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Pre-Algebra II—Semester A

We've got the powers.

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

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If math just sat still, like a bump on a log, it wouldn't be of much use to anyone. Not even mathematicians would get excited about it—and you should see some of the things they get worked up over. Lucky for everyone, then, that math is full of sound and fury, signifying something awesome.

(Levels of awesome may vary.)

In this Common Core-aligned course, we'll peel back the veil and uncover the mysteries of all the algebra that comes before Algebra. With boatloads of problem sets, readings, and quizzes, we'll cover

  • rational and irrational numbers
  • radicals, exponents, and number theory
  • linear equations and inequalities with one and two variables
  • transformations of geometric figures
  • linear functions

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

Unit Breakdown

1 Pre-Algebra II—Semester B - 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?

2 Pre-Algebra II—Semester B - 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.

3 Pre-Algebra II—Semester B - 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.

4 Pre-Algebra II—Semester B - 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!

5 Pre-Algebra II—Semester B - 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.

6 Pre-Algebra II—Semester B - 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!

7 Pre-Algebra II—Semester A - Rational and Irrational Numbers

Get ready for the next level of numbers: rational and irrational numbers. Sure, they might be as different as apples and orangutans, but it's good to have some variety. We'll learn how to convert rational numbers into fractions, how to identify those pesky irrationals, and even how to approximate irrational numbers using rationals. We wouldn't suggest approximating apples with orangutans, though; that might get messy.

Recommended prerequisites:

  • Pre-Algebra I—Semester A
  • Pre-Algebra I—Semester B

    • Sample Lesson - Introduction

    Lesson 3.06: Solving Inequalities Using Multiplication and Division

    Addition and subtraction are great, but sometimes we need another level of solving power. It's just like when you exchange your handsaw for a chainsaw, or add extra thrusters to your rocket ship. Your tool has to be up to the challenge of your problem. For us, the extra boosters are multiplication and division.

    With these added boosters, there's no way the atmosphere is keeping us in this time.

    (Source)

    Thankfully, utilizing this new, heavier-duty solving mechanism doesn't actually make our solution more complex. In fact, multiplication and division in inequalities follow the same rules that addition and subtraction do, which is to say that they follow the same rules regular equations do. It all boils down to our Golden Rule of algebra: Everything you do to one side you have to do to both.

    There is one very important thing to not overlook. The information in this lesson only applies when we are talking about multiplying or dividing by a positive factor. If our factor is negative, the rules are slightly different, and all those rules are covered in the next lesson. Just remember to keep on the positive side of things for now and you'll be just fine.

    Sample Lesson - Reading

    Reading 3.3.06: Solving Inequalities using Multiplication and Division

    Dividing your inequalities by positive numbers won't really look any different than dividing a run-of-the-mill equation by a positive number. Again, we need whatever we do to take place on both sides. (But by now, you know that's basically a given.) We just have to choose the vale to multiply or divide which will allow us to cancel things off and simplify our statement. Then, we can draw conclusions about the values that can solve our inequality.

    This quick video will give us an example of real life equalities and division in action. Try not to get too caught up in the emotional cause at hand. We know blobfish are sympathetic, but keep your eyes on the math.

    Recap

    When we work with inequalities, the same rules for multiplication and division apply that do with normal equations. The exception here is when we are dividing or multiplying by a negative number, but we will get into much greater depth on the topic in the next lesson. For now just remember that when a coefficient or quotient is positive, nothing about the sign has to change. It's beautiful just the way it is.

    Sample Lesson - Activity

    1. What is the solution to the inequality 4b > 24?

    2. What is the solution to the inequality 3x + 8 ≤ 29?

    3. What is the solution to the inequality -3 + 0.5c ≥ 7?

    4. Remember that History exam you forgot to study for? Yeah, well, it's make up time. You need to average a 92 on the next four exams in order to bring your grade back up. Which of the following inequalities represents the total combined score you need on the four exams in order to improve your grade?

    5. What is the solution to the inequality x⁄9 + 15 ≤ 22?

    6. What is the solution to the inequality 12 > p⁄24?

    7. The Shmooze Brothers are coming to town and you are dying to rock out at their concert. Tickets are $75 each and you only have one night waitressing to earn the money. You work an eight-hour shift and earn $35 in tips. Which of the following inequalities shows the minimum you need to make per hour in order to earn enough for the ticket?

    8. Solve the inequality 5a + 4.25 > 9.25.

    9. What is the solution to the inequality ⅛t – 1 ≠ 0?

    10. Solve the inequality -11 ≥ 2b + 11.

    11. Your parents have saved and saved to send you to the finest institution of higher learning: Clown College. After paying for the boring stuff (i.e., tuition, room and board, books), you have $16,260 for entertainment, food, and clothes for the next four years of college. Before you head off to school, your brother decides it is the perfect time to pay you back that $300 he borrowed. After your brother paid you back, how much can you afford to spend per month over the next four years?

    12. Solve 3(x – 2) < 33 for x.