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From Toothpicks to Treetops
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From Toothpicks to Treetops
Quantity and Space in Mathematics

Foreword by Mahesh Sharma


Other Titles in:
Mathematics & Numeracy

June 2003 | 200 pages | Corwin
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:

Identification

Comparison

Combination

Separation

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

For instructors

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ISBN: 9781575178585
£29.99