Algebra FlexBook® for Middle School

Algebra FlexBook® for High School

For Middle School

For High School

Levels are CK-12's student achievement levels.

Basic
Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.

At Grade (Proficient)
Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.

Advanced
Students matched to this level are ready for material that requires superior performance and mastery.

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- Real Numbers
- Number Lines
- Inequalities on a Number Line
- Sets and Symbols
- Order of Operations
- Algebra Expressions with Fraction Bars
- Algebra Expressions with Exponents
- Calculator Use with Algebra Expressions
- Numerical Expression Evaluation
- Numerical Expression Evaluation with Basic Operations
- Numerical Expression Evaluation with Grouping Symbols
- Expression Evaluation with Powers and Grouping Symbols
- Polynomial Expression Evaluation
- Definition of Variable
- Mathematical Expressions
- Expressions with One or More Variables
- Patterns and Expressions
- Words that Describe Patterns
- Single Variable Expressions
- Expressions for Real-Life Situations
- Checking Solutions
- Checking Solutions to Equations
- Checking Solutions to Inequalities
- Variable Expressions
- Addition and Subtraction Phrases as Expressions
- Multiplication and Division Phrases as Expressions
- Sums and Differences of Single Variable Expressions
- Products and Quotients of Variable Expressions
- Working with Real Numbers
- Axioms for Real Numbers
- Mixed Numbers in Applications
- Rational Numbers in Applications
- Distributive Property
- Expressions and the Distributive Property
- When to Use the Distributive Property
- Distributive Property to Evaluate Formulas with Decimals
- Opposites and Absolute Values
- Additive Inverses and Absolute Values
- Absolute Value
- Operations with Real Numbers
- Properties of Real Number Addition
- Properties of Real Number Multiplication
- Simplify Expressions
- Simplify Variable Expressions Involving Integers
- Simplify Variable Expressions Involving Integer Addition
- Simplify Variable Expressions Involving Integer Subtraction
- Simplify Variable Expressions Involving Integer Multiplication
- Simplify Variable Expressions Involving Integer Division
- Simplify Single Variable Expressions
- Simplify Sums or Differences of Single Variable Expressions
- Simplify Products or Quotients of Single Variable Expressions
- Simplify Variable Expressions Involving Multiple Operations

- Linear Equations
- Equations that Describe Patterns
- Sentences as Single Variable Equations
- Addition and Subtraction Phrases as Equations
- Multiplication and Division Phrases as Equations
- Single Variable Equations from Verbal Models
- Input-Output Tables
- Function Rules for Input-Output Tables
- Input-Output Tables for Function Rules
- Extend Numerical Patterns
- One-Step Equations and Inverse Operations
- Single Variable Addition Equations
- Single Variable Subtraction Equations
- Mental Math for Addition and Subtraction Equations
- Inverse Property of Addition in Decimal Equations
- Inverse Property of Addition in Fraction Equations
- One-Step Equations Transformed by Multiplication/Division
- Single Variable Multiplication Equations
- Single Variable Division Equations
- Mental Math for Multiplication/Division Equations
- Division to Solve Decimal Equations
- Multi-Step Equations
- Two-Step Equations and Properties of Equality
- Two-Step Equations from Verbal Models
- Two-Step Equations with Addition and Multiplication
- Two-Step Equations with Addition and Division
- Two-Step Equations with Subtraction and Multiplication
- Two-Step Equations with Subtraction and Division
- Solving Real-World Problems with Two-Step Equations
- Multi-Step Equations with Like Terms
- Equations with Decimals, Fractions, and Parentheses
- Equations with Fractions
- Equations with Decimals
- Distributive Property for Multi-Step Equations
- Solving Real-World Problems Using Multi-Step Equations
- Equations with Variables on Both Sides
- Applications of One-Step Equations
- Problem-Solving Models
- Comparison of Problem-Solving Models
- Trends in Data
- Guess and Check, Work Backward
- Scale and Indirect Measurement Applications
- Formulas for Problem Solving
- Dimensional Analysis
- Applications Using Linear Models
- Problem Solving Plan, Mental Math

