The FOIL method is not that bad really for teaching multiplication of two binomials as long as it is derived from applying the distributive law or more officially known as the Distributive Property (over addition or subtraction).
The FOIL method is a mnemonic for First term, Outer term, Inner Term, Last term. It means multiply the first terms of the factors, then the outer terms, then the inner terms and the last terms. I would suggest the following sequence of examples before the teacher introduces product of two binomials: Click here for the complete description of how to teach this with meaning.
Simplify the following expressions
The FOIL method is also related to Line Multiplication. However, while the latter is applicable to any number of terms in the factors like the Distributive Law, the FOIL method is not. It only works for getting the factors of binomials. This is why it is not a powerful tool. The most powerful knowledge is still the distributive property of equality. Before the teacher should introduce any fancy way of calculating, he or she should make sure this knowledge is in place. Sample lesson on how to do this is presented in Sequencing Examples.
Want a more challenging problem for distributive law? Click Application of Distributive Law.