Math Decoded
Purchase
Description
Experience the joy of answering "why" in math class like never before
Mathematics often feels like a collection of disconnected rules, but what if you could uncover their underlying story? In Math Decoded: Explaining the Why Behind the Numbers and How They Operate, author James Tanton provides educators with a compelling and accessible guide to understanding the logic, purpose, and poetry behind numbers and arithmetic.
Move away from simply teaching formulas and procedures. Instead, discover the coherent and human story of mathematics that will enliven your classroom and deepen your own mathematical knowledge.
By addressing the "why" questions students frequently ask, this book offers clarity on tricky concepts such as dividing by zero, fractions, and negative numbers through these key features:
- Engaging Structure: Each chapter begins with a thought-provoking question, explores real-world scenarios, and culminates in bold insights and classroom activities.
- Grade-Banded Tasks: The book includes classroom activities for elementary to high school, ensuring relevance for multiple grade levels.
- Comprehensive Resources: The text is accompanied by videos, supplemental essays, and practical tools to deepen the learning experience.
- Accessible Style: The book is written in a friendly, relatable tone to explain mathematics’ most mystifying and rigorous topics.
With this book, educators will gain a newfound appreciation for the beauty, structure, and coherence of mathematics. Math Decoded will help you inspire your students to see math not just as a subject, but as an invitation to explore, discover, and think deeply about the joy of numbers.
Contents
On the Companion Website
On the Companion Website
List of Videos
List of Videos
Acknowledgments
Acknowledgments
About the Author
About the Author
Introduction
- The Why of This Book
- Who This Book Is For
- The Story Behind the Story
- What’s Inside
- What’s Outside(!)
- An Invitation
Chapter 1: Counting
- Something to Mull On
- Counting in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 2: Addition
- Something to Mull On
- Addition in the Real World
- The Number Zero
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- The Solitaire Game
- Some Sophisticated Jargon
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 3: Negative Numbers
- Something to Mull On
- Negative Numbers in the Real World
- Solitaire Again
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 4: Distributing the Negative Sign
- Something to Mull On
- Distributing the Negative Sign in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Question on Notation
- A Card Pile Mystery
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 5: Subtraction
- Something to Mull On
- Subtraction in the Real World
- A Key Takeaway
- Being Bold With the Math
- Generalizing Our Thinking a Wee Bit
- More Mulling and Some Classroom Tasks
- Wishful Thinking Across the Curriculum
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 6: Multiplication
- Something to Mull On
- Multiplication in the Real World
- Solitaire Yet Again!
- The Number 1
- A Key Takeaway
- Being Bold With the Math
- On the Question of What Multiplication Is
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 7: The Distributive Property
- Something to Mull On
- The Distributive Property in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 8: Multiplication and Zero
- Something to Mull On
- Multiplication and Zero in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 9: Multiplication and Negative Numbers
- Something to Mull On
- Multiplication and Negative Numbers in the Real World
- One Way Out
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 10: Division
- Something to Mull On
- Division in the Real World
- A Key Takeaway
- Being Bold With the Math
- Dividing Zero and Dividing by Zero
- The Curious Case of 0 ÷ 0
- More Mulling and Some Classroom Tasks
- A Task for All Grades
- For Extra Fun
- How Some Curricula Address the Issue
Chapter 11: The Reciprocal Numbers (The Building Blocks of Fractions)
- Something to Mull On
- Reciprocal Numbers in the Real World
- A Realistic Note
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle and High School Grades
Chapter 12: Fractions Are Answers to Division Problems
- Something to Mull On
- Fractions as Answers to Division Problems in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- The Definition of a Fraction
- A Task for All Grades
Chapter 13: Multiplying Fractions
- Something to Mull On
- Multiplying Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for All Grades
Chapter 14: Equivalent Fractions
- Something to Mull On
- Equivalent Fractions in the Real World
- Two Pieces of Language
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 15: Dividing Fractions
- Something to Mull On
- Dividing Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for Upper Grades
Chapter 16: Adding and Subtracting Fractions
- Something to Mull On
- Adding and Subtracting Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for All Grades
Chapter 17: Comparing Fractions
- Something to Mull On
- Comparing Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- Mixed Numbers
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 18: Exponents
- Something to Mull On
- Exponents in the Real World
- A Key Takeaway
- Being Bold With the Math
- Understanding 212
- More Mulling and Some Classroom Tasks
- The Value of 00
- A Task for Elementary School Grades
- A Task for Upper School Grades
Chapter 19: Fractions as Decimals
- Something to Mull On
- Fractions as Decimals in the Real World
- Leaning Into Reverse Multiplication
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- On Multiplying by Ten
- Understanding 0.9999 . . .
