- To reapportion Congressional districts, using Huntington’s method of least proportions. A useful social studies project could be to figure out how your state could be gerrymandered to benefit either Republicans or Democrats, given its voting habits, and how to apportion districts without gerrymandering.
- To investigate when the number of telephone area codes in the United States will run out, given the increasing number of uses for telephone lines, unanticipated at the time the system was designed. What are the alternatives the phone companies face?
- To figure out how much it cost to put out the oil fires in Kuwait. (Why were the original estimates so far off?) Involves chemistry, labor economics, math skills of estimation, size and scale, measure.
- To analyze statistically the frequency of letters in any document written in English, for the purpose of breaking various codes. (The same is possible in other languages, but frequencies differ from language to language.)
- In esthetics, to determine what proportions are pleasing to the human eye. The “golden section” is the result of dividing a line of length q into two lengths, r and s, so that the ratio of q to r is the same as the ratio of r to s. A simple mathematical derivation involving the quadratic formula can be used to show that the ratio of r to s is about 1.618. This ratio appears in architecture, art, various ratios of parts of the human body to each other, canned goods, and other places we find esthetically pleasing.
- To describe musical notes. If a length of musical string is divided in the ratio of 1:2, the note of the shorter section is exactly one octave higher than the note of the longer.

*Thanks to Stephen Willoughby , author of Mathematics Education for a Changing World (ASCD, 1990), and Herb Rosenfeld.*