Preface Foreword Introduction Part I: Definition 1. Getting a Grip on Number Sense Number Freedom Flexibility Through Composition and Decomposition of Numbers How Counting Can Make or Break Number Sense Ducks, Gauss, and George Keep in Mind 2. The Map of Number Symbol Territory The Shapes of Reading Numbers Is Subitizing About Another Shape to Recognize? Alphabet of Letters and Alphabet of Digits Writing Numbers and Reading Symbolism Keep in Mind 3. An Evolution of Number and Naming Rights Counting (Natural), and Whole Numbers Integers and Other Positive and Negative Absurd Numbers Rational Numbers Include Fractions and Other Number Comparisons Politics of Rational and Unutterable Irrational Numbers Infinity, Googol, and Other Very Large Ideas Keep in Mind Part II: Organization 4. Classify First Three Is Not Red Classification as an Essential Skill Different Classifications Lead to Increased Flexibility Keep in Mind 5. Whence Came Place Value? Digits Continue to be the Alphabet for Numbers Some Cautionary Tales About Learning Place Value Classifying by Size for Place Value Transitioning to Place Value Record-Keeping Charles' Overlays Decimals Continue the Same Organization, Just Smaller Keep in Mind 6. The Number Line Brings Numbers to Order First, Last, and In Between - The Nature of Order Repetition of Pattern in Sequential Order A Place for Everything Keep in Mind Part III: Relationships and Patterns 7. Pattern Ancestors Repeating Patterns Growing Patterns Ancestors of Figurate Numbers and Other Growing Patterns Patterns Inside EquivalencesExpressing Ancestral Rules as Algebra Relationships Keep in Mind 8.

Balance of Relationships and Patterns Flexibility Within Balance Balance in Fraction Equivalences Decimal Numbers Are Connections to the Other Side Finding Patterns With ViewfindersKeep in Mind 9. Number Personalities Even and Odd Numbers Prime and Composite Numbers Positive and Negative Integers Numbers Can Have Multiple Number Personalities Keep in Mind Part IV: Connections 10. Place Value LegaciesExponents and Logarithms Location Matters Reciprocals: A Location and an Inverse Who Moved My Decimal? Keep in Mind 11. Ratio: The Comparison Effect Predicaments Around Understanding Fraction as a Ratio Notation Ratio Pairs Can Make Proportions Percentage: A Location and a Rate Keep in Mind 12. More Order From the Number Line Number Lines Are Everywhere Coordinate Axes More Coordinate Connections Keep in Mind Conclusion: What Parents Can Do Ask Questions Advocate for Number Sense Find Your Math Voice Keep in Mind Glossary References About the Author.