Examines the factors influencing the use of a plan by four- and five-year-old children to judge the relative number of two sets by one-to-one correspodence. Results suggest that most children have one-to-one plans in long-term memory by age four. (Author/RWB)

Using factoring as an aid to mental multiplication is illustrated. Other suggestions for teaching mental computation are also included. (MNS)

Problems set in the real world help students see the relevance of mathematics. Topics that provide sources of real problems are discussed, with examples: mazes, packing, and networks. (MNS)

The rational plane, consisting of the points in the Cartesian plane having two rational coordinates, is a model in which certain properties do not hold. Nine theorems are discussed. (MNS)

Four ways of knowing about numbers are listed, with direct estimation emphasized. Using perceptual anchors is described, with several teaching tips on their use in estimation. (MNS)

Questioned is a method of having students tap reference points on numerals to count out sums, differences, and products. How the method works, educators' reactions, and problems noted in interviews with children are discussed. (MNS)

Three mathematical games which are developments of well-known games are described: Rummy, War, and Remembering. Seven packs of cards are illustrated. (MNS)

Two relevant applications of mathematics and computer science are presented: International Standard Book Numbers (ISBN) that appear in textbooks and universal product codes that appear on grocery products. A computer program is included. (MNS)

One mathematician's view of real problems is given. Described (with some humor) are magic retail numbers, the highway bypass, the elliptical table, and the senior-class schedule. (MNS)

Included are brief reports on an algebra quiz in a menu format; two activity sheets on base two; and an alternative method of teaching least common multiple and greatest common factor, and related ideas, with six lessons outlined. (MNS)

Two activities are presented. The first involves geometric concepts using the alphabet, while the second is a game to provide practice in finding factors of composite numbers. (MNS)

Simple patterns both in mathematics and music are discussed. Several activities using standard instruments and handmade devices are described. (MNS)

Three board games are presented, with playing directions and comments to the teacher (MNS)

Examples of diversions with cards that may be used to illustrate the concept of a cyclic group and structural properties of the integers modulo a prime are presented. (MNS)

Indicates how thinking strategies help children learn the basic facts for whole numbers, listing several strategies involved in addition, subtraction, multiplication, and division. Also lists books and articles for illustrations of the strategies and how to teach them, and two sources for research findings on thinking strategies for basic facts.…