## UNIT I. Number Basics M1.1 – M3.5​

### Math1    Number Sense

M1.1

Order of Operations
• Order of Operations (PEMDAS)
• Problems Involving Multiplication, Division, Addition, and Subtraction (no parentheses)
• Order of Operations Involving Parentheses
• Order of Operations Involving Parentheses, Brackets, and/or
• Exponents
• Conclusion

M1.2

Divisibility Rules
• Definitions
• Divisibility by 2, 5, and 10
• Divisibility by 4
• Divisibility by 3 and 9
• Divisibility by 6
• Conclusion

M1.3

Properties of Addition and Multiplication and Inverse Operations
• Mental Math Using Properties of Addition
• Properties of Multiplication
• Mental Math Using Properties of Multiplication
• Conclusion

M1.4

Distributive Properties
• Distributive Property Model 1-Digit Number
• Distributive Property Model 1-Digit Number Times 2-Digit Number
• Distributive Property of Multiplication Over Subtraction
• Applications of the Distributive Property
• Conclusion

M1.5

Estimation

• Estimation Strategies: Front-End Estimation
• Estimation Strategies: Rounding
• Estimation Strategies: Compatible Numbers
• Comparing and Combining Estimation Strategies
• Conclusion

### Math2    Whole Number Operations

M2.1

• Partial Sums Method for Addition
• Conclusion

M2.2

Large Numbers: Subtraction

• Understanding Regrouping
• Subtraction Using Blocks
• Column Subtraction Method
• Counting Up Method
• Conclusion

M2.3

Large Numbers: Multiplication

• Estimating and Multiplying with Zeros
• Partial Products Method for Multiplication
• Multiplication Using Base Ten Blocks
• Conclusion

M2.4

Large Numbers: Division

• Finding a Reasonable Quotient or Estimation
• Partial Quotients Method for Division
• Division Using Base Ten Blocks
• Interpreting Remainders
• Conclusion

M2.5

Large Numbers: Problem Solving Strategies

• Problem-solving Basics
• Draw a Diagram
• Look for a Pattern/Make a List
• Guess and Check
• Conclusion

### Math3    Integers

M3.1

Integers and Absolute Value

• Negative Numbers
• Opposite and Absolute Value
• Compare Integers
• Order Integers
• Conclusion

M3.2

• Adding Integers Using Counters Model
• Adding Integers Using Number Lines
• Conclusion

M3.3

Subtracting Integers

• Subtracting Integers Using Counters
• Subtracting Integers Using Number Lines
• Subtracting Integers Using Rules
• Conclusion

M3.4

Multiplying and Dividing Integers

• Multiplying Integers Using Counters
• Multiplying Integers Using a Number Line
• Multiplying and Dividing Integers
• Conclusion

M3.5

Solving Problems with Integers

• Solving Problems with Integers (Math Camp Swimming Pool)
• Solving Problems with Integers (Zeo’s Alienoon)

## UNIT II. NUMBER Operations M4.1 – M7.7

### Math4   Fractions, Decimals, Percents and Factors

M4.1

Concepts of Fractions, Ratios, and Percents

• Fractions
• Ratios: Part to Whole
• Ratios: Part to Part
• Percent
• Conclusion

M4.2

Concepts of Decimal Place Value and Fraction and Percent Equivalents

• Decimal Place Value and Fraction Equivalents
• Changing Decimals to Fractions and Fractions to Decimals
• Changing and Fraction to a Percent
• Benchmark Fraction and Fraction Equivalents
• Conclusion

M4.3

Factors and Prime Factorization

• Finding Factors of a Number
• Finding the Prime Factorization of a Number
• Common Factors and Greatest Common Factor
• Using Prime Factorization to Find the GCF

M4.4

Factors and Prime Factorization

• Least Common Multiple
• Using Prime Factorization to Find the LCM
• Applications Using the LCM of More Than Two Numbers
• Applications Using the GCF of More Than Two Numbers
• Conclusion

M4.5

Simplifying and Converting Fractions

• Rational Numbers and Equivalent Fractions
• Simplifying Fractions to Lowest Terms
• Converting an Improper Fraction to a Mixed Number
• Converting Mixed Number to Improper Fractions
• Conclusion

