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Pre-Algebra I—Semester B

Not all equations are created equal.

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

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We know why you're here. Either you thought that last semester was a blast and you're ready for more, or you're one of those nosy types with a magnifying glass and a funny detective hat, always looking for the final clue, that last unknown that solves the whole equation.

Yes, we have been reading a lot of Nancy Drew lately. How'd you guess?

If you're looking for a fast and furious journey into the unknown—unknown variables, that is—then look no further. Grab a pencil and notebook, and it can't hurt to bring along a magnifying glass and a sidekick, too. (Where would Sherlock be without his trusty Watson?)

In this Common Core-aligned course, you'll get practice problems, examples, and activities that cover

  • calculating the perimeters and areas of triangles, quadrilaterals, circles, and just about any polygon you can think of. We'll even get our feet wet with the 3D realm of geometry, too.
  • translating English into numerical and variable expressions. We suggest keeping a pocket dictionary handy.
  • writing and solving one-variable equations and inequalities as well as some simple two-variable ones.
  • conducting legit statistical studies, analyzing the data, and representing it appropriately.

With a mastery of expressions, equations, inequalities, and statistics under your belt, we imagine there's little you won't be able to take on in your post-Pre-Algebra life.

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

Unit Breakdown

7 Pre-Algebra I—Semester A - Number Theory

Compared to Quantum Theory, Relativity Theory, and the Lost Sock Theory (for washing machines), number theory is pretty concrete. Probably because we have so many concrete strategies to deal with it; things like prime factorization, factor trees, and the GCF and LCM. If those sound like a bunch of random words thrown together, don't worry. You'll see some concrete examples soon enough. 

8 Pre-Algebra I—Semester A - Ratios, Proportions, and Percents

Numbers don't just sit there, isolated from the rest of the world. They tell about…stuff. And things! Can't forget about the things. If you want some more details than that, then we can bring in ratios, proportions, and percents, which are all about how two things relate to each other. And we don't mean in a family tree kind of way.

9 Pre-Algebra I—Semester A - Coordinate Graphs

Even if you have a perfect sense of direction, a coordinate plane will still help you navigate the wild world of numbers. We can use it to plot points, find distances on the plane, and reflect things across both its axes. It's like a map, compass, and GPS all in one, and you only need paper and pencil to make it work. Handy!

10 Pre-Algebra I—Semester A - Scale Factors and Dilations

Well, we have these coordinate planes that we can put points and shapes on. We also know about ratios and proportions, which tell us how two different things are related to each other. What happens if we smash them together? We'll see that similar figures, scale factors, and dilations will all fall out of the aftermath. We suggest bringing an umbrella.

Recommended prerequisites:

  • Pre-Algebra I—Semester A

    • Sample Lesson - Introduction

    Lesson 8.05: Numerical Expressions

    This is the definition of a "don't care-ical" expression.

    (Source)

    Before we saddle up those bucking broncos known as variable expressions, let’s take a few turns around the pasture with numerical expressions. Numerical expressions are gentle old ponies that won’t try to throw you with fancy tricks like variables. These simple creatures are made up of only two things: numbers and operations.

    Friendly as they may be, numerical expressions still have their little quirks, and we’re going to get good and familiar with those before we head out on the trail. We might want to bring a carrot or two for them—just in case.

    Numerical expressions are math phrases that we use to describe real-world situations. Let's say you want to figure out how many honey badger posters it would take to completely cover your bedroom ceiling. Or maybe your situation is even real-er, and you're calculating how many cans of honey badger chow you need to buy to survive this month with all your body parts intact.

    A numerical expression will fearlessly wrangle these problems for you. No foe is too ferocious for numerical expressions. They're just crazy. They don't care.

    Sample Lesson - Reading

    Reading 8.8.05: The Anatomy of an Expression

    At this point, you've already performed thousands of operations in your math career: applying exponents, multiplying and dividing, adding and subtracting, and maybe the occasional ingrown toenail removal. When we do several types of operations on one patient—er, numerical expression—these procedures need to happen in a particular order. Don't start slicing and dicing before you've administered the anesthetic, for cryin' out loud!

    Let's change into our scrubs, wash our hands for an hour or so, and review the standard operating procedure with this reading.

    Old news, you say? Did you get antiseptic in your eyes, or are those tears of boredom? Never fear, Mathketeers; we're going to toss a new beat into the mix to keep you on your toes.

    An exponent is like a little fairy that floats above a number's shoulder, whispering how many times that number must be multiplied by itself. (If you want to see an exponent's tiny wings, you have to clap your hands and say, "I do believe in exponents!") In the example below, 7 is the exponent and 3 is the base (the number being multiplied):

    37 = 3 × 3 × 3 × 3 × 3 × 3 × 3

    Seven! Seven threes…ah ah ah! Ahem, please excuse our inner Sesame Street Count. To get the exponent's point of view, check out this video .

    When the number two is used as an exponent, we say that the base is being squared. Squaring five, for example, gives us 25: 52 = 5 × 5 = 25.

    Now here comes the dramatic tension—did you know that our little fairy exponent 2 has an evil twin? One who undoes all his efforts by reversing his spells? It's true. We call this little rebel the square root, and she belongs to a species known as radicals. Her symbol looks a bit like a checkmark, and when she's got a number in her clutches, it means that we need to figure out what base was squared in order to yield that number:

    √25 = 5
    √16 = 4
    √9 = 3

    The square root is just the tip of iceberg. There are oodles more radicals out there; in fact, every exponent ever invented has its own evil twin. Told you there'd be drama in the club tonight. For now though, we'll stick to the square root two-step in our numerical expression barn dance. No need to blow minds with any radical Bollywood moves until the moment is right.

     

    Recap

    • Numerical expressions are math phrases used to describe real-world situations.
    • Unlike variable expressions, numerical expressions contain only numbers and operators; no letters allowed! 
    • The rules of order of operations (abbreviated as PEMDAS) must be followed in order to correctly evaluate a numerical expression.

    Sample Lesson - Activity

    1. Is it true or false that numerical expressions are the same as variable expressions?

    2. Is it true or false that √2 2 = 2?

    3. Simplify the expression √32.

    4. Identify the base of the expression 42.

    5. Identify the exponent of the expression 12.

    6. Which operation is done first to simplify 9(8 + 2)?

    7. Which expression is equivalent to 4 × 4 × 4?

    8. Which expression is equivalent to 2 × 2 × 2 × 3 × 3?

    9. Identify the square root of 25.

    10. Mark and his brother are playing an intense game of Monopoly (we're talking elbows flying, here), and Mark starts with $1500.00.  He uses $500.00 to buy some property; however, the property's value falls flat, so he doesn't make any revenue.  If Mark ends up with a final amount of $1000.00, write an equation that describes how much money he ended the game with.

    11. Jennifer is going shopping for school clothes with her mom's credit card, which has a limit of $500.00.  If she buys four pairs of shoes, write an equation that describes how much money is left on the card after she has finished shopping.

    12. Jeff is planning on doing three dances at his school's talent show: The Stanky Leg, The Dougie, and The Nae-Nae.  However, before his performance he is told that he will only have time to complete one dance.  Write an equation that describes how many dances he actually performed.