Lessons for first-grade students deal with the numbers five and six. How groups of five and six differ is the focus of the comparing and counting activities. (MNS)

Several brief articles are included in this section. "Purple Puzzlers" are challenging problems for algebra students. "Linear Invaders" is a game to reinforce concepts of graphing lines. "The Diagonal Method" is used to prove that the real and natural numbers cannot be put into one-to-one correspondence. (MNS)

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)

Activities and manipulative materials that teach pupils regrouping, also known as borrowing or carrying, are reviewed. Several examples of typical student errors and the reasons for these mistakes are outlined. (MP)

Learning activities using a two-pan balance to teach the concept of equality are described. Construction of a poster board balance is illustrated. (MP)

Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)

Described are activities and games incorporating a technique of "one step" which is used with children with learning difficulties. The purpose of "one step" is twofold, to minimize difficulties with typical trouble spots and to keep the step size of the instruction small. (Author/TG)

Rule learning in mathematics among elementary school children is described. Samples of dialogue between experimenters and children are presented, and the concept of rule learning is described in relation to two subgroups, gifted children and "regular" ones. (MP)

Three methods of proof are analyzed as a means of aiding teachers in presenting arguments for certain number concepts. These are: (1) proof by contradiction, (2) Venn diagrams, and (3) method of exhaustion. (MP)

On a scale of "moja" to "kumi", African math studies rate "kumi" with kids. (Editor)

Presents an investigation, applicable for grades 3-6, that focuses on the concept of randomness and encourages children to conjecture and to conduct experiments which verify or contradict their intuitions. Involves using hands-on explorations, collecting data, and drawing conclusions on the basis of the information. (JRH)

Simple experiences with probability can extend third graders' understanding of the need for fractions. Three activities are given which build on language-arts experiences and incorporate concepts in multiplication, graphs, and fractions. (MNS)

Several problem-solving activities involving only 0-9 to be used with sets of ceramic tiles are presented. Finding specified sums, differences, or products is the object of most of the problems. (MNS)

The article relates the British PrIME (Primary Initiatives in Mathematical Education) Project to children with special educational needs doing mathematics. The project's main aim is to improve the mathematical understanding and teaching skills of primary teachers. Activities using calculators are described. (DB)

Discusses explorations that students can engage in using the interstate highway system. (MKR)