Viewing Life Mathematically plus Integrated Review

1.R.1 Introduction to Whole Numbers

• Examples
• Example 1: Understanding Place Value
• Example 2: Understanding Place Value
• Example 3: Writing Numbers in Expanded Notation
• Example 5: Reading and Writing Whole Numbers
• Example 7: Reading and Writing Whole Numbers
• Example 9: Application: Reading Tables

1.R.2 Rounding and Estimating with Whole Numbers

• Examples
• Example 1: Rounding Whole Numbers
• Example 2: Rounding Whole Numbers
• Example 3: Application: Rounding Whole Numbers
• Example 4: Estimating a Sum of Whole Numbers
• Example 6: Estimating a Difference of Whole Numbers
• Example 7: Application: Estimating a Difference of Whole Numbers
• Example 8: Estimating Products of Whole Numbers
• Example 9: Estimating Products of Whole Numbers
• Example 10: Estimating Quotients of Whole Numbers
• Example 11: Estimating Quotients of Whole Numbers
• Example 13: Estimating Quotients of Whole Numbers

1.R.3 Exponents and Order of Operations

• Examples
• Example 1: Identifying the Base and Exponent
• Example 3: Evaluating Exponential Expressions
• Example 4: Evaluating Exponential Expressions
• Example 5: Using the Order of Operations with Whole Numbers
• Example 6: Using the Order of Operations with Whole Numbers
• Example 7: Using the Order of Operations with Whole Numbers
• Example 8: Using the Order of Operations with Whole Numbers
• Example 9: Using the Order of Operations with Whole Numbers

1.R.4 Problem Solving with Whole Numbers

• Examples
• Example 1: Application: Adding Whole Numbers
• Example 2: Application: Multiplying Whole Numbers
• Example 3: Application: Dividing Whole Numbers
• Example 4: Application: Calculating Loan Amounts
• Example 5: Application: Balancing a Checking Account
• Example 6: Application: Finding the Area of Rectangles
• Example 7: Calculating an Average
• Example 8: Application: Calculating an Average
• Example 9: Application: Calculating an Average
• Example 10: Application: Calculating an Average

1.R.5 Translating English Phrases and Algebraic Expressions

• Examples
• Example 1: Translating English Phrases into Algebraic Expressions
• Example 2: Application: Translating English Phrases
• Example 3: Translating Algebraic Expressions to English Phrases
• Example 4: Translating Equations into Word Problems

1.R.6 Solving Linear Equations: ax + b = c

• Examples
• Example 1: Solving Linear Equations of the Form ax + b = c
• Example 2: Solving Linear Equations of the Form ax + b = c
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations Involving Decimals
• Example 5: Solving Linear Equations Involving Fractions
• Example 6: Solving Linear Equations Involving Fractions

1.1 Thinking Mathematically

• Examples
• Example 1: Using Inductive Reasoning
• Example 2: Using Inductive Reasoning
• Example 3: CounterExamples
• Example 4: Reasoning with Sequences
• Example 5: Reasoning with Patterns
• Example 6: Using Deductive Reasoning
• Example 7: Inductive versus Deductive Reasoning

1.2 Problem Solving: Processes and Techniques

• Examples
• Example 1: Working Backwards
• Example 2: Guess and Test
• Example 3: Solve a Simpler Problem
• Example 4: Find a Pattern
• Example 5: Draw a Diagram
• Example 6: Make a List
• Example 7: Use a Variable

1.3 Estimating and Evaluating

• Examples
• Example 1: Using Pólya's Problem-Solving Steps in Estimation
• Example 2: Using Deductive Reasoning in Estimation
• Example 3: Estimating Using Graphs

2.R.1 The Real Number Line and Absolute Value

• Examples
• Example 1: Finding the Opposite of an Integer
• Example 2: Graphing Integers on a Number Line
• Example 3: Identifying Types of Numbers
• Example 4: Graphing Sets of Numbers
• Example 5: Graphing Sets of Numbers
• Example 6: Verifying Inequalities
• Example 7: Finding Absolute Values
• Example 8: Verifying Absolute Value Inequalities
• Example 9: Solving Absolute Value Equations
• Example 10: Solving Absolute Value Equations
• Example 11: Application: Solving Absolute Value Equations

2.R.2 Addition with Real Numbers

• Examples
• Example 1: Adding Real Numbers with Like Signs
• Example 2: Adding Real Numbers with Unlike Signs
• Example 3: Adding More Than Two Real Numbers
• Example 4: Adding Three or More Real Numbers

2.R.3 Subtraction with Real Numbers

• Examples
• Example 1: Finding Additive Inverses
• Example 2: Subtracting Real Numbers
• Example 3: Application: Calculating Change in Value
• Example 4: Application: Calculating Change in Value
• Example 5: Application: Calculating Net Change
• Example 6: Application: Calculating Net Change

2.R.4 Multiplication and Division with Real Numbers

• Examples
• Example 1: Multiplying Positive and Negative Real Numbers
• Example 2: Multiplying Two Negative Real Numbers
• Example 3: Multiplication by $0$
• Example 4: Dividing Real Numbers
• Example 5: Dividing Fractions and Decimals
• Example 6: Application: Calculating an Average
• Example 7: Application: Calculating an Average
• Example 8: Application: Calculating an Average

2.R.5 Order of Operations with Real Numbers

• Examples
• Example 1: Using the Order of Operations with Real Numbers
• Example 2: Using the Order of Operations with Real Numbers
• Example 3: Using the Order of Operations with Real Numbers
• Example 4: Using the Order of Operations with Real Numbers
• Example 6: Using the Order of Operations with Real Numbers
• Example 7: Using the Order of Operations with Real Numbers

