Box Folding: An
Exercise in Prediction, Measurement, and Analysis

Main Page | Folding Boxes | Gathering Data | Organizing Data | Using the Applet | Questions | Formulas and GraphsIntroduction: 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
- Spreadsheet program (files included here were made in Excel®)
- scissors
- puffed rice or other space filling material
- Graphing calculator (optional)

- 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)

- Take a piece of the grid
paper and cut the blank strips
from around the edges so that only the grid itself remains.

- 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.

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

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

Proceed to next page.

*See, for example, Burns, M., & Humphreys, C. (1990).