Junior high students are required to find the mathematical expression or equation to describe a given pattern. Guess and check is not an efficient method for figuring out the expressions or ‘rules’ for a given pattern. When Galileo worked with number sequences, he noticed patterns within the patterns and used those observations to determine the constant acceleration of falling objects. During this session, participants will use the power of observing patterns, first and second differences within responding data, to discover the code for the one-dimensional matrices that efficiently produce the equation (function) that models the data. This historical and creative approach will illustrate many connections between junior high and senior high mathematics learning outcomes regarding sequences, functions (linear, quadratic, cubic, and other), and introductory matrices.