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# Geometric Structures An Inquiry-Based Approach for Prospective Elementary and Middle School Teachers

**by**Aichele, Douglas B.; Wolfe, John

### 9780131483927

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## Summary

## Author Biography

**John Wolfe, Oklahoma State University: **John recently was promoted to professor emeritus at Oklahoma State University. After graduating from the University of California at Berkeley in 1971 he was active in mathematics research including several publications and National Science Foundation research grants in Banach Space Theory. His enthusiasm for teaching has been recognized by awards from both the Mathematical Association of America and the Regents of Oklahoma State University. Over the past several years educational issues with a special passion for geometry have been the focus of his professional life. Woodworking, travel, camping and grandkids are becoming increasingly important in his life.

**Douglas B. Aichele, Oklahoma State University: **Douglas grew up in Great Neck, NY. He received his undergraduate and graduate education in mathematics at the University of Missouri-Columbia. He has been a faculty member at Oklahoma State University for many years and was appointed Regents Professor in 1989. He is currently serving as Associate Head of the Department of Mathematics. Good teaching of mathematics has always been important to him and he has been recognized over the years by such institutions/organizations as the OSU Blue Key Alumni Association, Mathematical Association of America, and the University of Missouri-Columbia.His other interests reside mainly in the outdoors - particularly spending time with his family in the mountains of Colorado at a log cabin that he built by hand. He is an avid backpacker and hiker; he has climbed most of Colorado's Fourteeners (mountains with elevations greater then 14,000 ft.) and several mountains and glaciers near Juneau, Alaska.

## Table of Contents

Paper Folding | |

Warm Up Activities | |

Introduction | |

Folding Polygons from a Circle | |

Making Squares | |

Two Congruent Halves | |

Dissecting Figures | |

Polygons and the Angle Relationships | |

Introduction | |

Parallel Line Grid - Triangle Angle Sum | |

Envelope Fold - Triangle Angle Sum | |

Triangle and Quadrilateral Angle Sums by Tearing | |

Polygon Angle Sums: How many Triangles? | |

The Angles of a Polygon | |

When Does Erika's Idea Work? | |

The Greedy Triangle | |

Problems: Angle Sums and Angle Relationships | |

Four Kinds of Related Angles | |

Figuring Angles and Checking by Measurement | |

Parallel Lines: How to Recognize Them | |

Measuring Sides and Angles of Triangles | |

Convex: Different Ways to Make Sense of It | |

Angle Problems - Version A | |

Angle Problems - Version B | |

Angle Probems - More | |

How Do I Know if I Understand? | |

Conjecturing ABout Quadrilaterals | |

Possible or Not? | |

True or False (with Example) | |

Under What Conditions? | |

Quadrilaterals and Their Definitions | |

Introduction | |

Checking Properties of Quadrilaterals | |

Properties of Quadrilaterals | |

Marking Quadrilateral Properties | |

Properties of Diagonals of Quadrilaterals | |

Checking Quadrilaterals by Folding | |

Read Carefully: Every Word Counts! | |

Checking Examples Visually or Physically | |

Exploring Medial Quadrilaterals | |

Problems: Properties of Quadrilaterals, Version A | |

Problems: Properties of Quadrilaterals, Version B | |

More Problems: Properties of Quadrilaterals | |

A Deeper Understanding of Definitions | |

Special Cases of Quadrilaterals | |

Definitions: Inclusive or Exclusive | |

Problems: Inclusive and Exclusive Definitions | |

What Is a Kite? Equivalent Definitions | |

Problems: Definitions of Quadrilaterals, Version A | |

Problems: Definitions of Quadrilaterals, Version B | |

More Problems: Definitions of Quadrilaterals | |

How Do I Know if I Understand? Prologue: Four Contexts for Geometric Constructions Prologue to Chapters 3, 10, 12, and 14 | |

Constructions by Paper Folding | |

Introduction | |

Introducing CDs: Two Basic Constructions | |

CD Problem: A Parallel Line | |

CD Problem: The Median | |

CD Problem: An Equilateral Triangle | |

CD Problem: A Square | |

Circumscribing Circle | |

Inscribed Circle | |

Balance Point of a Triangle | |

Additional CD Problems Using Basic Construction Steps | |

Group Problem: Inscribed Circles | |

Folding a Six-Pointed Star or a "Snowflake" | |

Problems Involving Paper Folding | |

How Do I Know if I Understand? | |

Explorations in Three-dimensional Geometry | |

Introduction | |

Polyhedra (Solids) from an Envelope | |

Roll-and-Fold Prism and Pyramid Activities | |

Net Project A: Prisms | |

Prisms | |

Makiing Sense of Volume: A Basic Relationship | |

Net Project B: Pyramids | |

Pyramids | |

Edges, Faces, and Vertices of Polyhedra | |

Special Kinds of Polyhedra | |

Riddles with Solids | |

Volumes Prisms, Pyramids, and Spheres | |

Volume of a Pyramid | |

What Does Volume Really Mean? | |

Volume of Solids: First Try | |

Solid-Geometry Problems, Version A | |

Solid-Geometry Problems, Version B | |

More Solid-Geometry Problems Addendum: Unit Origami: An Introduction | |

Instructions for the Basic Parallelogram Unit | |

Project for the Whole Class: Monster Stellated Icosahedron | |

Uni | |

Table of Contents provided by Publisher. All Rights Reserved. |