Teaching fractions as pizza slices entails dividing the circle into 6ths, say, and shading in 5 slices[1]. The wedge in the circle shows relative magnitude; it

Teaching fractions as pizza slices entails dividing the circle into 6ths, say, and shading in 5 slices[1]. The wedge in the circle shows relative magnitude; it depicts the fraction as a portion (numerator) of the whole (denominator) regardless of how big the circle is. The magnitude of the fraction is depicted only relative to 1. On a number line, the magnitude of the fraction is depicted relative to any number. In this sense, we capture the "absolute magnitude" of the fraction, by placing on a line relative to the integers. ---1-----0-----1-----2-----3--- ^ ^ 5/6 13/6 An individual fraction, as a single-dimensional magnitude, is best represented in an infinite single-dimensional space, where magnitude increases forever in exactly one direction. A circle, on the other hand, has a finite amount of space. Maybe you're right: perhaps it is the infinite nature of the number line that lends itself to "absolute magnitude" rather than the fact that it is one-dimensional. On the other hand (this is increasingly pedantic): While we could depict 1d magnitude "infinitely" in 2d with concentric circles of area 1, 2, 3, etc, using 2d area to depict a 1d magnitude is not intuitive. The natural alternative is to subdivide the space into units and show multiple discrete units. In 2d, 13/6ths would be two whole pizzas and one 1/6th-filled pizza. But in 1d, the units can be placed adjacent to each other according to the direction of increasing magnitude. In this sense, 1d lends itself to a natural depiction of absolute 1d-magnitude, but 2d does not. [1] http://www.primarygames.com/fractions/images/pizza_5-6.gif http://www.primarygames.com/fractions/images/pizza_5-6.gif