Patterns and relationships found in the multiplication table of the numbers zero through nine are discussed as a means to helping students understand certain concepts. (MP)

A model for multiplication is described and used to discuss the properties of division. (SD)

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

Using the methods described, pattern representation of operations in modular systems can be developed. (SD)