2.1 Set Notation

• Examples
• Example 1: Using the Roster Method to Represent a Set
• Example 2: Determining Equal and Equivalent Sets
• Example 3: Using Set-Builder Notation to Represent a Set
• Example 4: Determining Empty Sets
• Example 5: Determining the Complement of a Set

2.2 Subsets and Venn Diagrams

• Examples
• Example 1: Interpreting Venn Diagrams
• Example 2: Interpreting Venn Diagrams
• Example 3: Drawing a Venn Diagram with Subsets
• Example 4: Identifying Proper Subsets
• Example 5: Determining the Number of Subsets

2.3 Operations with Sets

• Examples
• Example 1: Determining the Intersection of Sets
• Example 2: Using a Venn Diagram to Find the Intersection
• Example 3: Determining the Union of Sets
• Example 4: Combining Intersection and Union
• Example 5: Identifying Disjoint Sets
• Example 6: Using De Morgan's Laws
• Example 7: Determining the Cardinal Number of a Union
• Example 8: Applying the Inclusion-Exclusion Principle

2.4 Applications and Survey Analysis

• Examples
• Example 1: Interpreting a Venn Diagram of Three Sets
• Example 2: Constructing a Venn Diagram of Three Sets
• Example 3: Drawing a Venn Diagram for Survey Analysis
• Example 4: Drawing a Venn Diagram for Survey Analysis

3.1 Logic Statements and Their Negations

• Examples
• Example 1: Identifying Statements
• Example 2: Negating a Statement
• Example 3: Using Logic Symbols for Compound Statements Involving and
• Example 4: Using Logic Symbols for Compound Statements Involving or
• Example 5: Using Logic Symbols for Compound Statements Involving Implications

3.2 Truth Tables

• Examples
• Example 1: Constructing a Truth Table for a Conditional Statement
• Example 2: Constructing a Truth Table for a Disjunction
• Example 3: Constructing a Truth Table from Words
• Example 4: Constructing a Truth Table for a Tautology

3.3 Logical Equivalence and De Morgan's Laws

• Examples
• Example 1: Writing Variations of a Conditional Statement
• Example 2: Writing the Contrapositive of a Conditional Statement
• Example 3: Writing a Biconditional Statement
• Example 4: Applying De Morgan's Laws
• Example 5: Writing the Negation of a Conditional Statement
• Example 6: Writing the Negation of a Conditional Statement

3.4 Valid Arguments and Fallacies

• Examples
• Example 1: Determining the Validity of an Argument
• Example 2: Determining the Validity of an Argument
• Example 3: Determining Sound Arguments
• Example 4: Determining Sound Arguments
• Example 5: Identifying Fallacies

4.R.1 Introduction to Fractions and Mixed Numbers

• Examples
• Example 1: Understanding Fractions
• Example 2: Understanding Fractions
• Example 3: Understanding Proper Fractions
• Example 4: Understanding Improper Fractions
• Example 5: Evaluating Fractions Involving 0
• Example 6: Graphing Proper Fractions
• Example 7: Graphing Improper Fractions
• Example 8: Identifying Types of Fractions and Mixed Numbers
• Example 9: Application: Understanding Mixed Numbers
• Example 10: Application: Understanding Mixed Numbers
• Example 11: Graphing Mixed Numbers
• Example 12: Changing Mixed Numbers to Improper Fractions
• Example 14: Changing Improper Fractions to Mixed Numbers
• Example 15: Changing Improper Fractions to Mixed Numbers

4.R.2 Introduction to Decimal Numbers

• Examples
• Example 1: Reading and Writing Decimal Numbers
• Example 2: Reading and Writing Decimal Numbers
• Example 3: Reading and Writing Decimal Numbers
• Example 4: Comparing Decimal Numbers
• Example 5: Comparing Decimal Numbers
• Example 6: Comparing Decimal Numbers
• Example 7: Rounding Decimal Numbers
• Example 8: Rounding Decimal Numbers

4.R.3 Decimals and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ to Percents
• Example 2: Changing Decimal Numbers to Percents
• Example 3: Changing Percents to Decimal Numbers

4.R.4 Fractions and Percents

• Examples
• Example 1: Changing Fractions to Percents
• Example 2: Changing Fractions to Percents
• Example 3: Changing Mixed Numbers to Percents
• Example 5: Changing Fractions to Percents
• Example 5: Application: Changing Fractions to Percents
• Example 7: Changing Percents to Fractions
• Example 8: Changing Percents to Mixed Numbers

4.R.5 Solving Percent Problems Using Proportions

• Examples
• Example 1: Finding the Amount
• Example 2: Finding the Base
• Example 3: Finding the Percent
• Example 4: Application: Finding the Amount
• Example 5: Application: Finding the Percent

4.1 Rates and Unit Rates

• Examples
• Example 2: Identifying Rates
• Example 3: Working with Miles per Gallon
• Example 5: Finding Unit Rates

4.2 Ratios

• Examples
• Example 6: Using Multiple Ratios
• Example 7: Using Ratios to Find Quantities

4.3 Proportions and Percentages

• Examples
• Example 1: Changing Fractions to Percentages
• Example 2: Finding Proportions and Percentages
• Example 3: Using Proportions to Find Quantities
• Example 4: Working with Ratios and Proportions
• Example 6: Finding Proportions and Ratios
• Example 7: Using Percentages

4.4 Using Percentages

• Examples
• Example 1: Finding the Percentage Change
• Example 2: Shifting Reference Points

5.R.1 The Cartesian Coordinate System

• Examples
• Example 1: Plotting Ordered Pairs
• Example 2: Plotting Ordered Pairs
• Example 3: Finding Ordered Pairs
• Example 4: Finding Ordered Pairs
• Example 6: Locating Points on the Graph of a Line

