TX-Algebra I TX Essential Knowledge and Skills 2009 · PDF fileTX-Algebra I TX Essential...

TX-Algebra I TX Essential Knowledge and Skills 2009

Standard ID Standard Text Edgenuity Lesson Name

Algebra I

Foundations for functions.

A.1 The student understands that a function represents a dependence of one quantity on another and can be

described in a variety of ways.A.1.A describe independent and dependent quantities in functional relationships;

Inequalities and Their Graphs

Functions

Slope-Intercept Form

Graphing Inequalities

Scatter Plots

Graphing Linear Functions

Relations

Writing Rules for Linear Functions

Understand Functions

Linear Inequalities

Relations and Functions

Function Notation

Graph Functions

Write Function Rules

Standard Form of a Linear Equation

Graph Linear Inequalities

Write Equations in Slope-Intercept Form

Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

©Edgenuity Inc. Confidential of 36



A.1.B gather and record data and use data sets to determine functional relationships between quantities;

Functions

Linear Equations and Two Variables

Slope


Writing Linear Equations

Scatter Plots

Identifying and Writing Proportions

Algebra: Solving Proportions


Relations


Mathematical Modeling

Growth and Decay Factors

Consecutive Growth and Decay Factors

Exponential Functions

Use Exponential Functions

Population Growth

Equations of Exponential Functions

Inverse Variation

Constant of Variation


Function Notation

Graph Functions



Scatterplots

Direct and Inverse Variation


Growth and Decay




A.1.C describe functional relationships for given problem situations and write equations or inequalities to answer

questions arising from the situations;Writing Two-Step Equations


Functions



Scatter Plots

Interpreting Graphs

Relations



Domain and Range


Slope

Write Linear Equations using Slope & y-Intercepts

Write Linear Equations using Two Points

Break-Even Points

Linear Inequalities


Equations as Mathematical Models

Translate and Solve Written Statements

Literal Equations

Model and Solve Problems with Multi-Step

EquationsWrite and Solve Inequalities


Graph Functions






Point-Slope Form

Parallel Lines




A.1.C describe functional relationships for given problem situations and write equations or inequalities to answer

questions arising from the situations; (Cont'd.)Perpendicular Lines

Equations of Lines

Model and Solve Problems with Linear Systems

Scatterplots

Solve by Factoring

Model and Solve Problems with Quadratics

A.1.D represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal

descriptions, equations, and inequalities; andWriting Two-Step Equations

Using Proportions

Functions


Graphing Linear Equations Using Intercepts

Slope

Rate of Change




Scatter Plots



Scatter Plots

Interpreting Graphs


Relations


Problem-Solving

Patterns

Expressions and Formulas

Proportional Reasoning

Unit Analysis


Domain and Range





descriptions, equations, and inequalities; and (Cont'd.)Mathematical Modeling

Write and Solve Equations

Slope

Systems of Equations

Break-Even Points

Quadratic Functions

Quadratic Equations

Parabolas

Solving Quadratic Equations





Population Growth


Direct Variation

Inverse Variation


Real Number Operations

Use Variables to Represent Numbers

Properties of Real Numbers

Simplify Expressions



Literal Equations


EquationsProperties of Inequality

Write and Solve Inequalities

Two-Step Inequalities

Multi-Step Inequalities

Compound Inequalities






descriptions, equations, and inequalities; and (Cont'd.)Function Notation

Graph Functions






Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Solve a Linear System Graphically

Solve a Linear System by Substitution

Solve a Linear System by Elimination


Quadratic Equations in Standard Form

Intercepts and Zeros

Quadratic Equations in Vertex Form

Convert Between Standard and Vertex Form

Making Connections: Daredevil Danny

Model Problems with Quadratic Functions




Growth and Decay




A.1.E interpret and make decisions, predictions, and critical judgments from functional relationships.


Solving Inequalities by Adding and Subtracting

Solving Inequalities by Multiplication and Division

Functions



Slope

Rate of Change




Scatter Plots



Scatter Plots

Interpreting Graphs


Relations




Linear Inequalities





Population Growth


Inverse Variation


Graph Functions






A.1.E interpret and make decisions, predictions, and critical judgments from functional relationships. (Cont'd.)

Slope




Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots







Growth and Decay

A.2 The student uses the properties and attributes of functions.

A.2.A identify and sketch the general forms of linear (y = x) and quadratic (y = x²) parent functions;






Quadratic Functions

Quadratic Equations

Parabolas

Graph Functions


Slope








A.2.A identify and sketch the general forms of linear (y = x) and quadratic (y = x²) parent functions; (Cont'd.)



