Lesson Structure

First Weeks of School

A Story of Units (Grades PK–5)

Every lesson follows the same four-part structure: Fluency, Concept Development, Application Problem, Student Debrief. Because every lesson follows the same arc, students develop a rhythm that reduces anxiety and frees cognitive resources for the math itself.

• Fluency: Activates prior knowledge and gives students distributed practice with previously learned concepts. Use this time to set the tone, rhythm, and purpose.
• Concept Development: The heart of the lesson. Students engage with new content through direct instruction, guided practice, and collaborative tasks. This section also includes the Problem Set for independent practice. Plan to spend the majority of your instructional time here.
• Application Problem: A problem that connects prior learning to the new concept. Students work independently or in pairs, and discussion follows. The Application Problem helps facilitate discussion around problem-solving strategies.
• Student Debrief: The lesson closes with this critical component. You’ll engage students in a whole-group discussion, inviting them to share their thinking. This allows you to gauge student understanding and surface misconceptions before the Exit Ticket.

A Story of Ratios (Grades 6–8) and A Story of Functions (Grades 9–12)

Lesson formats vary on the content being taught. Regardless of the type of lesson, each has an associated Problem Set—keep your use case for these flexible and based on student needs. Mathematical modeling intensifies at each grade level in high school, making this the most common lesson format at grades 9–12.

• Problem Set Lesson: Teacher-led examples are followed by guided exercises, with short discussions helping students make connections.
• Socratic Lesson: Used for more complex concepts. These lessons are primarily teacher-student dialogue designed to develop understanding through discussion.
• Exploration Lesson: Students work in partners or small groups on exploratory challenges, activities, and exercises aimed at a common goal.
• Modeling Lesson: Students apply math to real-world problems. These lessons appear at least three times per grade level in middle school.