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7th Grade Math—Semester A

Keeping proportions in proportion.

Fractions and decimals might seem pretty rational, but what happens when we start replacing them with letters? Before you know it, you'll wind up with a math problem that looks more like a Shakespearean play than a number line. Good thing Shmoop's 7th Grade Math course is here to turn those incomprehensible variables into alphabet soup: easily digestible, not to mention delicious.

After a solid review of rational numbers in all their forms, we'll start working with a little algebra. Once we get our feet wet with variables and expressions, we'll deep-dive straight into one- and two-variable equations. Then comes another wave of numbers—ratios, proportions, and percents—and finally, we'll finish up our math expedition with scale factors and dilations. (Hope you brought your scuba gear!)

With all the readings, projects, and problem sets you could ever want, this Common Core-ified course gives you the 7th grade lowdown with lesson plans on:

  • performing operations with fractions, decimals, and negative numbers.
  • simplifying and evaluating expressions.
  • solving both one- and two-variable equations and inequalities.
  • representing and working with ratios, proportions, and percents.
  • understanding scale factors and drawing dilations of shapes.

P.S. 7th Grade Math is a two-semester course. You're looking at Semester A, but you can check out Semester B here.

Here's a sneak peek at a video from the course. BYOP (bring your own popcorn).

Course Breakdown

Unit 1. Rational Numbers

Numbers can take all kinds of forms, and we have to be ready for any that sneak up on us. We'll review how to defend ourselves against fractions and decimals, and practice the martial art of taking down integers. (Tip: aim for their negative signs.) With number lines, operations, and rational numbers, this unit will warm us up and prepare us for combat with any number.

Unit 2. Linear Expressions

From variables and PEMDAS to word problems, this unit will teach you how to express yourself more suavely in all kinds of situations—mathematical and otherwise. Unfortunately, there's no lesson on snappy comebacks. All of our best zingers show up three days late, too.

Unit 3. Solving Equations and Inequalities in One Variable

We'll start off covering the basic rules of solving equations. That means treating both sides of the equation exactly the same. No playing favorites! From there, we'll move onto inequalities, the hippie relatives of equations. They don't care about single values as much; as long as answers fall within a certain range, they'll go with the flow. Pretty groovy, huh?

Unit 4. Equations and Inequalities in Two Variables

We'll learn all about how two-variable equations can describe all sorts of different relationships—except your love-hate relationship with Lost. Those feelings are sort of inexplicable.

Unit 5. Ratios, Proportions, and Percents

Ratios, proportions, and percents were designed to work with groups of objects or to make comparing things directly easier. We can use them to do everything from comparing the prices of regular and jumbo packs of batteries to figuring out our savings per battery. (Four whole cents? Score!)

Unit 6. Scale Factors and Dilations

Now that we're well-versed in ratios and proportions, we'll apply these babies to two-dimensional shapes. Ever heard of dilations and similarity? We'll learn how to recognize and prove that two shapes really are related, kind of like they do on Maury—only with less swearing and more geometry.

Sample Lesson - Introduction

Lesson 4: Graphs of Proportional Relationships

A photo of two chocolate wafer cookies filled with white cream.
What are Oreos if not the combination of two great things (cookies and cream) to make something so much greater?


Here's where we combine everything we've learned about fractions and ratios with the actual meat (or tofu, if you prefer) of algebra. Like soldering pieces of silver together to make a beautiful ring or fusing two atoms of hydrogen together to power our whole solar system, we're about to join two great things to make an even greater third thing. Brace yourself.

To be fair, we only start the fusing process here. It'll take a little while until we've got a full-fledged solar system on our hands. But as we continue exploring these different topics, we can expect to see a lot of topics mix and mingle more than middle-aged singles.