8th Grade Math—Semester A
Time to hit the slope-intercept form.
If you've ever thought that math was a bit too irrational—boy, you don't know the half of it. (On second thought, maybe you do.) Thank goodness Shmoop's Common Core-aligned 8th Grade Math course makes it all a little more rational.
Right off the bat, we'll be introduced to irrational numbers and learn the ins and outs of exponents. After delving into expressions and equations for a bit, we'll get our doodle on with some geometric transformations. Once we've covered the basics of linear functions, we'll move onto graphing them on the coordinate plane. (Complimentary peanuts not provided.)
With more readings, drills, problems, and projects than you can shake a stick at, we'll cover:
- approximating and comparing rational and irrational numbers.
- using integer exponents and scientific notation.
- solving one-variable linear equations.
- performing geometric transformations.
- understanding and working with functions.
- graphing linear equations and inequalities.
P.S. 8th Grade Math is a two-semester course. You're looking at Semester A, but you can check out Semester B here.
Course BreakdownPurchase units individually *
*Purchasing by unit includes course material only.
Unit 1. Rational and Irrational Numbers
We'll review the ins and outs of rational numbers and get to know their enigmatic counterparts, irrational numbers. They've been shrouded in mystery, but we'll answer all the questions you ever had about them. What kind of music do they like? What's their favorite Ben and Jerry's flavor? Where do they belong on a number line? (Answers: classic rock, Chunky Monkey, and it depends—in case you were curious.)
Unit 2. Radicals, Exponents, and Number Theory
This unit will be all about understanding the ins and outs of exponents and radicals. The two are opposite operations, which means that one undoes the other. You don't want a number to be squared anymore? Throw a radical over it. Radicals ruining your day? Invite exponents over to set them straight.
Unit 3. Expressions
In this unit, we'll cover the order of operations, the distributive property, and how to translate from English to Algebrese, all of which are important tools in actually using expressions. We'll even simplify your life by teaching you how to simplify and evaluate expressions. By the end, you'll be able to express yourself in more variables than one.
Unit 4. One-Variable Equations
By putting an equal sign between two expressions, one-variable equations dare us to find those values that make them true. The trouble is that equations aren't always going to hand those solutions over easily. They'll hide behind exponents and coefficients, try to intimidate us with cubed roots, or overwhelm us by having infinitely many solutions. But after this unit, solving equations will be a cinch.
Unit 5. Geometric Transformations
If you're sick of numbers and letters, this might just be the unit for you. Aside from a few tricky definitions and a coordinate plane that might give you some turbulence, we're all about movin' and groovin' with figures. Just be careful; some of those shapes have pointy edges. The last thing you want is to be poked in the stomach mid-disco.
Unit 6. Linear Functions
This will be our first glance at functions, so we'll start with the very basics: learning the definition of a function, seeing how they can be identified in tables and graphs, and visualizing them on the coordinate plane. Then, we'll look at linear functions and all of their different parts and pieces—no dissection necessary. Leave that for science class.
Unit 7. Graphing Linear Equations and Inequalities
Our knowledge of linear equations can only get us so far if we don't know how to graph them. Shockingly, graphs of linear equations have a purpose other than looking really cool; they can make problems easier to understand and solve—especially when there are real-world applications to be made. Of course, looking really cool doesn't hurt.
Sample Lesson - Introduction
Lesson 9: Word Problems with Expressions
They say life is like a box of chocolates. Eating nothing but chocolate every day doesn't sound that healthy, though. Now if life were like a box of vegetables, our parents would probably be happy, and we wouldn't be so afraid of losing all our teeth.
Word problems are a bit like a box of chocolates and vegetables. At first we're like, "Yay, words. We use those all the time." They'll be nice and sweet like a chocolate treat. The thing with word problems is that we need to do a bunch of mathematical thinking before we even get to the actual math part. That's like expecting to bite into a milk chocolate with caramel and actually getting a Brussels sprout.
We're going to help you go through this word problem box so that you can eat your vegetables and snack on sweets, all without the taste bud whiplash. If you can handle translating problems into expressions, word problems are a cinch. As long as we keep an additional rule of thumb in mind, word problems should be no more intimidating than a pile of fresh vegetables.
Sample Lesson - Reading
Reading 3.9: Expressing Word Problems with Expressions
We work through word problems the same way we do any other kind of problem. First, figure out what the problem is asking. Second, determine what the variables are. Finally, connect the parts together to give an expression that captures what the problem is asking. No surprises there, unless you lost your memory after our last lesson.
One thing to keep an eye on, though, is units. A lot of word problems deal with physical situations, which means we'll have units and measurements of stuff in the real word. We need to keep our variables and units straight.
For example, if part of the problem requires us to calculate a speed using the expression d/t, we need to know whether d is in millimeters, meters, or kilometers, and whether t is in seconds, minutes, or hours. Otherwise, we'll end up confusing ourselves or misinterpreting the results or making an incorrect substitution, and nobody wants that.
Word problems are filled with code words that we can latch onto and translate directly into parts of an expression. We still have to do a lot of thinking about how all the pieces fit together, though. The phrases for subtracting, for instance, are often backwards from what they look like at first. As the problems get bigger, we have to be more careful to pick out the parts we need. And all the while, we need to keep an eye on our units; when they don't match up, that's a sign that something else is going on with the problem.
Sample Lesson - Activity
Activity 3.9c: Problem Set
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- Course Length: 18 weeks
- Grade Levels: 8
- Course Type: Basic
7th Grade Math—Semester A
7th Grade Math—Semester B
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following standards are covered in this course:CCSS.Math.Content.8.EE.A.1