Park City Mathematics Institute Geometry Project Abstract

Geometry Transformed

Twitter: #pcmigeo

Authors: Jim King, Gabe Rosenberg, Robert Garber, Jennifer Katz, Dan Kerns, Elizabeth McGrath, Vince Mucciolli, Brian Shay, Jennifer Tate

 

Logistics

• Each of the 5 synchronous sessions will be approximately 60-90 minutes
• Each day will also include a pre-activity, possibly including a video (less than 30 minutes)
• Each day will also include a problem set after the lesson

One of the challenges that teachers have is the transition from the old state standards for Geometry to the new Common Core standards, especially the increased role for transformations. This online professional development seeks to highlight key principles, as well as some tools that teachers can use to demonstrate these new concepts to their students. Over five sessions, participants will cover a variety of topics.

 

The course was offered for the first time in April 2016. The materials were based on the work of the Geometry Working Group of 2015. The task posed to the group in summer 2016 was to develop some additional material to flip some content outside the synchronous sessions and some material to make the sessions more interactive.

 

The materials archived for this year include (1) the materials used in Spring 2016 and (2) new materials developed in 2016. A revised version of the course will based on this.

 

The days will be broken down in the following manner:

Day 1 - Congruence

General definition of congruence using Rigid Mtions

Reasoning from definitions

Congruence of segments using reflections

Proof of SAS triangle congruence criterion

Day 2 - Rigid Motions

Rigid Motions as tools for proofs

Rotations and Reflections as compositions of reflections

Glide reflections

Day 3 - More Congruence and Rigid Motions

Fixed points of Rigid Motions

Classification Theorem for Rigid Motions

Coordinates and formulas

Symmetry

Day 4 - Similarity

Dilations and definition of similarity

SAS, AA, and SSS triangle similarity tests

Dilations and Euclidean Parallel Postulate

Day 5 - Geometry and the Standards

Examine key Standards in light of the course

Symmetry in the whole plane

Rotation and trigonometry

More Problems and examples

download zipped folder Spring2016course.zip and Summer2016products.zip [generic login required]

Back to Index