### Math5    Decimal Operations, Exponents and Powers

M5.1

Rounding and Comparing Decimals

• Rounding Decimals to a Given Place Value
• Comparing Positive Decimals
• Comparing Negative Decimals
• Conclusion

M5.2

Converting, Comparing, and Ordering

• Ordering Fractions, Decimals, and Integers
• Comparing Fractions, Decimals, and Percents
• Conclusion

M5.3

• Estimation of Decimal Sums and Differences
• Adding Decimals Using Models and Standard Algorithm
• Subtracting Decimals Using Models
• Standard Decimal Subtraction
• Conclusion

M5.4

Multiplying Decimals

• Model Multiplication of Decimals
• Multiply Decimals by Powers of Ten
• Estimating Decimal Products
• Multiplying Decimals Using the Standard Method
• Conclusion

M5.5

Dividing Decimals

• Estimating Quotients using Front-end Estimation, Rounding, and Compatible Numbers
• Dividing Decimals Using Models
• Dividing Decimals by Whole Numbers
• Dividing Decimals by Decimals
• Conclusion

M5.6

Exponents and Powers

• Exponents and Powers
• Using Exponents and Powers in Expressions
• Zero and Negative Exponents
• Solving Problems with Exponents and Powers
• Conclusion

M5.7

Scientific Notation

• Powers of 10 with Integers Exponents
• Multiply by a Power of Ten with an Integer Exponent
• Scientific Notation
• Converting Between Standard and Scientific Notations (Numbers Greater than One)
• Conclusion

### Math6    Computational Fluency of Fractions

M6.1

Adding and Subtracting Fractions with Like Denominators

• Adding Fractions with Like Denominators
• Subtracting Fractions with Like Denominators
• Conclusion

M6.2

• Model Adding Fractions with Unlike Denominators
• Adding Fractions with Unlike Denominators
• Conclusion

M6.3

Subtracting Fractions with Unlike Denominators

• Model Subtracting Fractions with Unlike Denominators
• Subtracting Fractions with Unlike Denominators Using the LCM/LCD
• Conclusion

M6.4

• Subtracting Mixed Numbers
• Conclusion

M6.5

Multiplying Fractions

• Multiplying Fractions with or without Models
• Simplifying Fractions before Multiplying
• Multiplying with Mixed Numbers
• Conclusion

M6.6

Dividing Fractions

• Fraction or Mixed Number Divided by a Nonzero Whole Number Using Models and the Invert-and-Multiply Algorithm
• Whole Number, Mixed Number, or Fraction Divided by a Fraction Using Models and the Denominator Algorithm
• Conclusion

### Math7    Ratio, Proportion and Percent

M7.1

Square Roots

• Number Models
• Perfect Squares and Their Square Roots
• Problem Solving Using Squares and Square Roots
• Conclusion

M7.2

Finding Percents

• Percent and Ratio
• Finding the Percent of a Number
• Proportions
• Conclusion

M7.3

Decimal and Percent Equivalents

• Decimal and Percent Equivalent for Proper Fractions
• Decimal and Percent Equivalent for Repeating Decimals
• Decimal and Percent Equivalent of Mixed Numbers
• Conclusion

M7.4

Ratios, Rates, and Proportional Reasoning

• Ratios, Rates, and Unit Rates
• Use Ratios and Proportions to Solve Problems
• Comparing Rates
• Conclusion

M7.5

Percent Proportions

• Use the Percent Proportion to Write Fractions as Percents
• Estimate a Percent of a Number
• Determine the Percent of a Number and Solve Problems
• Conclusion

M7.6

Using Percent Equations

• Find the Percent of a Number
• Find the Percent One Number is of Another
• Find a Number When a Percent is Given
• Conclusion

M7.7

Problem Solving with Percents

• Percent of Increase and Percent of Decrease
• Simple Interest
• Compound Interest
• Conclusion

## UNIT III. Geometry M8.1 – 11.5

### Math8    Points, Lines, Angles and Triangles

M8.1

Language of Geometry

• Basic Terms of Geometry
• Angles
• Conclusion

M8.2

Angle Classification and Line Relationships

• Angle Classification
• Line Relationships
• Conclusion

M8.3

Angle Relationships and Parallel Lines

• Angle Relationships
• Intersecting Lines and Transversals
• Parallel Lines and Transversals
• Conclusion

