The observations of a five-year-old girl about the mutliplication tables are presented. The results are compared to structures in modern algebra. The incident is suggested as an example of Bruner's hypothesis: Any subject can be taught effectively in some intellectually honest form to any child at any stage of development. (LS)

The author suggests having students work on the related inequalities to given equations comparing and graphing the three solutions on the same number line. Using individual activity cards, the student picks replacements and computes, continuing this process until they can determine the complete solution. (LS)

This article displays the graphs of number patterns obtained by writing each number in the pattern as an ordered pair, plotting the ordered pairs, and joining consecutive points by straight lines. (DT)

Meanings of the word square'' are explored; the square as a figurate number, the sum of consecutive odd numbers, dissections of the square, and magic squares are discussed. (DT)

Starting from the concept of one-to-one correspondence, an introduction to the different types of infinities is presented. The usual problems concerning the infiniteness of the rational numbers, the real numbers, and the unit interval are given. Several other theorems follow. (LS)