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8th Grade Math—Semester A

Time to hit the slope-intercept form.

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

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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.

Here's a sneak peek at a video from the course. BYOP (bring your own popcorn).

Unit Breakdown

1 8th Grade Math—Semester B - Systems of Linear Equations and Inequalities

In this unit, we're going to work with two of the most common algebraic tools that humans use to plan and strategize: systems of linear equations and systems of linear inequalities. You can use them to plan your entrepreneurial ventures, strategize your rise to power, and orchestrate your eventual takeover of the free world. Useful stuff, isn't it?

2 8th Grade Math—Semester B - Functions and Relations

By the end of this unit, you'll have so many new function friends, you'll need to build a bigger tree fort. We'll get familiar with what our function pals look like in algebraic or in graph form, what kinds of x and y values they have, their favorite One Direction song, and what their food allergies are. You know; all those little details that friends should know about each other.

3 8th Grade Math—Semester B - Triangles and the Pythagorean Theorem

Triangles are really basic stuff, right? After all, how many permutations of three sides and angles can there be? Sure, the shapes themselves are pretty simple and predictable—but that doesn't mean there isn't a lot to say about them. We'll explore these three-legged creatures in their natural habitats and even use the Pythagorean Theorem to prove that some are more right than others.

4 8th Grade Math—Semester B - 3D Geometry

This unit is all about getting to know cylinders, cones, and spheres inside and out—and we're literally talking about the insides and outsides of these solids. We'll learn their volume and surface area formulas and even dive into a bit of density, so it may help to break out the calculator for this one. We'll finish off with a hands-on project that'll get students psyched about circular solids.

5 8th Grade Math—Semester B - Statistics

In this unit, we're going to cover the basics of collecting and analyzing bivariate data, or data that explains the relationship between two variables. With two-way frequency tables and scatterplots abound, we'll guide you through the complexities of nonlinear associations, linear models, and both numerical and categorical data. By the time we're through, lines of best fit will be your very best friends. Get the scrapbook ready.

6 8th Grade Math—Semester A - 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.)

7 8th Grade Math—Semester A - 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.

Recommended prerequisites:

  • 7th Grade Math—Semester A
  • 7th Grade Math—Semester B

    • Sample Lesson - Introduction

    Lesson 3.09: 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 3.3.09: 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.

    Recap

    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

    1. When solving problems, it's always best to evaluate the expression from left to right. Is this true or false?

    2. Bobby has twice as many pants and four times as many shirts as his sister, Sally. If the number of pants and shirts Sally owns are p and s, which expression represents the total items of clothing Bobby has?

    3. We look for the sum and product when working with division and subtraction. Is this true or false?

    4. Tyler found three times as many Easter eggs as Andy did at the Easter egg hunt. As they were leaving, Tyler dropped his basket, six Easter eggs fell out and rolled down the hill. Andy, in his glee at Tyler's misfortune, dropped his basket and lost three of his own eggs. If e represents the number of eggs Andy found, which of the following expresses the number of eggs Andy and Tyler have total?

    5. Batman is, secretly, a very neat and orderly superhero. Today, he is grouping his 70 Batarangs in groups of 5. When he's done organizing, he looks out the window to see the Bat Signal and orders Alfred to grab three groups of Batarangs to go. How many groups of Batarangs are left?

    6. Larry is driving from Boise, Idaho to Akron, Ohio for the most delicious White Castle burgers he has ever had. The trip is 2045 miles one way. How can we express the number of nonstop hours Larry has to drive if he drives at a speed of r miles per hour?

    7. Amanda, Mary, and Tamera all play the piccolo, so why not have a concert showcasing their musical talents? Amanda plays twice as many piccolo pieces as Mary, while Tamera plays one piece less than Mary. If we let m represent the number of piccolo pieces Mary plays, which of the following expresses the number of piccolo pieces played in the entire concert?

    8. Andi had $100. She gave Mike some money and then gave Brian twice that amount. Which of the following expresses the amount of money Andi has left over?

    9. Declan found 45 pencils and gives his sister p of them (you know, because he's nice like that). If he splits up his remaining pencils into groups of 5, write an expression that represents the groups of pencils that Declan has.

    10. Andy has g green Legos. He has eight more white Legos than green Legos, 10 more yellow Legos than green Legos, and three less red Legos than green Legos. Write an expression that represents all the Legos that Andy has, and explain what that expression tell us.

    11. Patrick baked twice as many cookies as Angela. Angela baked three more cookies than Sally. Write an expression that gives the number of cookies Patrick baked in terms of the number of cookies Sally baked.

    12. The expression 4p + 32 could express which of the following values?