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.
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
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.
Sample Lesson - Reading
Reading 11.5: Solving Equations: Stuff Just Got Real
Setting up real world equations is easy, once you understand what the problem is asking for. Sometimes it helps to go over what you know, in order to figure out what you want to know. That way you know what you know, and you know what you don't know…you know? Ow, that made our heads hurt.
Let's use the examples in the unit intro to begin.
How about the shirts? We know that we have twenty shirts total. We know that twelve shirts are dirty. What we want to know is how many shirts are clean.
What else do we know, but didn't say up above? We know that our shirts are either clean or dirty—so our total number of shirts must equal the number of dirty ones plus the number of clean ones. Here's how this looks as an equation:
Total Shirts = Clean shirts + dirty shirts.
We'll call our unknown value(s) x, just because that's what we like to do. You can call yours Jason or Ashley or whatever you want. It's a free country. We just think x is a bit more efficient. In this case, the unit of measurement of our unknown value is "clean shirts". We know there are 20 total shirts and 12 dirty shirts. Plugging all of this info into our equation, we get:
20 = x + 12
Our answer will be expressed in clean shirts.
The magazine problem is just as easy. We know how much each magazine weighs in pounds, and we know how many pounds of magazines we have. What we want to know is how many magazines we have.
What else do we know? We know that the weights of all the magazines add up to make the total weight—but since each magazine weighs the same amount, we can multiply them instead of adding them. So the weight of each magazine times the number magazines equals the total weight of all the magazines. Our equation looks like this:
Total weight of magazines = weight of each magazine × total number of magazines.
Our unknown x is the number of magazines. Substituting, we get:
60 = ½(x)
If we included the units, it would look like:
60 pounds = ½ pound per magazine × x magazines
We can double-check our units to make sure they match on both sides of the equation. We can write pounds per magazine as pounds/magazine, and see if the units cancel out in the numerator and the denominator. Let's check.
60 pounds = ½ pound/magazine × x magazines
It works! We have pounds on both sides of the equation.
For the room-cleaning problem, we know that Mom will crack in 30 days if you don't clean your room and two weeks have already passed. What we don't know is the number of days until Mom cracks, so we'll call that x. Using the same methods we can set up the equation
30 = 2 + x
Wait, that doesn't look right. Let's check the units.
30 days = 2 weeks + x days until Mom cracks.
Aha! We need to change weeks to days. We know there are 7 days in a week so we could add a term:
30 days = (2 weeks × 7 days/week) + x days until Mom cracks.
Simplifying, we get
30 days = 14 days + x days until Mom cracks.
If that isn't a handy real-world equation, we don't know what is. There are some more examples of equations here for you to check out as well. Now that we've set all of these equations up, how about you solve each of them and check to see if your solutions are correct? Come on, you're quickly becoming a pro at this solving equations thing. We have faith in you!
To set up real world equations, think about what the unknown value is—in other words, the answer you want to find out. It helps to list what you know as well as what you want to know. You will use those things to make your equation.
Make sure you know what the units are, and that they match up on both sides of the equation. You can cancel out units that appear in both the numerator and the denominator on the same side of the equation.
Sample Lesson - Activity
Activity 11.5: Problem Set
- Credit Recovery Enabled
- Course Length: 1 weeks
- Grade Levels: 6
- Course Type: Basic
6th Grade Math—Semester A
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following standards are covered in this course:CCSS.ELA-Literacy.CCRA.L.2