I would express this in a diagram with a dotted line around the set under consideration. When dealing with thirds, make a diagram containing three objects with their respective properties, and end by drawing a dotted line around the set. When switching to sixths, add three more objects, erase the line around the first three, and draw a new dotted line around the whole set of six. Then go on to sevenths by adding one more object, erasing the dotted line for the six and drawing it around all seven.

If I do it this way, my 4th grader can add fractions just like numbers without resorting to common denominators.