ABSTRACT
Rational numbers measure directed distances of certain points from zero in terms of some unit distance. Under the measure interpretation, a fraction is usually the measure assigned to some interval or region, depending on whether people are using a one- or two-dimensional model. In a one-dimensional space, a fraction measures the distance of a certain point on the number line from zero. Obviously, partitioning plays a major role in the measurement interpretation of fractions, as does reasoning up and down. Through successive partitioning, children quickly learn about equivalence and common denominators. Aided by the arrow notation, multiplication and division are the first operations to develop. Students understand fractions as measures when they are comfortable with successive partitioning; are able to find any number of fractions between two given fractions; and are able to compare any two fractions.
