# A Model for Multiplication

## Developing an Algorithm for Fraction Multiplication

For CMP2 Unit Bits and Pieces II, Investigation 3: Multiplying with Fractions

For CMP3 Unit Let's Be Rational, Investigation 2: Building on Multiplication with Fractions

Students develop an algorithm for multiplying improper fractions during the exploration of Problems 3.1 and 3.2. The video focuses on the learning trajectory from first exposure to a model for representing a part to developing an algorithm for the computation.

This video starts with the teacher's comments on her goals for the lesson and what difficulties students might encounter. Most of the discussions occur around Problem 3.1. At the end of Problem 3.2 students are ready to write down an algorithm for multiplying improper fractions. The focus is on student understanding.

Real time is 3 class periods.

As you view the video, consider the following:

• What evidence is there of students' understanding and reasoning? What prior understandings do you see students using or building upon?
• What is the evidence of students' use of the Mathematical Practices from the Common Core Standards for Mathematics (CCSSM)? To what extent are students growing in their sophistication of using the Mathematical Practices?
• Were there any "aha" moments?
• How is the teacher facilitating the development of students' understanding and reasoning?
• As a teacher, how would you use this information from this lesson to plan the next lesson?

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