2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

If students are going to spend years exploring a foreign country, they'd better be able to speak the language pretty fluently. Relying on phrasebooks, dictionaries, and Google Translate is okay in the very beginning, but it doesn't capture the multiple meanings that certain terms might have. You don't want to ask for the nearest restroom and accidentally wind up insulting someone's grandmother. Oops.

The same exact thing goes for algebra, and students should start getting comfortable with the lingo—and fast. Thankfully, they're less likely to dish out unintentional familial insults in Algebrese than in other foreign languages.

Students should know certain mathematical and algebraic buzzwords—term, constant, coefficient, factor, variable, etc.—and use them correctly to identify and describe parts of an expression. If you give them an algebraic or numerical expression, they should be able to identify each piece individually without losing the forest for the trees.

In addition to the buzzwords, teach students to recognize important subtleties within expressions. For instance, parentheses might contain multiple terms, but we can treat them and everything inside them as a single term. There are lots of ways to look at algebraic and numerical expressions, and make sure your students give 'em all a try.

And no, we didn't mean upside-down, so get down from there before you break your neck.