What is Pre-algebra?
Pre-algebra: The mathematical skills required to perform the basic operations assumed in algebraic manipulations.
This is (to my mind) a very good question, especially considering the confusion in posting questions in "Algebra" and "Pre-Algebra".
If I were to define Algebra as
the component of mathematics in which general symbols are used and manipulated in the representation of values in expressions and equations;
then (at least some of) the elements I would consider essential in Pre-Algebra would be:
- Basic numeric manipulation using addition, subtraction, multiplication, division, and exponentiation.
- Standard order of operations.
- Associative and distributive properties.
- Different forms of numeric representation: integers, fractions, improper fractions, mixed fractions, decimal fractions, scientific notation.
- Conversion between common units of measurement (distance, temperature, time, volume, etc.)
- Representation of numbers on a number line (and possibly relations between numbers on a graph).
- Basic understanding of equality and inequalities (including "less than", "less than or equal to", "not equal to" , etc.)
- Knowledge of meaning of basic geometric shapes.
- General formulae for geometric forms (perimeter and area of rectangles, triangles, circles).
(There are probably more items that should be included here, but this is a reasonable starting point, IMHO).