Presents two vignettes of mathematics lessons and describes fourth-grade students' discussions of fractions, percents, decimals, time, and money while investigating the various interpretations of the word "quarter." (ASK)

Presents a mathematics activity that illustrates how such adjectives as elegant, surprising, concise, and challenging can be, and in fact are, attributed to proofs by a not very expert audience. (ASK)

Explains that, although mathematics is essential for calculating time, the calendar is an historical construct. Demonstrates why there is no true way of measuring time and looks at the historical roots of the western calendar. Offers further readings on calendars, time, and the millennium. (ASK)

Presents a game to capture student interest in probability by giving them an opportunity to explore the idea of various outcomes and the likelihood of the occurrence of one of those outcomes to explain the benefits of using a large sample rather than a small one. (ASK)

Presents an activity that led to the discovery of the role of ratios and percentages in discussions about triple-jump performances, and a range of tasks that provide important information about students' understanding of key mathematical concepts. (ASK)

Discusses the importance of using children's previous experiences with geometric figures to build foundations for developing geometric thinking. Describes how children's play with unit blocks can be structured to give them experiences with geometric concepts. Contains 12 references. (ASK)

Describes a third-grade class's discoveries when students were asked to develop a method to find the area of a trapezoid on the basis of their prior work with finding the area of rectangles. (ASK)

Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. (ASK)

Presents a hands-on activity in which students use the tools to derive the basic procedure used by wildlife biologists worldwide for estimating the sizes of wildlife populations. Helps students gain the feelings of power and ownership of a statistical method that they derive themselves. (ASK)

Presents an activity that focuses on the composition of functions in the context of jawbreakers. (ASK)

Presents an activity that utilizes the mathematical models of forest fires and oil spills that were generated (in the first part of this activity, published in the November 1998 issue) by students using probability and cellular automata. (ASK)

Presents the general postage-stamp problem on Diophantine equations. Discusses ways to uncover all solutions to the problem. (ASK)

Calculus students have great trouble visualizing solids of revolution and their cross sections. Illustrates the use of props in order to help students understand the solid revolution. (ASK)

Introduces students to nonperiodic tiling and allows them to construct their own sets of kites and darts through a series of explorations, conjectures, and discoveries. (ASK)

Investigates the problem of finding all triangles that have natural-number sides for which the area is numerically equal to the perimeter. (ASK)