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8th grade (U.S.)

8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life (no way to avoid the miseries of wedding planning), but at least your mathematical life. Seriously, we're not kidding. If you get the equations and functions and systems that we cover here, most of high school will feel intuitive (even relaxing). If you don't, well.. at least you have high school to catch up. :) On top of that, we will sharpen many of the skills that you last saw in 6th and 7th grades. This includes extending our knowledge of exponents to negative exponents and exponent properties and our knowledge of the number system to irrational numbers! (Content was selected for this grade level based on a typical curriculum in the United States.)
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Relationships and functions
All content in “Relationships and functions”

Graphing and analyzing proportional relationships

In proportional relationships, the ratio between one variable and the other is always constant. In the context of rate problems, this constant ratio can also be considered a rate of change. This tutorial allows you to dig deeper into this idea. Common Core Standard: 8.EE.B.5

Intercepts of linear functions

There are many ways to graph a line and this tutorial covers one of the simpler ones. Since you only need two points for a line, let's find what value an equation takes on when x = 0 (essentially the y-intercept) and what value it takes on when y = 0 (the x-intercept). Then we can graph the line by going through those two points.

Slope of a line

If you've ever struggled to tell someone just how steep something is, you'll find the answer here. In this tutorial, we cover the idea of the slope of a line. We also think about how slope relates to the equation of a line and how you can determine the slope or y-intercept given some clues. Common Core Standard: 8.F.B.4

Triangle similarity and slope

In this tutorial, we use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. We'll connect this idea to the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Common Core Standard: 8.EE.B.6

Function notation

f(x), g(x), etc. What does this mean? Well they are ways of referring to "functions of x". This is an idea that will show up throughout more advanced mathematics and computer science so it is a good idea to understand them now!

Recognizing functions

Relationships can be any association between sets of numbers while functions have only one output for a given input. This tutorial works through a bunch of examples of testing whether something is a valid function. As always, we really encourage you to pause the videos and try the problems before Sal does! Common Core Standard: 8.F.A.1

Linear and nonlinear functions

Not every relationship in the universe can be represented by a line (in fact, most can't be). We call these "nonlinear". In this tutorial, you'll learn to tell the difference between a linear and nonlinear function! Have fun! Common Core Standare: 8.F.A.3