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…

Introduces addition, subtraction, multiplication, and division of fractions using area models such as rectangles and circles, or linear models such as the number line and fraction strips. (ASK)

Presents problem situations that support students when discovering the multiplication principle, permutations, combinations, Pascal's triangle, and relationships among those objects in a concrete context. (ASK)

Discusses the interpretation given to the multiplication symbol ("x") in elementary school textbooks, the meaning of multiplication, and how it should be introduced to children. Also considers several aspects of multiplication, including: (1) equal steps on a line; (2) the array; (3) equal groupings; and (4) allocation (rate). (JN)

Use of an ancient method of mental calculation with aliquot parts is illustrated. Other tips for helping children reason are also included. (MNS)

Provides a brief historical explanation of the multiplication sign in mathematics. (ASK)

A classroom illustration of a multiplication game is presented followed by an analysis of the game. (MNS)

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)

Having children create and solve their own story problems is a valuable activity to use for them to think carefully about and apply a concept to create and solve a problem. Describes using two books to help children learn about the concept of multiplication. (ASK)

Research on students' attainment on multiplication facts, common errors, and meaningful instruction is briefly cited in this review. (MNS)

Activities are presented that focus on attributes of numbers. The activities highlight such attributes as more than, equal to, greater than, less than, LCM, prime and factor. The activities provide practice in motivational game-oriented situations. (RH)

How to develop multiplicative magic squares is discussed. Various types of numbers are used in the examples. (MNS)

Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

Activities with triangular, square, pentagonal, hexagonal, and octagonal numbers are briefly discussed. (MNS)

Arrays are seen as excellent models for beginning multiplication examples, but that they are often put aside by teachers when they become unwieldly for greater factors, possibly depriving learners just when they need the help. The use of grids made on paper marked in squares is suggested. (MP)