An activity is described which can be used to introduce students to the general divisibility test for nine. (JP)

A card trick that can be explained and justified using first-year algebra is presented. It illustrates the power of mathematics to unmask seemingly complex situations. (MNS)

An unusual way of using the long multiplication algorithm to solve problems is presented. It is conceptually harder, since it involves negative numbers but is easier to perform once mastered, since the size of the multiplication table required is smaller than the standard one. (MP)

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)

Presented are the purposes served by mathematical investigation--the exploration of open situations in a relatively unstructured way--and an example (investigating numbers adding to 13), with numerous questions and conjectures. (MNS)

Patterns and relationships are shown between the Pythagorean theorem, Fibonacci sequences, and the golden ratio. Historical references also include the works of Euclid and Euler. These unexpected relationships can be used to motivate secondary students. (DC)

Domino games are used to illustrate problem-solving techniques in a college principles-of-mathematics course. Students develop tables and use Pascal's triangle to find the total number of pips and the sum of numbers on the pieces. (DC)