The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

Demonstrates the logical relationship between percentage composition and an empirical formula using a technique that depends on determining a minimum molar mass for the compound based on the mass percent of each element. (DDR)

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

Presents three methods invented by fourth graders for obtaining the arithmetic mean. This presentation is in support of the idea that encouraging children to invent their own mathematical processes is a good way for them to clarify the idea of representativeness and consequently the teacher can facilitate the students' construction of higher…

The dynamics of some common sports, such as race walking, running, cycling, jumping, and throwing, are presented. Rough estimates of the relevant physical quantities required for these individual sports are discussed. General mathematical formulas are derived which can be used for judging the performance of any athlete. (Author/KR)

A series of well-defined steps is given for solving titrimetric problems, based on the mole concept. An example is given, including calculations from the first step to the last. (SA)

Describes two activities for developing computational skills, discovering patterns, checking answers, and factoring quadratics and equivalent fractions. Provides worksheets for the activities. (YP)

The application of the programmable calculator to evaluating complicated formulas is illustrated by considering the formula for finding the area of any triangle when only the lengths of the three sides are known. Other advantages of the programmable calculator are discussed such as freeing the student to explore more challenging problems and…

The article describes the Mental Mathematics System, a number of formulas designed to develop mathematical skills in elementary and junior high school gifted and talented students. Formulas are provided for multiplication. The formulas for mental mathematics are noted to promote student interest in the subject. (SBH)

Provided is a rebuttal to an argument concerning the use of Ka values for water and the hydronium ion. The derivation of new values as a result of the treatment of the water as the solvent and using a Raoult's Law standard state is discussed. (CW)

Presents number tricks appropriate for use in workshops, mathematics clubs or at other times when stressing recreational mathematics. (PK)

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)

Building mathematical sentences is the focus, with worksheets for practice with basic facts and fractions in a problem-solving setting, using logical reasoning. (MNS)

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)

This project involves devising and evaluating a sales tax schedule to meet the specific revenue needs of a hypothetical state in the United States. Conducting this unit involves many mathematical skills in a learning environment familiar to the student. The essential parts of the project consist of student preparation of a tax schedule and class…