Smith, M. S., & Stein, M. K. (2018). 5 Practices for Orchestrating Productive Mathematics Discussion (2nd ed). National Council of Teachers of Mathematics.

Illustration videos, via Dan Meyer: https://us.corwin.com/en-us/nam/the-five-practices-in-practice/book260532

Big inspiration for Desmos activity builder.

Q. What are the 5 practices?
A. anticipate, monitor, select, sequence, connect

1. anticipating likely student responses to challenging mathematical tasks and questions to ask to students who produce them;
2. monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups);
3. selecting particular students to present their mathematical work during the whole-class discussion;
4. sequencing the student responses that will be displayed in a specific order; and
5. connecting different students’ responses and connecting the responses to key mathematical ideas.

Q. What two categories of things are teachers meant to “anticipate”?
A. likely student responses, questions to ask about those responses

Q. What two categories of things are teachers meant to “connect” to?
A. student responses to each other, and to key mathematical ideas