A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

An activity sequence is described. Several aspects of a population problem are developed using isoperimetric graph paper and symmetry principles to derive general rules. (SD)

When a simple game was presented as a challenge to a primary-school girl, she solved the problem, and went on to generalize her solution. (SD)

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)

Activity sheets posing problems in which students must examine and test various possibilities are presented. (SD)

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)

A computer program is presented for the billiard ball problem. It can be integrated into a lesson on inductive reasoning and suggests several ways to do so. (MNS)