Calculate density from mass and volume, and use density to identify an unknown substance or predict floating and sinking.
Density is how much mass is packed into a given volume: density = mass / volume, usually in g/mL or g/cm^3 (note that 1 mL and 1 cm^3 are the same volume). Density is a physical property that does not depend on how much of a substance you have -- a huge block of aluminum and a tiny aluminum paperclip have the exact same density, 2.70 g/cm^3, because density is about how tightly packed the matter is, not how much of it there is.
Density lets you identify an unknown material: measure its mass on a balance, measure its volume (directly for a regular shape, or by water displacement for an irregular one -- drop it into a graduated cylinder of water and see how much the water level rises), divide, and compare the result to known reference densities.
Density also predicts floating and sinking: an object floats in a fluid if it is less dense than that fluid, and sinks if it is more dense. Water is 1.00 g/mL, which is why ice (about 0.92 g/mL) floats but a steel ball bearing (about 7.9 g/mL) sinks.
Mastery looks like: They calculate density correctly from mass and volume (including by water displacement) and use it to identify a substance or predict floating and sinking.
Common stumbles: Dividing volume by mass instead of mass by volume; forgetting to subtract the initial water level when using displacement, which inflates the volume and throws off the density.