8th Grade Math—Semester B
Move over, Pythagoras.
- Credit Recovery Enabled
- Course Length: 18 weeks
- Course Type: Basic
- Category:
- Math
- Middle School
Schools and Districts: We offer customized programs that won't break the bank. Get a quote.
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.
Here's a sneak peek at a video from the course. BYOP (bring your own popcorn).
Unit Breakdown
8 8th Grade Math—Semester A - 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.
9 8th Grade Math—Semester A - 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.
10 8th Grade Math—Semester A - 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.
11 8th Grade Math—Semester A - 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.
12 8th Grade Math—Semester A - 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.
Recommended prerequisites:
Sample Lesson - Introduction
Lesson 8.02: 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 8.8.02: 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.
Recap
- 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
- Credit Recovery Enabled
- Course Length: 18 weeks
- Course Type: Basic
- Category:
- Math
- Middle School
Schools and Districts: We offer customized programs that won't break the bank. Get a quote.