A.2.B identify mathematical domains and ranges and determine reasonable domain and range values for given

situations, both continuous and discrete;Systems of Equations

Functions



Slope


Scatter Plots

Interpreting Graphs


Relations



Domain and Range


Parabolas





Scatterplots





A.2.C interpret situations in terms of given graphs or creates situations that fit given graphs; and

Functions



Slope

Rate of Change




Scatter Plots

Interpreting Graphs

Relations




Reading Graphs


Function Notation

Graph Functions


Slope




Scatterplots









Growth and Decay




A.2.D 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.Slope-Intercept Form


Scatter Plots

Line Graphs

Scatter Plots


Scatterplots

Organizing Data

Graph Functions


Scatterplots



A.3 The student understands how algebra can be used to express generalizations and recognizes and uses the

power of symbols to represent situations.A.3.A use symbols to represent unknowns and variables; and

Solving Equations by Adding or Subtracting

Solving Equations by Multiplying or Dividing

Solving Two-Step Equations

Writing Two-Step Equations

Using Proportions






Slope



Scatter Plots

Scatter Plots





A.3.A use symbols to represent unknowns and variables; and (Cont'd.)


Problem-Solving

Patterns



Unit Analysis


Domain and Range




Break-Even Points




Zero and Negative Exponents

Multiply with Like Bases

Divide with Like Bases

A Quantity to a Power

Apply Laws of Exponents

Addition and Multiplication Properties of Equality

Two-Step Equations

Equations with Like Terms

Equations with Variables on Both Sides


Solve Equations Using the Distributive Property

Simplify and Solve Equations


Literal Equations


Equations




A.3.A use symbols to represent unknowns and variables; and (Cont'd.)

Properties of Inequality






Graph Functions







Add and Subtract Polynomials

Multiply and Divide by a Monomial

Multiply Polynomials

Special Products

Simplify Polynomial Expressions

The Greatest Common Factor

Factor by Grouping

Factor Trinomials with Leading Coefficient of One

Factor Trinomials with a Leading Coefficient Other

than OneSpecial Cases

Factoring Polynomials

The Quadratic Formula





A.3.B look for patterns and represent generalizations algebraically.



Scatter Plots


Problem-Solving

Patterns



Unit Analysis


Solving an Equation














EquationsWrite and Solve Inequalities

Function Notation

Graph Functions





Special Products

Divide Polynomials




A.3.B look for patterns and represent generalizations algebraically. (Cont'd.)



Factor by Grouping









Solve by Factoring

A.4 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.A.4.A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as

necessary in problem situations;Solving Equations by Adding or Subtracting




Using Proportions

Solving Multi-Step Equations

Solving Equations with Variables on Both Sides

Solving Equations with Grouping Symbols




Solving an Equation



Break-Even Points

Linear Inequalities




A.4.A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as

necessary in problem situations; (Cont'd.)Solving Quadratic Equations












Two-Step Equations







Literal Equations


EquationsFunction Notation








Special Products

Divide Polynomials





A.4.A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as

necessary in problem situations; (Cont'd.)The Greatest Common Factor

Factor by Grouping







Solve by Factoring

Complete the Square


Irrational Roots


A.4.B use the commutative, associative, and distributive properties to simplify algebraic expressions; and









Break-Even Points

Linear Inequalities












A.4.B use the commutative, associative, and distributive properties to simplify algebraic expressions; and (Cont'd.)



Two-Step Equations






Literal Equations














Special Products

Divide Polynomials



Factor by Grouping





Solve by Factoring




A.4.B use the commutative, associative, and distributive properties to simplify algebraic expressions; and (Cont'd.)


Irrational Roots

A.4.C connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.


Functions






Relations


Domain and Range

Linear Inequalities

Quadratic Functions



Function Notation

Graph Functions



Slope




Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines







Linear functions.

A.5 The student understands that linear functions can be represented in different ways and translates among

their various representations.A.5.A determine whether or not given situations can be represented by linear functions;

Functions




Relations


Slope

Function Notation



Slope

Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots

A.5.B determine the domain and range for linear functions in given situations; and




Slope

Rate of Change




Line Graphs


Relations


Domain and Range

Scatterplots




A.5.B determine the domain and range for linear functions in given situations; and (Cont'd)

Organizing Data

Linear Inequalities


Function Notation

Graph Functions



Slope



Equations of Lines

A.5.C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear

functions.Writing Two-Step Equations

Using Proportions



Functions



Slope

Rate of Change



Line Graphs


Relations




Scatterplots

Organizing Data






A.5.C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear

functions. (Cont'd.)Write Linear Equations using Two Points

Properties of Inequality



Graph Functions






Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots

A.6 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.A.6.A develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic

representations;Functions



Slope

Rate of Change



Scatter Plots


Relations


Slope





A.6.A develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic

representations; (Cont'd.)Write Linear Equations using Slope & y-Intercepts



Slope



Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots

A.6.B interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;



Slope

Rate of Change



Scatter Plots

Line Graphs

Scatter Plots


Scatterplots

Organizing Data

Slope




Slope



Point-Slope Form

Parallel Lines




A.6.B interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

(Cont'd.)

