Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

This guide describes 47 number and numeration learning activities that can be used with elementary school students. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in developing further…

Utilizing word problems relevant to the field of environmental health, this workbook presents a concept-oriented approach to competency development in 14 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3)…

The converse of a familiar construction problem is explored, and a partial solution presented. The general problem is "Given a segment with length whose square is x, construct a segment with length 1." (SD)

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)

The relationships between arithmetic, geometric, and harmonic means and the root mean square of two numbers are examined. The problem of generalizing these relationships to three variables is discussed. (SD)

A calculator activity, described as a bingo game, emphasizes speedy calculations as well as problem solving. (JT)

A problem is discussed in which students investigate the properties of the perfect triangle. (MNS)

License plates are used to give students experiences in solving problems, following directions, developing numeracy, and writing number sentences. Four activities for different levels are given on the four worksheets. (MNS)

Three games in which the calculator plays an important facilitating role are presented. It promotes a "guess then adjust your guess" strategy. The games are described within the context of elementary, junior high, and secondary classrooms. (MNS)

Involving students in generating and solving their own problems is proposed. A method for generating problems by using a number puzzle is presented. Ideas for using the "what if not" technique are also given. (MNS)

Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)