Describes several activities to provide opportunity for the discovery of number patterns and shows the need for care in the descriptions of such patterns. (Author)

A discussion is given on the probability of winning at the game of craps. Variations are discussed in terms of probabilities. (MP)

Patterns emerging when two-digit numbers in various bases are operated on by squaring and summing the digits. (SD)

Four answers to a probability problem involving a perceived coincidence are discussed. (MNS)

The probabilities of six-card poker hands are derived and compared to those of the five-card poker hands. (JT)

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

Strategies for winning in the game of NIM are discussed and explained through applying a base 2 representation for the numbers involved. (DT)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

A formula for predicting population, given past data, is presented. Decade census reports for the United States are used to analyze problems that might occur in prediction. (MP)

Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)