Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

The importance of having children manipulate small objects that can be grouped, arranged, and counted is discussed. Learning activities for one-to-one correspondence, numerals, and the four operations are given. (MNS)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

Specific instruction in different contexts provide needed background for solving addition and subtraction problems. The categories of problems and relative difficulties are presented, followed by an explanation of a successful instructional sequence. (MNS)

Activities involving spinners and dice are presented. Making the materials is noted, followed by activities on counting, computation, probability, fractions, and other ideas. (MNS)

The use of developmental algorithms to develop skills is described. Children make the transition from using concrete materials to using a standard algorithm. (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 use of counting sticks as a concrete manipulative material in the development of number understanding and the concept of place value is strongly urged. (JT)

Lessons are suggested which involve dice in the instruction of various number concepts. Activities are presented under: (1) Early Number Concepts; (2) Meaningful Addition and Subtraction; (3) Place Value Practice; and (4) Extensions for the Intermediate Grades. The primary advantage of dice is their adaptability to student ability levels and…

Findings from a study with first-grade children on addition and subtraction help make a case for a conceptual rather than a mechanized approach to the operations. How base ten blocks were used in the program is illustrated. (MNS)

Activities to develop counting skills are given. (MK)

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (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)

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

Described is a study in which three instructional approaches were applied in second grade classes. Discussed are proportional materials, nonproportional materials, nonproportional materials with pictorial models. Findings, results, and recommendations are presented. (CW)