CurrICuluM DeSIgn | 29Daily lessons in the modules are designed to be 45 minutes in duration and are desig-
nated as one of the four lesson types described in the next paragraphs. The lesson type
designation is given using one of the four icons shown (Figure 4.1) and provides the teacher
with a general idea of what to expect from the structure of the lesson.
In the Problem Set Lesson, teachers and students work through a sequence of examples
and exercises to develop or reinforce a concept. The majority of the class period is spent
alternating between the teacher working through examples followed by students completing
exercises either individually or in pairs.
In the Socratic Lesson, the teacher leads students in a conversation with the aim of
developing a specific concept or proof. This approach is often used when conveying an idea
that students cannot learn or discover on their own. The teacher asks guiding questions to
pull information from the students and draw them into the discussion. Other activities may
occur during the lesson in the minutes that remain. For example, a fluency activity may open
the lesson, or there may be a debrief or application problem at the end of the lesson.
The Exploration Lesson involves students working independently or in small groups for
a sustained period of time on one or more exploratory challenges, followed by a debrief with
the goal of clarifying, expanding on, or developing a concept, definition, theorem, or proof.
Because of the rigorous nature of the exercise, allowing students to collaborate in pairs or
groups should be a consideration. The class comes back together to discuss the challenge,
draw conclusions, and consolidate understandings.
In the Modeling Cycle Lesson, students and teacher work through the modeling cycle
to complete an application problem over one or two days. The lesson may involve students
practicing all or part of the modeling cycle. In Grades 6–8, a reduced form of the modeling
cycle is typical, whereas in Grades 9–12, the modeling cycle in its entirety is generally
incorporated into lessons. The typical problem that students encounter in this lesson type is
ill-defined and has a real-world context. Students are likely to work in groups on these types
of problems, but teachers may want students to work for a period of time individually before
collaborating with their group members.
The lessons incorporate guidance for teachers in several ways. Narratives appear
throughout the lessons to help teachers understand the content being delivered and how to
Figure 4.1