Three lessons on division for grade 4 are presented, the first using manipulative materials; the second, the computer; and the third, the calculator. Advantages and disadvantages of each are discussed. (MNS)

Fourth-grade students' understanding of the order and equivalence of fractions was investigated in an 18-week teaching experiment. Three related characteristics of thinking are hypothesized to be related to success of such tasks, involving flexibility and reasoning that becomes increasingly independent of specific concrete embodiments. (MNS)

Some answers are given to questions that teachers ask about the preprimary mathematics program. A point of view is presented and a model provided outlining a scope and sequence for choosing experiences for children about five years old. (MNS)

The abacus method for instruction on addition, subtraction, and multiplication with integers is explained. How to represent the integers for each operation is detailed with words and illustrations. (MNS)

Activities are given for solving verbal subtraction problems. Take-away and comparison situations are described, and three levels of activities to model the situations are given: one involving concrete materials and verbal descriptions; the second with these plus written symbols; and the third encouraging mental images. (MNS)

A method is explained for using right triangles on a geoboard for determining the greatest common factor and least common multiple of two numbers. (DT)

Instructions are given for making a solid from unit cubes joined face to face. Activities lead to design and construction of the SOMA cube, along with other cube puzzles. (DT)

A Mira is described, then several uses of the Mira are suggested. (DT)

Discussed is development of a manipulative system which used dots on numerials for teaching basic mathematical concepts to mentally or variously handicapped children in kindergarten through grade 2. (MC)

Three worksheets are provided; the aim is to develop skill in visualization of the cube from two-dimensional patterns. (DT)

A classification scheme provides for discussion of manipulative devices by type as well as individually. Characteristics of good devices, general guidelines for uses, and means of evaluation are given. Besides specific examples, there is a listing of commercial sources and a selected bibliography. (LS)

Directions are given for seven activities involving the folding of paper strips to illustrate geometric concepts. Properties of pentagons, triangles, hexagons, and Mobius bands resulting from the various foldings are discussed. (DT)