This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Discusses the mistakes of Kirschner, the German philosopher and mathematician, in calculating factorials of large numbers by hand in the 1600s. Uses computer technology to calculate those numbers now. (ASK)

Using the calculator to do addition and multiplication in base 2 is discussed, with the stress on how to change numbers from one base to another using the calculator. (MNS)

A learning disabled student was drilled on multiplication facts, with records of his performance used to help him reach mastery. A sequence in which the 0 facts, 1 facts, etc., are taught is used. (MNS)

Using factoring as an aid to mental multiplication is illustrated. Other suggestions for teaching mental computation are also included. (MNS)

Presents a technique for multiplying two-digit numbers whose tens digits are equal and whose units digits have a sum of 10. Then various mental calculations with other types of two-digit and larger numbers are discussed. (MNS)

Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)

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)

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)

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)

This book provides regular classroom and special education teachers with alternative, individualized methods of teaching math computation skills. Learning activities are designed to appeal to auditory, visual, and kinesthetic learning modalities. Six mathematics topics addressed include modeling addition and subtraction, basic facts for addition…

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)

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…