Viewing Life Mathematically Plus Integrated Review, 2nd Edition

1.R.1 Introduction to Whole Numbers

1.R.2 Rounding and Estimating 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 Orders 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

1.2 Estimating and Evaluating

1.3 Problem Solving: Processes and Techniques

2.R.1 Introduction to Integers

• Examples
• Example 1: Finding the Opposite of an Integer
• Example 2: Graphing Integers
• Example 3: Verifying Inequalities
• Example 4: Finding Absolute Value
• Example 5: Finding Absolute Value
• Example 6: Simplifying Expressions Containing Absolute Value
• Example 7: Verifying Absolute Value Inequalities
• Example 8: Solving Absolute Value Equations
• Example 9: Solving Absolute Values Equations

2.R.2 Addition with Integers

2.R.3 Subtraction with Integers

2.R.4 Multiplication, Division, and Order of Operations with Integers

2.1 Set Notation

2.2 Subsets and Venn Diagrams

2.3 Operations with Sets

2.4 Applications and Survey Analysis

3.1 Logic Statements and Their Negations

3.2 Truth Tables

3.3 Logical Equivalence and De Morgan's Laws

3.4 Valid Arguments and Fallacies

4.R.1 Introduction to Fractions and 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 Positive Decimal Numbers
• Example 5: Comparing Positive Decimal Numbers
• Example 6: Comparing Negative Decimal Numbers
• Example 7: Rounding Decimal Numbers
• Example 8: Rounding Decimal Numbers

4.R.3 Multiplication and Division with Decimal Numbers

• Examples
• Example 1: Multiplying Decimal Numbers
• Example 2: Multiplying Decimal Numbers
• Example 3: Multiplying Decimal Numbers
• Example 5: Application: Multiplying Decimal Numbers
• Example 6: Multiplying by Powers of 10
• Example 7: Dividing Decimal Numbers
• Example 8: Dividing Positive and Negative Decimal Numbers
• Example 9: Dividing Decimal Numbers
• Example 10: Dividing Decimal Numbers
• Example 11: Application: Calculating Average Amount per Unit
• Example 12: Application: Calculating Total Distance Traveled
• Example 13: Dividing by Powers of 10

4.R.4 Basics of Percentages

• 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
• Example 4: Changing Fractions to Percents
• Example 5: Changing Fractions to Percents
• Example 6: Changing Mixed Numbers to Percents
• Example 8: Changing Fractions to Percents
• Example 9: Application: Changing Fractions to Percents
• Example 10: Changing Percents to Fractions
• Example 11: Changing Percents to Mixed Numbers

4.R.5 Scientific Notation

• Examples
• Example 1: Writing Decimals in Scientific Notation
• Example 2: Using Scientific Notation while Simplifying
• Example 3: Application: Scientific Notation

4.1 Proportions, Percentages, and Ratios

4.2 Using Percentages

4.3 Rates, Unit Rates, and Rates of Change

4.4 Using Rates for Dimensional Analysis

4.5 Proportionality

5.R.1 Operations with Real Numbers

• Examples
• Example 1: Addition with Like Signs
• Example 2: Addition with Unlike Signs
• Example 3: Application: Reading a Table
• Example 4: Application: Calculating the Perimeter of a Rectangle
• Example 5: Subtraction with Real Numbers
• Example 6: Application: Calculating Change in Value
• Example 7: Multiplication with Positive and Negative Real Numbers
• Example 8: Application: Calculating the Area of a Rectangle
• Example 9: Division with Positive and Negative Real Numbers
• Example 10: Division with 0

5.R.2 Simplifying Algebraic Expressions

5.R.3 Solving One-Step Linear Equations

• Examples
• Example 1: Checking Given Solutions in Equations
• Example 2: Solving Linear Equations of the Form x + b = c
• Example 3: Solving Linear Equations of the Form x + b = c
• Example 4: Solving Linear Equations of the Form x + b = c
• Example 5: Solving Linear Equations of the Form x + b = c
• Example 6: Simplifying and Solving Linear Equations
• Example 8: Solving Linear Equations of the Form ax = c
• Example 9: Solving Linear Equations of the Form ax=c
• Example 10: Solving Linear Equations of the Form ax = c
• Example 12: Application: Solving Linear Equations

