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Thinking Outside the Box -- or Maybe Just About the Box

Thomas Hern (Bowling Green State Univ.) and David Meel (Bowling Green State Univ.)

Discussing Dundas's (1984) analysis

In a paper by Dundas (1984), he looked at a variety of box problems and one of them was configured like the RSC. The tactic that Dundas (1984) took was to look at the problem from the perspective of a piece of cardboard of fixed area rather than a fixed dimensions. We find this choice mathematically sound but problematic to the exploration of the real-world situation since cardboard is not typically sold by area but rather constrained by manufacturable lengths and widths. Consequently, when Dundas (1984) explored the function,

\[ V(l) = T\left( {{1 \over 2} - T} \right)\left( {{A \over l} - T} \right) \]

there was no way to convey to the reader information about the length and width of the cardboard (since the cardboard area was being restricted to A square inches). In addition, a critical piece of the problem is what the lengths of the cuts should be, since that transforms the problem from a multiple-variable problem to a single-variable problem. Unfortunately for a student reading the paper, it was never motivated or explained. It is these particular elements that we wish to revisit and illustrate using text and a set of applet-based activities to lead students to similar conclusions without making the activity all about pushing algebra around on a page.