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)

The construction and use of bean sticks, an easily produced and inexpensive manipulative material, is promoted. Activities and games designed to teach place value and related mathematical concepts are also presented. (MP)

Many learning activities designed to make metric measurement meaningful to children are described. The manufacture and use of play dough is featured. Several simple recipes for preparing dough are included. (MP)

The game "Order Out", which uses manipulative and pictorial aids, is effective in teaching the ordering of common fractions. The use of manipulative or pictorial aids during instruction did not significantly affect achievement. Gender-related achievement trends were observed. (CJ)