CPM Glossary

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Talk Moves

Although IRE is the most common type of Teacher-Student discourse, talk moves are a better option.  The secret to talk moves is not to evaluate, but question for better discourse without acknowledging if the response was right or wrong.  Talk moves can work at the small team level or in a whole class discussion. Here are the four types of talk moves. (O'Connor and Chapin)

Elicit Student Thinking (what are the students thinking and saying?)

  • Turn and Talk "Share your thinking with your partner"

  • Revoicing "Are you saying that.....?"

  • Say More "Could you give us an example?" or "Would someone else say that in their own words?" or "I'm not sure I understand what you are saying, could you say more?"

Orient Students to the Thinking of Others (Are the students listening and understanding what others are saying?)

  • Repeating "Who can repeat what was said?"

  • Sharing Out "What did your partner think?"

  • Surveying Access "Can everyone hear what is being said?"

  • Focusing Attention on Student Thinking "As we listen to this response, think about how it is the same or different than what we talked about yesterday?"

Deepen Student Understanding (How can I make this more meaningful?)

  • Press for Reasoning "Why do you think that?"

  • Having Reasoning Repeated in Multiple Ways "Who can put that in their own words?"

  • Find a Student Who is Unconvinced "Erin is not convinced, Who can explain why that is true?"

  • Turn and Talk, Prompting students to make sense of reasoning "Talk about Marla's idea"

Students Response to the Reasoning of Others (How can students build on this idea?)

  • Press for reactions "Do you agree or disagree? Why?" or "What does Marla's statement make you think of?"

  • Compare or Contrast "Is what Erin said the same or different than what Marla said? How?"

  • Invite Challenges "Who sees it differently?" or "Can someone make a counter-argument?"

  • Turn and Talk "Talk to your partner about whether or not you agree with Erin?"

Task Manager

The Task Manager keeps the team focused on the assignment of the day. He or she works to keep the team discussing the math at hand and intervenes if anyone is talking outside of her/his team. Additionally, a Task Manager helps the team focus on articulating the reasoning behind the math statements they make as the well as the answers that are proposed.

Typically, a teacher could expect to hear a Task Manager saying:

“Ok, let’s get back to work!”

“Let’s keep working.”

“What does the next question say?”

“Explain how you know that.”

“Can you prove that?”

“Tell me why!”

Tasks that Promote Reasoning

One of the eight Mathematics Teaching Practices from Principles to Actions that needs to be a consistent component of every mathematics lesson.  Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Teacher Toolkit

The Teacher Toolkit - Collaboration, Pacing, and Routines is a module within the Professional Learning Portal that provides teacher testimonials from experienced teachers regarding the routines and procedures they use to support student learning in their own classrooms.

Teacher Transparency

When implementing new instruction strategies, it is not only important to make obvious the intellectual practices involved in completing and evaluating learning tasks, but also to explain the intent of your practice to your students. Each strategy and classroom expectation should be accompanied by an explanation of how that intentional act will positively impact the students' learning.

Read the article Teacher Transparency , by John Hayes, in the May 2020 CPM Newsletter.  

Team Roles

CPM resources are designed around four Team Roles: Resource Manager, Facilitator, Recorder/Reporter, and Task Manager.  Click on the individual roles to see their descriptions.

Teammates Consult

Mode of Instruction: Teamwork           Purpose: Team discussion and decision making

Objective: To establish mathematics goals to focus learning, teams utilize an established routine to begin problem solving by making sure all members know the goals and learning progression.

Teammates Consult is an effective strategy to use for problem solving and concept development situations. It allows the students an opportunity to think and discuss the problem before actually writing anything down.

  • All pencils and calculators are set aside (no writing).

  • Students read the problem or question individually.

  • Students get approximately 1 minute of individual think time.

  • Students take turns sharing and discussing the problem for clarity.

  • Students share possible strategies or next steps.

  • Teacher gives okay for pencils to be picked up and written work to begin.

They Say..., I Say..., So What...? Protocol

A reading strategy where text is read silently and individuals are asked to describe what they say (the authors say) about the topic; interpret what the reader thinks about the topic (I say); and then the reader writes what the topic means to them (so what). This is shared with a partner, group and/or whole class. 


This could be done on your Learning Management System or on a document that all students have access to.

You could assign each student a Team Role ahead of time and then pair up team roles (i.e. Facilitators are paired with Resource Manager)

In your LMS, create a Forum with your prompt. Students write an entry and then read and comment on another a partners entry.  Partners are determined by their team role.

On a Google Doc, put the prompt at the top.  Have each student write an entry and then read their partners and comment or question on what they read.

Think Ink Pair Share-Socially Distanced

This could be done with whiteboards so that the writing is large enough for distanced students to see each others work.

It could also be done with a Google Doc.  The teacher posts a prompt in a document or sheet. Have each student write an entry and then read their partners and comment or question on what they read.  Teachers would monitor the time and give students verbal feedback about the amount of time left.

Think Ink Pair Share-Synchronous

This could be done on a document or a spreadsheet.  The advantage of a spreadsheet is that you could lock some of the columns or rows so that students could not change the data.  

The teacher posts a prompt in a document or sheet. Have each student write an entry and then read their partners and comment or question on what they read.  Teachers would monitor the time and give students verbal feedback about the amount of time left.

You could also do this with Private Chats or Breakout Rooms but be mindful that you may not always be able to monitor these chats.


