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 9th-grade 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:

  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.

Meta-reflection:

  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:

Resources:

  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 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.

  1. Adding/Subtracting Polynomials [ task | slides | posters ]
  2. Area Model and Factoring #1 [ task | slides | posters ]
  3. Area Model and Factoring #2 [ task | slides | posters ]
  4. Area Model with Division [ task | slides | posters ]
  5. Arithmetic Sequences 1 [ task | slides | posters ]
  6. Arithmetic Sequences 2 [ task | slides | posters ]
  7. Bar Models and Operations [ task | slides | posters ]
  8. Calculations and Arrays [ task | slides | posters ]
  9. Comparing values on a graph [ task | slides | posters ]
  10. Completing the Square [ task | slides | posters ]
  11. Distance vs Time Graphs [ task | slides | posters ]
  12. Division of Integers [ task | slides | posters ]
  13. Equations and Number Lines #1 [ task | slides | posters ]
  14. Equations and Number Lines #2 [ task | slides | posters ]
  15. Equations and Sentences [ task | slides ]
  16. Exponents [ task | slides | posters ]
  17. Function or Not [ task | slides | posters ]
  18. How Many Birds? [ task | slides | posters ]
  19. Linear Equations and Graphs [ task | slides | posters ]
  20. Matching solutions to bar models #1 [ task | slides | posters ]
  21. Matching solutions to bar models #2 [ task | slides | posters ]
  22. Matching Solutions to Number Lines [ task | slides | posters ]
  23. Mean and Standard Deviation [ task | slides | posters ]
  24. Order of Operations [ task | slides | posters ]
  25. Quadratic Formula, Axis of Symmetry, and Roots [ task | slides | posters ]
  26. Rational Exponents on The Number Line [ task | slides | posters ]
  27. Sequences and Visual Patterns [ task | slides | posters ]
  28. Simple Quadratic Functions and Tables [ task | slides ]
  29. Simplifying Radicals on The Number Line [ task | slides | posters ]
  30. Solving Quadratic Equations Graphically [ task | slides | posters ]
  31. Systems of Linear Inequalities on Graphs [ task | slides | posters ]
  32. Tables to Factored Form [ task | slides ]
  33. Tape Diagrams to Situations [ task | slides | posters ]
  34. Vertex Form vs Factored Form [ task | slides | posters ]
  35. Volume of a Rectangular Prism [ task | slides | posters ]
  36. x-squared vs 2x vs x + 2 [ task | slides | posters ]

 

Last modified: Friday, 1 September 2023, 4:40 PM