ABSTRACT
A quantity is a measurable quality of an object—whether that quality is actually quantified or not. Before dealing with rational numbers symbolically, it is important to get children to discuss the relationships among quantities in real-world situations. The study of relationships begins on a visual level and may be clarified and extended when children develop a vocabulary, talk about those relationships, and analyze them. For fraction instruction, the fact that rods are three-dimensional is unimportant. It is the length of the rods that is critical. Thus, it is easy and inexpensive to cut Cuisenaire-like pieces out of card stock so that all children can have access to these tools. Human beings seem to have a built-in capability to recognize objects whether they are large or small in size, whether they are the real thing, or whether they are photographs or models with only some of the characteristics of real things.