5.R.2 Graphing Linear Equations in Two Variables

• Examples
• Example 1: Graphing a Linear Equation in Two Variables
• Example 2: Graphing a Linear Equation in Two Variables
• Example 3: Graphing a Linear Equation in Two Variables
• Example 4: Using Intercepts to Graph Linear Equations
• Example 5: Using Intercepts to Graph Linear Equations
• Example 7: Graphing Horizontal Lines
• Example 8: Graphing Vertical Lines

5.R.3 Rules for Exponents

• Examples
• Example 1: Using the Product Rule for Exponents
• Example 2: Using the Product Rule for Exponents
• Example 3: Evaluating the Exponent 0
• Example 4: Using the Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients
• Example 6: Negative Exponents
• Example 7: Combining Rules for Exponents

5.R.4 Greatest Common Factor (GCF) of a Set of Terms

• Examples
• Example 1: Finding the GCF

5.R.5 Factoring Trinomials: x^2 + bx + c

• Examples
• Example 1: Factoring Trinomials with Leading Coefficient 1
• Example 2: Factoring Trinomials with Leading Coefficients of 1
• Example 4: Finding a Common Monomial Factor

5.R.6 Factoring Trinomials: ax^2+bx+c

• Examples
• Example 1: Using the Trial-and-Error Method
• Example 2: Factoring Trinomials

5.R.7 Special Factoring Techniques

• Examples
• Example 1: Factoring the Difference of Two Squares
• Example 2: Factoring the Sum of Two Squares (Not Factorable)
• Example 3: Factoring Perfect Square Trinomials

5.R.8 Quadratic Equations: The Quadratic Formula

• Examples
• Example 1: The Quadratic Formula
• Example 2: The Quadratic Formula
• Example 3: The Quadratic Formula
• Example 4: The Quadratic Formula
• Example 5: Cubic Equations
• Example 6: Finding the Discriminant
• Example 7: Understanding the Discriminant
• Example 8: Understanding the Discriminant

5.1 The Language of Functions

• Examples
• Example 1: Evaluating Functions
• Example 2: Exploring Mathematical Relationships

5.2 Linear Growth

• Examples
• Example 1: Using Direct Variation
• Example 2: Applying Linear Functions

5.3 Discovering Quadratics

• Examples
• Example 1: Graphing Quadratic Functions
• Example 2: Application of Quadratic Functions

5.4 Exponential Growth

• Examples
• Example 1: Introducing Exponential Growth
• Example 2: Application of Exponential Functions
• Example 4: Percent Increase

5.5 Logarithmic Growth

• Examples
• Example 1: Equivalent Logarithmic and Exponential Functions
• Example 2: Equivalent Logarithmic and Exponential Functions
• Example 3: Evaluating Logarithmic Functions
• Example 4: Application of Logarithmic Functions Involving Earthquakes
• Example 5: Application of Logarithmic Functions Involving Earthquakes
• Example 6: Application of Logarithmic Functions Involving Earthquakes
• Example 8: Human Memory Capacity and Logarithms

6.R.1 Proportions

• Examples
• Example 1: Verifying Proportions
• Example 3: Solving Proportions
• Example 4: Solving Proportions
• Example 5: Solving Proportions
• Example 6: Solving Proportions
• Example 8: Application: Solving Proportions
• Example 9: Application: Solving Proportions
• Example 10: Application: Solving Proportions
• Example 13: Application: Solving Proportions Written in Medical Notation

6.R.2 Square Roots and the Pythagorean Theorem

• Examples
• Example 1: Evaluating Perfect Squares
• Example 2: Evaluating Square Roots
• Example 3: Calculating Square Roots Using a Calculator
• Example 4: Verifying Right Triangles
• Example 5: Finding the Length of the Hypotenuse
• Example 6: Finding the Length of the Hypotenuse
• Example 7: Finding the Length of the Hypotenuse

6.R.3 Simplifying Algebraic Expressions

• Examples
• Example 1: Combining Like Terms

6.R.4 Evaluating Algebraic Expressions

• Examples
• Example 1: Evaluating Algebraic Expressions
• Example 2: Simplifying and Evaluating Algebraic Expressions
• Example 4: Simplifying and Evaluating Algebraic Expressions
• Example 5: Simplifying and Evaluating Algebraic Expressions

6.R.5 Working with Formulas

• Examples
• Example 1: Application: Evaluating Formulas
• Example 2: Evaluating Formulas
• Example 3: Application: Evaluating Formulas
• Example 4: Evaluating Formulas
• Example 5: Solving for Different Variables
• Example 6: Solving for Different Variables
• Example 7: Solving for Different Variables
• Example 8: Solving for Different Variables

6.1 Everyday Geometry and Applications

• Examples
• Example 1: Determining the Length of a Line Segment
• Example 2: Complementary Angles
• Example 3: Supplementary Angles
• Example 4: Complementary and Supplementary Angles
• Example 5: Converting Decimal Degrees to Degrees, Minutes, and Seconds
• Example 6: Converting Degrees, Minutes, and Seconds to Decimal Degrees
• Example 8: Determining Location
• Example 9: Using GPS to Determine Location and Distance

6.2 Circles, Polygons, Perimeter, and Area

• Examples
• Example 1: Using Similar Triangles
• Example 2: Finding Perimeter
• Example 3: Finding Area
• Example 5: Finding the Area of a Parallelogram
• Example 6: Finding the Area of a Triangle
• Example 9: Using Area