M8.4

Triangles

• Defining Triangles
• Classifying Triangles
• Triangle Sum Property
• Conclusion

M8.5

Congruent Traingles

• Congruence
• Determine Whether Triangle are Congruent
• Conclusion

M8.6

Similar Triangles

• Similar Triangles
• Using Similar Triangles
• Conclusion

M8.7

Right Triangles

• The Pythagorean Theorem
• Using the Converse of the Pythagorean Theorem
• Conclusion

### Math9    Characteristics of Geometry Shapes

M9.1

Polygons

• Convex and Concave Polygons
• Classifying Polygons According to Sides
• Regular and Irregular Polygons
• Conclusion

M9.2

• Conclusion

M9.3

Circles

• Circles
• Circumferences
• Conclusion

M9.4

Similar Polygons

• Similar Polygons
• Finding Unknown Lengths
• Enlargements and Reductions
• Scale Drawings
• Conclusion

M9.5

Inductive and Deductive Reasoning

• Inductive Reasoning
• Deductive Reasoning
• Conclusion

### Math10    Coordinate Geometry and Spatial Visualization

M10.1

Points in a Coordinate Plane

• Writing Ordered Pairs for Points in a Coordinate Plane
• Plotting Points in a Coordinated Plane
• Conclusion

M10.2

Classifying Geometric Figures Using Points

• One-dimensional Figures on a Coordinate Plane
• Two-dimensional Figures on a Coordinate Plane
• Conclusion

M10.3

Coordinate Geometry

• Distances on a Coordinate Plane
• Slope
• Parallel and Perpendicular Lines
• Conclusion

M10.4

Three-dimensional Shapes

• Polyhedra: Prisms and Pyramids
• Spheres, Cylinder, and Cones
• Conclusion

M10.5

Building Models

• Nets for Three-dimensional Figures
•
• Views of Three-dimensional Figures
•
• Conclusion

### Math11    Transformation of Shapes

M11.1

Translations and Reflections

• Translations
• Reflections
• Conclusion

M11.2

Rotations

• Rotations of Two-Dimensional Figures
• Rotations Using Ordered Pairs
• Conclusion

M11.3

Dilations

• Dilations
• Dilations on the Coordinate Plane
• Conclusion

M11.4

Symmetry

• Line Symmetry
• Rotational Symmetry
• Point Symmetry
• Conclusion

M11.5

Tessellations

• Geometric Patterns
• Tessellations
• Conclusion

## UNIT IV. Measurement M12.1-13.7

### Math12    Attributes and Tools

M12.1

Measurement Systems

• The Customary System
• The Metric System
• Conclusion

M12.2

Same System Conversions

• Converting Customary Units
• Converting Metrics Units
• Converting Time Units
• Conclusion

M12.3

Measurement: Time

• Elapsed Clock Time
• Elapsed Calendar Time
• Problem Solving with Two or More Elapsed Times
• Conclusion

M12.4

Measurement: Distance

• Draw and Measure Customary Distance/Length
• Draw and Measure Metric Distance/Length
• Problem Solving with Customary Distances
• Problems Solving with Metric Distances
• Conclusion

M12.5

Measurement: Weight and Mass

• Using a Scale
• Customary Weight
• Metric Weight
• Conclusion

### Math13    Perimeter, Area and Volume

M13.1

Perimeter and Circumference

• Perimeter
• Circumference
• Conclusion

M13.2

Area

• Area of Rectangles and Parallelograms
• Area of Triangle, Trapezoids, and Circles
• Find Different Areas of a Given Perimeter
• Conclusion

M13.3

Irregular Shapes

• Estimating Areas of Irregular Shapes
• Areas of Combined Shapes
• Conclusion

M13.4

Surface Area: Prisms, Cylinders, and Spheres

• Surface Area of a Prism
• Surface Area of a Cylinder
• Surface Area of a Sphere
• Conclusion

