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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.

Cognitive Delays in Processing

Students who have the ability to engage with the mathematics but need more time and supports may struggle to keep up.

Supporting Question to Ask:
Can assignments be extended or modified to allow more time? Are there opportunities for extra help available?

PDF document Students Who Sometimes Struggle Position Paper.pdf

Collaborative Learning

Research says students learn ideas more deeply when they discuss ideas with classmates.

Collaborative learning is evident in a classroom when

  • Students and teachers are aware of the purpose for and value of working in teams. 
  • Students and teachers are familiar with team norms and roles.

Concept Goals

Concept Goals are those focused on the mathematics students learn.  Teachers may have particular success criteria attached to these Learning Goals that explain how and when students may demonstrate their proficiency level.

Connect-Extend-Challenge protocol

This is a reading strategy used for longer passages where students are asked to make connections to things they already know, extend their thinking by finding new ideas in the material, identify ideas that challenge them, and then share these with their group or the class.



Connecting

  • Craft questions to make the math visible.
  • Compare and contrast 2 or 3 students' work. What are the mathematical relationships?
  • What do parts of a student's work represent in the original problem? The solution? Work done in the past?

Connecting is Step 5 of the 5 Practices for Orchestrating Productive Math Discussions. 

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