From Toothpicks to Treetops: Quantity and Space in Mathematics serves the needs of the math whiz and the non-mathematically inclined alike by exploring and applying mathematical constructs to everyday situations.
By providing a vantage point from which to discern how students' prior knowledge can be used to help expand their mathematical thinking and increase their ability to communicate, author Rita Corbett outlines four ways students can begin to engage in problem solving:
Each method is used to reveal connections between mathematical thoughts, topics, and applications, and activities at the end of each chapter help students understand the relationship of mathematics to their surroundings.
Forword by Dr. Mahesh Sharma Preface Introduction Chapter 1 - What Is Elementary and Middle School Mathematics? Mathematical Thought and Communication Mathematical Thought: Four Arenas Mathematical Communication: Three Stages Conclusion Selected Readings Student Activities Chapter 2 - Our Number System Identifying Types of Numbers in Our Number System Comparing Irrational Numbers in Our Number System: Counting vs. Quantity Combining Numbers in Our Number System: Place Value Separating Mathematical Thought from Mathematical Symbols Selected Readings Student Activities Chapter 3 - Whole Numbers Thoughts Identifying Whole Numbers Comparing Whole Numbers Combining Whole Numbers Separating Whole Numbers Introducing Integers Selected Readings Student Activities Chapter 4 - Fractional Thoughts An Overview of Expressing Fractions Identifying Fractions Comparing Fractions Selected Readings Chapter 5 - Communicating Fractional Thought Combining Fractions Separating Fractions Selected Readings Student Activities Chapter 6 - Spatial Geometry Thoughts Introducing Spatial Geometry van Hieles' Levels of Geometric Constructs Identifying Geometric Constructs Comparing Geometric Space Separating Space Selected Readings Student Activities Chapter 7 - Communicating Spatial Thoughts with Measurement Measuring Non-Dimensional Space Measuring One-Dimensional Space Measuring Two-Dimensional Space Measuring Three-Dimensional Space Measuring Time Measuring Temperature Measuring Weight Selected Readings Student Activities Chapter 8 - Solving Problems Reading and Understanding the Problem Making a Plan Solving the Problem Clarifying the Solution Using Graphic Organizers to Solve Problems Conclusion Selected Readings Student Activities Glossary Bibliography Index