All common fractions can be written in decimal form. In this Discovery article, the author suggests that teachers ask their students to calculate the decimals by actually doing the divisions themselves, and later on they can use a calculator to check their answers. This article presents a lesson based on the research of Bolt (1982).

This article presents a hands-on experiment that covers many areas of high school mathematics. Included are the notions of patterns, proof, triangular numbers and various aspects of problem solving. The problem involves the arrangements of a school of fish using split peas or buttons to represent the fish. (Contains 4 figures.)

Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the…

Reams of paper come in a standardised system of related sheet sizes. Most people are familiar with the international paper sizes A4, A3 and B4, but there are others. The ratio of the sides of any sheet in the series is such that if the paper is cut or folded in half on itself then the ratio of the sides remains unchanged. Due to this property of…

Sets of numbers where not only their sums are equal but the sums of other powers are also equal have been called multigrades. This article presents several mathematical equations that portray how multigrades are generated. By further extension of the process outlined in this article, students can generate higher-order multigrades. (Contains 1…

For many years I have been advocating the use of hands-on materials to assist students in the understanding and application of mathematical concepts. Some of the methods have been introduced as small parts of earlier Discovery articles, (de Mestre, 1994, 1996, 1998, 1999a, 1999b, 1999c, 2000a, 2000b, 2001), but here I propose to devote the whole…

Computers were invented to help mathematicians perform long and complicated calculations more efficiently. By the time that a computing area became a familiar space in primary and secondary schools, the initial motivation for computer use had been submerged in the many other functions that modern computers now accomplish. Not only the mathematics…

This paper describes a "hands-on task" called Number Tiles, which is Task 43 in the collection constructed for the Mathematics Task Centre Project, and available at www.blackdouglas.com.au or www.curriculum.edu.au. This task is rich in possibilities and directions. It should be used as a planned curriculum experience at several year levels to…

This paper examines the difference between mass and weight, which is discussed very early in most physics courses. Those who indulge in mathematical problems involving weights should know the difference. Mass is often defined as the amount of matter in an object. This usually means the sum of the masses of all the atoms that constitute that…

Tennis is a sport in which the mathematics involves an unusual scoring system together with other applications pertinent to the draw for different types of tournaments and the relative ratios of points won and lost. The name of the sport is thought to have originated from the French word "tenez", which translates roughly as "to receive (the…

Samples of materials available to students from grades 4 through 12 at a Mathematics Center are reviewed. The examples are part of a collection of more than 200 mathematical tasks using solid materials in a new approach to problem solving. (MP)

Presents a hands-on mathematics task that can be investigated experimentally to produce a sequence of numbers. Describes ways to extrapolate values of the table of numbers by formulating and verifying a conjecture related to the pattern in the numbers. (MDH)