Translating from English to mathematical notation

Word problems are the bane of every algebra student. In helping students solve word problems, I have found the main difficulty is usually translating the words of the problem into algebraic expressions (and more generally into mathematical notation). I call this step translating from English to "Algebraic". Algebraic is a language that you must learn to be successful, however a surprising number of students seem to have missed learning this language. Oh, they know how to manipulate the symbols once they're written down, but they don't grasp the language itself. This manifests itself in difficulty solving word problems, as well as trouble in other areas of mathematics such as reciting a proof from memory.

In this article, I will offer some general advice on getting started translating from English to Algebraic. Along the way, I'll introduce some word problems to illustrate the procedure. Click "Introduction" to continue, or for specific advice on particular types of word problem, click one of the specialized topics below the Introduction.