| Module | Lesson Title and Descriptor | TEKS |
| 1
Functional Relationships | Describing Independent and Dependent Quantities (Verbal/Symbolic) | A.1A
(A.1A) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to describe independent and dependent quantities in functional relationships. |
| Analyzing Functional Relationships: Dependency Statements | A.1A
(A.1A) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to describe independent and dependent quantities in functional relationships. |
| Writing Equations to Describe Functional Relationships (Table → Equation) | A.1B
(A.1B) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to gather and record data and use data sets to determine functional relationships between quantities. |
| Determining if a Relationship is a Functional Relationship | A.1B
(A.1B) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to gather and record data and use data sets to determine functional relationships between quantities. |
| Writing Equations to Describe Functional Relationships | A.1C
(A.1C) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations. |
| Writing Inequalities to Describe Relationships (Verbal → Symbolic) | A.1C
(A.1C) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations. |
| Writing Inequalities to Describe Relationships (Graph → Symbolic) | A.1D
(A.1D) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. |
| Writing Inequalities to Describe Relationships (Symbolic → Graph) | A.1D
(A.1D) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. |
| Connecting Multiple Representations of Functions | A.1D
(A.1D) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. |
| Writing the Symbolic Representation of a function (Graph → Symbolic) | A.1D
(A.1D) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. |
| Determining the Graphical Representation of a Function (Symbolic → Graph) | A.1D
(A.1D) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. |
| Describing a Relationship (Graph → Verbal) | A.1E
(A.1E) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships. |
| Describing a Relationship (Verbal → Graph) | A.1E
(A.1E) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships. |
| Interpreting Functional Relationships (Verbal/Symbolic Descriptions) | A.1E
(A.1E) Foundations for Functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships. |
| 2
Properties and Attributes of Functions | Determining Parent Functions (Verbal/Graph) | A.2A
(A.2A) Foundations for Functions. The student uses the properties and attributes of functions. The student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions. |
| Determining Reasonable Domains and Ranges (Verbal/Graph) | A.2B
(A.2B) Foundations for Functions. The student uses the properties and attributes of functions. The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. |
| Interpreting Graphs | A.2C
(A.2C) Foundations for Functions. The student uses the properties and attributes of functions. The student is expected to interpret situations in terms of given graphs or creates situations that fit given graphs. |
| Interpreting Scatterplots | A.2D
(A.2D) Foundations for Functions. The student uses the properties and attributes of functions. The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. |
| Making Predictions and Critical Judgments (Table/Verbal) | A.2D
(A.2D) Foundations for Functions. The student uses the properties and attributes of functions. The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. |
| Collecting Data and Making Predictions | A.2D
(A.2D) Foundations for Functions. The student uses the properties and attributes of functions. The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. |
| 3
Algebraic Symbols and Symbolic Manipulation | Writing Expressions and Equations to Solve Problems (Verbal//Pictorial → Symbolic) | A.3A
(A.3A) Foundations for Functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to use symbols to represent unknowns and variables. |
| Writing Expressions to Model Patterns (Table/Pictorial → Symbolic) | A.3B
(A.3B) Foundations for Functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to look for patterns and represent generalizations algebraically. |
| Finding Specific Function Values (Verbal/Symbolic) | A.4A
(A.4A) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. |
| Simplifying Polynomial Expressions (Verbal/Symbolic) | A.4A
(A.4A) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. |
| Solving Equations and Inequalities | A.4A
(A.4A) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. |
Solving One-Variable Inequalities | A.4A
(A.4A) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. |
| Factoring to Solve Problems (Verbal/Symbolic) | A.4A
(A.4A) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. |
| Simplifying Algebraic Expressions (Symbolic) | A.4B
(A.4B) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressions. |
| Connecting Function Notation and Equation Notation | A.4C
(A.4C) Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1. |
| 4
Linear Functions | Determining Linear Functions (Verbal → Symbolic) | A.5A
(A.5A) Linear Functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to determine whether or not given situations can be represented by linear functions. |
| Determining Linear Functions (Symbolic → Verbal) | A.5A
(A.5A) Linear Functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to determine whether or not given situations can be represented by linear functions. |
| Determining the Domain and Range for Linear Functions | A.5B
(A.5B) Linear Functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to determine the domain and range for linear functions in given situations. |
Connecting Multiple Representations of Linear Functions | A.5C
(A.5C) Linear Functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. |
| Determining the Meaning of Slope and Intercepts | A.6B
(A.6B) Linear Functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. |
| Analyzing the effects of the changes in m and b on the graph of y = mx + b | A.6C
(A.6C) Linear Functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b. |
| Writing Equations of Lines | A.6D
(A.6D) Linear Functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. |
| Determining Intercepts and Zeros of Linear Functions | A.6E
(A.6E) Linear Functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations. |
| Predicting the Effects of Changing Slope and y-intercept in Problem Situations | A.6F
(A.6F) Linear Functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations. |
| 5
Linear Equations and Inequalities | Formulating Linear Equations to Solve Problems | A.7A
(A.7A) Linear Functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. |
| Formulating Linear Inequalities to Solve Problems | A.7A
(A.7A) Linear Functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. |
| Investigating Methods for Solving Linear Equations and Inequalities | A.7B
(A.7B) Linear Functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities. |
| Solving Linear Equations and Inequalities | A.7B
(A.7B) Linear Functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities. |
| Determining Reasonableness of Solutions (Linear Equations) | A.7C
(A.7C) Linear Functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities. |
| Determining Reasonableness of Solutions (Linear Inequalities) | A.7C
(A.7C) Linear Functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities. |
| Formulating Systems of Equations (Verbal → Symbolic)
| A.8A
(A.8A) Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems. |
| Solving Systems of Equations (Concrete Models) | A.8B
(A.8B) Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods. |
| Solving Systems of Equations with Graphs | A.8B
(A.8B) Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods. |
| Solving Systems of Equations with Tables | A.8B
(A.8B) Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods. |
| Solving Systems of Equations with Algebraic Methods | A.8B
(A.8B) Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods. |
| Determining Reasonableness of Solutions (System of Equations) | A.8C
(A.8C) Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to interpret and determine the reasonableness of solutions to systems of linear equations. |
| 6
Quadratic and Other Non-Linear Functions | Determining the Domain and Range for Quadratic Functions | A.9A
(A.9A) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to determine the domain and range for quadratic functions in given situations. |
| Analyzing the effects of the changes in a on the graph of y = ax2 + c | A.9B
(A.9B) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c. |
| Analyzing the effects of the changes in c on the graph of y = ax2 + c | A.9C
(A.9C) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to investigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c |
| Solving Quadratic Equations (Concrete Models) | A.10A
(A.10A) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods. |
| Solving Quadratic Equations (Algebraic Methods) | A.10A
(A.10A) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods. |
| Quadratics: Connecting Roots, Zeros and x-intercepts | A.10B
(A.10B) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. |
| Applying the Laws of Exponents (Verbal/Symbolic) | A.11A
(A.11A) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations. |
| Analyzing Situations Involving Inverse Variation (Graphs) | A.11B
(A.11B) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods. |
| Analyzing Situations Involving Inverse Variation (Algebraic Methods) | A.11B
(A.11B) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods. |
| Analyzing Situations Involving Exponential Growth and Decay (Tables) | A.11C
(A.11C) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. |
| Analyzing Situations Involving Exponential Growth and Decay (Graphs) | A.11C
(A.11C) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. |
| Analyzing Situations Involving Exponential Growth and Decay (Algebraic Methods) | A.11C
(A.11C) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. |