Other Lesson ideas using SimSurface

Science 7

Observation and Record keeping

In order to meet the curriculum objective "Observe and accurately record objects and events by counting, comparing, estimating, and measuring" a class might be directed to conduct several annealings, varying whatever conditions they choose (for example, changing the number of charges or the charge on the walls). Annealing is the general term applied to the process a substance goes through as it hardens, or "freezes" into a solid state. The recording of observations could be accomplished in journal style with a notebook or a word processor document. Students should understand that both qualitative and quantitative observations should be recorded. Much of the process of recording quantitative observations is facilitated by features of SimSurface. It is important, however, that the students also "describe what they see" (for example, "higher charge on the walls makes the charges gather at the center" or "with more than x charges, the final pattern is less regular" or something as simple as "for each particular number of charges, the final patterns are almost always the same"). If they notice something irregular, they could attempt to reproduce the irregularity, and perhaps attempt to guess what caused the irregularity based on their previous observations. The teacher might suggest to them a way to test their conjectures. They can

observe the annealed pattern of, say, ten runs each of 1 charge, then 2 charges, etc. and try to come up with a general pattern
use the tool palette to fix the locations of some number of charges, randomize the positions of the rest, and see what happens. Can they predict the final configuration based on the initial configuration?
measure the distances between adjacent charges in some lattice and find the mean, median, and range of this data
move the charges around after the annealing (or before the annealing) to see if they can achieve a lower energy. How much lower? What makes the energy lower?

We again emphasize the fact that the point is not to give the students a detailed "behavior prescription." They should be encouraged to branch out on their own and pursue their own questions. In the real world, major discoveries are often made because some individual looked at a problem in a different way. (In fact, people described as "smart" or "brilliant" are frequently people who are, above all else, "observant.") The teacher's role here is not to tell the students what they should be thinking, but to help the students develop good observation and record keeping skills. Carefully recorded observations are frequently the key to solving extremely complex mysteries. Freedom to explore is often the key to sparking and retaining students' interest. The ideal lesson plan will embody both of these qualities.

Graphing Data

Here are some activities demonstrating a method (electronic) of graphing data:

Have the students complete an annealing and copy the data from the run into some program capable of graphing the data. The data file contains a listing of the number of charges, the temperature, the step size, and the energy for each iteration. Use the graphing feature of the spreadsheet to graph the energy as a function of time.
Now have the students change something (for example, the number of charges, the charges on the walls, etc) and anneal again. Save and graph the data as before. Now plot both graphs on the same set of axes. (What they observe will depend, of course, on what they changed. They may get an almost identical graph, or something slightly or radically different.)
If the students are letting the program anneal automatically, the temperature and the step size will decrease according to a preset rule. If the students graph these quantities they should notice that nothing they do (short of actually interfering while the annealing is in progress) changes this graph.
Depending on the level of the students, it may be instructive to have them graph the number of charges as a function of time (supposing that they didn't add or delete any charges as they went, this will be a flat line).
To reinforce understanding (or just for fun) the students might want to "interfere" with the annealing and see the result on the graph. For example, if charges are added during the process, they can observe a corresponding energy spike on the iteration at which this happened.

Tabular Representation of Data

Have the students organize the data saved from a run in various types of tables. A table showing wall charge, number of charges, cooling rate and iterations per temperature, and the final energy might be instructive.