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)

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)

Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. (ASK)

Presents an activity in which attribute blocks help middle school students understand the fundamental counting principle and the multiplication rule. Demonstrates how these materials can aid students in building a conceptual understanding of multiplication and the counting principle. (ASK)

Pupils progress through a relatively small number of key stages called growth points in numeracy learning. Identifies growth points in developing numeracy and suggests that better support can be offered to children when teachers are aware of the growth points. (ASK)

One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the…

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)

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)

Provides four pages of practice problems covering the skills of multiplication, addition, and subtraction. Follows the premise that many arithmetic operations be done in working toward a solution. The sheets could be photocopied as worksheets or handouts. (JM)

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)

Activities are described which make use of rectangular arrays as a means of illustrating multiplication facts and the distributive property. (DT)

The Mayan system of numeration, which used 20 as the base, is discussed. The material presented has been used to stir the curiosity of students in different systems of numeration. It has been helpful in promoting a speedier and better understanding of base 10. (MP)

An introductory multiplication lesson, used successfully with second graders, is detailed. The method takes advantage of prior knowledge acquired in a geometry unit of study. The lesson is seen to have potential for other grades teaching multiplication for remedial work, and explaining the commutative law. (MP)

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)