M13.5

Volume: Prism, Cylinders, Speheres

• Volume of a Rectangle Prism
• Volume Cylinder and Sphere
• Conclusion

M13.6

Surface Area: Pyramids and Cones

• Surface Area of a Pyramid
• Surface Area of a Cone
• Conclusion

M13.7

Volume: Pyramids and Cones

• Volume of a Cone
• Volume of a Pyramid
• Conclusion

## UNIT V. EXPRESSIONS AND OPERATIONS A1.1 – A2.5

### Algebra1    Getting Ready for Algebra

A1.1

Concepts of Fractions, Ratios, and Percents

• Elements of a Set
• Subsets
• Disjoint Sets
• Intersection of Two Sets
• Empty Set
• Union of Sets
• Natural Numbers, Whole
• Numbers, Integers
• Rational Numbers
• Irrational Numbers
• Number Line
• Conclusion

A1.2

Simplifying Expressions with Integers
• Subtracting Integers
• Multiplying Integers
• Dividing Integers
• Conclusion

A1.3

Simplifying Expressions with Rational Numbers
• Operations with Fractions
• Multiplying Fractions
• LCD
• Subtracting Fractions
• Dividing Fractions
• Subtracting Decimals
• Multiplying Decimals
• Dividing Decimals
• Conclusion

A1.4

Simplifying Expressions with Rational Numbers
• Operations with Fractions
• Multiplying Fractions
• LCD
• Subtracting Fractions
• Dividing Fractions
• Subtracting Decimals
• Multiplying Decimals
• Dividing Decimals
• Conclusion

A1.5

Applying the Order of Operations
• Order of Operations without Grouping Symbols or Exponents
• Order of Operations without Grouping Symbols
• Order of Operations Using All Steps
• Order of Operations with Two Levels of Nested Grouping Symbols
• Conclusion

### Algebra2 Writing and Simplifying Algebraic Expressions

A2.1

Using the Language of Algebra

• Variable
• Algebraic Expression
• Term
• Monomials
• Coefficients
• Polynomials
• Special Polynomial
• Degree of a Monomial
• Degree of a Polynomial
• Conclusion

A2.2

Translating Word Phrases into Algebraic Expressions

• Expressions with One Operation
• Exponents
• More than One Operation
• Conclusion

A2.3

Identifying Algebraic Properties

• Commutative Property of Multiplication
• Associative Property of Multiplication
• Zero Property of Multiplication
• Identity Property of Multiplication
• Multiplicative Inverse
• Distributive Property
• Conclusion

A2.4

Combining Like Terms

• Term and Coefficient
• Subtracting Polynomials
• Conclusion

A2.5

Evaluating Expressions

• Algebraic Expression
• Baseball Application Problem
• Evaluating Exponential Expressions
• Evaluating Expressions with Roots
• Evaluating Formulas

## UNIT VI. Linear Equations of One Variable A3.1 – A6.5

### Algebra3    Solving Linear Equations of One Variable

A3.1

Identifying Properties of Equality

• Equality
• Reflexive Property of Equality
• Symmetric Property of Equality
• Transitive Property of Equality
• Subtraction Property of Equality
• Multiplication Property of Equality
• Division Property of Equality
• Algebraic Proof
• Conclusion

A3.2

Solving Equations by Expression

• Solving Addition Equations by Inspection
• Solving Subtraction Equations by Inspection
• Solving Multiplication Equations by Inspection
• Solving Division Equations by Inspection
• Conclusion

A3.3

Solving One-Step Linear Equations

• Solving One-Step Equations Using Division
• Solving One-Step Equations Using Multiplication
• Solving One-Step Equations Using Addition
• Solving One-Step Equations Using Subtraction
• Conclusion

A3.4

Solving Two Step-Linear Equations

• Working Backwards
• Solving Two-Step Equations
• Conclusion

A3.5

Solving Multi-Step Linear Equations

• Solving Multi-Step Equations-Combining Like Terms
• Solving Multi-Step Equations-Variable Terms on Both Sides of the Equation
• Identity Equations
• Solving Multi-Step Equations-No Solution
• Solving Multi-Step Equations-Distributive Property
• Solving Multi-Step Equations-Fractions
• Conclusion

A3.6

Rewriting Formulas

• Defining Formula
• Using the Area Formula
• Rewriting the Area Formula

### Algebra4    Problem Solving with Linear Equations of One Variable

A4.1

Translating Sentences into Algebraic Equations

• Writing a Sentence as an Equation
• Writing a Sentence as an Equation with Parentheses
• Writing a Sentence as an Equation for Real-World Situations
• Conclusion

