# Pre-Algebra II—Semester B

Scatter plots, not scatter brains.

People often ask, "Which came first, the chicken or the egg?" as though it were some kind of super stumper. It's really not, though; you kind of need an egg before you can get a chicken. Hatching from eggs is something they are kind of famous for.

It's pretty much the same thing with Pre-Algebra and Algebra. Before we can move on to the big bad world of Algebra, we need to master the tools of Pre-Algebra and get them under our belt. Don't worry—it's a pretty big belt. In this Common Core-aligned course, we'll use loads of drills, examples, and projects to cover

- systems of linear equations and inequalities
- functions and relations
- triangles, triangles, and maybe some more triangles
- the basics of three-dimensional geometry
- statistics and probability

Are you ready for the egg of truth to be turned into an omelet of understanding?

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

## Course Breakdown

### Unit 8. Systems of Linear Equations and Inequalities

Get out your thinking cap and your scheming scarf, because we're going to start working with two of the most common algebraic tools that people use to plan and strategize: systems of linear equations and linear inequalities. You can use them to make a business plan, strategize your rise to power, and orchestrate your eventual conquering of the world. Pretty useful, right?

### Unit 9. Functions and Relations

We've only recently been introduced to functions, but we're already becoming fast friends. They've been telling us all about themselves: what they look like in algebraic or graph form, what kinds of *x* and *y* values they like, their favorite Fall Out Boy song, and what food allergies they have. You know; all the little details that friends should know.

### Unit 10. Triangles and the Pythagorean Theorem

Triangles are really simple, right? How many ways can there be of putting three sides and angles together? Well, the shapes themselves might be simple and predictable, but there's still a lot to say about them. We're going to study these three-legged creatures in their natural habitat, and even use Pythagoras's theorem to prove that some of them are more right than others.

### Unit 11. 3D Geometry

We'll be spending this unit getting to know cylinders, cones, and spheres inside and out: literally. We're going to talk about their insides and outsides (i.e., their volumes and surface areas). There will be formulas galore, so it will help to pull out the calculator for this one. We'll end things with a hands-on project to get psyched up about circular solids. Whoo!

### Unit 12. Statistics

Are two pieces of data related in some way? We're going to try to find out in this unit, using plenty of two-way frequency tables and scatterplots. We'll guide you through nonlinear associations, linear models, and both numerical and categorical data. By the end of it all, you'll be BFFs with lines of best fit. Get the scrapbook ready.

### Unit 13. Probability

It's time to start unlocking the secrets to predicting the future. (Think less divination and more blackjack.) We'll make tables and diagrams to show the probabilities of different events, calculate our chances of getting a winning poker hand or lottery ticket, and dabble in the black art of simulation. All to bring probability to life. Mwahaha!

## Sample Lesson - Introduction

#### Lesson 3: Domain and Range

(Source)

Humans are fascinated by transformation; just look at our classic comic book heroes. A hapless nerd gets bitten by a spider or blasted by gamma radiation and—poof!—he's transformed into a heavy hitter with a cool (yet tragic) backstory. Most supervillains also have some major transformation in their personal histories. A little lab accident here, a little acid in the face there, and another well-meaning physicist or politician turns to a life of crime.

Even before they're old enough to hold a comic book right-side up, kids love to watch something turn into something else. Did you ever push Play-Doh through that gadget that turns it into a pile of green spaghetti? Maybe you were preparing for a career as a mad (culinary) scientist. Or maybe it's just that children are deeply rooted to life's bottom line: inputs and outputs. (Changed any diapers lately? Then you know exactly what we're talking about.)

Like toddlers (and evil geniuses), functions are all about turning things into other things. Sometimes, we'll even replace *y* with *f*(*x*) when dealing with functions, but all that *f*(*x*) really means is, "We're gonna push *x* through this here contraption, and you'd best believe that something else will be coming out the other end." Let's just hope it's as pungent as what comes out of babies' other end.

Since inputs and outputs are at the heart of functions, we're going to spend some time playing with them. If you're lucky, maybe we'll let you use our Squeezy Freezy function to transform lemonade into delicious lemonade slushies.

- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 7, 8
- Course Type: Basic
- Category:
- Math
- Middle School

- Prerequisites:

Pre-Algebra I—Semester A

Pre-Algebra I—Semester B

Pre-Algebra II—Semester A

Just what the heck is a Shmoop Online Course?

Courses Tutorial

### Common Core Standards

The following Common Core Standards are covered in this course:

CCSS.Math.Content.7.G.A.2CCSS.Math.Content.7.G.A.3

CCSS.Math.Content.7.G.B.5

CCSS.Math.Content.7.SP.C.5

CCSS.Math.Content.7.SP.C.6

CCSS.Math.Content.7.SP.C.7

CCSS.Math.Content.7.SP.C.8

CCSS.Math.Content.8.EE.A.2

CCSS.Math.Content.8.EE.B.6

CCSS.Math.Content.8.EE.C.8

CCSS.Math.Content.8.F.A.1

CCSS.Math.Content.8.F.A.2

CCSS.Math.Content.8.F.A.3

CCSS.Math.Content.8.F.B.4

CCSS.Math.Content.8.F.B.5

CCSS.Math.Content.8.G.A.2

CCSS.Math.Content.8.G.A.4

CCSS.Math.Content.8.G.A.5

CCSS.Math.Content.8.G.B.6

CCSS.Math.Content.8.G.B.7

CCSS.Math.Content.8.G.B.8

CCSS.Math.Content.8.G.C.9

CCSS.Math.Content.8.SP.A.1

CCSS.Math.Content.8.SP.A.2

CCSS.Math.Content.8.SP.A.3

CCSS.Math.Content.8.SP.A.4