The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…