- Linear Inequalities
- Inequalities that Describe Patterns
- Inequality Expressions
- Inequalities with Addition and Subtraction
- Inequalities with Multiplication and Division
- Inequalities with Multiplication
- Inequalities with Division
- Multi-Step Inequalities
- Inequalities with Like Terms
- Inequalities with the Distributive Property
- Compound Inequalities
- Solutions to Compound Inequalities
- Absolute-Value Equations and Inequalities
- Absolute Value Equations
- Graphs of Absolute Value Equations
- Absolute Value Inequalities
- Graphs of General Absolute Value Equations with Technology
- Graphs of Absolute Value Inequalities
- Applications with Inequalities
- One-Step Inequalities

- Function Notation
- Domain and Range of a Function
- Functions that Describe Situations
- Points in the Coordinate Plane
- Ordered Pairs in Four Quadrants
- Coordinate Locations on a Map
- Graphs in the Coordinate Plane
- Functions on a Cartesian Plane
- Graphs of Functions based on Rules
- Function Rules based on Graphs
- Graphs of Inequalities in One Variable
- Linear and Non-Linear Function Distinction
- Linear and Non-Linear Patterns of Change
- Algebraic Functions
- Vertical Line Test
- Function Notation and Linear Functions
- Graph of a Linear Equation in Two Variables
- Graphs of Linear Equations
- Horizontal and Vertical Line Graphs
- Intercepts by Substitution
- Intercepts and the Cover-Up Method
- Graphs of Linear Functions
- Applications of Linear Graphs
- Problem Solving with Linear Graphs
- Linear Inequalities in Two Variables
- Testing Solutions for Linear Inequalities in Two Variables
- Slope
- Rates of Change
- Slope of a Line Using Two Points
- Slope-Intercept Form
- Graphs Using Slope-Intercept Form
- Graphs of Linear Models of Direct Variation
- Forms of Linear Equations
- Standard Form of Linear Equations
- Slope-Intercept Form of Linear Equations
- Linear Equations in Point-Slope Form
- Write a Function in Slope-Intercept Form
- Comparing Equations of Parallel and Perpendicular Lines
- Equations of Parallel Lines
- Equations of Perpendicular Lines
- Families of Lines
- Determining the Equation of a Line
- Write an Equation Given the Slope and a Point
- Write an Equation Given Two Points
- Fitting Lines to Data
- Linear Interpolation and Extrapolation
- Problem Solving with Linear Models

- Systems of Equations and Inequalities
- Systems of Linear Equations in Two Variables
- Checking a Solution for a Linear System
- Graphs of Linear Systems
- Linear Systems with Addition or Subtraction
- Linear Systems with Multiplication
- Solving Systems by Multiplying One Equation
- Solving Systems by Multiplying Both Equations
- Comparing Methods for Solving Linear Systems
- Systems Using Substitution
- Consistent and Inconsistent Linear Systems
- Determining the Type of Linear System
- Applications of Linear Systems
- Graphs of Systems of Linear Inequalities in Two Variables
- Checking for Solutions to Systems of Linear Inequalities
- Systems of Linear Equations in Three Variables
- Mixture Problems
- Systems of Linear Inequalities
- Linear Programming

- Polynomials and Factoring
- Addition and Subtraction of Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Polynomials in Standard Form
- Multiplication of Monomials by Polynomials
- Multiplication of Polynomials by Binomials
- Multiplying Polynomials
- Multiplying Binomials Mentally
- Factoring Completely
- Monomial Factors of Polynomials
- Special Products of Polynomials
- Factor Polynomials Using Special Products
- Factorization using Difference of Squares
- Factorization using Perfect Square Trinomials
- Factorization of Quadratic Expressions
- Factorization of Quadratic Expressions with Negative Coefficients
- Factoring when the Leading Coefficient Equals 1
- Factoring by Grouping
- Sum and Difference of Cubes
- Applications of Factoring
- Zero Product Principle
- Solving Problems by Factoring

