This report presents mathematics benchmarks organized into instructional sequences by topic. Each sequence is based upon an analysis of the order of content as it appears among a set of highly rated state standards. The report is intended to inform and guide state or district curriculum directors or others who, starting from content that is placed…

A game with dice that can be adapted for use at various levels of understanding is presented. (MS)

Derives a formula for the number of years a given resource will last as a function of constant yearly growth rates in the resource usage. Suggests such a calculation to account for environmental problems. (CC)

"Capture" is a game that requires players to perform several computations on each turn and to choose an optimal move, thus promoting higher-order thinking and probability notions. Rules are given, playing is described, and extension activities are noted. (MNS)

Students in grades four-six were asked to complete multiplication examples and write a story problem (reported earlier, SE 533 279). Their stories were categorized in terms of their logic and realism. Many errors were noted, leading to the conclusion that knowledge of multiplication does not necessarily lead to logical multiplication. (MNS)

Calculators have made the arithmetic curriculum obsolete in both scope and sequence. Calculators can perform each operation as easily as any other. We should be asking if there is ever a time when we should trust paper-and-pencil computation. (MNS)

A nine-year-old's conception of fractions was compared with his knowledge of units. He had effective schemes for solving some partition problems but did not consistently use units of different sizes in interpreting fractions. His solutions to equivalence problems showed no coherent method of verification. (MNS)

Lists and explains a computer program written in BASIC which calculates teacher salaries using a salary index. Modification of this payroll program is suggested as a student project in schools which teach computer programing. (JJD)

Eighty-seven pupils in grades 4-6 completed five multiplication examples and wrote a problem for another example. They were reasonably proficient, with mean scores of 82 percent in grade 4, 75 percent in grade 5, and 97 percent in grade 6. They did less well on developing a problem. (MNS)

Discusses approach to integrating computer programing into a calculus-based physics survey college course which stresses three major uses of computers: data reduction, calculation, and simulation. An initial programing exercise and practical constraints--time a student can allot to course and student's level of confidence--are mentioned. (EJS)

The use of a type of magic square as a tool for student drill in the basic operations is emphasized. Methods for constructing "Sneaky Squares" are outlined and the logic behind them explained. The approach is seen as convenient for a variety of basic drill work. (MP)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

Discusses computer applications to school administration tasks, in particular word processing, computations, and data base management systems. Advantages and disadvantages of program software and a chart containing an overview of application programs available are included. (JJD)