5.R.4 Solving Multi-Step Linear Equations

• 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 Fractions
• Example 5: Solving Equations of the Form ax + b = cx + d
• Example 6: Solving Equations of the Form ax + b = cx + d
• Example 7: Solving Linear Equations Involving Decimals
• Example 8: Solving Linear Equations Involving Fractions
• Example 9: Solving Equations Involving Parentheses
• Example 11: Determining Types of Equations
• Example 12: Determining Types of Equations
• Example 13: Determining Types of Equations

5.R.5 Solving Linear Inequalities

• Examples
• Example 1: Graphing Intervals
• Example 2: Graphing Intervals
• Example 3: Graphing Intervals
• Example 4: Graphing Intervals
• Example 5: Solving an Inequality and Graphing the Solution Set
• Example 6: Solving an Inequality and Graphing the Solution Set
• Example 7: Solving an Inequality and Graphing the Solution Set
• Example 8: Solving an Inequality and Graphing the Solution Set
• Example 9: Solving Linear Inequalities
• Example 10: Solving Linear Inequalities
• Example 11: Solving Linear Inequalities
• Example 13: Application: Using Inequalities

5.R.6 The Quadratic Formula

5.R.7 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.8 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.9 Introduction to Functions

5.1 Linear Equations and Functions

5.2 Linear Modeling

5.3 Solving Linear Systems of Equations in Two Variables

5.4 Linear Inequalities in Two Variables

5.5 Linear Programming

5.6 Modeling with Quadratics

5.7 Exponential and Logarithmic Functions

6.R.1 Estimating and Order of Operations with Decimal Numbers

• Examples
• Example 1: Estimating Sums of Decimal Numbers
• Example 3: Estimating Products of Decimal Numbers
• Example 4: Estimating Quotients of Decimal Numbers
• Example 5: Application: Estimating with Decimal Numbers
• Example 6: Using the Order of Operations with Decimal Numbers
• Example 7: Using the Order of Operations with Decimal Numbers
• Example 8: Using the Order of Operations with Decimal Numbers

6.R.2 Percentages

• Examples
• Example 1: Changing between Percents and Decimal Numbers
• Example 2: Changing between Percents and Fractions
• Example 3: Finding the Amount
• Example 4: Finding the Base
• Example 5: Finding the Percent
• Example 6: Application: Finding a Discount
• Example 7: Application: Calculating Sales Tax
• Example 8: Application: Determining Commission
• Example 9: Application: Finding the Percent Increase
• Example 10: Application: Finding the Percent Decrease
• Example 11: Application: Calculating Percent of Profit

6.R.3 Reading Graphs

• Examples
• Example 1: Reading a Bar Graph
• Example 2: Reading a Circle Graph
• Example 3: Reading a Line Graph
• Example 4: Reading a Histogram

6.1 Understanding Interest

6.2 Saving and Investing

6.3 Borrowing Money

6.4 Federal Revenue

6.5 Budgeting

7.R.1 The Decimal System

7.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 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

7.R.3 Multiplication with Whole Numbers

• Examples
• Example 1: Recognizing the Properties of Multiplication
• Example 3: Using the Distributive Property
• Example 4: Multiplying Whole Numbers
• Example 5: Multiplying Whole Numbers
• Example 6: Multiplying Whole Numbers
• Example 7: Multiplying Whole Numbers that End with $0$s
• Example 8: Application: Calculating the Area of a Rectangle