6.3 Volume and Surface Area

• Examples
• Example 1: Determining Volume
• Example 2: Using Volume to Meet Restrictions
• Example 4: Finding the Volume of a Right Circular Cylinder
• Example 5: Finding the Volume of a Right Circular Cone
• Example 6: Finding the Volume of a Square Pyramid
• Example 9: Finding the Surface Area of a Right Circular Cylinder
• Example 11: Using Surface Area

7.R.1 Multiplication and Division with Fractions and Mixed Numbers

• Examples
• Example 1: Multiplying Fractions
• Example 2: Application: Multiplying Fractions
• Example 3: Reducing Fractions to Lowest Terms
• Example 5: Application: Reducing Fractions to Lowest Terms
• Example 6: Multiplying and Reducing Using Prime Factors
• Example 7: Multiplying and Reducing Using Prime Factors
• Example 8: Multiplying and Reducing Using Prime Factors
• Example 9: Application: Multiplying and Reducing Fractions
• Example 10: Multiplying and Reducing Using the Division Method
• Example 11: Multiplying and Reducing Using the Division Method
• Example 12: Multiplying and Reducing Using the Division Method
• Example 13: Finding Reciprocals
• Example 14: Finding Reciprocals
• Example 15: Dividing Fractions
• Example 16: Dividing and Reducing Fractions
• Example 18: Finding a Missing Number
• Example 19: Application: Dividing Fractions
• Example 20: Application: Multiplying and Dividing Fractions
• Example 21: Multiplying Mixed Numbers
• Example 22: Multiplying and Reducing Mixed Numbers
• Example 24: Finding Fractional Parts of Mixed Numbers
• Example 25: Dividing and Reducing Mixed Numbers
• Example 27: Application: Dividing Mixed Numbers

7.R.2 Least Common Multiple (LCM)

• Examples
• Example 1: Finding the Least Common Multiple (LCM)
• Example 2: Finding the Least Common Multiple (LCM)
• Example 4: Finding the Least Common Multiple (LCM)
• Example 5: Finding the Least Common Multiple (LCM)
• Example 6: Finding the Least Common Multiple (LCM)
• Example 7: Finding the Least Common Multiple (LCM)
• Example 9: Application: Finding the LCM
• Example 10: Finding Equivalent Fractions
• Example 11: Finding Equivalent Fractions

7.R.3 Addition and Subtraction with Fractions

• Examples
• Example 1: Adding Fractions with the Same Denominator
• Example 2: Finding the Least Common Denominator (LCD)
• Example 3: Adding Fractions with Different Denominators
• Example 4: Adding Fractions with Different Denominators
• Example 5: Adding Three Fractions with Different Denominators
• Example 6: Application: Adding Fractions
• Example 7: Application: Adding Fractions
• Example 8: Subtracting Fractions with the Same Denominator
• Example 9: Subtracting Fractions with Different Denominators
• Example 10: Subtracting Fractions with Different Denominators
• Example 11: Subtracting Fractions with Different Denominators
• Example 12: Application: Subtracting Fractions with Different Denominators

7.R.4 Decimals and Fractions

• Examples
• Example 1: Changing Decimal Numbers to Fractions
• Example 2: Changing Decimal Numbers to Fractions
• Example 3: Changing Decimal Numbers to Fractions
• Example 4: Changing Fractions to Decimal Numbers
• Example 5: Changing Fractions to Decimal Numbers
• Example 6: Changing Fractions to Decimal Numbers
• Example 7: Changing Fractions to Decimal Numbers
• Example 8: Simplifying Expressions with Decimals and Fractions
• Example 9: Comparing Decimal Numbers and Fractions
• Example 10: Application: Decimal and Fraction Expressions

7.1 Introduction to Probability

• Examples
• Example 1: Determining Sample Spaces
• Example 3: Calculating Classical Probability
• Example 4: Empirical Probability with Multiple Trials
• Example 5: Classical vs. Empirical Probability

7.2 Counting Our Way to Probabilities

• Examples
• Example 1: Using the Fundamental Counting Principle with Replacement
• Example 3: Calculating Factorials
• Example 4: Using Combinations
• Example 5: Using Permutations
• Example 6: Using Permutations

7.3 Using Counting Methods to Find Probability

• Examples
• Example 1: Calculating Classical Probability Using Combinations
• Example 2: Calculating Classical Probability Using Permutations
• Example 3: Finding the Complement of an Event
• Example 4: Finding Probability Using Complements

7.4 Addition and Multiplication Rules of Probability

• Examples
• Example 1: Applying the Addition Rule for Probability
• Example 2: Applying the Addition Rule for Probability
• Example 3: Applying the Addition Rule for Mutually Exclusive Events
• Example 4: Applying the Addition Rule for Mutually Exclusive Events
• Example 5: Independent vs. Dependent Events
• Example 6: Multiplication Rule for Independent Events
• Example 7: Multiplication Rule for Independent Events
• Example 8: Multiplication Rule for Dependent Events

7.5 Expected Value

8.R.1 Decimals and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ to Percents
• Example 2: Changing Decimal Numbers to Percents
• Example 3: Changing Percents to Decimal Numbers

8.R.2 Fractions and Percents

• Examples
• Example 1: Changing Fractions to Percents
• Example 2: Changing Fractions to Percents
• Example 3: Changing Mixed Numbers to Percents
• Example 5: Changing Fractions to Percents
• Example 5: Application: Changing Fractions to Percents
• Example 7: Changing Percents to Fractions
• Example 8: Changing Percents to Mixed Numbers