- Rational Expressions
- Division of Polynomials
- Excluded Values for Rational Expressions
- Simplifying Rational Expressions
- Zero, Negative, and Fractional Exponents
- Negative Exponents
- Fractional Exponents
- Evaluating Exponential Expressions
- Operations with Rational Exponents
- Operations with Rational Expressions
- Products and Quotients of Rational Expressions
- Multiplication of Rational Expressions
- Division of Rational Expressions
- Addition and Subtraction of Rational Expressions
- Applications of Adding and Subtracting Rational Expressions
- Sums and Differences of Rational Expressions with Unequal Denominators
- Adding and Subtracting Rational Expressions where One Denominator is the LCD
- Complex Fractions
- Rational Expressions in Open Sentences
- Percent Problems
- Rational Expressions in Equations and Problems
- Clearing Denominators in Rational Equations
- Solving Rational Equations using Cross-Multiplication
- Solving Rational Equations using the LCD
- Number Problems
- Ratio, Proportion, and Variation
- Rational Equations Using Proportions
- Proportions with Variable in the Numerator
- Proportions with Variable in the Denominator
- Direct Variation
- Applications Using Direct Variation
- Inverse Variation Models
- Graphs of Rational Functions
- Horizontal and Vertical Asymptotes
- Determining Asymptotes by Division
- Inverse Variation Problems
- Oblique Asymptotes
- Joint and Combined Variation
- Applications Using Rational Equations

- Square Roots and Irrational Numbers
- Properties of Rational Numbers versus Irrational Numbers
- Evaluation of Square Roots
- Evaluation of Perfect Square Roots
- Rational Square Roots
- Irrational Square Roots
- Estimation of Square Roots
- Pythagorean Theorem and its Converse
- Solving Equations Using the Pythagorean Theorem
- Applications Using the Pythagorean Theorem
- Distance Formula
- Midpoint Formula
- Expressions with Radicals
- Simplification of Radical Expressions
- Multiplication and Division of Radicals
- Raising a Product or Quotient to a Power
- Addition and Subtraction of Radicals
- nth Roots
- Radical Equations
- Equations with Radicals on Both Sides
- Applications Using Radicals
- Equations with Square Roots
- Radical Equations with Variables on Both Sides
- Graphs of Square Root Functions
- Shifts of Square Root Functions

- Quadratic and Exponential Equations and Functions
- Solutions Using the Discriminant
- Use Square Roots to Solve Quadratic Equations
- Square Root Applications
- Completing the Square
- Vertex Form of a Quadratic Equation
- Completing the Square when the Leading Coefficient Equals 1
- Quadratic Formula
- Discriminant
- Using Quadratic Equations to Solve Problems
- Comparing Methods for Solving Quadratics
- Graphing Quadratic and Other Polynomial Functions and Equations
- Quadratic Functions and Their Graphs
- Vertical Shifts of Quadratic Functions
- Use Vertex Form of Quadratics
- Graphs of Quadratic Functions in Intercept Form
- Graphing Calculator to Graph Quadratic Functions
- Transformations of Quadratic Functions
- Roots to Determine a Quadratic Function
- Quadratic Functions and Equations
- Use Graphs to Solve Quadratic Equations
- Polynomial Functions
- Exponential Properties and Functions
- Exponent Properties with Variable Expressions
- Exponential Properties Involving Products
- Exponential Properties Involving Quotients
- Exponent of a Quotient
- Exponential Terms Raised to an Exponent
- Solving Equations with Exponents
- Solving Equations with Fractional Exponents
- Scientific Notation
- Scientific Notation with a Calculator
- Comparison of Numbers in Scientific Notation
- Operations with Numbers in Scientific Notation
- Exponential Growth and Decay
- Exponential Growth
- Exponential Decay
- Geometric Sequences and Exponential Functions
- Applications of Exponential Functions
- Graphs of Exponential Functions
- Logarithms
- Linear, Exponential, and Quadratic Models
- Applications of Function Models
- Identification of Quadratic Models

- Matrices
- Matrices to Represent Data
- Matrix Algebra
- Adding and Subtracting Matrices
- Multiplying Matrices by a Scalar
- Matrix Multiplication
- Limitations of Matrix Multiplication
- Determinants
- Cramer's Rule
- Matrix Equations
- Solving a Matrix Equation
- Row Operations and Row Echelon Forms
- Augmented Matrices
- Writing and Solving a Matrix Equation for a Linear System
- Solving Linear Systems Using Matrices and Technology
- Inverse Matrices
- Applications of Matrices
- Partial Fraction Expansions

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