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.
 Adding/Subtracting Polynomials [ task  slides  posters ]
 Area Model and Factoring #1 [ task  slides  posters ]
 Area Model and Factoring #2 [ task  slides  posters ]
 Area Model with Division [ task  slides  posters ]
 Arithmetic Sequences 1 [ task  slides  posters ]
 Arithmetic Sequences 2 [ task  slides  posters ]
 Bar Models and Operations [ task  slides  posters ]
 Calculations and Arrays [ task  slides  posters ]
 Comparing values on a graph [ task  slides  posters ]
 Completing the Square [ task  slides  posters ]
 Distance vs Time Graphs [ task  slides  posters ]
 Division of Integers [ task  slides  posters ]
 Equations and Number Lines #1 [ task  slides  posters ]
 Equations and Number Lines #2 [ task  slides  posters ]
 Equations and Sentences [ task  slides ]
 Exponents [ task  slides  posters ]
 Function or Not [ task  slides  posters ]
 How Many Birds? [ task  slides  posters ]
 Linear Equations and Graphs [ task  slides  posters ]
 Matching solutions to bar models #1 [ task  slides  posters ]
 Matching solutions to bar models #2 [ task  slides  posters ]
 Matching Solutions to Number Lines [ task  slides  posters ]
 Mean and Standard Deviation [ task  slides  posters ]
 Order of Operations [ task  slides  posters ]
 Quadratic Formula, Axis of Symmetry, and Roots [ task  slides  posters ]
 Rational Exponents on The Number Line [ task  slides  posters ]
 Sequences and Visual Patterns [ task  slides  posters ]
 Simple Quadratic Functions and Tables [ task  slides ]
 Simplifying Radicals on The Number Line [ task  slides  posters ]
 Solving Quadratic Equations Graphically [ task  slides  posters ]
 Systems of Linear Inequalities on Graphs [ task  slides  posters ]
 Tables to Factored Form [ task  slides ]
 Tape Diagrams to Situations [ task  slides  posters ]
 Vertex Form vs Factored Form [ task  slides  posters ]
 Volume of a Rectangular Prism [ task  slides  posters ]
 xsquared vs 2x vs x + 2 [ task  slides  posters ]