8.R.3 Working with Formulas

• Examples
• Example 1: Application: Evaluating Formulas
• Example 2: Evaluating Formulas
• Example 3: Application: Evaluating Formulas
• Example 4: Evaluating Formulas
• Example 5: Solving for Different Variables
• Example 6: Solving for Different Variables
• Example 7: Solving for Different Variables
• Example 8: Solving for Different Variables

8.R.4 The Cartesian Coordinate System

• Examples
• Example 1: Plotting Ordered Pairs
• Example 2: Plotting Ordered Pairs
• Example 3: Finding Ordered Pairs
• Example 4: Finding Ordered Pairs
• Example 6: Locating Points on the Graph of a Line

8.R.5 Graphing Linear Equations in Two Variables

• Examples
• Example 1: Graphing a Linear Equation in Two Variables
• Example 2: Graphing a Linear Equation in Two Variables
• Example 3: Graphing a Linear Equation in Two Variables
• Example 4: Using Intercepts to Graph Linear Equations
• Example 5: Using Intercepts to Graph Linear Equations
• Example 7: Graphing Horizontal Lines
• Example 8: Graphing Vertical Lines

8.R.6 Slope-Intercept Form

• Examples
• Example 1: Finding the Slope of a Line
• Example 2: Finding the Slope of a Line
• Example 3: Finding the Slope of a Horizontal Line
• Example 4: Finding the Slope of a Vertical Line
• Example 5: Using Slope and the y‑Intercept to Graph a Line
• Example 6: Using Slope and the y-Intercept to Graph a Line
• Example 7: Finding Equations Given the Slope and the y‑Intercept

8.R.7 Evaluating Radicals

• Examples
• Example 1: Evaluating Square Roots
• Example 2: Evaluating Square Roots
• Example 3: Estimating Square Roots
• Example 4: Evaluating Cube Roots

8.1 Collecting Data

• Examples
• Example 1: Identifying Parts of a Survey
• Example 2: Identifying Sampling Techniques

8.2 Displaying Data

• Examples
• Example 1: Interpreting a Frequency Distribution
• Example 2: Constructing a Frequency Distribution
• Example 3: Constructing a Grouped Frequency Distribution
• Example 4: Interpreting a Frequency Distribution
• Example 5: Interpreting Bar Graphs
• Example 6: Interpreting Bar Graphs with Multiple Populations
• Example 7: Interpreting a Histogram
• Example 8: Reading Graphs

8.3 Describing and Analyzing Data

• Examples
• Example 1: Finding the Mean
• Example 2: Finding the Median
• Example 3: Finding the Mode
• Example 4: Finding the Mean, Median, and Mode
• Example 5: Finding the Range
• Example 6: Calculating Standard Deviation by Hand
• Example 9: Interpreting Percentiles

8.4 The Normal Distribution

8.5 Linear Regression

• Examples
• Example 1: Identifying Correlations

9.R.1 Introduction to Whole Numbers

• Examples
• Example 1: Understanding Place Value
• Example 2: Understanding Place Value
• Example 3: Writing Numbers in Expanded Notation
• Example 5: Reading and Writing Whole Numbers
• Example 7: Reading and Writing Whole Numbers
• Example 9: Application: Reading Tables

9.R.2 Addition and Subtraction with Whole Numbers

• Examples
• Example 1: Adding Whole Numbers
• Example 2: Adding Whole Numbers When Carrying is Required
• Example 3: Adding Whole Numbers Using Sums of $10$
• Example 4: Adding Whole Numbers
• Example 5: Recognizing the Properties of Addition
• Example 6: Calculating the Perimeter of a Polygon
• Example 7: Application: Calculating the Perimeter of a Rectangle
• Example 8: Subtracting Whole Numbers
• Example 9: Subtracting Whole Numbers
• Example 10: Subtracting Whole Numbers by Borrowing
• Example 11: Subtracting Whole Numbers by Borrowing
• Example 12: Finding a Missing Addend
• Example 13: Application: Subtracting Whole Numbers
• Example 14: Application: Adding and Subtracting Numbers

9.R.3 Exponents and Order of Operations

• Examples
• Example 1: Identifying the Base and Exponent
• Example 3: Evaluating Exponential Expressions
• Example 4: Evaluating Exponential Expressions
• Example 5: Using the Order of Operations with Whole Numbers
• Example 6: Using the Order of Operations with Whole Numbers
• Example 7: Using the Order of Operations with Whole Numbers
• Example 8: Using the Order of Operations with Whole Numbers
• Example 9: Using the Order of Operations with Whole Numbers

9.R.4 Introduction to Decimal Numbers

• Examples
• Example 1: Reading and Writing Decimal Numbers
• Example 2: Reading and Writing Decimal Numbers
• Example 3: Reading and Writing Decimal Numbers
• Example 4: Comparing Decimal Numbers
• Example 5: Comparing Decimal Numbers
• Example 6: Comparing Decimal Numbers
• Example 7: Rounding Decimal Numbers
• Example 8: Rounding Decimal Numbers

9.R.5 Decimals and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ to Percents
• Example 2: Changing Decimal Numbers to Percents
• Example 3: Changing Percents to Decimal Numbers

9.R.6 Solving Percent Problems Using Equations

• Examples
• Example 1: Finding the Amount
• Example 2: Finding the Base
• Example 3: Finding the Percent
• Example 4: Finding the Amount
• Example 5: Finding the Base
• Example 6: Application: Finding the Base
• Example 7: Application: Finding the Amount

9.R.7 Simplifying and Evaluating Algebraic Expressions

• Examples
• Example 1: Identifying Like Terms
• Example 2: Combining Like Terms
• Example 3: Evaluating Algebraic Expressions
• Example 4: Simplifying and Evaluating Algebraic Expressions
• Example 5: Simplifying and Evaluating Algebraic Expressions
• Example 6: Simplifying and Evaluating Algebraic Expressions

