Volume and surface area of rectangular prisms: a maximum-minimum problem for the grades

To emphasize the distinction between perimeter and area, a useful lesson is one in which pupils use graph paper to draw many different rectangles of a given perimeter and then notice that these rectangles all have different areas. Since a lesson like this can be presented even in primarylevel classes, this discussion is limited for implicity's sake to integral values for the dimensions. For instance, rectangles of perimeter 16 could be 1 × 7, 2 × 6, 3 × 5, and 4 × 4. Students doing several such sets of rectangles with a given perimeter will discover the pattern: For a given perimeter, the square or the rectangle with length and width most nearly equal has the greatest area.