# Student Discourse

## Developing an Algorithm for Fraction Multiplication

Various segments of discourses that the classes engage in as they develop multiplication algorithms are highlighted in this video. The focus is on how the discourse promotes and illustrates understanding.

All clips orginate in the same week, when students were studying Bits and Pieces II, Investigation 3 in CMP2 (Let's Be Rational, Investigation 2 is the CMP3 equivalent).

As you view the video, consider the following:

- What mathematical idea is being discussed in each clip?
- From what we can hear do you think that students understand this mathematical idea?
- What would you ask to clarify or extend student thinking?
- Is this a student-student or student-class or teacher-student or teacher-class interchange?
- Who initiates the discussion? A student or the teacher?
- Who takes responsibility for continuing the discussion? A student or the teacher?
- How would you characterize the discussion?
- What is the value of the explore time?
- How do you set the stage for this kind of student discourse?
- How can you foster curiosity and engagement in reasoning in your class? (See Teri’s reflection for Day 2, and her extended interview in the appendix.)

- Full Length Video (14:29)
- Problem 3.3
- Goals
- Estimate products of fractions
- Use models to represent the product of two fractions
- Understand that finding a fraction of a number means multiplication
- Develop and use strategies and models for multiplying combinations of fractions, whole numbers, and mixed numbers to solve problems
- Determine when multiplication is an appropriate operation
- Explore the relationships between two numbers and their product
- Develop and use an efficient algorithm to solve any fraction multiplication problem

- Video Transcript
- Suggestions for organizing Professional Development