Density Curriculum

Section 2—Lesson 3: What Patterns Can Be Found Between Mass, Volume, and Density?

Background Information

Finding the Pattern in the Relationship Between Mass and Volume to Discover Density

This lesson focuses on helping students discover the pattern in the relationship between mass and volume. As one variable changes for a given substance, how does the other change? The next lesson covers what most units on density typically cover—information on how to calculate density. However, this lesson looks first at the patterns between mass, volume, and density for a given substance. Instead of stressing the use of formulas to calculate density, it emphasizes using the relationship between mass and volume to infer the intensive quantity of density. By focusing on this relationship, students develop a strong mental model and a strong relational understanding of density.

Scientists define density as the mass of a substance per unit of volume. It is the relationship between the mass (or weight) of one unit of a material and the volume of that one unit. Neither mass nor volume is sufficient to define density. Students need to reason about the relationship between mass and volume and understand that if the relationship between them changes, density will change. If you know the mass and volume of something, 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). There is no reason to memorize all three formulas. If you understand the relationships involved, you can easily figure them out.

It can be difficult to directly memorize three formulas that are different yet share similarities. The lesson attempts to help students to understand density conceptually—as the relationship between an object's mass and its volume—so they can generate the formulas themselves instead of just memorizing them.

Introducing the Concept of Relational Causality

This lesson formally introduces the concept of Relational Causality. By using social examples such as the ages of siblings, it presents to students the idea that some variables are either defined by or caused by a relationship between two other variables. From a developmental stance, late childhood and early adolescence are ideal times to introduce these concepts because students have an ability to hold more information in their heads and are able to think about relationships between multiple variables. Increasingly, research shows that when you control for how much information a student has to hold in his or her head (known as cognitive load), even young children are able to reason about relationships to a greater extent than earlier research suggested. Students will discover that Relational Causality is a powerful concept, not just for understanding density, but also for understanding other concepts in the world around them.

Relating the Patterns to the Visual Models

This lesson also attempts to have students connect the patterns that they find between mass, volume, and density to the models that they considered in Lesson 2 and Lesson 3. Keeping the visual images in mind will help to reinforce the concept of a mass-volume relationship as well as the mathematical concepts that they will learn later. This makes it more likely that students will develop an enduring concept of density as a relationship and that they will be able to deduce the formulas on their own in the event that they forget them later.

Prerequisite Understandings About the Nature of Matter

As discussed in the introduction, it is very important that your students have a firm understanding of the nature of matter before they attempt to learn about density. For this lesson, in addition to understanding the particulate nature of matter, they will need to know how to mass an object and how to figure out the volume of regularly and irregularly shaped objects.