Integrating technology into the mathematics classroom means more than just new teaching tools--it is an opportunity to redefine what it means to teach and learn mathematics. Yet deciding when a particular form of technology may be appropriate for a specific mathematics topic can be difficult. Such decisions center on what is commonly being…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

This article describes several ways that calculus students can develop a deeper understanding of related rates by getting actively involved in the lesson.

Four worksheets are given to enhance the understanding of and facility with numerical concepts and relations for students in grades seven through nine. The focus is on enhancing deductive reasoning abilities with Venn diagrams and arrow diagrams. Teaching ideas are included. (MNS)

Two problem-solving skills, guess-and-test and simplification, are introduced and reinforced through a variety of motivating problem situations. Solutions of sample problems and extensive directions for the teacher encourage the use of Polya's four-step model of problem solving. (MNS)

The estimation strategies of "using compatible numbers,""averaging," and "rounding" are used. The first two worksheets review easy arithmetic facts and ask students to identify compatible numbers. Worksheet Three introduces averaging and provides practice with rounding, while the fourth worksheet contains problems for group practice. (MNS)

Activities that provide opportunities for students to investigate solving linear equations using both a physical and a pictorial model are given. Students should discover a method that will permit them to solve such equations at the symbolic level. (MNS)

Activities concern exploring data and using the stem-and-leaf plot for displaying data. The three worksheets present activities, with brief directions for the teacher included. (MNS)

Activities focus on the use of computers as an instructional tool. Three worksheets provide experiences with: perimeter and areas of squares; area of parallelograms and triangles; and properties of triangles. A Logo computer program is included. (MNS)

Drawing accurate regular polygons with a specified edge length is the focus of three activities. Angle measurement and related geometric concepts are reinforced with three worksheets. (MNS)

Activities to extend the core curriculum through the study of the periodicity of rational numbers to help students develop calculator and research skills are presented. Four worksheets are included, to be used as discovery activities. A computer program is listed, as well as examples of periodic pictures. (MNS)

The activity uses an area model to analyze probabilities associated with games of chance. Three activity sheets are included, with teaching suggestions. (MNS)

Topics from graph theory are introduced at an informal level and thereby made accessible to the majority of secondary school students. Three worksheets are included. (MNS)

Using four activity sheets, students learn to identify fractions that are easy to use in estimation situations. (MNS)

Stressed is a conceptual approach to absolute value, based on the visualization of the graphs of absolute-value equations. An important by-product is predicting a graph on the basis of certain constraints. Four worksheets plus teacher comments are included. (MNS)