Density Curriculum

Section 1—Lesson 1: How Can Objects of the Same Volume Differ in Mass?

Background Information

Realizing that Density Exists

The purpose of this lesson is to help students realize that density exists. It accounts for differences between masses of different kinds of materials when volume is held constant. Density is an intensive quantity. It is called intensive because it cannot be directly measured. It is determined by the relationship between mass and volume, a quantity because it can be calculated mathematically. This means that you can't measure it directly. It must be inferred. This is different from other types of measurements that students may be familiar with, such as measurements of mass, volume and weight, which are extensive quantities.

We often miss non-obvious variables and focus on those that more easily grab our attention. This lesson controls for volume so that differences in mass become more obvious. The lesson uses two metal cylinders of the same volume, but with noticeably different masses. As students reach out to grasp the two cylinders in this lesson, observe the amount of arm drop that they experience. This reveals the discrepancy between their expectations for how much mass each cylinder should have and the actual mass of each cylinder.

Mental Models of Density

This lesson attempts to help students develop a mental model of density—to realize that something is going on that they cannot see to account for differences between materials. While many density curricula stress density as an "unchanging property of the material," this module uses these terms lightly. Instead, it stresses the relationship between mass and volume.

Many students end up drawing crowdedness models. This is particularly common in classes where students have studied the nature of matter. Crowdedness models usually depict a certain number of dots or particles in a given amount of space. They connect nicely with density models in population studies. They capture the concept of the amount of stuff in a given amount of space nicely, and fit with the second cause of density at the micro-level—the strength and structure of the atomic and molecular bonds (studied in Section 3).

Other students explain the difference between the cylinders as having to do with one being hollow. This is especially common in classes where students do not have a strong background in the nature of matter. As students will learn, a hollow object is essentially a case of mixed density—the density of the surrounding material and the density of the air inside it.