8th Grade Math—Semester B
Move over, Pythagoras.
Baffled by how dysfunctional functions can be? Upset that most triangles feel more wrong than right? Dismayed that despite your best efforts, lines of best fit are your worst enemies?
Well, not anymore.
We'll guide you through complex systems of linear equations and help you identify functions and relations. (Just a tip: those Groucho glasses aren't fooling anyone.) After we buckle down and prove the Pythagorean Theorem, we'll slide on our 3D glasses and get cozy with cones, cylinders, and spheres. By the time we finish up with scatter plots and lines of best fit, you'll be wishing the math party never ended.
Chock-full of problem sets, activities, and quizzes, this Common Core-aligned course covers:
- solving systems of linear equations and inequalities.
- comparing and describing functions and relations.
- proving and applying the Pythagorean Theorem.
- calculating volumes of 3D solids.
- graphing scatter plots and analyzing lines of best fit.
P.S. 8th Grade Math is a two-semester course. You're looking at Semester B, but you can check out Semester A here.
Unit 8. 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?
Unit 9. 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.
Unit 10. 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.
Unit 11. 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.
Unit 12. 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.
Sample Lesson - Introduction
Lesson 2: Solving Systems of Linear Equations by Elimination
It was a sultry late afternoon in the bustling city of Algebropolis. Suzy Limination, private mathematician, sat slumped at her desk, dripping sweat in spite of the electric fan clattering just inches from her face.
Suddenly the door burst open, and a trio of attackers charged into the room. Suzy recognized the villainous Dr. Pseudoscience and the Bad Data twins, Spin and Skew. The twins rushed Suzy from either side, each brandishing an old CRT television heavy enough to smoosh her clever noggin to pulp. Suzy dropped to the ground and quickly rolled under her desk to safety. Spin and Skew each caught the other's TV set directly in the frontal lobe and slumped to the ground in identical heaps.
Now Suzy was free to focus her full attention on Dr. Pseudoscience. Listening as his footsteps came around the desk to her hiding place, she sent out a sweeping roundhouse kick that caught his ankle and sent him sprawling backwards over the unconscious twins. A light tap to the temple with one of the TVs ensured that he'd be napping along with them for awhile.
With her unexpected visitors comfortably settled in, Suzy locked the door to her office behind her and took off down the sidewalk at full speed. Dealing with multiple adversaries always made her hungry, and Dmitri's Deli would be closing in 10 minutes. If she hurried, she could decide what to do about the mess in her office over a falafel gyro with extra onions.
The above story might read like a cheap paperback, but it contains a valuable moral for the budding algebraist. "Oil your noisy fan already so you can hear your arch nemesis sneaking up on you" is good advice, but not the main message here.
The take-home lesson is to deal with things one at a time, no matter how many come at you at once. Keep this pearl of wisdom in mind as we learn how to solve systems of linear equations algebraically.
Sample Lesson - Reading
Reading 8.2: Resistance Is Futile; You Will Be Eliminated
Solving systems of linear equations algebraically is more accurate than solving them by graphing, but it can feel a little overwhelming. So many equations; so many variables. Where to begin?
We begin by looking for a way to make the problem simpler. An equation with just one variable is much easier to solve than an equation with two (or three!) variables. This lesson and the one that follows it will each cover a different way of solving systems of linear equations one variable at a time.
Today's method is to add two equations together so that one of their variables cancels out. Suzy demonstrated this by letting the Bad Data twins eliminate each other before she tackled the problem of Dr. Pseudoscience. Watch in amazement as we apply the same approach to systems of linear equations in this reading.
We call this method solving by elimination. ("Solving by addition" might be a better description, but it doesn't have the same sinister ring to it.) Notice that in two of the sample problems from the reading, one or both equations had to be multiplied by a coefficient so that x would be eliminated from the sum. Sometimes those pesky critters just won't go quietly.
- The first step in solving systems of linear equations algebraically is to get an equation with just one variable in it.
- We can cancel out variables by adding equations from the same system together.
- It's sometimes necessary to multiply one or both equations by a coefficient to get a variable to cancel out in their sum.
- Once we've figured out one variable, we plug its solution back into one of the original equations to find the value of the second variable.
- It's still a good idea to check our solution by running both variables' values through all the equations in the system.
Sample Lesson - Activity
Activity 8.2c: Problem Set
- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 8
- Course Type: Basic
7th Grade Math—Semester A
7th Grade Math—Semester B
8th Grade Math—Semester A
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.2