Perpendicular Lines

Equations of Lines

Scatterplots

A.6.C investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

Functions



Slope

Rate of Change



Line Graphs


Relations


Scatterplots

Organizing Data

Slope



Slope



Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots




A.6.D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and

y-intercept;Functions



Slope



Scatter Plots

Line Graphs


Relations


Scatterplots

Organizing Data




Graph Functions

Slope



Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines




A.6.E determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables,

and algebraic representations;Functions



Rate of Change




Relations





Graph Functions


Slope




Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots

A.6.F interpret and predict the effects of changing slope and y-intercept in applied situations; and



Slope

Rate of Change



Slope


Slope




A.6.F interpret and predict the effects of changing slope and y-intercept in applied situations; and (Cont'd.)



Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines

Scatterplots

A.6.G relate direct variation to linear functions and solve problems involving proportional change.

Using Proportions

Slope

Rate of Change


Unit Analysis

Direct Variation

Inverse Variation



A.7 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.A.7.A analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;


















A.7.A analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

(Cont'd.)



Solving an Equation


Linear Inequalities







Literal Equations








Point-Slope Form

Parallel Lines

A.7.B 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; andSolving Equations by Adding or Subtracting




Using Proportions









properties of equality, select a method, and solve the equations and inequalities; and (Cont'd.)











Solving an Equation


Linear Inequalities


Two-Step Equations







Literal Equations














properties of equality, select a method, and solve the equations and inequalities; and (Cont'd.)

Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines


A.7.C interpret and determine the reasonableness of solutions to linear equations and inequalities.





Using Proportions










Rate of Change





Solving an Equation


Linear Inequalities


Two-Step Equations






A.7.C interpret and determine the reasonableness of solutions to linear equations and inequalities. (Cont'd.)





Literal Equations







Slope




Point-Slope Form

Parallel Lines

Perpendicular Lines

Equations of Lines


A.8 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.A.8.A analyze situations and formulate systems of linear equations in two unknowns to solve problems;



Break-Even Points








A.8.B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods; and



Break-Even Points





A.8.C interpret and determine the reasonableness of solutions to systems of linear equations.



Break-Even Points





Quadratic and other nonlinear functions.

A.9 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.

A.9.A determine the domain and range for quadratic functions in given situations;

Quadratic Functions

Quadratic Equations

Parabolas

Graph Functions







Solve by Factoring

Complete the Square


Irrational Roots




A.9.B investigate, describe, and predict the effects of changes in a on the graph of y = ax² + c;

Quadratic Functions

Quadratic Equations

Parabolas







A.9.C investigate, describe, and predict the effects of changes in c on the graph of y = ax² + c; and

Quadratic Functions

Quadratic Equations

Parabolas







A.9.D analyze graphs of quadratic functions and draw conclusions.

Quadratic Functions

Quadratic Equations

Parabolas








Solve by Factoring





A.10 The student understands there is more than one way to solve a quadratic equation and solves them using

appropriate methods.A.10.A solve quadratic equations using concrete models, tables, graphs, and algebraic methods; and

Quadratic Functions









Solve by Factoring

Complete the Square


Irrational Roots


A.10.B 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.Solving Quadratic Equations











Solve by Factoring

Complete the Square





A.10.B 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. (Cont'd.)Irrational Roots


A.11 The student understands there are situations modeled by functions that are neither linear nor quadratic and

models the situations.A.11.A use patterns to generate the laws of exponents and apply them in problem-solving situations;

Exponents and Multiplication

Exponents and Division

Scientific Notation

Rate of Change

Negative Exponents

Quadratic Functions

Quadratic Equations

Parabolas





Population Growth










Factor by Grouping








A.11.B analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or

algebraic methods; andRate of Change



Direct Variation

Inverse Variation




Growth and Decay

A.11.C analyze data and represent situations involving exponential growth and decay using concrete models, tables,

graphs, or algebraic methods.Growth and Decay Factors




Population Growth



Growth and Decay


TX-Algebra I TX Essential Knowledge and Skills 2009 · PDF fileTX-Algebra I TX Essential...

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