A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

A rationale is given for the Russian-peasant algorithm for multiplication indicating why it works as well as how it works. (DT)

The Russian-peasant algorithm for multiplication is described and then extended to developing an algorithm for renaming base ten numbers in other number bases. (DT)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

Work with recurring decimals provides pupils with an opportunity for exploration and examination of a wide variety of mathematical ideas and strategies. Examples of work done by one group of pupils who were presented with an opportunity to explore such decimals is featured. (MP)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (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)

Alternative algorithms, "tricks," and shortcuts are viewed as ideally suited for inclusion in a systematic program of practice because of their motivational effect and the mental stimulation involved in discovering why they work. (MP)