- Believing 0.9999 . . . Is Meaningful
- Final Conclusion
- The Geometric Series
- A Task for All Grades
Chapter 20: Not Every Number is a Fraction
- Something to Mull On
- Numbers That Are Not Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling
Final Thought: Are there more Numbers
Final Thought: Are there more Numbers
What's Next?
- But How?
- Now That You Have Read This Book
- Be Bold!
References
References
Index
Index
Resources
Companion Website
https://companion.corwin.com/courses/mathdecodedAdditional materials
Description
Experience the joy of answering "why" in math class like never before
Mathematics often feels like a collection of disconnected rules, but what if you could uncover their underlying story? In Math Decoded: Explaining the Why Behind the Numbers and How They Operate, author James Tanton provides educators with a compelling and accessible guide to understanding the logic, purpose, and poetry behind numbers and arithmetic.
Move away from simply teaching formulas and procedures. Instead, discover the coherent and human story of mathematics that will enliven your classroom and deepen your own mathematical knowledge.
By addressing the "why" questions students frequently ask, this book offers clarity on tricky concepts such as dividing by zero, fractions, and negative numbers through these key features:
- Engaging Structure: Each chapter begins with a thought-provoking question, explores real-world scenarios, and culminates in bold insights and classroom activities.
- Grade-Banded Tasks: The book includes classroom activities for elementary to high school, ensuring relevance for multiple grade levels.
- Comprehensive Resources: The text is accompanied by videos, supplemental essays, and practical tools to deepen the learning experience.
- Accessible Style: The book is written in a friendly, relatable tone to explain mathematics’ most mystifying and rigorous topics.
With this book, educators will gain a newfound appreciation for the beauty, structure, and coherence of mathematics. Math Decoded will help you inspire your students to see math not just as a subject, but as an invitation to explore, discover, and think deeply about the joy of numbers.
Contents
On the Companion Website
On the Companion Website
List of Videos
List of Videos
Acknowledgments
Acknowledgments
About the Author
About the Author
Introduction
- The Why of This Book
- Who This Book Is For
- The Story Behind the Story
- What’s Inside
- What’s Outside(!)
- An Invitation
Chapter 1: Counting
- Something to Mull On
- Counting in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 2: Addition
- Something to Mull On
- Addition in the Real World
- The Number Zero
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- The Solitaire Game
- Some Sophisticated Jargon
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 3: Negative Numbers
- Something to Mull On
- Negative Numbers in the Real World
- Solitaire Again
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 4: Distributing the Negative Sign
- Something to Mull On
- Distributing the Negative Sign in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Question on Notation
- A Card Pile Mystery
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 5: Subtraction
- Something to Mull On
- Subtraction in the Real World
- A Key Takeaway
- Being Bold With the Math
- Generalizing Our Thinking a Wee Bit
- More Mulling and Some Classroom Tasks
- Wishful Thinking Across the Curriculum
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 6: Multiplication
- Something to Mull On
- Multiplication in the Real World
- Solitaire Yet Again!
