Overview

Session 4 established key properties and conventions of the number line and explored students’ thinking about the representation.

Session 5 extends the work in Session 4 by examining two central practices of teaching mathematics: narrating the construction and use of a representation and analyzing tasks. In particular, this session focuses on:

• Narrating the construction and use of a number line to compare fractions
• Analyzing the instructional possibilities of fraction comparison problems

In this module, “narrating” refers to the practice of “talking through” the construction and use of a representation during instruction. Narrating is a practice that explicitly aims to expand students’ access to and understanding of mathematical representations and the ideas being conveyed.

This session maps out a process for narrating and identifies qualities that make a narration productive. It also considers the mathematical knowledge narrating representations requires. These ideas help teachers to narrate representations with their students and to support students in narrating representations.