This set of activity activities are designed to help students to structure their thinking so that they are afforded the opportunity to make sense of the idea of division of fractions. The goal of this collection of activities is to allow the division algorithm to emerge from quality thinking and reasoning about the mathematics needed to divide fractions. While students will engage in many (all?) of the Standards for Mathematical Practices, the primary practice that is the focus of these activities is Practice #8: Look for and express regularity in repeated reasoning. As a result of developing this and the other mathematical practices, division of fractions will become part of a well-connected network of understanding.
The activities in this series of lessons have just a few questions in each. However, each question will likely take much time and were designed to elicit much conversation, discussion, debate, explanation, etc. That is, students should be thinking deeply about what they are doing and why they are doing it. Teachers should be challenging students to explain what “it” means as students describe the methods they used to answer each question.
This is also an excellent example of why the worksheets alone may not accomplish the intended goal if the user does not understand the purpose. By combining the workshop experience with the solutions, my hope is that the worksheets will accomplish the intended goal: for students to engage in repeated reasoning for the purpose of creating an algorithm for dividing fractions.