Connecting Representations
This instructional routine is intended to support students in making sense of mathematical ideas through mathematical structure and to learn how to have mathematical discussions with each other. It was created by Amy Lucenta and Grace Kelemanik of Fostering Math Practices.
Watch a video of an overview of the routine used with 9thgrade students here:
Connecting Representations: Algebra I Distributive Property [8 minutes] from New Visions for Public Schools on Vimeo.
In the routine students are given two sets of mathematical representations that on the surface may appear different but behave mathematically the same. Through their work together, students make matches between the given sets of representations, eventually creating their own representation.
The flow of the instructional routine is
Orient to the task: 

Tell students why they are doing this activity and how the activity will run. 
Make Connections: 

Students look for connections individually then share their connections with a partner. 
Share Connections: 

Selected pairs of students share their connections with the whole class. At the end of the presentations, each pair of matching representations should be matched and one representation should be left unmatched. 
Create a Representation: 

Students create the missing representation with a partner then selected pairs of students share their created representations with the whole class. 
Metareflection: 

Students write independently, students share what they wrote with a partner, then selected students share their reflections with the whole class. 
Learn more about the routine: 
Resources: 
Adapted from Routines for Reasoning: Fostering the Mathematical Practices in All Students AmyLucenta@gmail.com and GraceKelemanik@gmail.com
Resources for each task are available below. The tasks can also be found by searching here. Many of the tasks were created for New Visions for Public Schools and are released under a Creative Commons license as a result.
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