Farey Fraction Number Line
A Farey Sequence consists of all fractions between 0 and 1 with denominator less than or equal to a particular value. This applet shows Farey Sequences on a number line. Note that past denominator 9, the labels won't fit. If this applet is too big for your screen; here's one that splits the number line in half: http://www.geogebratube.org/student/m12722.
What patterns do you notice in the Farey Fractions? Also see the Farey Fraction Pattern Graph Applet at http://www.geogebratube.org/material/show/id/12780 to explore more.