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.


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:

  1. Launch: (1 - 2 minutes)

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

Make Connections:

  1. Individual Think Time: (10 - 30 seconds) 

  2. Pair-Share: (2 - 5 minutes)

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

Share Connections:

  1. Full group share: (2 - 4 minutes per match)

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:

  1. Think & Pair: (3 - 6 minutes)

  2. Share: (4 - 8 minutes)

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


  1. Individual writing: (1 - 2 minutes) 

  2. Pair: (30 seconds) 

  3. Share: (2 - 3 minutes)

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:


  1. Detailed description

  2. Planning Document

  3. Lesson Plan

  4. Sample Slides

  5. Sample Tasks

Adapted from Routines for Reasoning: Fostering the Mathematical Practices in All Students and 


Last modified: Wednesday, 21 August 2019, 8:36 AM