algebra = a study of variables

the notion of a variable has several facets

students might find it helpful to consider the following products of two 'things'

using letters (as symbols) and the equals sign in ways that might seem fairly different:

• in an equation: 7 = 5n
• stating a relationship (general form of a direct proportion): y = mx
• as a formula: A = b.h or d = s.t
• in a (general rule) identity: 1 - n^2 = (1 – n)(1 + n)          (with a big equals, an equivalence)
• stating a general arithmetical (and algebraic) property/rule: 1 = n.(1/n) or k^8 = k^3 x k^5