There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

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.)

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

This book is designed to prepare students for taking the SAT I--Reasoning Test using a problem-solving focus. It clarifies the purpose, structure, and use of the SAT I and provides meaningful instructional material and explanations which illuminate the necessary skills. The book begins with a review of essential fundamentals, including useful…

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)

Motivational classroom materials that provide direct instruction on problem-solving skills are given. The activity highlights and provides opportunities for practice with two problem-solving skills, make a drawing and work backward. (MNS)

The problems in this book are intended mainly for students in junior high school and junior secondary classes, but many will interest students at higher levels. Most of the problems fit quite easily into the regular curriculum, and could be used by both teachers and parents. The book has 11 chapters, all but one of which contain problems and their…

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in January 1985, it contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the…

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in June 1985, it contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the…

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

An activity is described as an example of an application that draws on the behavior of current in electrical circuits to create a symbolic algebra. Five worksheets are included, with discussion of their use. (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)

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. It contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the provincial education department. (RH)