This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five building blocks of elementary mathematics: numbers, the place value system, whole number operations, fractions and decimals, and problem solving. It stresses the need for precision otherwise ambiguity creeps in and we are no longer dealing with mathematics. It notes that abstraction is part of the underlying power of mathematics and it should be taught from the earliest grades. It also notes that the structure of mathematics is hierarchical and dictates that certain topics must be taught and mastered before others.