View all courses

Algebra I—Semester A

Invariable fun with variables.

  • Credit Recovery Enabled
  • Course Length: 18 weeks
  • Course Type: Basic
  • Category:
    • Math
    • Middle School
    • High School

Schools and Districts: We offer customized programs that won't break the bank. Get a quote.

Get a Quote

Shmoop's Algebra I course has been granted a-g certification, which means it has met the rigorous iNACOL Standards for Quality Online Courses and will now be honored as part of the requirements for admission into the University of California system.

This course has also been certified by Quality Matters, a trusted quality assurance organization that provides course review services to certify the quality of online and blended courses.

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.

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

Unit Breakdown

1 Algebra I—Semester A - 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.

2 Algebra I—Semester A - 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.

3 Algebra I—Semester A - 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.

4 Algebra I—Semester A - 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?

5 Algebra I—Semester A - 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.

Recommended prerequisites:

  • 7th Grade Math—Semester A
  • 7th Grade Math—Semester B
  • 8th Grade Math—Semester A
  • 8th Grade Math—Semester B

    • Sample Lesson - Introduction

    Lesson 4.01: Solving Linear Equations One Variable

    black and white group photograph
    They might not be smiling, but rest assured, they're having a lot of fun.

    (Source)

    There's an unfortunate stereotype about mathematicians being loners. That they are the kind of people who mostly like to sit by themselves with just pencils and paper, spending most of their time without any human contact. Although many mathematicians do work alone, that doesn't mean they don't like to hang out once the working day is done. Some mathematicians even have friends.

    That said, no matter how sociable the mathematician, there's one domain where they all love isolation: solving linear equations of one variable. We'll be putting the variable on lockdown, isolating it so that we can solve all kinds of problems. Well, except for crippling loneliness.

    Sample Lesson - Reading

    Reading 4.4.01: One Good Way to Solve Linear Equations of One Variable

    To solve a linear equation of one variable, you have to find the value that will make this equation true. That is to say, the value that, were you to substitute it in for all occurrences of the variable, you'd get a true equation.

    To find this value, you have to isolate the variable, performing operations on both sides until you're left with an equation that's just the variable on one side, and a constant on the other. In other words, find an equation that states: "This variable is equal to this constant."

    This process is easier to understand once you've tried it a few times. Let's take the linear equation 5x – 21 = 2x. If we want to isolate x, it'd be a good idea to get all the instances of x on one side, and all the constants on the other. So let's start by subtracting 2x from both sides, since any operation has to be performed on both sides:

    5x – 21 = 2x

    (5x – 21) – 2x = (2x) – 2x

    3x – 21 = 0

    Now we can get all the constants on the other side by adding 21 to both sides:

    3x – 21 = 0

    3x – 21 + 21 = 0 + 21

    3x = 21

    Although we now have the variable on one side and a constant on the other, we still need to divide both sides by 3 to completely isolate the variable:

    3x = 21

    3x/3 = 21/3

    x = 7

    And that's it. We now literally have a mathematical statement that says: "x is equal to 7."

    One bonus that comes with solving linear equations of one variable is that it gives us an easy way to check whether our solution is correct. To check your answer, just substitute the result back into the original equation, to see whether it still gives a true equation. If it works, you're golden. If it doesn't, you might want to check your solution, because something definitely went wrong at some point.

    To see this in action, let's take a look at our example. We found that x = 7, so let's try substituting this result back into the original equation:

    5x – 21 = 2x

    5(7) – 21 = 2(7)

    35 – 21 = 14

    14 = 14

    Since 14 does, in fact, equal 14, we know our solution is correct.

    For another example, feel free to check out this video.

    Recap

    • To solve a linear equation of one variable, you have to find the value that will make this equation true.
    • To find this value, you have to isolate the variable, performing operations on both sides until you're left with an equation that's just the variable on one side, and a constant on the other. Operations we can do include addition, subtraction, multiplication, and division (but, as always, not by 0).
    • To check your answer, just substitute the result back into the original equation, to see whether it still gives a true equation.

    Sample Lesson - Activity

    1. What are we trying to do when "solving" an equation with one variable?

    2. If we do an operation to one side of an equation, what must we also do?

    3. What is the value of x in x – 5 = 4?

    4. What is the value of x in 6x = 24?

    5. What is value of x in 2x – 4 = 18?

    6. What is the value of x in 3x + 6 = 2x – 4?

    7. What is the value of x in 5x – 10 = 7x?

    8. Why is it important to check our answer after solving an equation?

    9. What can we say if, when solving an equation, the variable totally cancels out and leaves us with an equation that is not true (like in 2x – 8 = 2x, which ends up as -8 = 0)?

    10. What can we say if the variable of an equation totally cancels out and leaves us with an equation that is true (like in x + 4 = x + 4, which turns into 4 = 4)?

    11. The solution to 3x – 5 = 10 is x = 5.

    12. The solution to 4x + 8 = 44 is x = 8.