Quantitative Literacy: Essential Mathematics for Everyday Life, School, and Work
Author(s): Michael J. Cullinane
Edition: 1
Copyright: 2022
Pages: 356
Choose Your Platform | Help Me Choose
This book develops quantitative literacy by teaching the mathematical concepts and reasoning needed to interpret information, solve problems, and make informed decisions. Topics include number systems, arithmetic, algebra, fractions, ratios, proportional reasoning, decimals, percentages, measurement, probability, statistics, data analysis, functions, linear regression, and correlation. The text concludes with applications to personal finance, including interest, saving, retirement planning, credit, and loans, emphasizing the practical use of mathematics in everyday life.
CHAPTER 1 Introduction and Preview
Why Quantitative Literacy Matters
Reading and Interpreting Quantitative Information
Using Quantitative Concepts and Methods to Solve a Problem
Using Quantitative Concepts and Methods to Support an Argument
The Role of Mathematics in Quantitative Literacy
Problems
CHAPTER 2 Types of Numbers
Whole Numbers
Fractions
Negative Numbers
Number Terminology
The Ordering of the Real Numbers
Problems
CHAPTER 3 Whole Number Arithmetic
The Concept of Addition
The Concept of Subtraction
Counting Using the Inclusion-Exclusion Principle
The Concept of Multiplication
Counting the Number of Ways to Perform a Multi-Step Process
The Concept of Division
Remainders in Division
Problems
CHAPTER 4 More Arithmetic and Some Algebra
Variables and Variable Expressions
Equations
Some Algebraic Properties of Addition and Multiplication
Even and Odd Numbers Revisited
Arithmetic and Algebra with Positive and Negative Numbers
Multiplicative Inverses and Division
Positive Integer Exponents
Combining Operations
Solving Equations
Solving an Equation Containing More than One Variable
Problems
CHAPTER 5 Fractions, Ratios, and Proportional Reasoning
Fractions Revisited
Multiplying Fractions
Equivalent Fractions
Reducing Fractions
Multiplying Fractions Revisited
Dividing Fractions
Adding and Subtracting Fractions
Ratios
Proportions
Proportional Reasoning
Problems
CHAPTER 6 Rational and Irrational Numbers
Square Roots and Cube Roots
Rational Numbers and Irrational Numbers
Triangles
Right Triangles and the Pythagorean Theorem
The Circumference and Area of a Circle
Problems
CHAPTER 7 Place Value and Decimals
Base Ten Representation of Whole Numbers
Base Two (Binary) Representation of Whole Numbers
Zero and Negative Exponents
Decimal Fractions
Rounding Numbers
Representing Rational and Irrational Numbers in Decimal Form
Scientific Notation
Problems
CHAPTER 8 Working with Percentages
Percentages
Percentages and Rounding
Absolute and Relative Change
Percentage Points vs. Percentages
Absolute and Relative Difference
Index Numbers
Problems
CHAPTER 9 Measurement Units
Converting Units of Measurement
The Metric System
Rates
Converting Units of Area and Volume
Density and Concentration
Measurements Expressed in Scientific Notation
Approximation, Measurement Error, and Error Propagation
Problems
CHAPTER 10 Probability
Experiments, Outcomes, and Sample Spaces
Events of a Sample Space
The Complement of an Event
The Intersection of Events
The Union of Events
Using Venn Diagrams to Depict Events within a Sample Space
Assigning Probabilities
Equally Likely Outcomes
The Complement Rule
The General Addition Rule
Conditional Probability
Problems
CHAPTER 11 Data and Statistics
Data, Populations, and Samples
Issues in Sampling: Representativeness and Bias
Randomized Sampling
Variables: Quantitative and Categorical
Organizing and Displaying Categorical Data
Grouping Quantitative Data
Histograms
Using Desmos to Make a Histogram
Misleading Graphical Displays
Dotplots
Outliers
Measures of Center for Quantitative Data
Weighted Averages
Measuring How Quantitative Data Values Are Spread Out
The Range
Measuring Spread Relative to the Mean: The Standard Deviation
Standardizing Data Values
Measures of Relative Location
Measuring Spread Relative to the Median: The Interquartile Range
Identifying Outliers
Boxplots
Problems
CHAPTER 12 Modeling Relationships between Quantitative Variables
Ordered Pairs and the Coordinate Plane
Methods for Representing Quantitative Relationships
Linear Functions
Piecewise-Defined Functions
Average Rate of Change
Exponential Functions
Problems
CHAPTER 13 Linear Regression and Correlation
Nondeterministic Relationships and Regression Analysis
Scatterplots
The Line of Best Fit
Extrapolation
Linear Correlation
Correlation vs. Causation
Problems
CHAPTER 14 Personal Finance
Simple and Compound Interest
Saving Money: Bank Accounts and Certificates of Deposit
Sums of Consecutive Powers
Saving for Retirement
Withdrawing Money in Retirement
Credit Cards
Installment Loans
Problems
Mike Cullinane is a Professor of Mathematics at Keene State College. He earned his B.S., M.S., and Ph.D. in Mathematics from the University of New Hampshire and previously served on the faculty at North Carolina Wesleyan College. His professional interests include topology, mathematical analysis, mathematical proof, and undergraduate mathematics education. His work includes research publications, presentations at regional and national conferences, and experience teaching mathematics at both the undergraduate and graduate levels.
