Models for developing addition, subtraction, and multiplication with integers are given. (MNS)

A model, easily constructed by students, is used to assist in seeking basic Pythagorean identities used to prove more complex ones. (MNS)

The "positive-negative charge" model is described and demonstrated with all four operations on integers. Its major advantages are that it is both concrete and complete. (MNS)

Describes several activities of the Data and Chance program involving third and fourth graders. Students use real-life situations to investigate probability. (MKR)

Considers some changes that the use of graphics calculators impose on the assessment of calculus and mathematical modeling at the undergraduate level. Suggests some of the ways in which the assessment of mathematical tasks can be modified as the mechanics of calculation become routine and questions of analysis and interpretation assume greater…

Presented is an example meant to enable students with a scant mathematical education to grasp the meaning of the limit of the binomial distribution. (Author/TG)

Presents a diagrammatic proof for classroom use to demonstrate the quasi-convexity of the indirect utility function. Includes a variation of the price indifference curve. Suggests an exercise in which the student is asked to show that the tangency condition is a restatement of Roy's identity. (DK)

Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

Presents an activity in which the subject is the identity of the team in the greatest jeopardy of becoming the big loser in a basketball tournament. Explores several facts about the big loser, offering them in a hierarchy appropriate for creating various short- and long-term projects for a high school mathematics class. (ASK)

Discusses a precalculus project in which students create a model United Nations to present and discuss the long-term prognosis for individual countries given data on population growth and food production. Students compare exponential and linear functions to determine whether starvation will occur and prepare oral and written presentations of their…

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (MNS)

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)