http://www.teachengineering.org/view_lesson.php?url=collection/duk_/lessons/duk_boxes_mary_less/duk_boxes_mary_less.xmllessontext/xmlEngineering K-Ph.D. Program, rectangular prismcubevolumesurface area

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren’t packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

Students learn to think like packaging engineers while considering ways in which consumer goods are boxed. They must consider not only the most efficient designs, but also how those designs will be used by the public. Students will be able to determine the dimensions of a cube when given its volume. Students will be able to assert that a cube has less surface area than a rectangular prism of the same volume, and then prove this assertion with examples. 3.5TeachEngineering.orgMary R. Hebrank (Project Writer and Consultant), Duke Universityhttp://www.teachengineering.org/collection/duk_/lessons/duk_boxes_mary_less/letter.pdfS101DA63North_CarolinaMath2.01 Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.66S101F83ENorth_CarolinaMath2.02 Solve problems involving perimeter/circumference and area of plane figures.66S10018BENorth_CarolinaMathb. Build from various views.77United StatesCopyright 2012 - Engineering K-Ph.D. Program, Pratt School of Engineering, Duke Universityhttp://www.teachengineering.org/policy_ipp.phphttp://www.teachengineering.org/2009-01-207Teacher