Pool Table with Numbered Squares
This applet is similar to the Animated Pool Table Applet (http://www.geogebratube.org/student/m93224), but it shows the whole path of the ball at once and numbers the squares the ball passes through. You can highlight multiples of a particular number or show the squares' numbers in various mods (uncheck "Show Numbers" so number displays don't overlap).
Look for patterns in where particular multiples appear and using various mods. These patterns can be linked to the questions in the Animated Pool Table Applet.