Overview

This part focuses on analyzing a set of fraction-comparison problems to identify and compare possible solution strategies and representations.

Carefully analyzing the mathematical possibilities of tasks provides an important foundation for teaching. It helps teachers hear the mathematics in what students say, guides selection and modification of problems, and yields mathematical considerations that can be coordinated with a teacher’s knowledge of student thinking and instructional goals to make decisions.

Key Points

• One approach to analyzing the mathematics of a task is to think through the different strategies, representations, and solutions that are possible, without initially limiting the possibilities to those that are likely to be generated by students.