It is beneficial for students to discover intuitive strategies, as opposed to the teacher presenting strategies to them. Certain proportional reasoning tasks are more likely to elicit intuitive strategies than other tasks. The strategies that students are apt to use when approaching a task, as well as the likelihood of a student's success or…

"Concept study" is described in this article as a collaboration of teachers to investigate images, analogies, metaphors, exercises, and other experiences that are used to support students' understandings of concepts. The discussion is illustrated with the examples of multiplication and prime numbers. (Contains 3 figures.)

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 systematic search is given for products where reversing the digits does not change the answer. Related questions are suggested that can be solved by the same discovery approach. (MP)

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

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…

Key factors in mathematics remediation for high school students are examined. Levels of learning are discussed, and suggestions are given for working at different learning levels. Examples are given for remedial activities with area, multiplicain, and decimals and percent, and additional references are included. (MNS)

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)

This article explores the mathematics involved in the NCAA basketball tournament including data analysis, basic probability, expected value, and the multiplication principle. A fun activity is presented that applies these concepts and involves students shooting Ping-Pong balls to discover a best strategy. (Contains 3 tables and 3 figures.)

Activities are described in which number patterns in two-digit multiplication exercises are investigated. (DT)

Discusses a method of teaching the multiplication of integers to eighth-grade students that utilizes videotape recordings to represent positive and negative rates. Videotapes of students walking forward and backward in the play and rewind modes illustrate that the product of two negatives is positive. (MDH)

Uses of calculators to teach the concept of exponents are described. Topics covered on activity sheets include powers of two, number systems, and powers as repeated multiplication. Cooperative learning is emphasized. (KR)