Mode of Instruction: Independent/Partner/Teamwork           Purpose: Individual reflection prior to discussion

Objective: To elicit and use evidence of student thinking, students utilize intentionally planned think time before responding to and sharing out understanding.

To emphasize the importance of think-time, the teacher poses a question/problem for students to silently think about. After a short period of time, students write an explanation to share. When the teacher indicates, partners share explanations. Partners may share within the team or the whole class.

Think-Pair-Share (Think-Ink-Pair-Share variation)

Students receive a question—possibly about concepts covered in a unit, Diamond Problems, or mental math—and silently think for a short period of time. Without writing, partners discuss explanations of the question. Partners may then share out with the rest of the team or class.

  • Teacher poses a question/problem.

  • Students think for a period of time—one or two minutes.

  • Students silently prepare an explanation in writing to share.

  • Partners take turns sharing written explanations.

  • Partners may then share out with the rest of the team or class.

Third CPM Principle of Assessment

Students should be assessed only on content with which they have been meaningfully engaged, and with which they have had ample time to make sense of.


Related problems and/or lessons intentionally sequenced within and between courses to help students both deepen conceptual knowledge and build procedural fluency.


2kzpZqPIrDIYw5aoENW5md3NYg4ED8CeQXj75V0XO_huSaBi8oMjk68ikxT-FT_GdQEzVDRpzs4WnEhkM4WEfY8XeyuBDTDC0YzLmRrwkWk_6MOtVB7XjTnE91C3dekj_ET2jq5d Working documents in which students write Learning Logs, interact with Math Notes and create other personal reference tools.

Tools and Technology Outcome 1

Learn how to access CPM’s Synthesis of Research and course preparation resources

Tools and Technology Outcome 2

Experience how to engage students with content using Desmos and other eTools

Tools and Technology Outcome 3

Understand the structure and organization of the teacher and student ebooks

Tools and Technology Outcome 4

Locate Closure and Assessment resources

Tools and Technology Outcome 5

Know how to utilize Chapter Opening and Lesson Teacher Notes

Tools and Technology Outcome 6

Understand how to access Team Support and Strategies to establish and maintain classroom expectations

Tools and Technology Outcome 7

Examine Universal Access and Literacy resources to support the learning of all students

Tools and Technology Outcome 8

Learn how to access and navigate CPM’s Learning Management System

Tools and Technology Outcome 9

Locate resources to support parent and public relations

Traveling Salesperson

Mode of Instruction: Teamwork/Teacher-led           Purpose: Communicate mathematical ideas

Objective: To implement tasks that promote reasoning, students solve a problem and decide on an effective strategy within a team. One team member shares that strategy with other teams.

Teams receive a topic or problem—same/different from other teams—and a presentation is prepared. Teams plan and practice within teams. Then one team member—Traveling Salesperson—rotates to another team to pitch the presentation. The team asks clarifying questions. Then the Traveling Salesperson returns to the team so that roles may rotate. The use of Numbered Heads allows all team members to rotate. The teacher circulates to make informed instructional decisions about which team member is assigned the role of Traveling Salesperson.

  • Teams receive a topic or problem from the teacher.

  • Teams complete the problem by planning a presentation.

  • Team Member (1) shares the presentation with another team.

  • The process continues with another topic or problem, and roles may rotate.

Tuning Protocol

Mode of Instruction: Teamwork           Purpose: Receive feedback

Objective: To promote meaningful mathematical discourse, students share, analyze, and compare teammates' approaches and arguments.

Team Member (1) presents an explanation to a problem to other team members in a short period of time—one or two minutes. The presentation may be a portfolio project, a report, a math problem, Learning Log, etc. When the time is up, team members ask Team Member (1) any questions or clarifications—about one minute. Then Team Member (1) turns away from the team while team members discuss the presentation and deepen understanding of the problem—five minutes—, while Team Member (1) listens and writes notes. Team Member (1) turns back and shares a reflection of the discussion. The role may rotate to Team Member (2) and the process continues. The teacher uses discretion for length of activity.

  • Team Member (1) presents an explanation to a problem in teams.

  • Team Members ask Team Member (1) questions or clarifications.

  • Team Member (1) turns away from the team while listening and writing notes.

  • Team Member (1) shares a reflection of the discussion.

  • The role is rotated to Team Member (2) and the process continues.

Turn and Talk

Mode of Instruction: Partner Work           Purpose: Share understanding

Objective: To promote productive struggle with a topic before mastery is expected, two students share mathematical ideas with each other. Teacher monitors through circulation.

To discuss a procedure or concept without writing, one team member explains while the other team member listens. If there is a disagreement, students continue to discuss the solution and agree on a single explanation. When partners have an explanation, they share with the rest of the team.

  • Students work in pairs.

  • Team Member (1) explains while Team Member (2) listens.

  • Team Member (2) asks clarifying questions to Team Member (1).

  • Partners agree on one explanation to share with other members of the team.

  • Roles are reversed for the next problem.

Two Stars and a Wish

Mode of Instruction: Independent/Teamwork           Purpose: Reflection and feedback

Objective: To establish goals to focus learning, students identify strengths and areas for growth. Teacher monitors students’ understanding to guide instructional decisions.

During any presentation, students record two things they really liked—Two Stars—and one suggestion that might improve the presentation—a Wish. At times, a team member may be present to explain or answer questions about the presentation.

  • Students record two things they like about a presentation.

  • Students record one thing that would improve the presentation.

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