On the Companion Website
List of Videos
Acknowledgments
About the Author
Introduction
The Story Behind the Story
Chapter 1: Counting
Counting in the Real World
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
Addition in the Real World
More Mulling and Some Classroom Tasks
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
Negative Numbers in the Real World
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
Distributing the Negative Sign in the Real World
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 5: Subtraction
Subtraction in the Real World
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
Multiplication in the Real World
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
The Distributive Property in the Real World
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
Multiplication and Zero in the Real World
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
Multiplication and Negative Numbers in the Real World
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
Division in the Real World
Dividing Zero and Dividing by Zero
The Curious Case of 0 ÷ 0
More Mulling and Some Classroom Tasks
How Some Curricula Address the Issue
Chapter 11: The Reciprocal Numbers (The Building Blocks of Fractions)
Reciprocal Numbers in the Real World
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
Fractions as Answers to Division Problems in the Real World
More Mulling and a Classroom Task
The Definition of a Fraction
Chapter 13: Multiplying Fractions
Multiplying Fractions in the Real World
More Mulling and a Classroom Task
Chapter 14: Equivalent Fractions
Equivalent Fractions in the Real World
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
Dividing Fractions in the Real World
More Mulling and a Classroom Task
Chapter 16: Adding and Subtracting Fractions
Adding and Subtracting Fractions in the Real World
More Mulling and a Classroom Task
Chapter 17: Comparing Fractions
Comparing Fractions in the Real World
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 18: Exponents
Exponents in the Real World
More Mulling and Some Classroom Tasks
A Task for Elementary School Grades
A Task for Upper School Grades
Chapter 19: Fractions as Decimals
Fractions as Decimals in the Real World
Leaning Into Reverse Multiplication
More Mulling and a Classroom Task
Understanding 0.9999 . . .
Believing 0.9999 . . . Is Meaningful
Chapter 20: Not Every Number is a Fraction
Numbers That Are Not Fractions in the Real World
Final Thought: Are there more Numbers
What's Next?
Now That You Have Read This Book
References
Index