The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

Computational algorithms from American textbooks copyrighted prior to 1900 are presented--some that convey the concept, some just for special cases, and some just for fun. Algorithms for each operation with whole numbers are presented and analyzed. (MNS)

Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

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

The multiplication and division algorithms that are taught in German schools are presented. It is suggested that these algorithms may be better than standard algorithms in terms of development of useful concepts and processes. (MK)

Three short essays provide teaching suggestions for lessons on base two, order of operations, and ratios used to motivate a number of mathematical ideas. (MK)

A collection of games and puzzles that teachers can use to replace or supplement the usual textbook subtraction examples involving large numbers is given. Most of the nine activities are self-checking. (MNS)

Symbols and shapes used in flowcharting are defined, reasons for incorporating flowcharts into instructional activities are listed, and eight different flowcharts are presented. (DT)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

Outlines various subtraction methods, such as the decomposition method, equal-addends method, and low-stress algorithm. Describes a subtraction method by addition of complements. Discusses the advantages and disadvantages of the method. (YP)

Renaming fractions with the dot method is described with illustrations. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved. (MNS)

Two worksheets are given, outlining algorithms to help students determine the day of the week an event will occur and to find the date for Easter. The activity provides computational practice. A computer program for determining Easter is also included. (MNS)

A model of the division algorithm is described which relates step-by-step to the standard algorithm. Use of the model in instruction requires the distribution of a special worksheet. The focus of the instruction is on students sharing some amount of money equally among several friends. (MP)

Typical instruction of the division algorithm fails to justify why one brings down a number during the process. The construction and use of an aid is described which can be used to help explain the process of division to students. The aid emphasizes place-value aspects. (MP)