- The Number 1
- A Key Takeaway
- Being Bold With the Math
- On the Question of What Multiplication Is
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 7: The Distributive Property
- Something to Mull On
- The Distributive Property in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 8: Multiplication and Zero
- Something to Mull On
- Multiplication and Zero in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 9: Multiplication and Negative Numbers
- Something to Mull On
- Multiplication and Negative Numbers in the Real World
- One Way Out
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 10: Division
- Something to Mull On
- Division in the Real World
- A Key Takeaway
- Being Bold With the Math
- Dividing Zero and Dividing by Zero
- The Curious Case of 0 ÷ 0
- More Mulling and Some Classroom Tasks
- A Task for All Grades
- For Extra Fun
- How Some Curricula Address the Issue
Chapter 11: The Reciprocal Numbers (The Building Blocks of Fractions)
- Something to Mull On
- Reciprocal Numbers in the Real World
- A Realistic Note
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle and High School Grades
Chapter 12: Fractions Are Answers to Division Problems
- Something to Mull On
- Fractions as Answers to Division Problems in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- The Definition of a Fraction
- A Task for All Grades
Chapter 13: Multiplying Fractions
- Something to Mull On
- Multiplying Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for All Grades
Chapter 14: Equivalent Fractions
- Something to Mull On
- Equivalent Fractions in the Real World
- Two Pieces of Language
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 15: Dividing Fractions
- Something to Mull On
- Dividing Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for Upper Grades
Chapter 16: Adding and Subtracting Fractions
- Something to Mull On
- Adding and Subtracting Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for All Grades
Chapter 17: Comparing Fractions
- Something to Mull On
- Comparing Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- Mixed Numbers
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
Chapter 18: Exponents
- Something to Mull On
- Exponents in the Real World
- A Key Takeaway
- Being Bold With the Math
- Understanding 212
- More Mulling and Some Classroom Tasks
- The Value of 00
- A Task for Elementary School Grades
- A Task for Upper School Grades
Chapter 19: Fractions as Decimals
- Something to Mull On
- Fractions as Decimals in the Real World
- Leaning Into Reverse Multiplication
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- On Multiplying by Ten
- Understanding 0.9999 . . .
- Believing 0.9999 . . . Is Meaningful
- Final Conclusion
- The Geometric Series
- A Task for All Grades
Chapter 20: Not Every Number is a Fraction
- Something to Mull On
- Numbers That Are Not Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling
Final Thought: Are there more Numbers
Final Thought: Are there more Numbers
What's Next?
- But How?
- Now That You Have Read This Book
- Be Bold!
References
References
Index
Index
Resources
Companion Website
https://companion.corwin.com/courses/mathdecodedAdditional materials
Reviews
December 2025 | 312 pages | Corwin
| Format | Published Date | ISBN | Price |
|---|---|---|---|
| Paperback | 10/03/2025 | 9798348809287 | $39.95 |
| Lifetime | 13/07/2025 | 9798348835873 | $36.00 |
Experience the joy of answering "why" in math class like never before
Mathematics often feels like a collection of disconnected rules, but what if you could uncover their underlying story? In Math Decoded: Explaining the Why Behind the Numbers and How They Operate, author James Tanton provides educators with a compelling and accessible guide to understanding the logic, purpose, and poetry behind numbers and arithmetic.
Move away from simply teaching formulas and procedures. Instead, discover the coherent and human story of mathematics that will enliven your classroom and deepen your own mathematical knowledge.
By addressing the "why" questions students frequently ask, this book offers clarity on tricky concepts such as dividing by zero, fractions, and negative numbers through these key features:
- Engaging Structure: Each chapter begins with a thought-provoking question, explores real-world scenarios, and culminates in bold insights and classroom activities.
- Grade-Banded Tasks: The book includes classroom activities for elementary to high school, ensuring relevance for multiple grade levels.
- Comprehensive Resources: The text is accompanied by videos, supplemental essays, and practical tools to deepen the learning experience.
- Accessible Style: The book is written in a friendly, relatable tone to explain mathematics’ most mystifying and rigorous topics.
With this book, educators will gain a newfound appreciation for the beauty, structure, and coherence of mathematics. Math Decoded will help you inspire your students to see math not just as a subject, but as an invitation to explore, discover, and think deeply about the joy of numbers.
