Today's class was filled with lots of fun and interesting mathematics concepts. Jon started students out with an activity related to the Chaos Game on the interactivate site. The activity was based on connecting three points with the help of the roll of a dice (the number you get from the roll is converted into a measurement, which allows the student to place a point in its appropiate place). The final outcome of all of the points is a triangle. After the activity, the class went to play the real Choas Game to test their experimental data. The Chaos Game is a game in which a given probability of the amount of color you will get in your triangle can be changed to suit your curiosity. Although you can change the probability, the class kept theirs at one because the probability of getting a certain number on a dice is one out of six (1/6). Real scientists experiment with numbers, so the class used their science skills by changing the probability of some of the colors.
Next, they went to the Sierpinski's Triangle site, where they can use the area of a triangle to find a pattern of how the area is derived during each calculation. The triangle that the class worked with had a pattern of 3/4, which means that you multiply the area by 3/4 each time to get the new area. Jon asked the class this question: "If the pattern kept performing, would the triangle eventually lose all area?" The class was split when it came to this question, so Jon gave examples to help everyone's decision.
Last on today's class agenda is the Mandlebrot Set. This is a fractal that allows you to test certain perspectives of images, while you interpret mathematical equations/concepts at the same time. Allyson used an example of the branches on a tree to help model a certain set. The class was then challenged to find an image that has thirteen extensions or branches coming from it. After this activity, the students learned that all fractals are forms of Self Similarity, and that the function of fractals are called Iterators.
Just as Jon had promised, the class was allowed to finish the problem about the area of the triangle. To model this, he took the class to Microsoft Excel® to model a bank loan situation, where you would have to eventually run out of money. After experimenting with different equations, they found one that was the most appropriate (in other words, we were able to let the numerical value of the money go to less than one cent, which is zero money).