math 2015
Shodor > SUCCEED > Workshops > Archive > math 2015

Designed for 6th to 8th grade students, the focus of this workshop was to explore different mathematical functions and bases using computational applications from Shodor’s Interactivate website. The workshop began by teaching the students how to count numbers in different bases with an introduction of binary: a base two system. The students learned how to express various numbers in the binary system by using modular arithmetic, a system of mathematics which takes a divisor input and gives a remainder output. Using modular arithmetic, students were given one, two, or three digit numbers to express in binary. Another focus of the class was that of functions, which the students explored through a number of Shodor’s Interactive programs. One such program was “Caesar’s Cipher,” an application which used a mathematical function to convert given text into a mess of incomprehensible letters. However, if one knew the mathematical function used, in this case a linear equation with a coefficient and a constant, one could easily decrypt the jumbled letters and find the original message. Letters “a” to “z” in this application were labeled 0 – 25 respectively. The students used this application to encrypt messages, determining the mathematical function themselves; to input text and determine the function by its given output; and to take a given output, the mathematical function provided, and determine the input. Finally, students explored the practice of estimation using Shodor’s Estimator program. This program gave the students various problems such as determining the area of a shape, the length of a curved line, or the number of particles on the screen. With the minimal amount of information given to solve these problems, students were encouraged to estimate the answers, helping them hone their innate mathematical abilities. Students were also encouraged to develop algorithms or methods to help them solve problems of different types. The students then applied these methods to compare two different problems and determine which had the greater area, length, or number of particles. Students were encouraged to work together to solve these problems, sharing their methods with one another, to help each other gain a deeper understanding of the material.