How the Lessons are Structured

What Is in Each Lesson?

Math Pathways & Pitfalls lessons use a consistent, easy-to-follow structured format with a core lesson and two follow-up mini lessons, each accompanied by a teaching guide. Teaching guides provide sample prompts and solution keys for each part of the lesson. Lessons rely on drawings for visuals and suggest — but do not require — manipulatives, allowing lessons to be used in schools where such resources are not readily available.

Every lesson employs a four-part instructional model:

  • Opener — Teacher engages and orients students by motivating inquiry into the mathematics and the pitfall.
  • Discussion — Teacher guides discussion around high interest mathematical problems.
  • Review and Practice — Students review and apply what they have learned about problem-solving habits of mind.
  • Assess and Reinforce — Students demonstrate mastery through mini lesson tasks and writing tasks.*

Together these elements provide multiple opportunities for students to develop, assess, and solidify their mathematical understandings.

*The lesson structure described here is applicable for grades 2–8. Lessons for kindergarten and grade 1 incorporate shorter intervals, fewer pages, and exclude the writing task mini lesson.

lesson structure

Each core lesson is designed to take approximately two 45-minute class periods. These class periods correspond to Day 1 and Day 2 of the lesson. Each mini lesson takes about 20–25 minutes and is completed about 1–2 days later.