A4.2

Solving Consumer/Business Problems using Equations of One Variable

• Steps to Solving Consumer/Business Problems
• Consecutive Integers
• Finding Percent in Consumers/Business Problems
• Percent Increase and Percent Decrease
• Conclusion

A4.3

Solving Geometry Problems Using Equations of One Variable

• Perimeter Problems
• Angle Sum Problems
• Conclusion

A4.4

Solving Mixture and Rate Problems Using Equations of One Variable

• Mixture Problems without Percents
• Mixture Problems with Percents
• Distance Problems
• Conclusion

### Algebra5    Problem Solving Linear Inequalities of One Variable

A5.1

Solving Linear Inequalities by Inspection

• Inequality Symbols
• Solution of an Inequality
• Graphing Linear Inequalities
• Conclusion

A5.2

Solving One-Step Linear Equations

• Solving One-Step Inequalities by Addition or Subtraction
• Solving One-Step Inequalities by Multiplying or Dividing by a Positive Number
• Solving One-Step Inequalities by Multiplying or Dividing by a Negative Number
• Conclusion

A5.3

Solving Two-Step Linear Inequalities

• Solving Two-Step Inequalities – Inequality Symbol Does Not Reverse
• Solving Two-Step Inequalities – Inequality Symbol Reverses
• Conclusion

A5.4

Solving Multi-Step Linear Inequalities

• Solving Inequalities with Variables on Both Sides
• Solving Multi-Step Inequalities Involving Simplifying Expression
• Conclusion

A5.5

Solving Conjunction Inequalities

• Defining Graphing Conjunctions
• Solving Multi-Step Conjuntions
• Conclusion

A5.6

Solving Disjunction Inequalities

• Defining Disjunctions
• Solving Multi-Step Disjunctions
• Conclusion

A5.7

Solving Problems Using Inequalities of One Variable

• Solving Problems with One-Step Inequalities
• Solving Problems with Two-Step Inequalities
• Solving Problems with Multi-Step Inequalities
• Conclusion

### Algebra6    Solving Absolute Value Equations and Inequalities

A6.1

Solving Basic Absolute Value Equations

• Absolute Value Defined
• Solve the Absolute Value of x=a, a>0
• Solve the Absolute Value of ax+b=k, k>0
• Solving Basic Absolute Value Equations with One or No Solution
• Conclusion

A6.2

• Isolating the Absolute Value One-Step
• Isolating the Absolute Value Two-Step
• Conclusion

A6.3

Solving Inequalities Using “Absolute Value is Less Than”

• Solving One-Step Inequalities Containing Absolute Value is Less Than
• Solving Two-Step Inequalities Containing Absolute Value is Less Than
• Isolating the Absolute Value Expression when Solving Inequalities with Absolute Value is Less Than
• Conclusion

A6.4

Solving Inequalities Using “Absolute Value is Greater Than”

• Explaining the Steps of Solving Inequalities Containing Absolute Value is Greater Than
• Solving “Two-Step” Inequalities Containing Absolute Value is Greater Than
• Isolating the Absolute Value Before Solving Inequalities with Greater Than
• Conclusion

A6.5

Solving Problems Using Absolute Value Equations and Inequalities

• Modeling with Inequalities Using Absolute Value Less Than
• Modeling Using Absolute Value Equations
• Modeling with Inequalities Using Absolute Value Greater Than

## UNIT VII. Equations and Inequalities of Two Variables and Functions A7.1 – A10.5

### Algebra7    Solving Linear Equations and Inequalities of Two Variables

A7.1

Defining Linear Equations of Two Variables and Their Solutions

• Solutions of a Linear Equation
• Cartesian Coordinate System
• Plotting Points
• Graph of the Solutions of a Linear Equation
• Showing All Solutions of a Linear Equation
• Special Case-Horizontal Lines
• Special Case-Vertical Lines
• Conclusion

A7.2

Graphing Linear Equations of Two Variables

• Graphing Linear Equations Using Tables
• Graphing Linear Equations Using Intercepts
• Graphing Linear Equations Slope-Intercept
• Negative Slope
• Positive Slope
• Conclusion