This book develops quantitative literacy by teaching the mathematical concepts and reasoning needed to interpret information, solve problems, and make informed decisions. Topics include number systems, arithmetic, algebra, fractions, ratios, proportional reasoning, decimals, percentages, measurement, probability, statistics, data analysis, functions, linear regression, and correlation. The text concludes with applications to personal finance, including interest, saving, retirement planning, credit, and loans, emphasizing the practical use of mathematics in everyday life.
CHAPTER 1 Introduction and Preview
Why Quantitative Literacy Matters
Reading and Interpreting Quantitative Information
Using Quantitative Concepts and Methods to Solve a Problem
Using Quantitative Concepts and Methods to Support an Argument
The Role of Mathematics in Quantitative Literacy
Problems
CHAPTER 2 Types of Numbers
Whole Numbers
Fractions
Negative Numbers
Number Terminology
The Ordering of the Real Numbers
Problems
CHAPTER 3 Whole Number Arithmetic
The Concept of Addition
The Concept of Subtraction
Counting Using the Inclusion-Exclusion Principle
The Concept of Multiplication
Counting the Number of Ways to Perform a Multi-Step Process
The Concept of Division
Remainders in Division
Problems
CHAPTER 4 More Arithmetic and Some Algebra
Variables and Variable Expressions
Equations
Some Algebraic Properties of Addition and Multiplication
Even and Odd Numbers Revisited
Arithmetic and Algebra with Positive and Negative Numbers
Multiplicative Inverses and Division
Positive Integer Exponents
Combining Operations
Solving Equations
Solving an Equation Containing More than One Variable
Problems
CHAPTER 5 Fractions, Ratios, and Proportional Reasoning
Fractions Revisited
Multiplying Fractions
Equivalent Fractions
Reducing Fractions
Multiplying Fractions Revisited
Dividing Fractions
Adding and Subtracting Fractions
Ratios
Proportions
Proportional Reasoning
Problems
CHAPTER 6 Rational and Irrational Numbers
Square Roots and Cube Roots
Rational Numbers and Irrational Numbers
Triangles
Right Triangles and the Pythagorean Theorem
The Circumference and Area of a Circle
Problems
CHAPTER 7 Place Value and Decimals
Base Ten Representation of Whole Numbers
Base Two (Binary) Representation of Whole Numbers
Zero and Negative Exponents
Decimal Fractions
Rounding Numbers
Representing Rational and Irrational Numbers in Decimal Form
Scientific Notation
Problems
CHAPTER 8 Working with Percentages
Percentages
Percentages and Rounding
Absolute and Relative Change
Percentage Points vs. Percentages
Absolute and Relative Difference
Index Numbers
Problems
CHAPTER 9 Measurement Units
Converting Units of Measurement
The Metric System
Rates
Converting Units of Area and Volume
Density and Concentration
Measurements Expressed in Scientific Notation
Approximation, Measurement Error, and Error Propagation
Problems
CHAPTER 10 Probability
Experiments, Outcomes, and Sample Spaces
Events of a Sample Space
The Complement of an Event
The Intersection of Events
The Union of Events
Using Venn Diagrams to Depict Events within a Sample Space
Assigning Probabilities
Equally Likely Outcomes
The Complement Rule
The General Addition Rule
Conditional Probability
Problems
CHAPTER 11 Data and Statistics
Data, Populations, and Samples
Issues in Sampling: Representativeness and Bias
Randomized Sampling
Variables: Quantitative and Categorical
Organizing and Displaying Categorical Data
Grouping Quantitative Data
Histograms
Using Desmos to Make a Histogram
Misleading Graphical Displays
Dotplots
Outliers
Measures of Center for Quantitative Data
Weighted Averages
Measuring How Quantitative Data Values Are Spread Out
The Range
Measuring Spread Relative to the Mean: The Standard Deviation
Standardizing Data Values
Measures of Relative Location
Measuring Spread Relative to the Median: The Interquartile Range
Identifying Outliers
Boxplots
Problems
CHAPTER 12 Modeling Relationships between Quantitative Variables
Ordered Pairs and the Coordinate Plane
Methods for Representing Quantitative Relationships
Linear Functions
Piecewise-Defined Functions
Average Rate of Change
Exponential Functions
Problems
CHAPTER 13 Linear Regression and Correlation
Nondeterministic Relationships and Regression Analysis
Scatterplots
The Line of Best Fit
Extrapolation
Linear Correlation
Correlation vs. Causation
Problems
CHAPTER 14 Personal Finance
Simple and Compound Interest
Saving Money: Bank Accounts and Certificates of Deposit
Sums of Consecutive Powers
Saving for Retirement
Withdrawing Money in Retirement
Credit Cards
Installment Loans
Problems
Mike Cullinane is a Professor of Mathematics at Keene State College. He earned his B.S., M.S., and Ph.D. in Mathematics from the University of New Hampshire and previously served on the faculty at North Carolina Wesleyan College. His professional interests include topology, mathematical analysis, mathematical proof, and undergraduate mathematics education. His work includes research publications, presentations at regional and national conferences, and experience teaching mathematics at both the undergraduate and graduate levels.

