By the 6th grade, you're starting to become a sophisticated mathemagician. You'll be able to add, subtract, multiply, and divide any non-negative numbers (including decimals and fractions) that any grumpy ogre throws at you. Mind-blowing ideas like exponents (you saw these briefly in the 5th grade), ratios, percents, negative numbers, and variable expressions will start being in your comfort zone. Most importantly, the algebraic side of mathematics is a whole new kind of fun! And if that is not enough, we are going to continue with our understanding of ideas like the coordinate plane (from 5th grade) and area while beginning to derive meaning from data! (Content was selected for this grade level based on a typical curriculum in the United States.)
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# Variables and expressions

Learning algebra is a little like learning another language. In place of words, algebra often uses symbols in the forms of variables (letters) which are sometimes combined with numbers to form expressions (words/phrases) and combined further to create equations or inequalities (sentences). Ok, that comparison may have a few flaws, but you get the idea. In this group of tutorials, we'll learn about and practice writing, evaluating, and adding expressions; order of operations; substitution; combining like terms; and solving equations and understanding inequalities.
All content in “Variables and expressions”

## Writing expressions

All the symbols you write in math are just a language or short-hand to represent real-world ideas. In this tutorial, we'll look at some of the short-hand including variables, expression terms, factors and coefficients. Mostly, however, we'll get experience writing algebraic expressions that elegantly represent real-life ideas. Common Core Standard: 6.EE.A.2, 6.EE.A.2b

## Evaluating numerical expressions

Mathematics wouldn't be so useful if, interpreted in different ways, the same expression could be viewed to represent different values. To combat this issue, the mathematical community defined "orders of operations" to remove ambiguity when evaluating an expression. Our acronym is PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction. Get it? Of course you. Let's talk more about order of operation and how will apply it.

## Evaluating expressions with variables

Wait, why are we using letters in math? How can an 'x' represent a number? What number is it? I must figure this out!!! Yes, you must. This tutorial is great if you're just beginning to delve into the world of algebraic variables and expressions. It will help guide your understanding of how variables can be substituted with different values and therefore giving us different outcomes. Common Core Standards: 6.EE.A.1, 6.EE.A.2b, 6.EE.A.2c

## Equivalent expressions

Using the combined powers of Chuck Norris and polar bears (which are much less powerful than Mr. Norris) to better understand what expressions represent and how we can manipulate them. We'll achieve a good understanding of the concept of "like terms" and combining expressions. Great tutorial if you want to understand that expressions are just a way to express things! Common Core Standards: 6.EE.A.3, 6.EE.A.4

## Solving equations and inequalities with substitution

The core underlying concepts in algebra are variables, expressions, equations and inequalities. You will see them throughout your math life (and even life after school). This tutorial won't give you all the tools that you'll later learn to analyze and interpret these ideas, but it'll get you started thinking about them. Common Core Standards: 6.EE.B.5, 6.EE.B.6, 6.EE.B.7

## Solving basic equations

Much of algebra seems obsessed with "doing the same thing to both sides". Why is this? How can we develop an intuition for which algebraic operations are valid and which ones aren't? This tutorial takes a high-level, conceptual walk-through of what an equation represents and why we do the same thing to both sides of it. Common Core Standard: 6.EE.B.7

## Variables and equations word problem: Super Yoga

Let's use our algebra tools to solve a problem of earth-shattering importance: which Super Yoga plan is the best value! In this word problem, you'll put to practice your knowledge of variables, substitution, and one-step equations. Common Core Standard: 6.EE.B.6

## Solving equations for beginners

Like previous tutorials in this topic, we'll introduce you to the most fundamental ideas of what equations mean and how to solve them. We'll then do a bunch of examples to make sure you're comfortable with things like 3x – 7 = 8. So relax, grab a cup of hot chocolate, and be on your way to becoming an algebra rockstar. And, by the way, in any of the "example" videos, try to solve the problem on your own before seeing how Sal does it. It makes the learning better! Common Core Standard: 6.EE.B.7

## Dependent and independent variables

We know that anything that is "independent" is not affected by other "dependent" forces. In math relationships (and algebra, in particular), one variable (the independent one) is thought to drive the behavior of the other one (the dependent one). This tutorial explores that relationship and how it can be expressed and interpreted. Common Core Standards: 6.EE.C.9

## Inequalities

Not all expressions are created equal, but we can still use some algebra to compare unequal numbers, variables, and/or expressions in interesting ways, like inequalities. You've heard of "greater than" and "less than," right? Terrific! First we'll express inequalities on a number line and then write them using information in word problems. Common Core Standard: 6.EE.B.8