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…

Discussed is the topic of least common multiple (LCM), a rationale for its importance, and suggestions for when and how to teach it. (RH)

Six activities useful in developing the idea of prime factorization are described. Some of these activities are best done with a calculator. (MK)

It is seen as important that mathematics teachers encourage open, imaginative investigations that give students an opportunity to probe, find patterns and relations, and derive new patterns and relations. The article focuses on multiplication tables and classes, including questions for further exploration. (MP)

Activities that can be used for maintenance of computational skills and can lead to the discovery of a pattern verifiable by an algebraic procedure are noted. The language of algebra is used in nonroutine settings, with several challenges for further exploration. (MP)

A new approach to teaching the division of common fractions is described. The approach is related to the multiplication operation and involves children working with concrete materials. (MK)

Offers suggestions for presenting multiplication to elementary students at the primary and intermediate levels. At the primary level, the emphasis is on introducing the concept of multiplication; at the intermediate level, the focus is on numeration and place value (using grids and a place value game). (SM)

Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)

Discusses a teaching method for multiplication using manipulative materials. Provides examples of the teaching method and activities using individual chalk boards. Two references are listed. (YP)

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

Discusses the generalization of the meaning of multiplication for whole numbers. Presents an example for multiplication of fractions. Provides several diagrams to help improve understanding. (YP)

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…

The use of graph paper to outline arrays of multidigit multiplication problems is promoted. (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)

This essay clarifies what it means to know mathematics by examining ways of knowing multiplication and explores what those ways of knowing imply for the teaching and learning of mathematics in schools. It reviews the perennial argument about whether computational skill or conceptual understanding should guide the school curriculum. A mathematical…