Students will consider the impact of significant digits in anticipation of a final scientific exploration in this unit.

Students attend to precision and strive to report their results to the greatest precision allowed by their instruments.

10 minutes

We begin a 2-3 day investigation trying to establish the specific heats of a variety of rocks. To get students thinking about the solution to this question, I provide a hot rock warmup question. This pencil-and-paper exercise mimics the calculation each student will need to perform in the upcoming investigation.

I expect this to be a straightforward problem whose only real value is to contextualize the lab work. Though straightforward, I allow plenty of time for students to complete this and spend a few minutes showing a solution at the end of this section. It is critical to the success of the investigation that each student understand the solution or, at least, has a model solution in their notebook.

The point of this warmup is to remove any mystery from the computational part of the upcoming investigation.

10 minutes

Before getting underway with our lab work, I want to introduce the concept of significant figures to my students. Historically, this is often met with resistance and deeply resented. . . to many students the idea of limiting one's answer is counter-intuitive to the idea of precision!

I break the issue into a few segments and hope to minimize confusion (while building buy-in) by staging the ideas in smaller chunks. Today's segment is limited to the rationale for using "sig figs": the fact that scientists (as opposed to mathematicians) use instruments whose precision is inherently limited.

The goal here is to get students to recognize that each measuring instrument has a smallest unit of measure that it can make. Using images of samples of measuring tools on the Smartboard, I present some thoughts about a few common instruments. This is a very teacher-driven section; I use these examples as a way of making the content (that each instrument has a limited precision) concrete. I focus on one instrument at a time and look carefully at the smallest increment of measure that each has to offer. Once that is established, I can add in the idea of "judgment:" one is allowed to split that smallest division in half with exceptions made for obvious (or large) gaps.

When this segment of the lesson is completed, I give the students some time to look at actual instruments to determine their limitations.

15 minutes

To focus the conversation on instrument precision, I direct students to look at a variety of tools and determine the smallest measurement that can be discriminated by them. Items include beakers, meter sticks, graduated cylinders, mass scales, and stopwatches. Students work in small teams, moving from item to item around the room, to determine the smallest measurement that can be made by each AND whether there is room for judgment (digital devices typically remove judgment from the user). This is a relatively casual time - students are not being assessed - though they are expected to report out on what they found in a few minutes. After 5-10 minutes, I ask students to return to their seats for a short, wrap-up discussion. During this time, I see if there's consensus on the precision of each instrument and reinforce the idea that we can report to within one-half of the smallest increment.

To follow-up, I assign two videos to watch for homework. They are "home-brew" Educreations videos that identify the rules for sig figs and discuss the difficulties with zeroes. Here is the link to the rules. Here is the link to the zeroes discussion. I also make available a review of the rationale for using sig figs. Students are told that they will lead a discussion on the content of the videos in the next class. By following the activity with this assignment, I hope students can see the connection between classwork and homework and appreciate the development of the sig figs idea over time.

Historically, I have found that the parts of the discussion of significant digits (rationale based on instrument precision, rules, and zeroes) can get conflated into a confusing blend of high concept and minutiae, with student resentment rising with confusion. By limiting today's discussion to precision, I hope to provide a baseline motivation for using sig figs. By delaying the discussion of the rules and the ambiguities of zeroes, I hope to achieve clarity.

15 minutes

I share the goals of this investigation by handing out this hot rocks lab prompt that will guide this three-day activity. As the mathematics of the problem have been completed earlier in the period, the discussion here focuses on lab techniques and the requirement of generating a distinct secondary question.

My pedagogical goals are threefold:

a) I want to make sure students understand some safety issues inherent in handling heated rocks.

b) I want to open students' minds to the idea that, while investigating, related questions will naturally arise . . . and students should record those questions as possibilities to explore.

c) I want to inform students that this investigation culminates with a team presentation based on their pursuit of a secondary question.

30 minutes

Students begin to collect data, generate secondary questions, and contribute to a common database of results. There are a small number of rocks (6 to 9) available, each named after a famous scientist (names are written on the rock in permanent marker).

As teams collect data and empirically determine the specific heat of their sample rock, they return their rock to me for re-heating and add the value to a common spreadsheet, which will be electronically shared for use by all students at the end of the investigation.

Rocks are heated in a small toaster oven and are randomly assigned to teams of students as they indicate their readiness.

Any given team will test most of the rocks throughout this investigation but, by chance, they'll test some more than others. The entire class, however, will wind up generating 8-12 samples calculations of the specific heat for each rock. By sharing the data set with all, I can reduce the student desire to collect data on a specific rock - which might entail needless waiting around - and provide students only with rocks whose initial temperatures are substantially above room temperature. This not only increases student time-on-task but increases the reliability of the trials; relatively cool rocks have little energy to deliver to the water bath and errors are far more likely to creep in.

The rocks heat in the toaster oven for some time before I provide them to student teams. I use tongs to extract the rocks and place them on a small paper plate for transport back to the lab benches. There, a student uses an infrared thermometer to measure the temperature of the rock just before it enters the water bath. Students return the cool, wet rocks to me for re-heating.

Students use Vernier LabQuest handheld data collectors, along with a Vernier temperature probe, to track the temperature of the water sample throughout a trial. Here's a sample graph that students should be able to generate:

As this is the first day of a multi-day investigation, I allow students to collect data until there's about five minutes remaining. At that time, we clean up and end class without much discussion; we will revisit this idea and this work in the next two lessons.