Have you ever wondered how Georg Pick discovered his formula for the area of a polygon drawn on dot paper? This activity will lead students through a discovery of his formula.
It is designed to be completed on square dot paper, an 11 by 11 geoboard, or a similar product.
Students begin by constructing several polygons that hold an area of 6. Then notice that they can build different polygons, but the number of boundary points and interior points change.
As students build additional shapes with different areas, they collect data, graph it and use the graphs to write equations of linear graphs. This leads to discovering Pick's Formula.
By the conclusion of the activity students have become very familiar with the formula and the conditions it describes about the polygon.
The lesson could be projected on a whiteboard, step by step, since each lesson slide is printed in large, easily visible type.
Students need to know how to write an equation of a linear function based upon its y-intercept and its slope.