Teaching Density in the Physics/Chemistry Lab, Step 1

by John R. Walkup, Ph,D.

I have worked with various other science professors at Fresno State University this past semester to prepare labs for Natural Science 1A. This course focuses on improving the science content knowledge of future K-12 teachers.

In this series of blogs, I will demonstrate how I created an standards-based science lab guided by the concept of Cognitive Rigor, which superposes Depth of Knowledge and Bloom's Revised Taxonomy.

Density

In science, a number of concepts arise immediately when we think of density:

1. Density is a property of a substance.
2. Density is a ratio between mass and volume.
3. The use of ratios to solve problems is called proportional reasoning.*
4. As a proportion, we can use density to predict how much mass a certain volume of a material contains.

Being a ratio, density shares many of the same characteristics as other ratios such as velocity, acceleration, fuel mileage, and so on. The real power in learning comes from learning overlying concepts/skills, such as the ratio and proportional reasoning, then relating how these overlying concepts relate to particular instances, such as density, velocity, fuel mileage, and so on.  Therefore, we will focus on the overlying concept of the ratio and how understanding the ratio helps us understand the concept of density.

The Standards

To teach a standards-based lesson, we first need to look at the standards.

Ratios

Density is a ratio between mass and volume, so students need a firm understanding of the concept of ratio to understand density. It turns out that the teaching of ratios is a typical middle school standard. In California, the Common Core Math Standards state the following:

• Use ratio and rate reasoning to solve real-world and mathematical problems. (6.RP.A.3)

I like the emphasis on solving real-world problems. We can do this in our lab with the right kind of culminating activity, which we will formulate in Step 2.

Density

No NGSS Performance Expectation or Disciplinary Core Idea (DCI) directly addresses the teaching of density. However, knowledge of density is assumed in the middle school Earth Systems Core Disciplinary Idea for ESS2.C: The Roles of Water in Earth’s Surface Processes. Specifically, middle school students studying earth systems will need to learn how:

• Variations in density due to variations in temperature and salinity drive a global pattern of interconnected ocean currents. (MS-ESS2-6) 

A middle school Performance Expectation for Matter and Its Interactions also relies on students understanding density:

• Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred. […] [Assessment is limited to analysis of the following properties: density, melting point, boiling point…] (MS-PS1-2)

To determine which grade in middle school these two standards target, we will need to go to specific state standards. In California, the DCI aligns to Grade 6, while the Performance Expectation aligns to Grade 7.

Mass

Much like density, the NGSS does not prescribe the teaching of mass either. Up through Grade 5 of the NGSS, the concept weight is mentioned in place of mass. Beginning in Grade 6, however, the concept of mass replaces weight. Therefore, an accurate definition of density should not be taught until Grade 6. However, to meet the NGSS, we will need to teach the concept of mass, a concept much tougher for students to understand than weight.

Do we teach mass in this lab, or in a previous classroom session? I think it would be best to teach it prior to this lab. We would need to use manipulatives of varying mass and have the students shake the objects back and forth across a table top, noting that the object with more mass is harder to shake back and forth. This resistance to change in motion is the essence of inertia; mass is the measure of inertia. (Note that mass scales don't really measure mass; rather, they indirectly measure the normal force required to support the object. So relying on mass scales to teach mass is fundamentally unsound.)

Volume

This lab will also focus heavily on volume. Elementary students can learn the general concept of volume; however, measuring volume is best left for middle school. In California, Grade 6 is the targeted grade level for this concept:

• Solve real-world and mathematical problems involving area, surface area, and volume. (6.G)

Statistical analysis

Because we are measuring a quantity (density) that should be fairly uniform for those items we plan to use in the lab, statistical variation is also a learning outcome. Grade 6 CCSS math standards include many references to statistical variability, such as the following:

• Summarize numerical data sets in relation to their context such as by (b) describing the nature of the attribute under investigation, including how it was measured and its units of measurement, (c) Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (6.SP.5. )

Oddly enough, distinguishing between accuracy and precision is not explicitly addressed in either the NGSS or CCSS standards; precision is only taught explicitly in high school in the Common Core. While I usually discourage teaching above grade level, I think the distinction between accuracy and precision is accessible to sixth graders.

Cross-cutting Concepts

I also find it instructive to examine the cross-cutting concepts in the NGSS for sixth grade. Since no specific DCI addresses density, then we are free to scan across all of the cross-cutting concepts in the NGSS. I found a few that our lab could potentially address:

• Scale/proportion/quantity 
• Structure and function
• Patterns
• Scientific knowledge assures an order and consistency in natural systems

Summary 

Based on the above, the teaching of density is appropriate for either Grades 6 or 7.

This lab focuses most attention on teaching ratios, with conceptual understanding of density targeted as a byproduct of the lesson. (A followup lesson could focus answering the formative question “How do we measure the density of liquids and gases?”)

In my next blog article, I will focus attention on using Depth of Knowledge to establish a culminating activity. Those interested in Project-Based Learning (PBL) may find it especially interesting.

* For a recent article on proportional reasoning, see http://robomatter.com/blog-proportional-reasoning/

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Seeking training at your school or district centered on Cognitive Rigor or Depth of Knowledge?  Call me at (559) 903-4014 or email me at jwalkup@standardsco.com. 

We will discuss ways in which I can help boost student engagement and deep thinking in your classrooms. I offer workshops, follow-up classroom observation/coaching, and curriculum analysis to anywhere in the country (and even internationally).