Using various aspects of mathematical structure as unifying concepts is stressed. Specific examples are given based on the concept of equivalent fractions and on the addition property of equality. (LS)

Suggestions for making number concepts and basic operations through counting with diagrams more meaningful are given. Discussions of specific instances with two children, ages 5 and 9, illustrate some ideas, inventions, and difficulties of children in this age range. (LS)

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)