Using an apparently simple problem, ''Design a cylindrical can that will hold a liter of milk,'' this paper demonstrates how engineering design may facilitate the teaching of the following ideas to secondary students: linear and non-linear relationships; basic geometry of circles, rectangles, and cylinders; unit measures of area and volume; solving systems of equations with at least two variables;minimization of area to control materials costs and to prevent heat exchange; packing geometry to minimize space for transportation and storage and for controlling for heat exchange; golden ratio as a design aesthetic; ergonomic factors in design including considerations of comfort of handling and safety; and strength of design for stacking and handling as well as for the prevention of accidental tipping. This interdisciplinary curriculum uses engineering design challenges to engage students with meaningful and fun group activities and discussions that also teach a multitude of diverse and powerful mathematical concepts.