At the beginning of this lesson, I want students to review the work they did with the calorimetry simulation in the last class. I have two goals here:
1) To have students articulate the basic observation that the equilibrium temperature falls somewhere between the two initial temperatures and
2) To have students consider the role that energy conservation plays in this process.
I'll use these thermal energy prompts to quickly get these thoughts flowing before moving on to the task in the next section. I provide a 90-second opportunity for students to write in their notebooks any repsonses they have to these two prompts.
The task of inducing a predictive equation for the equilibrium temperature is a very difficult one for high school students. With the right scaffolding, however, many can be successful.
The point of this part of the lesson is to provide student groups (same groups as in the previous lesson) time to re-visit their thinking about the Big Question ("Can we, from our collected data, background knowledge, and our developed intuition, create an equation that allows us to predict the final, equilibrium temperature?"), now that we've been explicit about the role of energy conservation.
I share this equilibrium temperature task (a re-focus of our Big Question) with students and ask them to enhance their thinking from the previous lesson. As resources, they have their data from the investigation, the hint about the conservation of energy, and the time to talk to one another and myself as they try to manufacture a working formula.
Students are not using computers at this time, though I make the simulation available on the projected Smart Board and encourage student groups to test their predictions with it. Specifically, when a team thinks it has a solution, I ask them to use their expression to compute the equilibrium temperature based on a new set of self-selected inputs (masses of water and hot object, the initial temperatures, and the specific heats of the materials), then input those values into the simulator to check their prediction. As the only computer available today is connected to the Smart Board, there's a bit of public drama with the test!
Though not every group will derive the correct expression, there is an opportunity for all and some positive tension about their outcomes.
My role during this time is to remind students about the power of the conservation of energy law. Without that fact, their work would be much more difficult.
In this part of the lesson, I ask a couple of successful student groups to come to the board to show their versions of the answer to the Big Question.
Here's a sample student result on the Smartboard (with a prediction for a novel situation, eventually confirmed by the simulator):
Here's a sample student response of the final question from the worksheet they have used to explore this phenomenon. Though there are some missing steps, one can see that this student was able to express the exchange of energy first in terms of numeric data:
As this is an exploratory exercise and somewhat informal, this kind of thinking and documentation is to be expected:
In the event that no group has a satisfactory response, I can provide this conservation of energy argument, which is the answer to our Big Question.
To formalize our learning about this, I distribute some thermal equilibrium notes. All students are thus supplied with the background necessary to predict equilibrium temperatures.
As a prelude to some guided practice, I work though one problem at the board, based on a common question from the simulation handout, to show how one would solve problems of these types. For some students, it is at this point that they will truly recognize the meaning of the equilibrium temperature - the common final temperature of the mixture.
For practice, I distribute a set of advanced calorimetry questions and ask students to work the odd-numbered problems first. These problems allow students the opportunity to practice the simplest versions of these questions - where the impact of the container is ignored. I encourage my students to compare their answers with one another and review their results with me. In this way, the learning is very self-paced and the class need not stop to review problems. Should I note a common misunderstanding, however, I do stop the activity and address the issue at the board. This is a key to formative assessment - precise and timely feedback based on ongoing observation of student work.
As students complete the odd-numbered questions, I ask them to consider the differences in the even-numbered questions. Here the impact of the containers must be considered. As we have done much thinking along these lines already, it is a simple extension to have THREE TERMS instead of just two in the conservation of energy equation. We can assume that the container and the water will share both initial and final temperatures.
This conversation happens in small groups and multiple times (for me) over the course of this practice time. It is important that the groups are ready for the conversation, a readiness that occurs once they've had some success with the simplest problems. I have found that introducing the extension too early can upset the sense of accomplishment. This is an example of "differentiation by readiness," as individual students work on the problems which are most relevant and valuable. In the next lesson, there will be some additional instruction that will bring all students to a common level of understanding.
As the time for guided practice comes to a close, I hand out our next assignment called calorimetry summary questions. I give my students a week to complete these problems, encourage them to start early, and suggest that they seek assistance from me should they get stuck.
As a final assessment in this lesson, I'll have students take an open notes 1-question calorimetry quiz.
I use this technique frequently and my students quickly come to expect it and, often, request it!! There are some interesting elements to this which I'll share here:
1) Students get to choose the lowest score out of 20 that they'd like to have count. If a student does not meet their personal threshold, I'll toss out the grade and give them an "exemption" in the grade book. This tends to diminish anxiety about "bombing the quiz" while simultaneously energizing the guided practice - knowing it's possible to get a 20/20 later in class provides an incentive for focused practice.
2) The single question is a simple variation on the kinds of problems we're doing on that day. In other words, the quiz question will mirror the guided practice questions.
3) It's remarkably quick to assess and I'll often have all quizzes graded before the end of class and can share the correct answer before students leave.
My goals are to collect a formative assessment of the group (how many showed mastery of this idea?) before the next class, to stimulate a focused guided practice session, and to do so with a very quick turnaround time for grading. The exercise, in no way, should feel like the traditional "pop quiz" which is often designed to catch students "napping." This is designed to catch students succeeding!