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Using the Finite Differences Method to Define a Function, Grades 7 – 12

With interlocking cubes, participants will build three-dimensional constructions following a growing pattern and record the number of blocks needed for each iteration. Participants will create a difference table to find the degree of the function that describes the growing pattern. Matching this table with a difference table for the standard form for that degree equation allows us to solve for the coefficients, beginning with the highest power of the function. We will do linear, quadratic, and cubic functions.