GPGC Weekly Class Report

6-22-2001 thru 6-28-2001

The third week included the introduction of several formulas and activities that blended the ancient world with the modern one. Communication was a key word that we focused in on this week. The students were given a process skills test that had paragraphs explaining many types of experiments. The students had to interpret graphs that depicted the data gathered from these experiments. They learned that the not only the gathering of data but the visual representation of this data many times helps us to see the data from a different perspective and therefore helps us to formulate a hypothesis or a conclusion about our hypothesis.

We discussed the various formulas for volume of different shapes and we talked about Archimedes and the important role he played in these formulae. The students were then given a handout activity that told the story of Hannibal and his impossible task of crossing the Alps and his surprise attack on the Romans who lay waiting for him in the valley. The students were given the scenario of 12 Roman scouts whose remains were found part way up on the Alps. All 12 of these scouts had the same number of strange colored stones or pebbles in a pouch that hung from their waste. It appeared to the archeologists that the scouts had been on their way back down the Alps to the Roman camp when they must have been ambushed by the Carthaginian soldiers of Hannibal. These scouts were trying to communicate something to the Romans but were unable to complete their mission. The students had to figure out what the strange stones were. The clues were given in the story that they read about Hannibal. Through their own discussions and discoveries they found out that the stones colored so strange were really just a tally of the enemy soldiers that they had seen on the mountain. They were on their way down the mountain to warn the Romans that Hannibal and his men were coming across the mountains and were going to attack. Like all good scouts they used a counting system to let their soldiers know how many were coming. The students not only were able to figure out what the stones represented, but they discovered the place value of each color or shape. Talk about communication. They even communicated through time. The students also compared this system to the abacus. What link does this story and activity have to do with Archimedes and the formulae of volume? Well, you see Hannibal attacked a small village in Spain that was under the protection of Rome. There had also been a treaty signed between Carthage and Rome that indicated neither would attack a city under the other’s protection. Hannibal attacked this village of Saguntum and ignored the treaty, thus starting the Second Punic War. During this war as the Romans slowly started to prevail, the Romans were conquering many lands. Sicily was one of these lands and the town of Syracuse in particular. After the capture of Syracuse during the Second Punic War, Archimedes was killed by a Roman soldier who found him drawing a mathematical diagram in the sand. It is said that Archimedes was so absorbed in calculation that he offended the intruder merely by remarking, “Do not disturb my diagrams.” I wonder what he was drawing in the sand?

The students also used this same concept to decipher a Japanese Code from WWII.

Here a group examine the strange artifacts found on one of the Roman scouts. NOTE: Common objects of marbles and poker chips were substituted for the real pebbles found on the 12 scouts.