A7.3

Gaphing Linear Inequalities of Two Variables

• Graphing an Inequality with One Variable on a Number Line
• Graphing an Inequality with Two Variables on a Coordinate Plane
• Boundary Line
• Test Point
• Conclusion

A7.4

Solving Consumer/Business Problems Using Linear Equations and Inequalities Of Two Variables

• Concession Stand Application Problem
• Football Tickets Application Problem
• DJ Service Application Problem
• Conclusion

### Algebra8    Writing Linear Equations of Two Variables

A8.1

Finding Slope

• Slope of a Line
• Comparing Slopes of Lines
• Negative Slopes
• Opposite Slopes
• Discovering the Slope Formula
• Slope Formula
• Horizontal Lines
• Vertical Lines
• Parallel Lines
• Perpendicular Lines
• Conclusion

A8.2

Writing Equations of Lines, Given the Slope and y-Intercept

• Equations and Lines
• Slope-Intercept Form
• Graphs and Slope-Intercept Form
• Determining Slope and y-intercept
• Writing Equations
• Parallel and Perpendicular Lines
• Reciprocals
• Conclusion

A8.3

Writing Equations of Lines, Given Point and  the Slope or Two Points

• Defining Point-Slope Form
• Using Point-Slope Form
• Application Problem
• Parallel and Perpendicular Lines
• Finding the Equation
• Conclusion

A8.4

Solving Linear Equations in Two Variables When Parameters are Changed

• Parameters
• Using Parameters to Determine an Equation
• Changing the Parameters m and b
• Perpendicular Lines
• Linear Equations
• Converting from Standard Form to Slope-intercept Form
• Conclusion

### Algebra9    Using Functions

A9.1

Defining Relationships and Functions

• Introduction to Function Machine
• Relations
• Domain and Range of a Relation
• Mapping Diagram
• Table
• Graph of a Relation
• Set-Builder Notation
• Ways to Represent a Relation
• Function
• Constant Function
• Linear Function
• Vertical Line Test
• Nonlinear Function
• Function Machine
• Conclusion

A9.2

Evaluating Functions

• Functions
• Domain and Range
• Function Notation
• Evaluating a Function
• Functions on the Coordinate Plane
• Conclusion

A9.3

Writing Functions from Patterns

• Input-Output Table
• Writing a Function from a Pattern
• Application Problem – Job
• Scatterplot
• Slope
• Function Mapping and Scatter Plots
• Conclusion

A9.4

Graphing Functions

• Definition of Linear Function
• Graphing the Linear Function
• Graphing the Constant Function
• Absolute Value Function
• Translating Parent Graph
• Graphing Piecewise Functions
• Conclusion

A9.5

Solving Problems Using Functions

• Real-World Application
• Formulas as Functions
• Real World Application #2
• Mowing Service
• Pizza Sharing Function
• Health-Related Function
• Conclusion

A9.6

Evaluating Composite Functions

• Sale Price Function
• Defining Composition of Two Functions
• Evaluating
• Example
• Real-World Application – Finding the Original Price
• Determining Inverses
• Conclusion

### Algebra10    Solving Systems of Linear Equations and Inequalities

A10.1

Solving Systems of Linear Equations by Graphing

• System of Linear Equations
• Determine Whether an Ordered Pair is a Solution
• Solving Systems of Linear Equations by Graphing
• Consistent, Inconsistent, Dependent, or Independent
• Conclusion

A10.2

Solving Systems of Linear Equations by Elimination

• Solutions to a System of Equations
• Elimination by Addition of a System
• Elimination by Multiplication of One Equation in a System
• Elimination by Multiplication of Both Equations
• Overview of Elimination Method
• System With No Solution
• System With Infinitely Many Solutions
• Conclusion

A10.3

Solving Systems of Linear Equations by Substitution

• Methods of Solving Systems of Linear Equations
• Solving of System of Linear Equations Using the Substitution Method
• Checking a Solution to a System of Linear Equations
• Solving a System of Linear Equations of Two Variables
• Solving a System of Linear Equations with Infinitely Many Solutions by Substitution
• Systems of Linear Inequalities Whose Graphs Have Parallel Boundaries
• Conclusion

