22. The Box Problem

Students build open top rectangular boxes from a standard sheet of paper by cutting congruent squares from each corner. Data is collected that pairs the length of the side of the cut out square with the volume of the resulting box. To describe a clear pattern shown in the scatter plot, students develop a function through analysis of the box design. Based on this function, the length of the side of the square is determined that will create a box of maximum volume, and two squares that will produce a box of equal volume.

Technology: Graphing calculator, Geometer’s Sketchpad sketch, Animation (from studio video) showing 3 different versions of how to make a box.

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• 3D Animation