Intuition in mathematics is essential but it must be based on good knowledge of mathematics. An example related to velocity, time, and area is presented and discussed, with models, visual approaches, and geometric arguments noted. (Author/KM)

A three-digit number is chosen, the digits reversed, and the smaller is subtracted from the larger. The difference is a page number in the textbook; the teacher tells the last word on that page. The learning begins when the class uses algebra to prove why the teacher's trick works. (KM)

By introducing elementary trigonometry earlier in a geometry course, a teacher can demonstrate how a variety of techniques can be brought to bear on the same problem. Eight theorems illustrate this. (Author/KM)

this article presents a way to stimulate the study of some properties of numbers. The number of points on the star to be drawn is predicted using the number of teeth on each wheel, the greatest common factor of those numbers, and the number of teeth in the movable wheel. (Author/KM)

This article presents a simple procedure to generate a sequence of rational numbers converging on the square root of 2, yielding common fraction approximations that motivate and illuminate the definition of real numbers based on rationals. Examples suggest that any irrational number can be approximated as closely as desired. A bibliography is…

A review lesson based on a sports car rally is described and illustrated. It teaches detailed map reading as well as providing drill on any subject desired. Pairing students is beneficial for several stated reasons. Some students may design their own rally for presentation to the class. (Author/KM)

Seven questions concerning the role of computation and the role of electronic calculators in arithmetic were posed to a sample of teachers, mathematicians, and laymen. Responses are given in percentage form and typical comments are included. (LS)

A method for generating 3x3 magic squares is developed. A series of questions relating to these magic squares is posed. An invesitgation using matrix methods is suggested with some questions for consideration. (LS)

The possibility of non-transitivity of preference choices is discussed. One example each from voting and from sports demonstrate some conditions where transitivity does not hold. Suggestions are made for using this type of problem in the classroom. (LS)