A10.4

Solving Systems of Linear Inequalities by Graphing

• Solving Linear Inequalities of Two Variables
• Graphing a System of Linear Equations of Two Variables
• Systems of Linear Inequalities Whose Graphs Have Horizontal and Vertical Boundaries
• Graphing a System of Three Linear Inequalities
• Systems of Linear Inequalities Whose Graphs Have Parallel Boundaries
• Conclusion

A10.5

Solving Problems Using Systems of Linear Equations and Inequalities

• Money Saving Problem – No Interest
• Problem – Solving Tips
• Money Saving Problem with Interest
• Rate/Time/Distance Problem
• Polygon Dimension Problem
• Mixture Problem
• Hours Worked/Salary Inequality Problem
• Conclusion

## UNIT VIII. Polynomial and Quadratic Equations A11.1 – A14.3

### Algebra11    Solving Linear Equations and Inequalities of Two Variables

A11.1

Applying Rules of Exponents

• Multiplying Powers with Like Bases
• Dividing Powers with Like Bases
• Power-of-a-Power Rule
• Power-of-a-Product
• Power-of-a-Quotient
• Conclusion

A11.2

Using Scientific Notation

• Understanding Scientific Notation
• Converting a Number from Scientific Notation to Standard Form
• Converting a Number from Standard Form to Scientific Notation
• Calculating Using Scientific
• Conclusion

A11.3

• Understanding Polynomials
• Subtracting Polynomials
• Conclusion

A11.4

Multiplying Monomials and Binomials

• Multiplying Monomials
• Multiplying a Binomial by a Monomial
• Multiplying a Binomial by a Binomial
• Conclusion

A11.5

Multiplying Monomials

• Special Products
• Multiplying General Polynomials
• Conclusion

A11.6

Dividing Polynomials by Monomials

• Dividing Monomials by Monomials
• Dividing Polynomials by Monomials
• Conclusion

A11.7

Dividing Polynomials Using long Division

• Dividing Polynomials Using Long Division
• Conclusion

### Algebra12    Simplifying Algebraic Expressions by Factoring Polynomials

A12.1

Factoring by Removing the Greatest Common Factor

• Introducing Factoring
• Greatest Common Monomial Factor
• Factoring Polynomials Containing More Than One Variable
• Conclusion

A12.2

Factoring by Grouping

• Common Binomial Factors
• Factoring by Grouping
• Conclusion

A12.3

Factoring the Difference of Two Squares

• How to Factor the Difference of Two Squares
• Recognizing Perfect Squares
• Factoring the Differences of Two Squares
• Factoring the Differences of Two Squares with a Leading Coefficient Than One
• Using the Difference of Square Rule Twice
• Conclusion

A12.4

Factoring x2 + b x + c

• Factoring Trinomials of the Form x2 + bx + c, b>0, c>0
• Factoring x2 + bx + c, b<0 and/or c<0
• Conclusion

A12.5

Factoring ax2 + b x + c

• Factoring ax2 + bx + c; Guess and Check
• Factoring ax2 + bx + c; Factoring by Grouping
• Conclusion

A12.6

Factoring Using Several Methods

• Review of Factoring Methods
• Factoring Using Several Methods
• Conclusion

A12.7

Dividing Polynomials Using Factoring

• Dividing Polynomial by Factoring: Factoring Numerator Only
• Dividing Polynomial by Using Factoring: Factoring Numerator and Denominator
• Conclusion

### Algebra13    Solving Quadratic Equations of One Variable

A13.1

Defining Quadratic Equations of One Variable

• Conclusion

A13.2

Solving Quadratic Equations by Evaluating Square Roots

• Solving Equations of the Form ax2=k
• Solving Equations of the Form ax2-b=k
• Solving Quadratic Equations of the Form a(x+b)^2=k
• Solving Quadratic Equations of the Form a(x=b)^2+c=k
• Conclusion

A13.3

• Solving Quadratic Equations by Factoring
• Conclusion

A13.4

Solving Quadratic Equations by Completing the Square

• Completing the Square and Factoring Perfect Square Trinomials
• Solving Quadratic Equations by Completing the Square
• Conclusion

