Scope & sequence

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
  • Properties of Addition
  • 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

  • Exact Answer or Estimate
  • Estimation Strategies: Front-End Estimation
  • Estimation Strategies: Rounding
  • Estimation Strategies: Compatible Numbers
  • Comparing and Combining Estimation Strategies
  • Conclusion

Math2    Whole Number Operations

M2.1

Large Numbers: Addition

  • Partial Sums Method for Addition
  • Column Addition Method for Addition
  • Standard Addition Model
  • 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

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

Adding and Subtracting Decimals

  • 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

Adding Fractions with Unlike Denominators

  • 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

Adding and Subtracting Mixed Numbers

  • Adding Mixed Numbers
  • 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

Quadrilaterals

  • Types of Quadrilaterals
  • Angles of Quadrilaterals
  • 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
  • Adding Integers
  • Subtracting Integers
  • Multiplying Integers
  • Dividing Integers
  • Conclusion

A1.3

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

A1.4

Simplifying Expressions with Rational Numbers
  • Operations with Fractions
  • Multiplying Fractions
  • LCD
  • Adding Fractions
  • Subtracting Fractions
  • Dividing Fractions
  • Adding Decimals
  • 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 Addition
  • Associative Property of Addition
  • Commutative Property of Multiplication
  • Associative Property of Multiplication
  • Identity Property of Addition
  • Zero Property of Multiplication
  • Identity Property of Multiplication
  • Multiplicative Inverse
  • Additive Inverse
  • Distributive Property
  • Conclusion

A2.4

Combining Like Terms

  • Term and Coefficient
  • Adding Polynomials
  • 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
  • Addition 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

Solving Advanced Absolute Value Equations

  • 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

Adding and Subtracting Polynomials

  • 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

  • Identifying Quadratic Equations
  • 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

  • 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

Solving Quadratic Equations by the Quadratic Formula

  • The Quadratic Formula
  • Using the Quadratic Formula
  • Using the Discriminant
  • Conclusion

A13.6

Solving Problems Using Quadratic Equations of One Variable

  • Rectangular Area Applications
  • Vertical Motion Applications
  • Conclusion

Algebra14    Graphing Quadratic Equations

A14.1

Graphing Simple Quadratic Relations

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

A14.2

Graphing Quadratic Relations by Analysis

  • 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

Solving Problems Using Quadratic Graphs

  • 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

  • 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

Algebra17    Simplifying Radical Equations

A17.1

Simplifying Radicals

  • 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

Adding and Subtracting Radicals

  • Adding and Subtracting Simplified Radicals
  • Simplify Before Adding and Subtracting Radicals
  • Adding and Subtracting Radicals with Variables
  • Conclusion

A17.3

Multiplying Radicals

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

A17.4

Dividing Radicals

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

Algebra18    Solving Radical Equations

A18.1

Solving One-Step Radical Equations

  • 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

Solving Multi-Step Radical Equations

  • Solving Two-Step Radical Equations
  • Solving Multi-Step Radical Equations
  • Conclusion

A18.3

Solving Problems Using Radical Equations

  • 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

Solving Advanced Probability Problems

  • Independent Events
  • Dependent Events
  • Conclusion

A20.4

Solving Discrete Mathematics Problems

  • Traversable Paths
  • Equivalent Graphs