Presents a mathematical problem on calculating the length of a groove on a long-playing record. Analyzes the problem-solving stages by using two methods of estimation or calculation. (ASK)

A distinction is made between estimation and checking, and an analysis of standard errors made on calculators when pupils are checking answers is given. (MP)

The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)