A13.5

• Using the Discriminant
• Conclusion

A13.6

Solving Problems Using Quadratic Equations of One Variable

• Rectangular Area Applications
• Vertical Motion Applications
• Conclusion

A14.1

• Defining Parabola
• Graphing Relations of the Form y=ax2+bx+c
• Conclusion

A14.2

• Graphing y=ax2
• Review of Graphics y=ax2
• Graphics Equations of the Form y=x2+k
• Graphing Equations of the Form y+a(x-h)^2+k
• Graphing Equations of the Form y=(x-h)^2
• Conclusion

A14.3

• Vertical Motion Application
• Sports Application
• Conclusion

## UNIT IX. Rational and Radical Equations A15.1 – A18.4

### Algebra15    Simplifying Rational Expressions

A15.1

Finding Restricted Values of Rational Expressions

• Rational Expression Restrictions Degree 1
• Rational Expression with More Than One Restricted Value
• Conclusion

A15.2

Simplifying Rational Expressions

• Simplifying Rational Expressions
• Negative One Technique
• Simplifying Rational Expressions Containing Trinomials
• Conclusion

A15.3

Multiplying and Dividing Rational Expressions

• Multiplying Rational Expressions with Monomials
• Multiplying Rational Expressions with Binomials and Trinomials
• Dividing Rationals Expressions
• Conclusion

A15.4

• Adding and Subtracting Rational Expressions with Like Denominators
• Adding and Subtracting Rational Expressions with Unlike Denominators
• Conclusion

### Algebra16    Solving Rational Equations

A16.1

Solving Rational Equations

• Solving Rational Equations
• Conclusion

A16.2

Solving Problems Using Direct Variation

• Direct Variation
• Applications of Inverse Variation
• Conclusion

A16.3

Solving Problems Using Inverse Variation

• Inverse Variation
• Applications of Inverse Variation
• Conclusion

A16.4

Solving Various Types of Problems Using Rational Equations

• Solving Work Problems
• Solving Uniform Motion Problems
• Conclusion

A17.1

• Square Roots
• Product Property of Square Roots
• Square Roots and Negatives
• Cube Roots
• Product Property of Cube Roots
• Roots of Variable Expressions
• Conclusion

A17.2

• Conclusion

A17.3

• Monomial Times Monomial
• Monomial Times Binomial
• Binomial Times Binomial
• Conclusion

A17.4

• Quotient Property of Square Roots
• Rationalizing the Denominator
• Conclusion

A18.1

• Solving Radical Equations of the Form sqrt x=a, a≥0
• Solving Radical Equations of the Form – sqrt x=a, a<0
• Solving Radical Equations Containing Negative Signs
• Solving Cube Roots and 4th Root Equations
• Conclusion

A18.2

• Conclusion

A18.3

• Length of a Skid Mark
• Distance to Horizon
• Speed of Sound
• Pythagorean Theorem Application
• Conclusion

A18.4

Solving Problems Using the Distance and Midpoint Formulas

• Pythagorean Theorem
• Distance on a Number Line
• Distance Formula
• Using the Distance Formula to Solve Problems
• Using the Midpoint Formula to Solve Problems
• The Midpoint Formula
• Conclusion

## UNIT X. Data Analysis, Probability, Statistics A19.1 – A20.4

### Algebra19    Analyzing Data and Statistics

A19.1

Finding Mean, Median, and Mode

• Calculating Mean, Median, and Mode
• Stem-and-Leaf Plot
• Conclusion

A19.2

Interpreting Graphs of Data

• Line Graphs
• Bar Graphs
• Circle Graphs
• Conclusion

A19.3

Analyzing and Describing Graphs

• Stem-and-Leaf Plot and Five-Number Summary
• Making Comparisons Using Box-and-Whisker Plots
• Histograms
• Conclusion

A19.4

Finding a Line of Best Fit

• Interpret Points on a Scatter Plot
• Writing Equations for Lines of Best Fit
• Conclusion

A19.5

Solving Statistics Problems

• Deviation from the Mean
• Mean Absolute Deviation
• Deviation from the Mean as a Measure of Dispersion
• Conclusion

### Algebra20    Solving Problems Using Probability, Statistics and Discrete Math

A20.1

Finding Permutations and Combinations

• Fundamental Counting Principle and Factorial Rule
• Factorial
• Permutations
• Combinations
• Conclusion

A20.2

Solving Basic Probability Problems

• Probability of an Event
• Experimental Probability
• Theoretical Probability
• Complementary Events
• Conclusion

A20.3