Density is how much of something sits in one unit of space, and finding it takes two steps: work out the area or the volume from the figure, then share the amount over it. These free printable worksheets draw the shape and give the amount; the size is the part a student finds.
If they get stuck
The answer key prints on a separate page.
Both of the standard's own examples are here. A rectangular piece of land with a population on it gives people per square mile — the number a census uses, and the reason two counties of different sizes can be compared at all. A rectangular block with a mass gives grams per cubic centimeter, which is the density of the MATERIAL: the same 11 g/cm³ whether the block of lead is small or large, and a student who notices that has understood what a rate per unit is for.
The reason it is a geometry sheet and not a rate sheet is the first step. The figure is labelled with its sides, not its size, so the area or volume has to be worked out before there is anything to divide. That is what modeling with geometry means: the shape carries the information, and reading it is part of the question.
People per square mile
