Density Curriculum

Section 2—Lesson 4: How Can We Calculate Density From The Relationship Between Mass and Volume?

Background Information

Using the Relationship Between Mass and Volume to Calculate Density

This lesson introduces information on how to calculate density by focusing on the relationship between mass and volume. Scientists define density as the mass of a substance per unit volume. It is the relationship between the mass (or weight) of one unit of a material and the volume of that one unit. Density is expressed in terms of grams per cubic centimeter (g/cm³) or grams per milliliter (g/ml).

If you know the mass and volume of an object or substance, you can figure out its density by dividing the mass by the volume (D = M/V). If you know the density and the volume, you can figure out the mass by multiplying the density times the volume (M = D x V). If you know the density and mass, you can figure out the volume by dividing the mass by the density (V = M/D). It can be difficult to directly memorize three formulas that are different but similar. However, there is no reason to memorize all three formulas. If students realize conceptually what is going on (that density is just the amount of matter for a given amount of space), they can easily figure out the formulas if they forget them.

This lesson builds on the concept of Relational Causality introduced in the last lesson by showing students that if just the mass or volume of an object could change, it would affect the relationship between them and the density would change.

Relating the Formulas to the Visual Models

This lesson also attempts to help students connect the mathematical formula for density with what is going on in the models of density that they considered in Lesson 1 and Lesson 2. Having a visual image of density helps to reinforce the mathematical concepts, and makes it more likely that students will develop an enduring concept of density as a relationship. It also increases the likelihood that they will be able to deduce the formulas on their own in the event that they forget them later. This is important because the formulas are difficult to remember without a deep understanding of what they mean to back them up. The surface similarities of the three formulas will instead cause them to blur together.