

4

Cross-check practice against exam expectations

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

5

Review and update as standards change

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

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

Why 240 Is Better Than Other Generic Study Guides

Not all study guides are built the same way. Here is what separates a test-aligned guide from a generic one — and why it matters when you are preparing for the TExES Math 4-8.

Generic

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

Test-aligned

240 Test-Aligned TExES 115 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 Math 4-8 Study Guide

The questions teacher candidates ask us most often about the TExES Math 4-8 study guide.

1

Is 240 a good study guide for TExES Math 4-8?

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

2

How closely does 240 align to the TExES 115 exam?

This guide is 92% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.

3

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.

4

What does “partially covered” mean?

Partially covered means the guide addresses the core parts of a competency, but some depth or subtopics may still be limited.

240's TExES Math 4-8 Study Guide Is 92% Test-Aligned