Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

Two games and one activity designed to be used with a hand-held calculator are presented. (MK)

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

Using a great variety of word problems drawn from many contexts can make multiplication and division rules more relevant to the student's needs. (SD)

Examples of student-developed methods for dividing fractions and dividing and multiplying whole numbers are presented. Both are selected to show mathematical creativity in general mathematics students which would often be overlooked. (MP)

Described are activities and games incorporating a technique of "one step" which is used with children with learning difficulties. The purpose of "one step" is twofold, to minimize difficulties with typical trouble spots and to keep the step size of the instruction small. (Author/TG)

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

A unit on problems involving large numbers can begin with calculating the amounts of ingredients needed to produce several thousand hamburgers. Other sources of computational problems are described. (SD)

Numerous studies indicate that performance in solving single step multiplicative word problems is influenced by both problem structure and the types of numbers involved in the problem. For example, including numbers less than one often increases the difficulty of a problem. What remains unclear is how problem structure and number type interact in…

Four worksheets and teaching suggestions are presented, with the focus on mental computation for levels 2-3; factors, levels 3-4; and nonroutine problems, levels 5-6 and 7-8. (MNS)

Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involving…

An unusual way of using the long multiplication algorithm to solve problems is presented. It is conceptually harder, since it involves negative numbers but is easier to perform once mastered, since the size of the multiplication table required is smaller than the standard one. (MP)

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

A learning pattern designed to help students cut down the amount of memorization needed in learning the basic multiplication facts is suggested and reviewed. (MP)