Presents the problem of finding the maximum area of a quadrilateral when three of the four sides are given. Incorporates several parts of the secondary school precalculus curriculum into the solution. Develops the formula to solve the problem. (MDH)

Examines the problem of determining the minimum center of mass for a can with a varying height of liquid in it. Uses PC SOLVE computer software to graphically represent the problem situation. (MDH)

Proposes lessons for algebra students using the context of tax calculations to learn about the concepts of slope, split functions, averages, rates, marginal rates, and percents. Students explore ramifications of possible tax revisions. (MDH)

Described is an activity that categorizes a two-digit number as "sneaky" if the continued process of taking the difference of the squares of its digits leads to a difference of zero. Other categorizations are determined by whether the difference process ends in a one-digit number or continues in a loop of numbers. (MDH)

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)

Emphasizes a real-world-problem situation using sine law and cosine law. Angles of elevation from two tracking stations located in the plane of the equator determine height of a satellite. Calculators or computers can be used. (LDR)

In recognition of the fact that young children develop informal number concepts and strategies for solving several basic types of verbal addition and subtraction problems before entering school, but lose this ability after a few years of schooling, the study created and tested an intervention designed to build on the children's early insights. A…

This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed.…

Presented is an activity in which students apply familiar concepts of geometry to novel settings. Using square dot paper and isometric dot paper, students trace routes and determine the geometry of each circle. (KR)

Investigates the probability of winning the largest prize at Bingo through a series of five simpler problems. Investigations are conducted with the aid of either BASIC computer programs, spreadsheets, or a computer algebra system such as Mathematica. Provides sample data tables to illustrate findings. (MDH)

Presents four cases of real-world probabilistic situations to promote more effective teaching of probability. Calculates the probability of obtaining six of six different prizes successively in six, seven, eight, and nine boxes of cereal, generalizes the problem to n boxes of cereal, and offers suggestions to extend the problem. (MDH)

Describes the importance of estimation in science for planning projects, conducting experiments, and developing theories. Defines order of magnitude. Provides explicit mathematical equations and calculations to estimate answers for seven provocative physics problems. Includes nine additional open-ended problems with hints and solutions. (PR)

Presents a problem to determine conditions under which two identical masses, constrained to move along two perpendicular wires, would collide when positioned on the wires and released with no initial velocity. Offers a solution that utilizes the position of the center of mass and a computer simulation of the phenomenon. (MDH)

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

From the equality of the ratios of the surface areas and volumes of a sphere and its circumscribed cylinder, the exploration of theorems relating the ratios of surface areas and volumes of a sphere and other circumscribed solids in three dimensions, and analogous questions relating two-dimensional concepts of perimeter and area is recounted. (MDH)