CPM Glossary


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A

Assessment Practices Outcome 5

Understand the purpose and value of team tests


Assessment Practices Outcome 6

Develop feedback and expectations for all forms of assessments


Attend to precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently and express numerical answers with a degree of precision appropriate for the problem context.


B

Board Report

Mode of Instruction: Teacher-led           Purpose: Self-assessment, Collaboration, Discourse

Objective: To facilitate meaningful mathematical discourse, students share and view others' solutions at the board. Teacher monitors learning through circulation and analysis of student work on board.


Teacher monitors student progress while students self-assess work and increase mathematical discourse. This is recommended for questions with short solutions, not for all questions from a lesson. If a problem requires choosing a tool and setting up an equation with many steps to solve, it is best if teams only report the end solution, or part of the solution.


  • Teacher creates a space in the classroom to write a row of problem numbers from the lesson.

  • When teams get to the problem listed on the board report, the team writes their answer on a sticky note.

  • A student from the team goes to the board to place the sticky note and compare to other teams.

  • Teacher monitors student work on board and through circulation. Based on work, teachers may ask specific teams to do a Swapmeet, or I Spy.

  • Repeat this process for each problem listed on the board, with a new student placing the sticky note each time.



Build Procedural Fluency from Conceptual Understanding

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 builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.


C

Carousel: Around the World

Mode of Instruction: Teamwork             Purpose: Brainstorm

Objective: To facilitate meaningful mathematical discourse, students share thinking and generate ideas by viewing multiple rounds of presentations. The teacher monitors learning through posing purposeful questions. 

Teams explore topics or questions displayed on poster paper around the classroom. After a brief discussion—two or three minutes, teams agree on a written statement to add to the poster. Teams rotate several times to discuss additional topics or questions. Teams read the previous written statements before adding to the list. Teacher monitors and determines when to conclude the activity. A Gallery Walk closure provides students time to read all of the written statements.


  • Display topics or questions around the classroom.

  • Provide a different colored marker for each team.

  • Assign one team to each topic or question to start.

  • Teams discuss and agree on a written statement to include about the topic.

  • Teams rotate to the next topic or question and repeat the process every few minutes.

  • For closure, facilitate a Gallery Walk to view all topics or questions.

Carousel: Index Card

Mode of Instruction: Teamwork           Purpose: Brainstorm 

Objective: To facilitate meaningful mathematical discourse, students share thinking and generate ideas by viewing multiple rounds of presentations. The teacher monitors learning through posing purposeful questions.


Teachers or students write one struggle about learning mathematics including time management, Review and Preview, partner work, teamwork, etc., on separate index cards. The index card rotates to other students that offer suggestions to support the struggles.


  • Students record one struggle/question/comment/concern on an index card.

  • Index card rotates within a team of students or to the next team.

  • Students or teams write suggestions on the index card.

  • Rotate the index card several times.

  • Index card is returned to the original student or can be displayed in class for all to benefit from.



Carousel: Station Rotation

Mode of Instruction: Teamwork           Purpose: Review

Objective: To facilitate meaningful mathematical discourse, students share thinking and generate ideas by viewing multiple rounds of presentations. Teacher monitors learning through posing purposeful questions.


Stations include review problems—possibly four to six—placed into a sheet protector. There should be more stations than teams. Teams record written explanations on a prepared sheet—in numerical order—to manage teacher review of work. After teams have completed a written explanation for a station, the paper is submitted to the teacher. Teams rotate to an available station.


  • Stations include several review problems.

  • Set up more stations than teams.

  • Teams record written explanations on a prepared record sheet.

  • Teams check in with the teacher.

  • Teams rotate to an available station.

  • Repeat until time is up or stations are complete.



Checkpoint Problem

LiwTtlrpE6cc1EX3sZA5xKdQEeKCgxLkNeUmx0eQKAL1iFVclzFha2YCV7axRoVmkn_2WRIN26S8GFjEXzWnq9l7qKsKsiXkAWIpg4B7M7OK6iaqphli58DpEWsC0B0HeZLz6aB4 These problems have been identified for determining if students are building skills at the expected level. Checkpoint problems are designed to support students in taking responsibility for the development of their own skills. When students find that they need help with these problems, worked examples and practice problems are available in the Checkpoint Problems section at the back of their book.



Checkpoint Problems

LiwTtlrpE6cc1EX3sZA5xKdQEeKCgxLkNeUmx0eQKAL1iFVclzFha2YCV7axRoVmkn_2WRIN26S8GFjEXzWnq9l7qKsKsiXkAWIpg4B7M7OK6iaqphli58DpEWsC0B0HeZLz6aB4 These problems have been identified for determining if students are building skills at the expected level. Checkpoint problems are designed to support students in taking responsibility for the development of their own skills. When students find that they need help with these problems, worked examples and practice problems are available in the Checkpoint Problems section at the back of their book.



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