Predicting Optimization

Overview

This activity should be done after you have discussed the idea of optimization in your classroom. To do this you may have looked at several examples of optimization such as the traveling salesman and/or the sweaty elevator, but your students should have a relatively good understanding of optimization.

Throughout this activity students will predict and then observe the optimization positions of different combination of electrons and charged walls. Students will record their predictions as well as their observations and will write an explanation in the end.

Preparation and Materials

Teachers should have access to a computer with the JAVA beta version of SimSurface installed and a projector to display the screen to the class.

You can use the predicting worksheet found on this website or create something similar to give to your students so that they can record their predictions and observations throughout the exploration.

Objectives

Students will be able to:

predict optimization arrangements for electrons in a charged box.
manipulate the settings for a program that generates random electron arrangements.
scientifically record their predictions and observations.
give written justification for the results of a scientific experiment.

Activities

Distribute a copy of the worksheet to the class. Explain to the students that they will be scientists today and discuss the importance of accurate record keeping in science.
Open SimSurface on the computer connected to the projector and explain the program and the settings to the students (If you are unfamiliar yourself, you should see the introduction materials.)
Explain to the students that you will be testing the optimization arrangement of several numbers of electrons in a charged box. The students will be expected to predict and draw the arrangement in the Prediction box, then perform the annealing and draw the observed arrangement in the Observation box. They should also record the final energy once the annealing is complete.
You will perform the first observation as a class, so have each student draw a prediction for the arrangement of one electron in a box with equally charged walls. Then simulate the annealing and have the students draw the observed arrangement.
Now you have the option of testing all of the arrangements as a class with the teacher or a student at the "driver seat" (adjusting the settings on the computer attached to the projector), or you may send the students off to work in groups at their own computers. Remind the students to make and record a prediction before they simulate the annealing for each scenario.

Discussion of Observations

Open a classroom discussion about whether the students were successful in predicting the optimization arrangments or not. Check to see if all groups found the same optimization arrangements? If they were different, which one actually yielded a lower energy? Talk about how they made their predictions when they were right and what they thought when they were wrong. Did some students think it was a mistake? Did they re-run the annealing process for this arrangement? Did they perform multiple annealing runs for any of the arrangements? For all of them?

Extension

You may want to have students write a paragraph or a page summary of the activity and their results addressing why they were or were not correct in their predictions and what that means for science.

You could encourage the students to try several additional numbers of electrons and to draw those pictures as well.

You may also encourage the students to change the charges on the walls and predict how that would effect the previously observed arrangements. New results should also be observed and recorded (in this case students will also need to make note of what charges they used): A good example is to choose 7 randomized charges, and set the initial wall charges to be 40. Have students predict and observe, as above. They should end up with a hexagonal orientation of the electrons with a high degree of symmetry. Repeat for wall charges 30, 20, 10. Your students should finish the activity with the impression that in science, while we may feel very certain about our predictions, we never actually know what will happen until we try. This can lead into a good discussion of theory versus experiment.