Unit 1

Foundations & the Language of Algebra

Variables, the equals sign as a balance, the number system & number line, order of operations, factors & exponents, negative numbers, expressions vs. equations

This unit is the language the rest of algebra is spoken in. Get comfortable here and everything after it has somewhere familiar to stand. If your everyday arithmetic feels fresh, the adding, subtracting, multiplying, and dividing you already do, you have all you need to begin.

A note before you start, and it holds for the whole book. You don't have to absorb a lesson in one sitting. If a page stops landing, that's a signal to take a break, not a verdict on you.

And when you come back to a new lesson, redo two or three problems from a lesson or two earlier from memory first. That small warm-up is one of the most useful things you can do, and you'll see why as the units build.

Here is what this first unit covers. You'll learn to read the equals sign so every later move makes sense, and map out the kinds of numbers so a strange-looking answer feels normal instead of wrong.

You'll also get steady with order of operations, meet the factors and exponents hiding inside ordinary numbers, work with negative numbers, and finally learn to tell apart the two things algebra is mostly made of. None of it needs anything beyond the arithmetic you already do.