Math Decoded (eBook)

Explaining the Why Behind the Numbers and How They Operate

James Tanton (Autor)

eBook Download: PDF

2026
313 Seiten
Corwin (Verlag)
979-8-3488-3588-0 (ISBN)

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 20.1.2026
• Reihe/Serie: Corwin Mathematics Series
• Verlagsort: Thousand Oaks
• Sprache: englisch
• Themenwelt: Schulbuch / Wörterbuch ► Schulbuch / Allgemeinbildende Schulen
• Schlagworte: Building math understanding • coherent story of mathematics • conceptual math teaching • dividing by zero explained • explaining math to students • grade banded math tasks • math activities elementary to high school • Math for Teachers • math pedagogy book • professional learning math teachers • real world math teaching • teaching fractions conceptually • teaching math concepts • teaching math with clarity • teaching math with joy • teaching math with meaning • teaching negative numbers • why behind math
• ISBN-13: 979-8-3488-3588-0 / 9798348835880