In the EOC Chemistry exam, there's a question that involves the relationship between temperature and volume of an ideal gas. Investigation into this relationship would be a good way of opening up discussion on Charles's Law, Boyle's Law, and the Ideal Gas Law.
Identification of Task
I would begin this ADI by reviewing definitions of volume and temperature and how they're measured. This would be designed to give students ideas for their experimental design. I would also ensure that students are familiar with the SI units involved. I would also make sure students understand the difference between real gases and ideal gases.
Generation of Data:
At this point I would divide the students into three or four groups. Each group would be assigned a specific aspect of the ideal gas law. For example, one group might be tasked with studying the difference between temperature and volume, while another group might examine the relationship between pressure and volume. A third group could be tasked with examining the relationship between moles and volume. Each of these three groups would be given a good bit of time in class to discuss ways to explore these relationships. Hopefully the students will be able to design experiments that remain within the realm of practicality for the classroom setting. If not, I will be moving from group to group and will be able to guide the students in the right direction. Once they come up with a solid experimental design, I will provide the materials they need (which I will hopefully have, provided I am able to successfully guide their experimental design) and they can get going.
Production of Tentative Argument:
From here, I would have students sit down in their groups and collaboratively summarize their experimental results and provide conclusions derived from the data they obtained. They would also discuss the sources of error for their experiments and discuss how real gas behavior might make experimental data more difficult to gather. I will also make sure that each student has their own copy of their work.
Once each group has been given enough time to draw conclusions and discuss their results, I'll split each group up and form new heterogeneous groups such that each new group has one or members of each old group. Within each group, each member will be required to present their own data and how they found it. If possible, other group members are encouraged to ask questions regarding their method or their results. Each group is also required to come up with one way they could improve upon their experiment (since this part is hypothetical, there is little to no need to bring in resource constraints).
Back in large group, we will together examine the relationships between all of the above properties, hopefully deriving something similar to the ideal gas law. We could also try and derive R from all the values they got, but given experimental constraints as well as the deviation of real gases from ideal gas behavior, it may be an exercise in futility. We could also use the volume temperature relationship to derive absolute zero, but again, given the behavior of real gases, it may not yield much. That said, once ideal gases are covered, this experiment could be brought up again, and the inaccuracies in our data could be used to strengthen students' understanding of real and ideal gases.