© 2016 Shmoop University, Inc. All rights reserved.

Pre-Algebra I—Semester A

"I graph, therefore I am."

Since elementary school, you've always been sort of a math whiz. Fractions were freakishly easy, times tables took no time at all, and geometry was practically art class. Honestly, you don't even need your calculator anymore; it's really just a paperweight at this point.

Okay, we get it. You're smart. Quit bragging.

If you're looking to step up your middle school math game, we've got just the ticket. In this Common Core-aligned math course, we'll take you through readings, examples, and problem sets that cover

  • rational numbers of all sorts, including those of the negative variety. (They're less pessimistic than they sound, we promise.)
  • breaking down whole numbers into fractions and decimals and performing arithmetic with 'em.
  • factors, prime numbers, and other helpful number theory tools.
  • ratios, proportions, rates, and percents. And expressing the same number about eighty different ways.
  • graphing, finding distances, and reflecting across the coordinate plane.
  • similarity, scale factors, and dilations of figures.

So if you thought that middle school math was Dullsville, USA, then think again. And maybe get a better GPS while you're at it.

P.S. Pre-Algebra I is a two-semester course. You're looking at Semester A, but you can check out Semester B here.

Course Breakdown

Unit 1. Integers and Rational Numbers

We're slapping on some scuba gear and diving down deep to find the negative numbers of the rational number line. We'll see integers, fractions, all sorts of decimals—all in positive and negative forms. While we're down here below zero, maybe we'll get lucky and get to visit the famous octopus's garden.

Unit 2. Fractions, Decimals, and Division

Working with positive whole numbers is old hat for us, but the world doesn't always make life easy. We need to be able to work with positive and negative fractions and decimals. That's not even counting when things take a turn for the worse and we need to start dividing all this stuff together. This unit will whip us into shape so that we'll be ready to take on the world at a moment's notice.

Unit 3. Number Theory

Compared to Quantum Theory, Relativity Theory, and the Lost Sock Theory (for washing machines), number theory is pretty concrete. Probably because we have so many concrete strategies to deal with it; things like prime factorization, factor trees, and the GCF and LCM. If those sound like a bunch of random words thrown together, don't worry. You'll see some concrete examples soon enough. 

Unit 4. Ratios, Proportions, and Percents

Numbers don't just sit there, isolated from the rest of the world. They tell about…stuff. And things! Can't forget about the things. If you want some more details than that, then we can bring in ratios, proportions, and percents, which are all about how two things relate to each other. And we don't mean in a family tree kind of way.

Unit 5. Coordinate Graphs

Even if you have a perfect sense of direction, a coordinate plane will still help you navigate the wild world of numbers. We can use it to plot points, find distances on the plane, and reflect things across both its axes. It's like a map, compass, and GPS all in one, and you only need paper and pencil to make it work. Handy!

Unit 6. Scale Factors and Dilations

Well, we have these coordinate planes that we can put points and shapes on. We also know about ratios and proportions, which tell us how two different things are related to each other. What happens if we smash them together? We'll see that similar figures, scale factors, and dilations will all fall out of the aftermath. We suggest bringing an umbrella.

Sample Lesson - Introduction

Lesson 3: Rules of Divisibility and Factor Trees

Hey, Rapunzel. How about meeting us down here for once?


Rapunzel, Rapunzel, let down your hair. Though, it would be way easier if you just took our advice and installed an elevator in that massive tower of yours. We know a guy who can build it on a low-interest installment plan.

Technically, we never said we were going to be knights in shining armor. But yes, this armor is pretty heavy, not to mention shiny, and we really don't feel like trudging all the way up this time. Maybe we've been barking up the wrong tower—er, tree—all along, and it's time we started calling on someone else instead.

Someone like a non-prime number. Because rather than towers, non-primes live in trees. And all those factorable branches make for easy climbing. Plus, numbers aren't really all that bad, are they? Or at least they're better than snooty princesses.

Start your free trial now

To get access to this product and hundreds more, start your free trial with Shmoop.
  • Credit Recovery Enabled
  • Course Length: 18 weeks
  • Grade Levels: 6, 7
  • Course Type: Basic
  • Category:
    • Math
    • Middle School

Just what the heck is a Shmoop Online Course?

Courses Tutorial