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]

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.