9.1 Understanding Personal Finance

• Examples
• Example 1: Determining Federal Income Tax
• Example 2: Determining Monthly Take Home Pay
• Example 3: Budgeting on a Given Income
• Example 5: Finding the Sale Price
• Example 6: Determining a Discount
• Example 7: Computing Percentage Decrease
• Example 8: Computing Percentage Increase

9.2 Understanding Interest

• Examples
• Example 1: Calculating Simple Interest
• Example 2: Calculating Simple Interest on Purchases
• Example 4: Comparing Compound Interest for Different Compounding Intervals
• Example 5: Calculating Continuous Compound Interest
• Example 6: Finding the Maximum Amount of Interest Possible in One Year
• Example 7: Annual Percentage Yield
• Example 9: Calculating Interest on Payday Loans

9.3 Saving Money

9.4 Borrowing Money

• Examples
• Example 1: Paying Off Credit Card Debt with a Fixed Payment
• Example 2: Purchasing a New Car
• Example 3: Determining Best New Car Incentive
• Example 4: Calculating Monthly Mortgage Payments

10.R.1 Addition and Subtraction with Whole Numbers

• Examples
• Example 1: Adding Whole Numbers
• Example 2: Adding Whole Numbers When Carrying is Required
• Example 3: Adding Whole Numbers Using Sums of $10$
• Example 4: Adding Whole Numbers
• Example 5: Recognizing the Properties of Addition
• Example 6: Calculating the Perimeter of a Polygon
• Example 7: Application: Calculating the Perimeter of a Rectangle
• Example 8: Subtracting Whole Numbers
• Example 9: Subtracting Whole Numbers
• Example 10: Subtracting Whole Numbers by Borrowing
• Example 11: Subtracting Whole Numbers by Borrowing
• Example 12: Finding a Missing Addend
• Example 13: Application: Subtracting Whole Numbers
• Example 14: Application: Adding and Subtracting Numbers

10.R.2 Introduction to Decimal Numbers

• Examples
• Example 1: Reading and Writing Decimal Numbers
• Example 2: Reading and Writing Decimal Numbers
• Example 3: Reading and Writing Decimal Numbers
• Example 4: Comparing Decimal Numbers
• Example 5: Comparing Decimal Numbers
• Example 6: Comparing Decimal Numbers
• Example 7: Rounding Decimal Numbers
• Example 8: Rounding Decimal Numbers

10.1 How to Determine a Winner

• Examples
• Example 2: Majority Rule Decision
• Example 3: Plurality Method
• Example 4: Borda Count Method
• Example 6: Pairwise Comparison Method

10.2 What's Fair?

• Examples
• Example 1: Condorcet Criterion and the Plurality Method
• Example 2: Majority Criterion and the Borda Count Method
• Example 3: Monotonicity Criterion and the Plurality with Elimination Method
• Example 4: Irrelevant Alternatives Criterion and the Pairwise Method of Comparison

10.3 Apportionment

• Examples
• Example 2: Distributing Money from the Super Bowl
• Example 3: Applying the Hamilton Method of Apportionment
• Example 4: Applying the Jefferson Method of Apportionment
• Example 5: Applying the Webster Method of Apportionment
• Example 6: Applying the Huntington-Hill Method of Apportionment
• Example 7: The Alabama Paradox

10.4 Weighted Voting Systems

• Examples
• Example 1: Weighted Voting System
• Example 2: Passing a Motion with a Coalition
• Example 4: Banzhaf Power Index
• Example 5: Determining a Pivotal Player
• Example 6: Number of Sequential Coalitions
• Example 7: Applying the SSPI

11.R.1 Decimal Numbers and Fractions

• Examples
• Example 1: Changing Decimal Numbers to Fractions
• Example 2: Changing Decimal Numbers to Fractions
• Example 3: Changing Decimal Numbers to Fractions
• Example 4: Changing Fractions to Decimal Numbers
• Example 5: Changing Fractions to Decimal Numbers
• Example 6: Changing Fractions to Decimal Numbers
• Example 7: Changing Fractions to Decimal Numbers
• Example 8: Simplifying Expressions with Decimals and Fractions
• Example 9: Comparing Decimal Numbers and Fractions
• Example 10: Application: Decimal and Fraction Expressions

11.R.2 Ratios, Unit Rates, and Proportions

• Examples
• Example 1: Application: Writing Ratios
• Example 2: Writing Ratios that Compare Mixed Numbers
• Example 3: Writing Ratios that Compare Decimal Numbers
• Example 4: Application: Writing Ratios from Graphs
• Example 5: Writing Ratios in Geometry
• Example 6: Writing Ratios that Compare Measurements
• Example 7: Writing a Rate
• Example 8: Application: Batting Average
• Example 9: Application: Writing a Unit Rate
• Example 10: Application: Writing a Unit Rate
• Example 11: Application: Writing a Unit Rate
• Example 12: Application: Comparing Unit Prices
• Example 13: Application: Comparing Unit Prices
• Example 14: Verifying Proportions
• Example 16: Solving Proportions
• Example 17: Solving Proportions
• Example 18: Solving Proportions
• Example 19: Solving Proportions
• Example 21: Application: Solving Proportions
• Example 22: Application: Solving Proportions
• Example 23: Application: Solving Proportions
• Example 26: Application: Solving Proportions Written in Medical Notation

