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TExES Mathematics 4-8 Online Center
This TExES Mathematics 4-8 Online Center brings together practice, lessons, worksheets, flashcards and review tools. Choose the resource that matches the skill you want to work on next.
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2 pop-up practice tests47 connected lessons1 complete flashcard deck
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TExES Mathematics 4-8 Practice Center
Take a full form, then read the explanation under every question you missed. Note that a quarter of this exam is not computation: Domains V and VI are about mathematical reasoning and about how students learn mathematics, and they need a different kind of study from the content domains.
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TExES Mathematics 4-8 at a glance
This is the Texas middle grades mathematics certification exam. The content reaches from place value through functions and coordinate geometry, which is what candidates expect. What they often do not expect is that a quarter of the exam is not content at all: Domain V is mathematical processes and reasoning, and Domain VI is about how students learn mathematics and how you would respond to their work.
| Test code | 115 (Mathematics 4-8) |
|---|---|
| Status | Current. No successor has been announced, and it is unaffected by the Core Subjects EC-6 retirement. |
| Number of questions | 100 selected-response questions. There is no constructed response. |
| Time limit | 5 hours total: 15 minutes for the tutorial and compliance agreement, then 4 hours 45 minutes of testing. |
| Calculator | An on-screen scientific calculator is provided, along with a Definitions and Formulas reference page. |
| Format | Computer-administered |
| Passing score | 240 on a scale of 100 to 300. |
Texas publishes weights by domain: Number Concepts 16 percent, Patterns and Algebra 21 percent, Geometry and Measurement 21 percent, Probability and Statistics 16 percent, Mathematical Processes and Perspectives 10 percent, and Mathematical Learning, Instruction, and Assessment 16 percent. That last pair is 26 percent between them, so more than a quarter of this exam is about reasoning and teaching rather than about computing.
The six domains, in plain language
Texas states each competency. Here is what each domain asks of you, with its published weight.
Domain II: Patterns and algebra (21 percent)
Relationships and how to represent them.
- Sequences and their rules
- Linear and non-linear functions
- Expressions, equations, and inequalities
- Systems of equations
- Modeling a situation algebraically
- Rate of change and slope
Domain III: Geometry and measurement (21 percent)
Figures, their measures, and how they move.
- Classifying figures by their properties
- Congruence, similarity, and the Pythagorean theorem
- Transformations and coordinate geometry
- Perimeter, area, surface area, and volume
- Units, conversion, and scale
Domain I: Number concepts (16 percent)
The number system and how to work in it.
- Place value and the structure of number
- Integers and rational numbers
- Ratio, proportion, and percent
- Exponents, roots, and number theory
- Estimation and judging reasonableness
Domain IV: Probability and statistics (16 percent)
Reading data and reasoning about chance.
- Data displays and what each one shows
- Measures of center and of spread
- Sampling and drawing conclusions
- Simple and compound probability
Domain VI: Mathematical learning, instruction, and assessment (16 percent)
How students learn mathematics.
- Reading a student’s work and naming what it shows
- Choosing a representation that fits the idea
- Sequencing instruction along a learning progression
- Common error patterns and their causes
- Assessment and what to teach next
Domain V: Mathematical processes and perspectives (10 percent)
Reasoning about mathematics itself.
- Problem solving and multiple approaches
- Reasoning, justification, and proof
- Representation and connections
- Communicating mathematical thinking
- The historical and cultural development of mathematics
A study routine for a 285-minute exam
Time is not the constraint here; almost five hours for a hundred questions is generous. The two things worth planning for are the formula page and the twenty-six percent of the exam that is not computation.
DiagnoseTake Practice Test 1 cold, using a scientific calculator. Score the four content domains separately from Domains V and VI.
Rebuild the weakest content domainPatterns and algebra and geometry and measurement are twenty-one percent each, so a weakness in either outweighs everything else.
Prepare for the teaching domains deliberatelyTwenty-six percent between them, and they cannot be studied by doing more mathematics. Practise reading a piece of wrong student work and naming the specific error before you look at the choices.
Learn the formula pageA Definitions and Formulas page is provided. Knowing what is on it, and therefore what you do not need to memorize, is worth an evening.
Prove itTake Practice Test 2 under time.
Complete topic map
Forty-seven lessons on the mathematics this exam expects, each opening in a new tab, followed by the descriptive statements Texas publishes for each competency.
Counting, place value, and operations
Fractions and decimals
Ratios, proportion, and percent
Algebraic thinking and patterns
The coordinate plane
Measurement and geometry
Data, statistics, and probability
Competency 001: Structure of Number Systems and Representations
- 48Analyzes the structure of numeration systems and the roles of place value and zero.
- 49Understands the relative magnitude of whole numbers, integers, rational numbers, and real numbers.
- 50Demonstrates an understanding of a variety of models for representing numbers, including concrete and pictorial models.
- 51Understands equivalency among different representations of rational numbers, including fractions, decimals, and percents.
- 52Selects appropriate representations of real numbers for particular situations.
- 53Understands the characteristics of number sets and their properties, including commutativity, associativity, distributivity, identity, inverse, and closure.
