Algebra I—Semester A
Invariable fun with variables.
Whether it's your saving grace or your worst enemy, there's no getting around it. Algebra is a part of life. The sooner we accept that, the better.
The fact is no matter where you go or what you do, you'll want a functional relationship with algebra. Its graphing skills are off the charts, and it can simplify your life like no other math can. Sure, it might be a bit radical and irrational from time to time, but it isn't half bad if you just give it a chance. Who knows? It might even be the start of an unlikely friendship. (You + Algebra = BFFs.)
Semester A is all about the essence of algebra: converting numbers to letters. And we'll do it via interactive readings, tons of examples, problem sets, fun activities… well, the list goes on. Needless to say, we've got all the Algebra help (and answers) you'll ever need.
In this Common Core-aligned course, we'll
- take an in-depth look at numbers, units, and how we can logically apply them to real life. Because, you know, real life is kind of important.
- convert between radicals and exponents, and interpret expressions accordingly. And by "accordingly," we mean "correctly."
- expand, factor, and combine polynomials of all shapes and sizes.
- derive the quadratic formula so that we can create and solve any one-variable equations thrown our way.
- write linear, quadratic, and exponential functions based on two-variable equations and sequences, and interpret them in context. Yeah, it's pretty exciting stuff.
P.S. Algebra I is a two-semester course. You're looking at Semester A, but you can check out Semester B here.
Unit 1. Real Numbers and Quantities
We'll kick off our Algebra learnin' with the good old backbone of mathematics: numbers and logic. Whether we're dealing with rational numbers or irrational ones, we aren't talking about them in a vacuum. (And if we are, get us out of here!) We'll learn how to think about more complicated combinations of numbers, and how to apply them to the real world and make sure our answers still make sense.
Unit 2. Radicals, Exponents, and Expressions
In this unit, we'll start off with a quick guide to exponents and radicals and then dive deep into expressions. We'll be introduced to our new best friends: lines, quadratics, and exponentials. (See? We're already on a first-name basis!) Of course, we can't really feel comfortable until we spend some quality time with them, so we'll finish up by learning how to interpret their behavior. Avoid their death glares like the plague.
Unit 3. Polynomials
Want to learn just about everything there is to know about polynomials? Well, you're in luck. After learning what a polynomial actually is, we'll smush them together and factor them apart using the distributive property, the FOIL method, inspection, trial and error, grouping—just about everything except for the kitchen sink. Actually, we'll probably need that, too.
Unit 4. One-Variable Equations and Inequalities
Much of what we learned about expressions will come in handy when we delve into one-variable equations and inequalities. We'll rearrange and solve equations, factor quadratics and find x values, and even do a little bit of drawing on the number line. Who says art and math don't go together?
Unit 5. Two-Variables Equations and Functions
First, we're going to learn what makes functions different from your run-of-the-mill equations. Then, we'll talk about the similarities and differences between functions and sequences. Finally, we'll use linear, quadratic, and exponential parent functions to answer problems about real world situations. By the end, we'll be able to model everything from movie ticket prices to your chances of surviving the zombie apocalypse.
Sample Lesson - Introduction
Lesson 5: Parts of a Linear Expression
At this point, our exponent pals are probably starting to get a little antsy. We know that their fondest dream is to be part of an expression, so we'll spend the next few lessons taste-testing three exponent-friendly flavors of expressions: linear, quadratic, and (here comes the oddball) exponential expressions.
If expressions were ice cream flavors, linear expressions would definitely be vanilla. They're simple, they're universally liked, and, in a pinch, they make a pretty good substitute for coffee creamer.
Linear expressions are used to describe situations in which something changes at a fixed rate. Time and distance are popular subjects of linear expressions, but they can also apply to things as varied as doubling recipes, saving a percentage of your paycheck, and collecting your monthly toenail clippings. What, you don't?
In case you're wondering why we're using the word "expression" instead of "equation," let's go over the difference between the two. An equation is a math sentence that tells us two things are equal, like 2x – 1 = 7. Every equation is made up of two expressions with an equals sign between them. So an expression is just a math phrase that describes a single value, like 2x – 1 (or 7).
Cool with you? Good; let's get to the fun stuff. We're gonna pull linear some expressions apart and see what they're made of.
Sample Lesson - Reading
Reading 2.5: Straighter Than the Sum of its Parts
Linear expressions are no-frills kind of guys. Each and every one of them has only three moving parts: a variable, a coefficient, and a constant. We generalize these pieces using the variables mx + b, where x is the variable, m is its coefficient, and b is some constant. Notice that this universal linear expression has two terms—the variable term mx, and the constant term b.
"So where are the exponents?" you ask. In linear expressions, x has two possible exponents to choose from: 0 and 1. That's it. Not very exciting perhaps, but that's life in the vanilla lane for you.
When the exponent on the variable is 0, the x effectively disappears and the expression becomes even simpler. Let's look at an example where m = 8 and b = -3.
8x0 – 3= 8(1) – 3
= 8 – 3
In its most simplified form, this expression is just a constant term. Totally legal in the super-minimalist world of linear expressions!
There are also linear expressions that consist of just the variable term. When b is equal to zero, the variable term mx is the only one we'll see. Thus, 3x or even just x are also perfectly acceptable linear expressions.
You may bump into some linear expressions who are trying to look like they have more terms than they actually do, like 2 + 4x – ⅓ or 7x – 3x. But if we reduce expressions like these to their simplest possible form, it becomes clear that they only have, at the most, one variable term and one constant term. No need to be frontin', guys. We like you for who you are.
- Linear expressions at their simplest have the two terms mx + b, where x is the variable, m is a coefficient on x, and b is some constant.
- x can have either the exponent 0 or the exponent 1. When its exponent is zero, the expression can be simplified to just a single constant term.
- b can be any fixed number, including zero. When b = 0, the expression consists of just the variable term.
Sample Lesson - Activity
Activity 2.5c: Problem Set
- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 8, 9, 10
- Course Type: Basic
7th Grade Math—Semester A
7th Grade Math—Semester B
8th Grade Math—Semester A
8th Grade Math—Semester B
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following standards are covered in this course:A-REI.4a