Instructional Design

The manner in which students encounter mathematical ideas can contribute significantly to the quality of their learning and the depth of their understanding. Core-Plus Mathematics units are designed around multi-day lessons centered on big ideas. Lessons are organized around cycles of instructional activities intended primarily for small-group work in the classroom and for individual work outside of the classroom.

In-Class Activities

The four-phase cycle of classroom activities,

is designed to actively engage students in investigating and making sense of problem situations, in constructing important mathematical concepts and methods, in generalizing and proving mathematical relationships, and in communicating their thinking and the results of their efforts.

Many classroom activities are designed to be completed by students working together collaboratively in heterogeneous groupings - in pairs or in groups of three or four.

Students in a CPMP classroom

Short clips of classrooms are available
at Parent Support: CPMP Classrooms.


Lessons begin with a full-class discussion of a problem situation and of related questions to think about. This discussion sets the context for the student work to follow and helps to generate student interest; it also provides an opportunity for the teacher to assess student knowledge and to clarify directions for the group activities. Teacher is director and moderator.

Sample launch


Classroom activity then shifts to investigating focused problems and questions related to the launching situation by gathering data, looking for patterns, constructing models and meanings, and making and verifying conjectures. As students collaborate in small groups, the teacher circulates from group to group providing guidance and support, clarifying or asking questions, giving hints, providing encouragement, and drawing group members into the discussion to help groups work more cooperatively. The unit materials and related questions posed by students drive the learning. Teacher is facilitator.

Sample exploration


Share and Summarize

A full-class discussion (referred to as a Checkpoint) of concepts and methods developed by different small groups then provides an opportunity to share progress and thinking. This discussion leads to a class summary of important ideas or to further exploration of a topic if competing perspectives remain. Varying approaches and differing conclusions that can be justified should be encouraged. Teacher is moderator.

Sample Checkpoint


Finally, students are given a task related to lesson objectives to complete on their own. The teacher circulates in the room assessing levels of student understanding. Teacher is intellectual coach.

Sample On Your Own

MORE: Out-of-Class Activities

In addition to the classroom investigations, Core-Plus Mathematics provides sets of MORE tasks, which are designed to engage students in

  • Modeling with
  • Organizing
  • Reflecting on, and
  • Extending their mathematical understanding.

These tasks, which are central to the learning goals of each lesson, are intended primarily for individual work outside of class.

Several MORE tasks are provided for each lesson. Selection of MORE tasks should be based on student performance and the availability of time and technology. Also, students should exercise some choice of tasks to pursue, and at times they should be given the opportunity to pose their own problems and questions to investigate.

Modeling tasks are related to, or provide new contexts to which students can apply, the ideas and methods that they have developed in the lesson.

Organizing tasks offer opportunities for integrating the formal mathematics underlying the mathematical models developed in the lesson and for making connections with other strands.

Reflecting tasks encourage thinking about thinking itself, about mathematical meanings, and about processes. They promote self-monitoring and evaluation of understanding.

Extending tasks permit further, deeper, or more formal study of the topics under investigation.

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