Algebra I—Semester B
Double the equations, double the fun.
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.
Unit 6. 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.
Unit 7. 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?
Unit 8. 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.)
Unit 9. 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!
Unit 10. 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.
Sample Lesson - Introduction
Lesson 5: 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 you would think that proving the method would not be very difficult. And 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 9.5: 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 9.5: 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.)
- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 7, 8, 9
- Course Type: Basic
Algebra I—Semester A
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following standards are covered in this course:CCSS.Math.Content.HSA-CED.A.2