# Preparation Manual

## Section 3: Overview and Exam Framework TX PACT: Mathematics: Grades 4–8 (715)

### Exam Overview

Table outlining the test format, number of questions, time, and passing score.
Exam Name TX PACT: Mathematics: Grades 4–8
Exam Code 715
Time 5 hours total appointment time
• 15 minutes for CAT tutorial and compliance agreement
• 4 hours and 45 minutes testing time
Number of Questions 125 selected-response questions
Format Computer-administered test (CAT)

The TX PACT: Mathematics: Grades 4–8 (715) exam is designed to assess whether a test taker has demonstrated the requisite knowledge and skills for admission to an educator preparation program. The 125 selected-response questions are based on the Mathematics: Grades 4–8 exam framework. Questions on this exam range from grades 4–8. Your final scaled score will be based only on scored questions.

### Domains and Competencies

Table outlining test content and subject weighting by sub area and objective.
Domain Domain Title Approx. Percentage of Exam
I Number Sense and Operations 17%
II Algebra and Functions 33%
III Measurement and Geometry 25%
IV Statistics, Probability, and Discrete Mathematics 25%

The content covered by this exam is organized into broad areas of content called domains. Each domain covers one or more of the standards for this field. Within each domain, the content is further defined by a set of competencies. Each competency is composed of two major parts:

• The competency statement, which broadly defines what an individual should know and be able to do in order to perform effectively in a Texas-approved educator preparation program.
• The descriptive statements, which describe in greater detail the knowledge and skills eligible for testing.

#### Domain I—Number Sense and Operations

##### Competency 001—Understand numbers.

For example:

1. Analyze the relationships between the subsets of the real numbers.
2. Analyze the role of place value in any number system.
3. Analyze the use of estimation in a variety of situations.
4. Translate between different representations of numbers.
5. Apply number-theory concepts (e.g., divisibility rules, prime factorization, greatest common factors) in problem-solving situations.
##### Competency 002—Understand operations.

For example:

1. Analyze relational and operational properties.
2. Analyze a variety of conventional and alternative algorithms.
3. Solve a variety of problems involving integers, fractions, and decimals.
4. Solve a variety of problems involving ratios, proportions, and percents.

#### Domain II—Algebra and Functions

##### Competency 003—Understand patterns, relations, and functions.

For example:

1. Analyze a variety of patterns.
2. Analyze the properties of relations and functions in multiple representations (e.g., tables, graphs, equations, words).
3. Analyze direct and inverse proportional relationships.
4. Determine the effects of transformations on the graph of a function or relation.
##### Competency 004—Understand algebraic techniques and applications.

For example:

1. Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor).
2. Solve linear and nonlinear equations and inequalities.
3. Connect appropriate algebraic notation to phrases and sentences.
##### Competency 005—Understand linear relations and applications.

For example:

1. Analyze the relationship between a linear equation or inequality and its representations.
2. Solve systems of linear inequalities or equations with a variety of methods.
3. Interpret the meaning of the slope and the y-intercept in various contexts.
4. Analyze a variety of real-world problems involving linear equations, systems, and inequalities.
##### Competency 006—Understand nonlinear relations and concepts of calculus.

For example:

1. Analyze relationships between multiple representations of a nonlinear equation or inequality.
2. Solve a variety of real-world problems involving nonlinear equations and inequalities.
3. Analyze function behavior in terms of limits, continuity, and rates of change.
4. Apply concepts of calculus to solve problems in real-world situations.

#### Domain III—Measurement and Geometry

##### Competency 007—Understand measurement principles, procedures, and applications.

For example:

1. Analyze the use of various units and unit conversions within the customary and metric systems.
2. Calculate or estimate measures of lengths, areas, and volumes.
3. Apply the concepts of similarity, scale factors, and proportional reasoning to solve indirect measurement problems.
4. Analyze precision, accuracy, and rounding in measurements and computed quantities.
##### Competency 008—Understand euclidean geometry in two and three dimensions.

For example:

1. Analyze properties of points, lines, planes, and angles.
2. Use the properties of triangles, quadrilaterals, and other polygons and circles to solve problems.
3. Apply principles of similarity and congruence.
4. Apply the Pythagorean theorem and its converse.
5. Use nets, cross sections, and projections to analyze three-dimensional figures.
6. Analyze geometric arguments using deductive reasoning.
##### Competency 009—Understand coordinate and transformational geometry.

For example:

1. Analyze two- and three-dimensional figures using coordinate systems.
2. Connect algebra and geometry by applying concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane.
3. Analyze transformations of figures in the coordinate plane.
4. Analyze figures in terms of symmetry, and tessellations of the plane.

#### Domain IV—Statistics, Probability, and Discrete Mathematics

##### Competency 010—Understand principles and techniques of statistics.

For example:

1. Analyze the effects of bias and sampling techniques.
2. Use appropriate formats for organizing and displaying data.
3. Analyze univariate and bivariate data in a variety of representations.
4. Make predictions from data presented in a variety of representations.
5. Analyze the use of measures of central tendency and spread.
##### Competency 011—Understand principles of probability and techniques for determining probability.

For example:

1. Determine probabilities of simple and compound events.
2. Use counting principles to calculate probabilities.
3. Use a variety of visual representations to calculate probabilities.
4. Demonstrate knowledge of methods for simulating probabilities.
##### Competency 012—Understand principles of discrete mathematics.

For example:

1. Apply concepts of permutations and combinations to solve problems.
2. Analyze sequences and series, including limits and recursive definitions.
3. Use finite graphs and trees to represent problem situations.
4. Apply set theory to solve problems.
5. Apply principles of logic to solve problems (e.g., conditional and biconditional statements, conjunctions, negations).