# SUCCEED

Math Explorations A 1998
Shodor > SUCCEED > Workshops > Archive > Math Explorations A 1998

Today's session began outside with an engaging activity. Bob2 initiated the activity by coughing on his hand and tapping people on the shoulder (or patting them on the back). Next, he handed out cards with "infected" or "safe" written on them. The students that had the "infected" cards took more cards and handed them out to people. They did this several times until most of the people were sick. Bob2 ended the activity and brought the students inside, telling them that they would model what they had just done on the computer.

Bob2 first told everyone to open a program called STELLA. He told them how to set up three boxes; one for the susceptible population, another for the infected population, and a final one for the recovered population. Then the students set up objects that would move people from one group to the next. He then listed an infection rate and a recovery rate that would simulate the 48 hour flu. Once all the items were set up the explorers decided which objects would effect the others. Finally, the students applied equations to the model and ran the finished product.

Next the students moved on to Geometry. Maria started by discussing the concept of dimensions. She spoke about how mathematicians often use the concept of points, lines and planes. She asked how many dimensions each of these elements had, and how they came to that conclusion. The hardest thing for the students to figure out was the concept of a point, because it has no dimensions. Once they had a good understanding of these concepts, Maria took out some objects and asked people what shape things would make if they were cut by a plane at different places. She used the surface of a bowl of water to help demonstrate why different shapes were made.

This led into the next topic: conics. Anne led this exploration into how you can intersect a plane with two cones. She used styrofoam to illustrate the shapes made. She told the class that there were four general shapes; parabolas, hyperbolas, circles and elipses. She then handed out a piece of paper to each student and told them to put a dot somewhere along the center line. She then told everyone to fold the paper lots of times so that the bottom of the paper touched the dot. When everyone had finished, they noticed that the lines created a curved area. Anne explained that the shape was a parabola. She elaborated that the dot was called a focus, and the bottom of the paper was called a directrix. Anne then explained that every point on the line they had formed was the same distance from the directrix as the focus. Next she showed the class a hyperbola that she had made using a similar method, but using a circle instead of a line. Finally she turned the students loose on a java program that could draw conics by changing the focus and changing the width of a circle.

To finish off the day the students played with a mobius strip. They first tried to count the sides and edges to discover there was only one of each. The explorers decided that the object was not a paradox, because there was no contradiction. Maria comented that the word "paradox" can mean different things for different people. The class also tried cutting the mobius strip in half, and discovered that it just formed another, larger loop. They cut that in half and discovered that they did get two strips, but they were interlocked. The explorers contemplated this as they wrote their reports to Richard.