6 mistakes learners make with density, each one named and explained.
Density is how much mass is packed into each unit of space, not how heavy something is.
You say density falls when mass rises, with the volume held the same.
Density is remembered as a fraction and the mass is put on the bottom by mistake.
Question. Volume stays at 20 cm^3 while mass rises from 60 g to 100 g
A common answer. the density falls
The answer. the density rises from 3 to 5 g/cm^3
Why. Mass is on top of the fraction, so more mass means more density.
Say the sentence out loud: mass divided by volume. Whatever is on top raises the answer.
You describe density in grams, or say something is dense because it is heavy.
Both words describe heaviness in ordinary speech, and only one of them is used at school.
Question. A kilogram of feathers and a kilogram of lead
A common answer. they have the same density because they have the same mass
The answer. the lead is far denser
Why. Same mass, very different volumes, so very different densities.
The unit gives it away. Density always carries a volume in it.
You judge density by how big something is, so the larger object is called the denser one.
Bigger is the most visible difference between two objects, so it becomes the one that matters.
Question. A beach ball and a marble
A common answer. the beach ball is denser because it is bigger
The answer. the marble is denser
Why. The marble packs much more mass into each cubic centimetre.
Density always needs both numbers. One on its own can never decide it.
You answer that density stays the same when the mass changes and the volume does not.
Density is taught as a property of a material, so it feels like a fixed number for the object too.
Question. Same volume, twice the mass
A common answer. the density is unchanged
The answer. the density doubles
Why. Density is fixed for a pure material, but this object is no longer the same object.
A material has a fixed density. An object only does if nothing about it changes.
You say an object floats when it is light and sinks when it is heavy, without mentioning volume.
It matches everyday experience, where the heavy things you pick up do sink.
Question. A large log and a small stone
A common answer. the log sinks because it is heavier
The answer. the log floats and the stone sinks
Why. The log has far more volume for its mass, so its density is lower than water.
Same material, opposite result. Mass alone cannot decide it, so it must be density.
g/cm^3 is matched to speed or force, because the unit is not read as a sentence.
Units are learned as labels to copy rather than as a description of the calculation.
Question. g/cm^3
A common answer. a unit of speed
The answer. a unit of density
Why. Grams for each cubic centimetre is mass for each unit of space, which is density.
Read the slash as the words for each. The unit then tells you the formula.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.