Table Of Contents:
- On the Companion Website
- List of Videos
- Acknowledgments
- About the Author
- Introduction
- The Why of This Book
- Who This Book Is For
- The Story Behind the Story
- What’s Inside
- What’s Outside(!)
- An Invitation
- Chapter 1: Counting
- Something to Mull On
- Counting in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 2: Addition
- Something to Mull On
- Addition in the Real World
- The Number Zero
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- The Solitaire Game
- Some Sophisticated Jargon
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 3: Negative Numbers
- Something to Mull On
- Negative Numbers in the Real World
- Solitaire Again
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 4: Distributing the Negative Sign
- Something to Mull On
- Distributing the Negative Sign in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Question on Notation
- A Card Pile Mystery
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 5: Subtraction
- Something to Mull On
- Subtraction in the Real World
- A Key Takeaway
- Being Bold With the Math
- Generalizing Our Thinking a Wee Bit
- More Mulling and Some Classroom Tasks
- Wishful Thinking Across the Curriculum
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 6: Multiplication
- Something to Mull On
- Multiplication in the Real World
- Solitaire Yet Again!
- The Number 1
- A Key Takeaway
- Being Bold With the Math
- On the Question of What Multiplication Is
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 7: The Distributive Property
- Something to Mull On
- The Distributive Property in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 8: Multiplication and Zero
- Something to Mull On
- Multiplication and Zero in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 9: Multiplication and Negative Numbers
- Something to Mull On
- Multiplication and Negative Numbers in the Real World
- One Way Out
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 10: Division
- Something to Mull On
- Division in the Real World
- A Key Takeaway
- Being Bold With the Math
- Dividing Zero and Dividing by Zero
- The Curious Case of 0 ÷ 0
- More Mulling and Some Classroom Tasks
- A Task for All Grades
- For Extra Fun
- How Some Curricula Address the Issue
- Chapter 11: The Reciprocal Numbers (The Building Blocks of Fractions)
- Something to Mull On
- Reciprocal Numbers in the Real World
- A Realistic Note
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle and High School Grades
- Chapter 12: Fractions Are Answers to Division Problems
- Something to Mull On
- Fractions as Answers to Division Problems in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- The Definition of a Fraction
- A Task for All Grades
- Chapter 13: Multiplying Fractions
- Something to Mull On
- Multiplying Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for All Grades
- Chapter 14: Equivalent Fractions
- Something to Mull On
- Equivalent Fractions in the Real World
- Two Pieces of Language
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 15: Dividing Fractions
- Something to Mull On
- Dividing Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for Upper Grades
- Chapter 16: Adding and Subtracting Fractions
- Something to Mull On
- Adding and Subtracting Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- A Task for All Grades
- Chapter 17: Comparing Fractions
- Something to Mull On
- Comparing Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling and Some Classroom Tasks
- Mixed Numbers
- A Task for Elementary School Grades
- A Task for Middle School Grades
- A Task for High School Grades
- Chapter 18: Exponents
- Something to Mull On
- Exponents in the Real World
- A Key Takeaway
- Being Bold With the Math
- Understanding 212
- More Mulling and Some Classroom Tasks
- The Value of 00
- A Task for Elementary School Grades
- A Task for Upper School Grades
- Chapter 19: Fractions as Decimals
- Something to Mull On
- Fractions as Decimals in the Real World
- Leaning Into Reverse Multiplication
- A Key Takeaway
- Being Bold With the Math
- More Mulling and a Classroom Task
- On Multiplying by Ten
- Understanding 0.9999 . . .
- Believing 0.9999 . . . Is Meaningful
- Final Conclusion
- The Geometric Series
- A Task for All Grades
- Chapter 20: Not Every Number is a Fraction
- Something to Mull On
- Numbers That Are Not Fractions in the Real World
- A Key Takeaway
- Being Bold With the Math
- More Mulling
- Final Thought: Are there more Numbers
- What's Next?
- But How?
- Now That You Have Read This Book
- Be Bold!
- References
- Index