LTG Materials

What are the Learning and Teaching Geometry PD materials?

The Learning and Teaching Geometry (LTG) materials are intended to support 54 hours of professional development to improve the teaching and learning of mathematical similarity based on geometric transformations. The LTG materials provide extensive opportunities for teachers to expand their mathematical knowledge for teaching in a focused content area, using an authentic, instructional context. The materials engage teachers in learning about similarity, congruence, and transformations through video cases in which specific and increasingly complex mathematical concepts are presented within the dynamics of classroom practice.

The Learning and Teaching Geometry materials are intended for use in the professional development of mathematics teachers serving grades 5–10. The materials are organized into five modules—the Foundation Module and four Extension Modules. Each module contains a sequence of video cases in which teachers explore the mathematics content; view, analyze and discuss video clips; compare and contrast issues across cases; and make links to their own instructional practice.


Foundation Module (ten 3-hour sessions)

The Foundation Module provides a thorough introduction to mathematical similarity in alignment with the Common Core State Standards. The module is intended to be completed prior to using any of the Extension Modules, and requires approximately 30 hours of face-to-face professional development time. The modules include mathematical tasks that interested teachers can bring into their own classrooms to promote their students’ learning.


The Foundation Module map  provides a relatively simple and accessible schematic of the 10 sessions. The map illustrates the mathematical storyline, showing both the central mathematical focus of each individual session and how the sessions are grouped together conceptually.

Four Extension Modules (two 3-hour sessions each)


Four Extension Modules are available, intended for use by groups of teachers who have completed the full 30 hours of the Foundation Module. Similar in nature and design to the Foundation Module, the Extension Modules offer the option to further explore topics related to the mathematical and pedagogical material covered by the Foundation Module. The Extension Modules are (1) Definitions of Similarity, (2) Justifying Claims Related to Similarity, (3) Representations and Tools for Learning Similarity, and (4) Communicating about Similarity. Each Extension Module consists of two 3-hour sessions.

Within the five modules there are a total of 53 video clips, comprising 2 hours and 47 minutes of video. The video clips are unedited segments selected from real classroom footage of 15 teachers’ un-staged mathematics lessons, representing a ranClassroom videoge of grade levels, geographic locations and student populations across the United States. The clips offer a window into a variety of issues related to content, student thinking, and pedagogical moves. By viewing classroom video across multiple and varied contexts, the materials provide insight into what an emerging understanding of similarity looks like as well as specific instructional strategies that can foster this understanding.

The LTG materials are highly specified—that is, they specify in advance particular learning goals, make explicit their design characteristics, and provide extensive supports and resources for facilitators. The sessions within each module have been organized into a sequence intended to build toward specific learning goals. Although optimal use of the materials is in a series of three-hour sessions, they may be adapted to fit a variety of professional development time frames.

How do I purchase the LTG materials?

The materials are available from WestEd: