This text provides a creative, inquiry-based experience with geometry that is appropriate for prospective elementary
and middle school teachers. The coherent series of text activities supports each student's growth toward being
a confident, independent learner empowered with the help of peers to make sense of the geometric world.
This curriculum is explicitly developed to provide future elementary and middle school teachers with
experience recalling and appropriately using standard geometry ideas,
experience learning and making sense of new geometry,
experience discussing geometry with peers,
experience asking questions about geometry,
experience listening and understanding as others talk about geometry,
experience gaining meaning from reading geometry,
experience expressing geometry ideas through writing,
experience thinking about geometry, and
experience doing geometry.
These activities constitute an "inquiry based" curriculum. In this style of learning and teaching, whole class
discussions and group work replace listening to lectures as the dominant class activity.
Table of Contents
Part I: Paper Folding
Chapter 0 - Warm Up Activities
0.0 Introduction
0.1 Folding Polygons from a Circle
0.2 Making Squares
0.3 Two Congruent Halves
0.4 Dissecting Figures
Chapter 1 - Polygons and the Angle Relationships
1.0 Introduction
1.1 Parallel Line Grid - Triangle Angle Sum
1.2 Envelope Fold - Triangle Angle Sum
1.3 Triangle and Quadrilateral Angle Sums by Tearing
1.4 Polygon Angle Sums: How many Triangles?
1.5 The Angles of a Polygon
1.6 When Does Erika's Idea Work?
1.7 The Greedy Triangle
1.8 Problems: Angle Sums and Angle Relationships
1.9 Four Kinds of Related Angles
1.10 Figuring Angles and Checking by Measurement
1.11 Parallel Lines: How to Recognize Them
1.12 Measuring Sides and Angles of Triangles
1.14 Convex: Different Ways to Make Sense of It
1.14a Angle Problems - Version A
1.14b Angle Problems - Version B
1.15 Angle Probems - More
1.16 How Do I Know if I Understand?
1.17 Conjecturing ABout Quadrilaterals