7.R.4 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

7.1 Numeral Systems Based on Position

7.2 Early Numeral Systems

7.3 Working with Base Number Systems

7.4 The Metric System

7.5 Converting between the US Customary System and the Metric System

8.R.1 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

8.R.2 Prime Numbers and Prime Factorizations

• Examples
• Example 1: Determining Prime Numbers
• Example 2: Determining Composite Numbers
• Example 3: Determining Whether a Number is Prime
• Example 4: Determining Whether a Number is Prime
• Example 5: Determining Whether a Number is Prime
• Example 7: Finding the Prime Factorization of a Number
• Example 8: Finding the Prime Factorization of a Number
• Example 10: Finding the Factors of a Composite Number
• Example 12: Using Factors of Counting Numbers

8.1 Prime Numbers

8.2 Modular Arithmetic

8.3 Fermat's Little Theorem and Prime Testing

8.4 Fermat's Little Theorem and Public-Key Encryption

9.R.1 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

9.R.2 Square Roots and 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

9.R.3 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

9.R.4 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

9.1 Two-Dimensional Geometry

9.2 Three-Dimensional Geometry

9.3 Angles and Trigonometry

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

• Examples
• Example 1: Understanding Fractions
• Example 2: Multiplying Fractions
• Example 3: Multiplying Fractions
• Example 4: Multiplying Fractions
• Example 5: Finding Equivalent Fractions
• Example 6: Finding Equivalent Fractions
• Example 7: Reducing Fractions to Lowest Terms
• Example 8: Reducing Fractions to Lowest Terms
• Example 9: Multiplying and Reducing Fractions
• Example 10: Multiplying and Reducing Fractions
• Example 11: Multiplying and Reducing Fractions
• Example 12: Dividing Fractions
• Example 13: Dividing and Reducing Fractions
• Example 14: Application: Writing and Reducing Fractions
• Example 15: Application: Dividing Fractions

10.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

10.R.3 Addition and Subtraction with Fractions

• Examples
• Example 1: Adding Fractions with the Same Denominator
• Example 2: Adding Fractions with the Same Denominator
• Example 3: Adding Fractions with Different Denominators
• Example 4: Adding Fractions with Different Denominators
• Example 5: Application: Adding Fractions
• Example 8: Subtracting Fractions with the Same Denominator
• Example 7: Subtracting Fractions with Different Denominators
• Example 8: Subtracting Fractions with Different Denominators

10.R.4 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

10.R.5 Determining Sample Spaces

10.1 Introduction to Probability

10.2 Counting Outcomes

10.3 Probability of Single Events

10.4 Addition and Multiplication Rules of Probability

10.5 Binomial Probability

10.6 Expected Value

11.R.1 Bar Graphs, Pictographs, Circle Graphs, and Line Graphs

• Examples
• Example 1: Reading a Bar Graph
• Example 2: Reading a Pictograph
• Example 3: Reading a Circle Graph
• Example 4: Reading a Line Graph

11.R.2 Constructing Graphs from Databases

• Examples
• Example 1: Constructing a Bar Graph
• Example 2: Constructing a Circle Graph

11.R.3 The Cartesian Coordinate System, Scatter Plots, and Linear Equations

• Examples
• Example 1: Graphing Ordered Pairs
• Example 2: Reading Points on a Graph
• Example 3: Creating a Scatter Plot
• Example 4: Graphing a Linear Equation in Two Variables
• Example 5: Graphing a Linear Equation in Two Variables
• Example 6: Graphing a Linear Equation in Two Variables
• Example 7: Using Intercepts to Graph Linear Equations
• Example 8: Using Intercepts to Graph Linear Equations

11.R.4 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

11.R.5 Evaluating Radicals

11.1 Statistical Studies

11.2 Displaying Data

11.3 Describing and Analyzing Data

11.4 The Normal Distribution

11.5 Confidence Intervals

12.1 The Science of Data

12.2 Data Wrangling

12.3 Data Exploration

12.4 Data Storytelling

13.1 How to Determine a Winner

13.2 Flaws in Voting Methods

13.3 Apportionment

13.4 Weighted Voting Systems

14.1 Introduction to Graph Theory

14.2 Trees

14.3 Matchings

14.4 Planar Graphs