Competency 002: Number Operations and Computational Algorithms
- 54Demonstrates proficiency in operations with real numbers and complex numbers.
- 55Analyzes the relationships among the properties of operations and standard and alternative computational algorithms.
- 56Uses concrete models and visual representations to illustrate the meaning of operations.
- 57Justifies procedures used in computational algorithms and analyzes errors in computation.
- 58Relates operations with real numbers to algebraic procedures.
- 59Extends operations to include integer exponents, rational exponents, and roots.
Competency 003: Number Theory and Modeling with Numbers
- 60Demonstrates an understanding of ideas from number theory, including divisibility, prime and composite numbers, factors, multiples, greatest common factor, and least common multiple.
- 61Uses numbers to quantify and describe attributes such as money, length, area, volume, time, and rate.
- 62Applies knowledge of place value and properties to perform mental mathematics and estimation.
- 63Uses counting techniques, including the fundamental counting principle, to solve problems.
- 64Applies properties of the real numbers to model and solve problems within and outside of mathematics.
Competency 004: Patterns, Variables, Expressions, Equations, Relations, and Functions
- 65Uses inductive reasoning to identify, extend, and generalize patterns.
- 66Formulates explicit and recursive rules to describe sequences, both numeric and geometric.
- 67Makes and tests conjectures about patterns and relationships.
- 68Justifies the steps used in manipulating algebraic expressions and solving equations and inequalities.
- 69Illustrates the concept of a function using tables, graphs, symbols, and verbal descriptions, and translates among these models.
- 70Uses transformations to explore the properties of relations and functions, including domain and range.
Competency 005: Linear Functions
- 71Understands the concept of a linear function through multiple representations and their connections.
- 72Connects linear functions to proportional reasoning, direct variation, and constant rate of change.
- 73Determines a line of best fit for a set of data and uses it to make predictions.
- 74Analyzes the relationship between a linear equation or inequality and its graph, including slope and intercepts.
- 75Models real-world situations with linear functions, equations, inequalities, and systems.
- 76Solves systems of linear equations using graphing, substitution, elimination, and matrices.
Competency 006: Nonlinear Functions and Relations
- 77Uses a variety of methods to investigate the roots, vertex, and axis of symmetry of a quadratic function.
- 78Understands the connections among the various representations of quadratic functions.
- 79Analyzes exponential functions and situations of exponential growth and decay.
- 80Understands the concept of proportional reasoning as it applies to rational functions and inverse variation.
- 81Analyzes the effects of parameter changes and transformations on the graphs of nonlinear functions.
- 82Applies the properties of nonlinear functions and relations to model and solve problems.
Competency 007: Conceptual Foundations of Calculus
- 83Relates topics in middle school mathematics to the concept of a limit in sequences and series.
- 84Relates the concept of average rate of change to the slope of a secant line, and instantaneous rate of change to the slope of a tangent line.
- 85Relates topics in middle school mathematics, such as areas of polygons, to the concept of area under a curve.
- 86Applies the concepts of rate of change, area, and accumulation to describe rates, volumes, and the behavior of functions.
Competency 008: Measurement as a Process
- 87Selects and uses appropriate units of measurement and appropriate measurement tools.
- 88Develops and applies procedures for converting within and between measurement systems.
- 89Applies dimensional analysis to derive units and to solve measurement problems.
- 90Describes the precision of measurement, significant digits, and the propagation of measurement error.
- 91Applies the Pythagorean theorem and right-triangle trigonometry to solve measurement problems.
Competency 009: Euclidean Geometry and Axiomatic Structure
- 92Understands concepts and properties of points, lines, planes, angles, lengths, and distances.
- 93Analyzes and applies the properties of parallel and perpendicular lines, including angle relationships formed by a transversal.
- 94Uses the properties of congruent triangles to explore geometric relationships and prove theorems.
- 95Describes and justifies geometric constructions.
- 96Applies the axiomatic structure of Euclidean geometry, including undefined terms, definitions, postulates, and theorems, to prove results.
Competency 010: Properties of Two- and Three-Dimensional Figures
- 97Derives, justifies, and applies formulas for lengths, perimeters, circumferences, areas, surface areas, and volumes.
- 98Applies relationships of similarity, including the effects of scale factor on length, area, and volume.
- 99Uses a variety of representations, including nets and cross sections, to analyze and solve problems involving figures.
- 100Analyzes the relationships among three-dimensional figures and their two-dimensional representations.
Competency 011: Transformational and Coordinate Geometry
- 101Describes and justifies geometric constructions, including those made with reflection devices and other tools.
- 102Uses translations, reflections, glide reflections, and rotations to describe congruence and to solve problems.
- 103Uses dilations to describe and analyze similarity relationships.
- 104Applies concepts of symmetry, including line and rotational symmetry, and analyzes tessellations.
- 105Applies the concepts of slope, midpoint, parallelism, perpendicularity, and distance in the coordinate plane.
- 106Performs and analyzes transformations of figures in the coordinate plane, including the effects on coordinates.
Competency 012: Exploring and Describing Data
- 107Organizes and displays data in a variety of formats, including tables, dot plots, stem-and-leaf plots, histograms, box plots, and scatter plots.
