The PE, PVC, and brass rods all have the same mass. Even without knowing anything about their atoms and molecules, how do you know that the smallest is the most dense, the largest is the least dense, and the middle-sized one has a density between the other two?

If different objects have the same mass, and the volume of one of them increases, its density decreases. If the volume decreases, density increases.

Explanation:

If all the brass rods have the same mass, and the volume increases, its density decreases. If the volume decreases, density increases.

Density measures how tightly gathered and how heavy are the molecules in an object, and it measures the amount of matter inside a particular volume.

Mass is the amount of matter, and volume is the amount of space the object takes up.  

The equation for Density is:

Mass (gr) ÷ Volume (c³)

If mass remains the same, a greater volume (a greater denominator) will result in a lower density.