Pre-Algebra I—Semester B
Not all equations are created equal.
We know why you're here. Either you thought that last semester was a blast and you're ready for more, or you're one of those nosy types with a magnifying glass and a funny detective hat, always looking for the final clue, that last unknown that solves the whole equation.
Yes, we have been reading a lot of Nancy Drew lately. How'd you guess?
If you're looking for a fast and furious journey into the unknown—unknown variables, that is—then look no further. Grab a pencil and notebook, and it can't hurt to bring along a magnifying glass and a sidekick, too. (Where would Sherlock be without his trusty Watson?)
In this Common Core-aligned course, you'll get practice problems, examples, and activities that cover
- calculating the perimeters and areas of triangles, quadrilaterals, circles, and just about any polygon you can think of. We'll even get our feet wet with the 3D realm of geometry, too.
- translating English into numerical and variable expressions. We suggest keeping a pocket dictionary handy.
- writing and solving one-variable equations and inequalities as well as some simple two-variable ones.
- conducting legit statistical studies, analyzing the data, and representing it appropriately.
With a mastery of expressions, equations, inequalities, and statistics under your belt, we imagine there's little you won't be able to take on in your post-Pre-Algebra life.
P.S. Pre-Algebra I is a two-semester course. You're looking at Semester B, but you can check out Semester A here.
Unit 7. Geometry
Every day we're surrounded by all kinds of shapes and solids, but we usually don't look too closely at them. Now we're going to break out the magnifying glass and give them a good stare-down. From triangles to trapezoids to even weirder shapes, we'll start to unlock all sorts of shape mysteries. After that, we'll take a sneak peek at working with a couple 3D shapes, too. Just relax, or you'll never see the 3D dolphin hidden on the page.
Unit 8. Expressions, Variables, and Basic Operations
We can say expressions in English, and we can make expressions with our faces (but not too much, or they'll stick that way), but how do we make mathematical expressions? In this unit, we'll learn what they're made of, how to work with them, and even how to translate a run-of-the-mill English sentence into Mathese. Once we throw variables into the mix, we'll be one big step closer to the mysterious land of algebra.
Unit 9. Equations and Inequalities
It's time to take our algebra learnin' up a notch or two. We'll cover setting up and solving equations with one or two variables. Then we'll meet the equation's fraternal twin, inequalities; they have a lot in common, but they're not quite identical. Because equations and inequalities are so useful, we'll also apply them to real-world situations. Who knows? Maybe they'll solve one of your long-standing problems, like who is in charge of the remote control.
Unit 10. Statistics
Statistics can seem like a hairy subject, so we've brought along our fine-toothed comb to this unit to help straighten everything out. We'll cover what statistics means, how we can summarize data, and the best ways to collect, analyze, and present it. By the way, we did a study and found that 99% of all statistics units end with students running their own study; it doesn't look like this one is going to break that trend.
Sample Lesson - Introduction
Lesson 5: Numerical Expressions
Before we saddle up those bucking broncos known as variable expressions, let’s take a few turns around the pasture with numerical expressions. Numerical expressions are gentle old ponies that won’t try to throw you with fancy tricks like variables. These simple creatures are made up of only two things: numbers and operations.
Friendly as they may be, numerical expressions still have their little quirks, and we’re going to get good and familiar with those before we head out on the trail. We might want to bring a carrot or two for them—just in case.
Numerical expressions are math phrases that we use to describe real-world situations. Let's say you want to figure out how many honey badger posters it would take to completely cover your bedroom ceiling. Or maybe your situation is even real-er, and you're calculating how many cans of honey badger chow you need to buy to survive this month with all your body parts intact.
A numerical expression will fearlessly wrangle these problems for you. No foe is too ferocious for numerical expressions. They're just crazy. They don't care.
Sample Lesson - Reading
Reading 8.5: The Anatomy of an Expression
At this point, you've already performed thousands of operations in your math career: applying exponents, multiplying and dividing, adding and subtracting, and maybe the occasional ingrown toenail removal. When we do several types of operations on one patient—er, numerical expression—these procedures need to happen in a particular order. Don't start slicing and dicing before you've administered the anesthetic, for cryin' out loud!
Let's change into our scrubs, wash our hands for an hour or so, and review the standard operating procedure with this reading.
Old news, you say? Did you get antiseptic in your eyes, or are those tears of boredom? Never fear, Mathketeers; we're going to toss a new beat into the mix to keep you on your toes.
An exponent is like a little fairy that floats above a number's shoulder, whispering how many times that number must be multiplied by itself. (If you want to see an exponent's tiny wings, you have to clap your hands and say, "I do believe in exponents!") In the example below, 7 is the exponent and 3 is the base (the number being multiplied):
37 = 3 × 3 × 3 × 3 × 3 × 3 × 3
When the number two is used as an exponent, we say that the base is being squared. Squaring five, for example, gives us 25: 52 = 5 × 5 = 25.
Now here comes the dramatic tension—did you know that our little fairy exponent 2 has an evil twin? One who undoes all his efforts by reversing his spells? It's true. We call this little rebel the square root, and she belongs to a species known as radicals. Her symbol looks a bit like a checkmark, and when she's got a number in her clutches, it means that we need to figure out what base was squared in order to yield that number:
√25 = 5
√16 = 4
√9 = 3
The square root is just the tip of iceberg. There are oodles more radicals out there; in fact, every exponent ever invented has its own evil twin. Told you there'd be drama in the club tonight. For now though, we'll stick to the square root two-step in our numerical expression barn dance. No need to blow minds with any radical Bollywood moves until the moment is right.
- Numerical expressions are math phrases used to describe real-world situations.
- Unlike variable expressions, numerical expressions contain only numbers and operators; no letters allowed!
- The rules of order of operations (abbreviated as PEMDAS) must be followed in order to correctly evaluate a numerical expression.
Sample Lesson - Activity
Activity 8.5: Problem Set
- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 6, 7
- Course Type: Basic
- Middle School
Pre-Algebra I—Semester A
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following Common Core Standards are covered in this course:CCSS.ELA-Literacy.CCRA.L.2