- 108Applies concepts of center, spread, shape, and skewness to describe a data distribution.
- 109Supports arguments, makes predictions, and draws conclusions using summary statistics and graphical displays.
- 110Understands measures of central tendency and measures of dispersion, including mean, median, mode, range, interquartile range, variance, and standard deviation.
- 111Analyzes the connections among concepts of center and spread and among different graphical displays of the same data.
- 112Calculates and interprets percentiles and quartiles.
Competency 013: Theory of Probability
- 113Explores concepts of probability through data collection, experiments, and simulations, and relates experimental to theoretical probability.
- 114Uses the concepts and principles of probability to describe the outcomes of simple and compound events.
- 115Generates, simulates, and uses probability models to represent situations.
- 116Determines probabilities by constructing sample spaces to model situations, including with tree diagrams and area models.
- 117Solves a variety of probability problems using combinations and permutations.
- 118Solves problems using binomial, geometric, and normal distributions.
Competency 014: Sampling and Statistical Inference
- 119Applies knowledge of designing, conducting, analyzing, and interpreting statistical experiments and studies.
- 120Understands random samples, sampling methods, sampling bias, and the concept of a confidence interval.
- 121Uses the concepts of probability to draw conclusions about a population from a sample.
- 122Makes inferences about a population using distributions of sample statistics.
- 123Uses scatter plots, correlation, and regression analysis to analyze bivariate data and make predictions.
Competency 015: Mathematical Reasoning and Problem Solving
- 124Demonstrates an understanding of proof, including direct proof, indirect proof, and counterexample.
- 125Applies correct mathematical reasoning to derive valid conclusions from a set of premises.
- 126Understands the roles of inductive and deductive reasoning in mathematics.
- 127Uses formal and informal reasoning to justify mathematical ideas and arguments.
- 128Recognizes that a problem may be solved in more than one way and compares solution strategies.
- 129Evaluates the reasonableness of a solution in the context of the original problem.
Competency 016: Mathematical Connections and Communication
- 130Recognizes and uses multiple representations of a mathematical concept and translates among them.
- 131Uses mathematics to model and solve problems in other disciplines, including science and social studies.
- 132Expresses mathematical statements using developmentally appropriate language, standard notation, and appropriate technology.
- 133Communicates mathematical ideas using a variety of representations, including verbal, graphical, numerical, symbolic, and physical.
- 134Understands the use of visual media, such as graphs, tables, diagrams, and animations, to communicate mathematical information.
- 135Uses appropriate mathematical terminology to express mathematical ideas precisely.
Competency 017: How Children Learn Mathematics
- 136Applies theories and principles of learning mathematics to plan appropriate instruction.
- 137Understands that students approach mathematical ideas in different ways and at different rates.
- 138Builds new mathematical learning on students’ prior knowledge and experience.
- 139Understands the appropriate use of manipulatives, models, and technology in developing mathematical understanding.
- 140Understands how to motivate students and encourage productive mathematical dispositions.
- 141Provides instruction that moves students from concrete to representational to abstract understanding.
Competency 018: Planning and Implementing Mathematics Instruction
- 142Demonstrates knowledge of a variety of instructional methods, strategies, and materials for teaching mathematics.
- 143Plans instruction that is interconnected and that builds coherently across the TEKS.
- 144Develops clear, measurable learning goals aligned to the TEKS.
- 145Establishes and manages transitions from concrete to abstract mathematical understanding within lessons.
- 146Applies a variety of instructional delivery methods, including direct instruction, guided discovery, and cooperative learning.
- 147Creates an inclusive learning environment that supports all students, including English learners and students receiving special education services.
Competency 019: Mathematics Assessment
- 148Understands the purposes and appropriate uses of formative and summative assessment in mathematics.
- 149Selects and uses appropriate assessment methods, including observation, interviews, performance tasks, portfolios, and written tests.
- 150Develops assessments that reveal students’ conceptual understanding and expose misconceptions.
- 151Evaluates the strengths and limitations of various assessment methods.
- 152Uses assessment results to modify, adapt, and differentiate mathematics instruction.
Before test day
The mistake to avoid is preparing for this as a pure content exam. More than a quarter of it asks about reasoning and about students, and those questions reward a different habit: on any item that shows you student work, name the specific error before you read the choices, because the wrong answers are written to be attractive to someone who has not. On the content side, unit conversion in two and three dimensions quietly costs more points than any single topic.
A USEFUL NEXT STEP
TExES Mathematics 4-8: study questions
What can I study in this TExES Mathematics 4-8 Online Center?
This TExES Mathematics 4-8 Online Center includes practice, lessons, worksheets, flashcards and review tools. Topics on the page include Domain II: Patterns and algebra (21 percent), Domain III: Geometry and measurement (21 percent), Domain I: Number concepts (16 percent).
How should I use the TExES Mathematics 4-8 resources?
Choose a topic or practice activity from this Online Center. Review the linked explanation, try the practice, and use the result to decide what to study next. Check each resource’s directions for its format and access requirements.
Resources from Effortless Math · Editorial standards