This routine is designed to help students learn to focus on the regularity in their process of counting, calculating, or building, rather than on the results of that process.

Repeated Reasoning "Looks Fors" are:
- repetition in their counting, calculating, or building that can be seen, heard, and felt.
- regularities in the process to identify a generalized statement about the mathematics.

A key to generalizing repetition is to connect an aspect of the repetition in the process to a quantity in the problem (such as the term of the series, the tower number, or one of the variables in the problem).

The first step in the instructional routine is to have students notice if calculations are repeated. The students should ask themselves, "Do I keep doing the same thing over and over again?" They should look for regularity in the way they are counting, calculating, and constructing. You eventually want them to find the process behind the results they are getting. Effective math doers record their counting, calculating and constructing processes in order to identify regularities in their process and ultimately create a general mathematical statement.

At this point, students are grouped in pairs to share their thoughts on the repetition. They should be looking for and listening for repetitions. Some thinking prompts are
.. Is there something in this problem context that repeats or suggests some regularity?
.. How can I create or use a repeated process to help me figure out what's going on in this problem?
..What was my process? Was it the same every time?
..Am I counting/ drawing/ building/ calculating in the same way each time?
..What about this process is repeating?
..How can I describe the repetition in words/ variables/ etc.
..What operations can I use to model this process?

Once students have worked in pairs to discuss the repetition, the student pairs now share their ideas with a larger group, such as the whole class. In addition to what is listed on the slide, other sentence frames that can be used are the following:
... The process that kept repeating was______.
... The repeated process we/they generalized was_____.
... The repetition we/they generalized was _____,

These are examples of sentence frames the support discourse among your students.

The focus now is to generate ideas to translate repetition into rules.Keep individual think time short. Give time enough to generate ideas they can share.

Students should ask, "How can I use the repetition to find _______?"

The should annotate repetitions and generalizations that are discovered.

Next they should share how they were thinking with a partner using questions such as
..What are the steps in my process?
..What operations can I use to model this process?
..Have I included every step?

Monitor pair sharing so that you can get sample diagrams to share/ discuss with the whole group. Ask students to record their diagrams without labels.

Ask one or two of the students who did not create the rule to discuss features of the rule.

Press students to determine if the generalization accurately captures the process, if it can be stated more precisely, and if the rule “works”.

The final and crucial step in the Instructional Routine is to have students reflect on their learning. This is when vital learning converges. On both this slide and the next are possible reflection prompts to elicit student thinking.

Other prompts that can be used are:
...When looking for repetition in a process, I learned to pay attention to __;
...When looking for repetition, I learned to ask myself __;
... __ helps me to notice repetition because __; or
... One way to identify repetition is to __.
... The key to generalizing the repetition I found is __.