Chess and Grains: Modeling Exponential Growth with a Spreadsheet

This GeoGebra example demonstrates the classic 'chessboard and grains' problem: place one grain on the first square, two on the second, four on the third, and so on, doubling each time, to observe how the total number of grains grows exponentially. The core mathematical concepts include exponential functions, geometric series summation, and the idea of limits. The construction uses GeoGebra's spreadsheet view to input formulas for the number of grains per square and the cumulative total, then visualizes the growth with a scatter plot or line chart. A slider can be added to adjust the number of squares and dynamically explore the total. This is suitable for middle school, high school, or introductory college mathematics, helping students understand exponential growth, series, and orders of magnitude in real-world contexts.