11.R.3 Angles and Triangles

• Examples
• Example 1: Measuring Angles
• Example 2: Classifying Angles by Their Measure
• Example 3: Identifying Complementary and Supplementary Angles
• Example 4: Calculating Measures of Angles
• Example 5: Identifying Congruent Angles
• Example 6: Calculating Measures of Angles
• Example 7: Finding Adjacent Angles
• Example 8: Calculating Measures of Angles
• Example 9: Classifying a Triangle by Its Sides
• Example 10: Determining Whether a Triangle Exists
• Example 11: Analyzing Triangles

11.R.4 Rules for Exponents

• Examples
• Example 1: Using the Product Rule for Exponents
• Example 2: Using the Product Rule for Exponents
• Example 3: Evaluating the Exponent 0
• Example 4: Using the Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients
• Example 6: Negative Exponents
• Example 7: Combining Rules for Exponents

11.R.5 Rationalizing Denominators

• Examples
• Example 1: Rationalizing Denominators Containing Square Roots
• Example 2: Rationalizing Denominators Containing Cube Roots
• Example 3: Rationalizing Denominators

11.R.6 Quadratic Equations: The Quadratic Formula

• Examples
• Example 1: The Quadratic Formula
• Example 2: The Quadratic Formula
• Example 3: The Quadratic Formula
• Example 4: The Quadratic Formula
• Example 5: Cubic Equations
• Example 6: Finding the Discriminant
• Example 7: Understanding the Discriminant
• Example 8: Understanding the Discriminant

11.1 Applications of Geometry to the Arts

• Examples
• Example 1: The Fibonacci Sequence
• Example 2: More on the Fibonacci Sequence
• Example 4: Golden Rectangles
• Example 5: Golden Rectangles in Modern Architecture

11.2 Tiling and Tessellations

• Examples
• Example 1: Finding Triangular Numbers
• Example 2: Representing Square Numbers
• Example 4: Archimedean Tiling

11.3 Mathematics and Music

• Examples
• Example 1: Determining Half Steps, Whole Steps, and Octaves on a Keyboard
• Example 2: Determining Frequencies of Octaves
• Example 3: Musical Notes as Exponential Functions
• Example 4: Finding Major and Minor Chords on a Piano
• Example 5: Finding Frequency Ratios of Perfect Fifths

12.R.1 Exponents and Order of Operations

• Examples
• Example 1: Identifying the Base and Exponent
• Example 3: Evaluating Exponential Expressions
• Example 4: Evaluating Exponential Expressions
• Example 5: Using the Order of Operations with Whole Numbers
• Example 6: Using the Order of Operations with Whole Numbers
• Example 7: Using the Order of Operations with Whole Numbers
• Example 8: Using the Order of Operations with Whole Numbers
• Example 9: Using the Order of Operations with Whole Numbers

12.R.2 Ratios, Unit Rates, and Proportions

• Examples
• Example 1: Application: Writing Ratios
• Example 2: Writing Ratios that Compare Mixed Numbers
• Example 3: Writing Ratios that Compare Decimal Numbers
• Example 4: Application: Writing Ratios from Graphs
• Example 5: Writing Ratios in Geometry
• Example 6: Writing Ratios that Compare Measurements
• Example 7: Writing a Rate
• Example 8: Application: Batting Average
• Example 9: Application: Writing a Unit Rate
• Example 10: Application: Writing a Unit Rate
• Example 11: Application: Writing a Unit Rate
• Example 12: Application: Comparing Unit Prices
• Example 13: Application: Comparing Unit Prices
• Example 14: Verifying Proportions
• Example 16: Solving Proportions
• Example 17: Solving Proportions
• Example 18: Solving Proportions
• Example 19: Solving Proportions
• Example 21: Application: Solving Proportions
• Example 22: Application: Solving Proportions
• Example 23: Application: Solving Proportions
• Example 26: Application: Solving Proportions Written in Medical Notation

12.R.3 Simplifying and Evaluating Algebraic Expressions

• Examples
• Example 1: Identifying Like Terms
• Example 2: Combining Like Terms
• Example 3: Evaluating Algebraic Expressions
• Example 4: Simplifying and Evaluating Algebraic Expressions
• Example 5: Simplifying and Evaluating Algebraic Expressions
• Example 6: Simplifying and Evaluating Algebraic Expressions

12.R.4 U.S. Measurements

• Examples
• Example 1: Basic Conversions in the US Customary System
• Example 2: Converting US Units of Measure Using Multiplication/Division
• Example 3: Application: Converting US Units of Measure
• Example 4: Using Unit Fractions to Convert US Units of Measure
• Example 5: Application: Converting US Units of Measure
• Example 6: Application: Converting US Units of Measure

12.R.5 The Metric System: Length and Area

• Examples
• Example 1: Converting Metric Units of Length
• Example 2: Application: Converting Metric Units of Length
• Example 3: Converting Metric Units of Length
• Example 4: Converting Metric Units of Length
• Example 5: The Prefixes Mega-, Giga-, and Tera-
• Example 6: Converting Metric Units of Area
• Example 7: Converting Metric Units of Area
• Example 8: Converting Metric Units of Area
• Example 9: Converting Metric Units of Land Area

12.R.6 US and Metric Equivalents

• Examples
• Example 1: Equivalent Measures of Temperature
• Example 2: Converting Units of Temperature
• Example 3: Converting Units of Temperature
• Example 4: Converting Units of Length
• Example 5: Converting Units of Area
• Example 6: Converting Units of Capacity (Liquid Volume)
• Example 7: Converting Units of Weight (Mass)

12.1 Baseball and Softball

12.2 Football

12.3 Basketball

12.4 Additional Sports: Tennis, Golf, and Track & Field

13.R.1 Solving Linear Equations: ax + b = c

• Examples
• Example 1: Solving Linear Equations of the Form ax + b = c
• Example 2: Solving Linear Equations of the Form ax + b = c
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations Involving Decimals
• Example 5: Solving Linear Equations Involving Fractions
• Example 6: Solving Linear Equations Involving Fractions

