Instructional Routines

Videos and information about two key instructional routines - Contemplate then Calculate & Connecting Representations - embedded within the New Visions math curriculum.

This video shows the instructional routine Contemplate then Calculate from a workshop setting. We recommend watching any of the videos all the way through and recording notes or questions as you do so.

Resources for this particular task are available here including the slides, pre-planner, lesson plan, and printable posters.

Interested in seeing more videos?

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Instructional Routines are “designs for interaction that organize classroom instruction.” Teachers are familiar with the use of routines that organize behavior, such as how students enter the room or how students turn in and get back homework. Instructional Routines are different because they are designed to organize thinking.

Instructional Routines are both flexible (the math changes depending on your goals) and consistent (the format remains the same). The consistency of the format reduces the number of decisions teachers need to make about managing behavior, allowing them to focus entirely on the parts of the lesson that are most important for student learning. The intention is that the teaching within a routine responds more directly to what students do as they engage in problem solving.

Two routines we use are Contemplate then Calculate and Connecting Representations. These two routines were designed by Amy Lucenta and Grace Kelemanik. Each instructional routine contains a launch to clarify the learning objectives for the day and a meta-reflection at the end so that students can reflect on what they have learned for the day. In between the launch and the meta-reflection, students engage in problem solving—first independently, then with a partner, and finally as a whole group working to study various solution strategies.


We believe that Instructional Routines provide a number of benefits for teachers and students. Specifically, they:

  • Shift cognitive load in the classroom so that students and teachers can focus less on what they are supposed to do next and more on actively listening and understanding each other's’ reasoning;
  • Provide instructional supports for English as a New Language Learners and students with disabilities without reducing access to the mathematics;
  • Provide opportunities for students to productively persist while engaging in authentic mathematical problem solving;
  • Allow students to develop fluency with mathematical language and to use this language to construct viable mathematical arguments;
  • Support teachers in embedding formative assessment strategies into daily instruction seamlessly;
  • Give groups of teachers working on the same routine more ability to talk concretely about their teaching practice.



Interested in Sharing Out Tasks? Click Here.

To create your own Contemplate then Calculate tasks or get a copy of the template files we use, fill out this form (and use a Google or Google Apps for Education email), you will be shared on a folder with the necessary template files.

To create your own Connecting Representations tasks or get a copy of the template files we use, fill out this form (and use a Google or Google Apps for Education email), you will be shared on a folder with the necessary template files.

If you fill out these forms, you agree to license your work under a Creative Commons, Share-alike, Derivatives license. You can do whatever you like with your tasks, but you agree that New Visions for Public Schools can distribute these tasks, with attribution to you as we are able, to the broader mathematics education community to use.

We encourage teachers to share their tasks back to the greater community so that every teacher can benefit from the collective work of individual teachers. To that end we have created forms to make it easier to get copies of the template files we use, modify those template files, and then potentially have work already being done by teachers available for everyone.


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