## Understanding by Design: Complete Collection

#### Title

Understanding Geometry as an Axiomatic System

#### Document Type

Instructional Material

2013

#### Abstract

After completing the Algebra I review and introducing several computational aspects of geometry including distance formula, midpoint formula, etc., we will introduce the idea of geometry as an axiomatic system. In this unit, we will decide what role rules play in governing behavior. Students will define and identify the four components of an axiomatic system; defined terms, undefined terms, axioms/postulates, and theorems. They will explore various axiomatic systems and decide how these systems dictate how appropriate behavior looks. We will explore Euclidean Geometry abstractly considering it at its most basic form, a set of rules that determine how geometric objects behave.

Students will be asked to create simple axiomatic systems. Since this task requires students to think very abstractly, it has been scaffolded to ensure that it is accessible to students at varying developmental levels. The unit has been designed to allow students the opportunity to explore both Euclidean and Non-Euclidean geometries, as well as, make connections between the mathematical world and the “real world”. The ultimate goal of this unit is to answer the questions: “When will I ever use this?” and “Outside of math class, why does this matter?”