Box Folding: An Exercise in Prediction, Measurement, and Analysis
by George Reese with an applet by Kristen Carvell

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

Introduction:
Many students at the middle and high school level experience difficulty understand the concept of volume. This venerable activity* has been used for decades
without technology to convey the conter-intuitive changes that occur in volume when folding boxes. With the addtion of the simulation tool, a java applet, and spreadsheets, we can collect more data and explore patterns in the data more easily.

Materials:
• colored grid paper(You will have to adjust the page settings to get the paper to print as a grid of square centimeters.)
• rulers
• scissors
• puffed rice or other space filling material
• Graphing calculator (optional)
Goals connected to learning standards: Students should be able to
• select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision (PSSM)
• Apply appropriate techniques, tools, and formulas to determine measurements (PSSM)
• understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders (PSSM)
Directions:
1. Take a piece of the grid paper and cut the blank strips from around the edges so that only the grid itself remains.
2. Next, cut away squares from each of the four corners.You may cut away a single square from each corner, or, say, a square that is a 3x3 square from each corner. Have other people in your group cut away squares of different sizes from the corners. For example, the grid with 3x3 squares and 6x6 squares cut away will look like those below.

3.  Grid paper with 3x3 squares cut away Grid paper with 6x6 squares cut away

4. Fold the paper into boxes. It does not matter if the grid is on the inside or the outside of the box.

Proceed to next page.

*See, for example, Burns, M., & Humphreys, C. (1990). A collection of math lessons from grades 6 through 8.White Plains, NY: Math Solutions Publications.