Box Folding: Questions

Main Page | Folding Boxes | Gathering Data | Organizing DataUsing the AppletQuestions | Formulas and Graphs

Here are some questions for students in different classes.

General questions
• How can you be convinced that you have found the biggest possible volume?
• If you're convinced that you've found it for a 22 x 19 piece of grid paper, how would you find it for an 8.5" x 11" piece of letter paper? Put the data in a spreadsheet and check the answer using the box folding applet for 8.5 x 11.
Algebra questions
• Think of the height as a variable "x", and express the volume of the box made from 22x18 grid paper in terms of x.
• What does the graph of equation look like? Graph it using a graphing calculator. For help, there is a page with the output.
• Explain what is happening with the boxes when the graph dips below the x-axis.
Pre-calculus questions
• Take the equation y = 4x3 - 80x2 + 396x  and find the local maxima betwen 0 and 9.
• How does this relate to the volume of the boxes?
• Come up with a general formula for the volume of a box created in this way, given L (the length of the original rectangle) and W (the width of the original rectangle).