View all courses

Algebra I—Semester B

Double the equations, double the fun.

  • 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.

It doesn't matter whether you love it or hate it. The fact remains that Algebra is around, and by golly, it's here to stay.

What's not to love about it, though? We'll admit that it might get a bit irrational from time to time, and there's no denying a few of its radical tendencies, but it can simplify your life in more ways than the square root of one. Besides, its graphing skills are off the charts. Why not give it a chance? Take it from us: there's a high probability of it working out.

Semester B is chock-full of stuff that we haven't come across in other math classes. In this Common Core-aligned course, we'll

  • graph all kinds of equations and inequalities (not just for lines, either).
  • revisit the slope of a line, and see it as the rate of change of a function.
  • solve and graph systems of equations.
  • finish up with probability and statistics. (Well, maybe. There’s a 99% chance we'll get there.)

Get ready for interactive readings, activities, and problem sets galore.

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

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

Unit Breakdown

6 Algebra I—Semester B - Graphing Equations and Inequalities

Tired of those unsightly function rules, equations, and inequalities? Long tables of inputs and outputs got you down? Had enough of sequences with numbers that seem to go on forever? We've got just the solution for you: whip out your paintbrush, dust off that palette, and get busy creating beautiful works of mathematical art. It's graphin' time.

7 Algebra I—Semester B - Graphing Nonlinear Functions

Get ready to see functions like you've never seen them before. Quadratics will take center stage first, flaunting their vertices, roots, and axes of symmetry. (Yeah, they're pretty hammy.) We'll use these guys to explore different properties of functions like domain, range, end behavior, and even what happens when we throw a monkey wrench—er, constant—into the function rule. We'll finish up with piecewise-defined and step functions, graphing them and using them as models. So yes, this unit's a biggie, but it's also a funnie. That's a word, right?

8 Algebra I—Semester B - Rate of Change

Knowing about rates of change and how they work allows us to know more about the world around us—especially from the perspective of linear and exponential functions. Whether it's gas prices, or bacteria growth, or crazy rich people, rates of change inform us about trends, patterns, and making good choices. (Tip: don't choose to be a crazy rich person and give away your money.)

9 Algebra I—Semester B - Systems of Equations and Inequalities

Systems of linear equations and inequalities shouldn't be all that new to you, which is why we aren't stopping there. Remember quadratics and exponentials? Yeah, we'll throw a few of those into our system just to mix things up a bit. By the end of this unit, we won't just be graphing and solving systems of equations; we'll be creating them and modeling with them, too!

10 Algebra I—Semester B - Statistics

We'll start this unit off with the kind of statistics you already know about: box plots, histograms, means, and standard deviations. But when univariate data just won't cut it, we'll need scatter plots to step in. Good thing we've been studying linear functions, too, because we'll need 'em when we analyze correlation coefficients, interpret slopes and y-intercepts, and distinguish correlation from causation.

Recommended prerequisites:

  • Algebra I—Semester A

    • Sample Lesson - Introduction

    Lesson 9.05: Proving the Elimination Method

    Don't panic. It won't take anywhere near 157 steps to prove the elimination method for solving systems of equations. We just think somebody likes chalk dust a little too much.

    It is fairly easy to see how the elimination method works once you use it, so if you think that proving the method would not be very difficult, you would be right. So how about you come back into the classroom and we'll get started. Really. It's okay.

    We're sorry we scared you. Come on back. Please?

    Sample Lesson - Reading

    Reading 9.9.05: Proving the Elimination Method

    It's not hard to prove the elimination method if you think about equality—and we're all about equality. We are multiplying by constants to get each equation in the form we want. Since we're doing that to both sides of the equation, we keep things nice and equal throughout every step.

    The activity in this lesson should help drive the point home. Or wherever the point needs to be driven to. Does the point have a curfew?

    Sample Lesson - Activity

    Activity 9.05: Driving Down the Elimination Highway

    Well, we said we were going to drive the point home, so everybody get in the car. We call shotgun!

    Wait, the car is out of gas. Guess we'll have to stick with paper, pencils, and graph paper. Since we have graph paper, let's start by graphing something. (By that logic, thank goodness we didn't have a jackhammer.)

    1. Graph this system of two equations: y = 2x + 1 and 2y = 7x – 4. These are linear equations, so you only have to pick two points to graph for each equation. List your x and y values below.

    2. Connect each pair of points to draw the two lines for the equations. Where do the lines intersect? If it helps, feel free to trace the lines with your fingers and run them together while making horrible crashing noises.

    3. If we were going to solve these equations by elimination, which equation would you change and what would you use for a multiplication factor? Remember, you want to make terms cancel out when the two equations are added together.

    4. Change the equation you chose, and graph it on the same coordinate plane as the original two equations. What does the resulting graph tell us about the changes that we made to the equation?

    5. We didn't bring you here just to show you two overlapping lines on a graph. Go ahead and use that equation you changed for its intended purpose: kicking one of our variables off the island, and solving for the other one. What do we end up with when we graph that solution?

    6. You probably know by now what happens next. We substitute that solved variable back into one of the original equations to find the value of the other variable. But wait—why is substitution part of the elimination method? Aren't they two different things?

      As methods for solving systems of equations, the elimination and substitution methods represent different approaches. However, the basic concept of substituting one expression for another, equivalent expression is like the duct tape of algebra. It's so handy that people reach for it in all kinds of situations…including in the elimination method.

      In fact, the principle of substitution is the reason that we can add one equation to another in the elimination method without messing up the system. Remember, we have to add the same thing to both sides of an equation to keep its meaning the same. So how is it that we can add some y-term to one side of an equation and an x-term to the other? Bonus points for putting your answer in the form of a haiku.

    7. Oh, we almost forgot—go ahead and solve for that second variable. Put your answer in the magic box below.

    Showing Work and Short Answer Rubric - 25 Points

    OutstandingProficientDevelopingNeeds Improvement
    Work is Shown

    All work is clearly and logically shown. Steps are clearly connected and legible. Necessary diagrams or graphs are included and labeled.

    (15)

    Work is logically laid out and understandable. Diagrams and graphs should still be shown, but it might have a few leaps in logic or skipped steps.

    (13)

    Work is shown, but doesn't always relate to the question at hand. Illogical arguments, absent crucial steps, and missing or insufficient graphs or diagrams.

    (9)

    Completely illegible and/or illogical work.

    (5)
    Answer

    All parts of the question are answered correctly, including proper units and notation.

    (10)

    Answer is mostly correct, but has rounding errors, incorrect units, or is expressed improperly.

    (9)

    Answer is incorrect, but reasonable.

    (6)

    Answer is clearly incorrect or missing.

    (4)