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6th Grade Math—Semester B

x marks the spot.

It's time to take a leap of faith. Off the rational number line, that is, and into the broader world of coordinate planes, expressions, equations, and inequalities.

If you're looking for an introduction to graphing, geometry, using variables (what's a letter like x think he's doing in our math homework, anyway?), solving equations, and working with real-world data, then this is the thrill-seeking course for you. So take a few deep breaths, strap that parachute on nice and tight, and prepare yourself for some mathematical adventures.

With practice problems, quizzes, and Common Core-aligned activities, we'll:

  • get cozy with coordinates by plotting points, distances, and reflections on the plane
  • calculate areas, surface areas, and volumes of polygons and 3D solids, no matter how corner-y (and ornery) they are
  • explore the building blocks of expressions and how to relate them to one another
  • solve simple one-variable equations and inequalities and even write a few of our own
  • work with simple two-variable equations
  • learn the basics of statistics, including collecting and representing data using numbers, plots, and graphs

If you're still nervous about leaping off from what we learned earlier, then grab some knee and elbow pads. But as long as you stick with us, we'll make sure you land on solid ground.

P.S. 6th Grade Math is a two-semester course. You're looking at Semester B, but you can check out Semester A here.

Course Breakdown

Unit 8. Coordinate Graphs

The coordinate plane is sort of like real estate; it's all about location, location, location. But it also allows us to plot points, find vertical and horizontal distances, and reflect things across the x- and y-axes. Can real estate help you do all that? Yeah, we didn't think so.

Unit 9. Geometry

In this unit, we're going to take a close look at some of the shapes and solids we take for granted every day. From triangles to trapezoids, every shape has some crazy mystical secrets it can impart to us. And then we'll flip things into full-on 3D, where we'll literally break geometric solids apart, unfold 'em into a flat pancake, and slide 'em back together again. Okay, fine. Maybe not literally.

Unit 10. Expressions, Variables, and Basic Operations

We know what expressions are in English and how to make expressions using our faces (and some Scotch tape), but what are mathematical expressions? In this unit, we'll learn how to identify the parts of an expression, how to simplify and evaluate expressions, and how to translate from English into Mathese. Chock-full of variables, exponents, and important properties, this unit will be our first expedition into the mysterious world of algebra.

Unit 11. Equations and Inequalities

This unit will take our algebra learnin' one step further. We'll learn how to set up and solve equations with one and two variables. We'll also talk about inequalities and how they're similar to and different from equations. Finally, we'll apply equations and inequalities to real-world situations that might come in handy. Who knows? Maybe they can solve the boundary dispute between you and your brothers and sisters—because clearly, the "Keep Out!" sign on your bedroom door won't do the trick.

Unit 12. Statistics

Statistics might seem like a pretty hairy subject, so in this unit, we'll take a fine-toothed comb and straighten everything out. We'll talk about what makes a statistical question, different centers, spreads, and shapes of data, and and how to represent information accurately and appropriately using charts, plots, and graphs. By the way, we've done a study and found that 99% of statistics units end with you conducting your own study…and yeah, looks like this one does, too.

Sample Lesson - Introduction

Lesson 5: Setting Up Real-World Equations

 A shot of a messy room covered in magazines, a mattress, blankets, a television, clothing, and other assorted junk.
There's a whole bunch of equations buried in here, along with who knows what else.

(Source)

Your Mom may see a revolting mess in this picture. You may see your room after what you call a cleaning. We see a lot of real world equations just waiting to be discovered. Are they hiding under the magazines? Desperately trying to get out from under the pile of dirty clothes? Hiding under the bed? Yes to all of those questions.

Can't see them? We'll give you some help. Here are some examples:

There are twelve dirty shirts on the floor. If there are twenty shirts total, how many are clean? Assume all the other shirts are clean and not crammed under the bed.

If you have 60 pounds of magazines to take to recycling and each magazine weighs ½ pound, how many magazines are you recycling?

If your room isn't cleaned at least once every thirty days, Mom will crack from the smell. If this picture was taken at the two-week point, how many more days will pass until Mom cracks? (Because you aren't cleaning your room without being told, that's for sure.)

When you finally have to clean your room for real, it takes you 1 hour to clean one-quarter of your room. How many hours will it take to clean your whole room?

What's that moving under that pile of clothes? That's not a math problem—we are just a little frightened. Do you have any missing pets, or has one of your socks come to life?

Now can you see the possibilities? There are equations to be found everywhere, even in this mess. We'll show you how to set them up. However, we are not helping clean your room, regardless of what is crawling around in your dirty clothes.