4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Man, languages are crazy. Translators are some of the most sought-after professionals in the world, and who wouldn't want to be fluent in Mandarin, Spanish, and Esperanto? Talk about job security.

Students should be able to "translate" word problems into the strangest language of all: algebra. And like any language, they'll need to learn some of the grammar first. Luckily, translating a sentence into a linear equation is a lot simpler than deciphering an Ancient Greek stone tablet.

Run your students through the basics: how the word "is" usually ends up representing an equal sign, the unknown quantity is the variable, etc. We want them to see something like "What is the width of a rectangle whose perimeter is 54 cm and whose length is 6 cm?" and have it immediately click in their brains that the math-speak version is 2x + 2(6) = 54.

They should also know that setting up an equation isn't the only way to solve these things. For simple linear word problems, it's also possible to just find the answer arithmetically, without translating first. We could always double the rectangle's length to 12 cm, then subtract that from 54 and divide by 2 to get the width. But putting everything into an equation will definitely help keep all our quantities neat and ordered, which means fewer time making math mistakes and more time watching America's Next Top Model.

A translator who's pretty fluent in Spanish or Greek might be able to hold a conversation in that language without mentally translating anything into English, but those of us who aren't fluent in math are probably better off translating a word problem into an equation first. Students should know that both algebraic and arithmetic versions will give the same answer, assuming they've translated everything right.

Now, where are those language tapes? We've got some Elvish to learn.