13.R.2 The Real Number Line and Absolute Value

• Examples
• Example 1: Finding the Opposite of an Integer
• Example 2: Graphing Integers on a Number Line
• Example 3: Identifying Types of Numbers
• Example 4: Graphing Sets of Numbers
• Example 5: Graphing Sets of Numbers
• Example 6: Verifying Inequalities
• Example 7: Finding Absolute Values
• Example 8: Verifying Absolute Value Inequalities
• Example 9: Solving Absolute Value Equations
• Example 10: Solving Absolute Value Equations
• Example 11: Application: Solving Absolute Value Equations

13.1 Introduction to Graph Theory

• Examples
• Example 1: Identifying Parts of a Graph
• Example 2: Identifying Parts of a Graph
• Example 3: Identifying a Walk
• Example 4: Identifying a Path
• Example 5: Identifying Connected and Disconnected Graphs
• Example 6: Identifying Different Views of the Same Graph
• Example 7: Identifying Parts of a Graph
• Example 8: Drawing a Graph Given the Edges

13.2 Trees

13.3 Matchings

13.4 Planar Graphs

14.R.1 Multiplication with Whole Numbers

• Examples
• Example 1: Recognizing the Properties of Multiplication
• Example 2: Using the Distributive Property
• Example 3: Multiplying Whole Numbers
• Example 4: Multiplying Whole Numbers
• Example 5: Multiplying Whole Numbers
• Example 6: Multiplying Whole Numbers that End with 0s
• Example 7: Application: Calculating the Area of a Rectangle

14.R.2 Division with Whole Numbers

• Examples
• Example 1: Understanding the Basic of Division
• Example 2: Understanding Division with 0
• Example 3: Dividing Whole Numbers
• Example 4: Dividing Whole Numbers
• Example 5: Dividing Whole Numbers
• Example 7: Using Division to Find Factors
• Example 8: Application: Dividing Whole Numbers

14.R.3 Tests for Divisibility

• Examples
• Example 1: Divisibility by 2
• Example 2: Divisibility by 3
• Example 3: Divisibility by 4
• Example 4: Divisibility by 5
• Example 5: Divisibility by 6
• Example 6: Divisibility by 9
• Example 7: Divisibility by 10

14.R.4 Rules for Exponents

• Examples
• Example 1: Using the Product Rule for Exponents
• Example 2: Using the Product Rule for Exponents
• Example 3: Evaluating the Exponent 0
• Example 4: Using the Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients
• Example 6: Negative Exponents
• Example 7: Combining Rules for Exponents

14.R.5 Power Rules for Exponents

• Examples
• Example 1: Using the Power Rule for Exponents
• Example 2: Using the Rule for Power of a Product
• Example 3: Using the Rule for Power of a Quotient
• Example 4: Using Combinations of Rules for Exponents
• Example 5: Using Two Approaches with Fractional Expressions and Negative Exponents
• Example 6: Simplifying a More Complex Example

14.R.6 Evaluating Radicals

• Examples
• Example 1: Evaluating Square Roots
• Example 2: Evaluating Square Roots
• Example 3: Estimating Square Roots
• Example 4: Evaluating Cube Roots

14.1 Prime Numbers

• Examples
• Example 1: Classifying a Number as Prime or Composite
• Example 2: Using a Factor Tree to Find a Prime Factorization
• Example 3: Classifying a Number as Prime or Composite
• Example 4: GCD Using Factor Trees
• Example 5: Using the GCD
• Example 6: Finding the GCD Using Euclid's Algorithm
• Example 7: Relatively Prime Numbers Using Euclid's Algorithm

14.2 Modular Arithmetic

• Examples
• Example 1: Completing the Modular Congruence Table
• Example 2: Finding Modular Congruence

14.3 Fermat's Little Theorem and Prime Testing

14.4 Fermat's Little Theorem and Public-Key Encryption

A.1 US Measurements

• Examples
• Example 1: Basic Conversions in the US Customary System
• Example 2: Converting US Units of Measure Using Multiplication/Division
• Example 3: Application: Converting US Units of Measure
• Example 4: Using Unit Fractions to Convert US Units of Measure
• Example 5: Application: Converting US Units of Measure
• Example 6: Application: Converting US Units of Measure

A.2 The Metric System: Length and Area

• Examples
• Example 1: Converting Metric Units of Length
• Example 2: Application: Converting Metric Units of Length
• Example 3: Converting Metric Units of Length
• Example 4: Converting Metric Units of Length
• Example 5: The Prefixes Mega-, Giga-, and Tera-
• Example 6: Converting Metric Units of Area
• Example 7: Converting Metric Units of Area
• Example 8: Converting Metric Units of Area
• Example 9: Converting Metric Units of Land Area

A.3 The Metric System: Capacity and Weight

• Examples
• Example 1: Common Metric Units of Capacity
• Example 2: Converting Metric Units of Capacity
• Example 3: Converting Metric Units of Capacity
• Example 4: Converting Metric Units of Capacity
• Example 5: Application: Converting Metric Units of Capacity
• Example 7: Converting Metric Units of Weight
• Example 8: Application: Converting Metric Units of Weight

A.4 US and Metric Equivalents

• Examples
• Example 1: Equivalent Measures of Temperature
• Example 2: Converting Units of Temperature
• Example 3: Converting Units of Temperature
• Example 4: Converting Units of Length
• Example 5: Converting Units of Area
• Example 6: Converting Units of Capacity (Liquid Volume)
• Example 7: Converting Units of Weight (Mass)