Science

Common mistakes in density

6 mistakes learners make with density, each one named and explained.

All common mistakes

Density is how much mass is packed into each unit of space, not how heavy something is.

Adding mass thought to lower density

What it looks like

You say density falls when mass rises, with the volume held the same.

Why it happens

Density is remembered as a fraction and the mass is put on the bottom by mistake.

A worked example

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.

Put the two side by side

More mass in the same space is denser.
More space for the same mass is less dense.

Say the sentence out loud: mass divided by volume. Whatever is on top raises the answer.

Density and mass treated as the same thing

What it looks like

You describe density in grams, or say something is dense because it is heavy.

Why it happens

Both words describe heaviness in ordinary speech, and only one of them is used at school.

A worked example

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.

Put the two side by side

Mass is measured in grams.
Density is measured in grams per cubic centimetre.

The unit gives it away. Density always carries a volume in it.

Density and volume treated as the same thing

What it looks like

You judge density by how big something is, so the larger object is called the denser one.

Why it happens

Bigger is the most visible difference between two objects, so it becomes the one that matters.

A worked example

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.

Put the two side by side

Volume is how much space it takes up.
Density is how much mass is in that space.

Density always needs both numbers. One on its own can never decide it.

Density thought fixed whatever you do

What it looks like

You answer that density stays the same when the mass changes and the volume does not.

Why it happens

Density is taught as a property of a material, so it feels like a fixed number for the object too.

A worked example

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.

Put the two side by side

Copper always has the same density.
This object has changed what it is made of.

A material has a fixed density. An object only does if nothing about it changes.

Heavy things sink, light things float

What it looks like

You say an object floats when it is light and sinks when it is heavy, without mentioning volume.

Why it happens

It matches everyday experience, where the heavy things you pick up do sink.

A worked example

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.

Put the two side by side

A steel nail sinks.
A steel ship floats.

Same material, opposite result. Mass alone cannot decide it, so it must be density.

Units not tied to what they measure

What it looks like

g/cm^3 is matched to speed or force, because the unit is not read as a sentence.

Why it happens

Units are learned as labels to copy rather than as a description of the calculation.

A worked example

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.

Put the two side by side

m/s is metres for each second.
g/cm^3 is grams for each cubic centimetre.

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.

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