Data-Driven Laboratory Activities: Density


Thanks again for spending some time with me in this blog. Over the course of my posts, I will share some ideas (and hoping for feedback) about data-driven instruction in science. So what the heck do I mean when I say "data-driven"?  Or you might be asking, isn't all science instruction data-driven? When posting about data-driven instruction, I will share examples about how laboratory activities can be used as the starting point for scientific model development rather than as the endpoint, or verification, of concepts presented in lecture. As I mentioned in my introductory post, the goal of data-driven instruction is to present students with a phenomena that will allow them to construct scientific meaning.

I've chosen to present in my first post a topic you likely discuss as an introductory course concept: density. The idea of density may seem like a simple and straightforward relationship to present in lecture, complete with the "density triangle" for problem solving. But could this actually be made into a data-driven experience, based on student reasoning?

With just a few different size cylinders of metal, this becomes an interesting challenge for students. For context, I would present this lab to students after discussion of the basic ideas of mass and volume. I usually like to use a variety of different size rods of copper and aluminum. After presenting the samples to the class for observations, ask if there is some type of relationship that might exist between the mass, or amount of 'stuff', in an object and the volume, or amount of space the 'stuff' takes up, for the cylinder under observation? What kind of measurements are required to show a relationship?

When ready to begin, measuring the amount of 'stuff' - the mass - in the cylinder is usually the easy part. Just use a balance! Volume is a little trickier, but students usually come up with ideas related to measuring dimensions and calculating volume of a cylinder, or using graduated cylinders and displacement of water (I usually keep a few rulers and graduated cylinders lying around to spur ideas). Once it is determined what data need to be collected, students go to work measuring the mass and volume of a variety of sizes of the cylinders and rectangular prisms available of the same metal.

After data are collected, students then construct a graph of their results. Sometimes I tell them to put mass on the vertical axis, other times I let them decide (Note: Discussing why this does or does not matter as lab results are shared is instructive in itself!). Once graphs are constructed, student groups usually present their results on whiteboards. Linear results are generally seen, and if two different metals are used, each metal displays a different mass/volume slope. The linearity of the data leads to a discussion of linear fit, the significance of a y-intercept, and the physical meaning of the slope of the best fit line. Eventually students conclude that the slope is the relationship between the metal's mass and volume, the y-intercept should be zero (zero volume should have zero mass), and that a general equation equation of y = mx + b can be more meaningfully written as  mass = (slope of the line) x (volume).  What is created is a data-based mathematical model describing the relationship between mass and volume.

Just what then is slope? Ensuing discussion can focus on a multiplicity of ideas depending on the direction the students take it (or the instructor guides it):

  • the units of the slope (amount of mass for every one unit of volume),
  • the observation that objects of a certain metal can have a variety of masses and volumes but the slope is always the same, 
  • comparing the mass-volume slopes of two different metals, and/or
  • discussing what does a "steeper slope" mean

Ultimately, the discussion should wrap up with the students concluding that the slope of the line for a mass vs. volume graph represents the density of a substance. Follow up work with density can involve the equation for the line:  mass = (slope) x (volume), which can now be re-written:  mass = (density) x (volume). As opposed to the standard definition d = m/v, the equation m = d x v can be viewed as stressing the functional relationship between mass and volume.