CPM Glossary

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Use and Connect Mathematical Representations

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 making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations


Walk and Talk

Mode of Instruction: Partner           Purpose: Movement and Communication

Objective: To implement tasks that promote reasoning, students respond to questions or prompts about a topic while walking. The teacher monitors for multiple points of entry into a topic.

To promote movement during learning, partners receive a topic or concept to discuss while walking—about the classroom, in the hallway, or outside. Partners summarize learning, clarify ideas, or ask questions. Partners report any remaining questions to the teacher after returning to desks.

  • Partners receive topics or concepts to discuss.

  • Partners summarize, clarify ideas, or ask questions while walking.

  • Partners share any remaining questions with the teacher after returning to their desks.


Mode of Instruction: Teamwork/Teacher-led           Purpose: Elicit final reflective comment

Objective: To facilitate mathematical discourse, students share understanding of a concept/topic and critique the sharing of others. Teacher uses this time to make instructional decisions about the concept/topic.

Students participate in a teacher-led discussion to share a final comment on a topic, concept, or lesson. Students turn in the direction of the speaker—possibly forming a circle around the classroom. Teacher states the topic or problem, and students take turns sharing brief comments. Students have the option to pass on their turn to share.

Team Whiparound (Whiparound variation)

Teams participate in a teacher-led discussion to share a final comment. Teams share out only one agreed upon response per team.

  • Teacher provides a prompt.

  • Students take turns sharing brief comments.

  • Students listen while others share.

Word Wall

A word wall is a collection of words which are displayed in large visible letters on a wall, bulletin board, or other display surface in a classroom.

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