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…

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)

Presents activities designed to help children understand the notion of a sample in a homogeneous group, a concept essential to understanding "R times E" problems. Underscores the importance of children's understanding the situation in a problem so that they can solve it. (JN)

The "count-by" technique of multiplication was taught to a fourth grade student with learning disabilities. The student learned to count by numbers not typically taught (e.g., fours, sevens, and eights). The method resulted in substantial increases in correct multiplications performed per minute, which were maintained and generalized to…

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)

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)

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

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Describes how five-year-old children responded to the investigation of looking for patterns in a multiplication square. Provides a 10 x 10 multiplication square for the investigation. (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)

Presented are several suggestions for teaching elementary school mathematics with technology. Activities use calculators and microcomputers for teaching multiples. (RH)

Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

Analyzes multiplication word problems to identify the origin of children's difficulty. Emphasis is given to problems involving the concept of combination. (JN)

Describes a mathematics lesson using digital sums that allows teachers to assess third grade students' understanding of reasoning, arithmetic, and geometry. (ASK)