Khan Academy on a Stick : Introduction to algebra

Khan Academy on a Stick

Algebra

Origins of Algebra
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Where did the word "Algebra" and its underlying ideas come from
Abstract-ness
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The general idea behind the word 'abstract'
The Beauty of Algebra
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Why the abstraction of mathematics is so fundamental
Descartes and Cartesian Coordinates
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Bridging algebra and geometry. What makes linear equations so linear.
Why all the letters in Algebra?
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Jesse Roe and Sal Khan talk about why we use letters in algebra

Overview and history of algebra

Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway? This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.

What is a variable?
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Understanding that a variable is just a symbol that can represent different values
Why aren't we using the multiplication sign
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Why we avoid using the traditional multiplication sign in algebra.
Example: evaluating an expression
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Variables and Expressions 1
Example: evaluate a formula using substitution
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Evaluate a formula using substitution
Evaluating exponential expressions 2
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Evaluating exponential expressions 2
Expressions with two variables
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Basics of expression with two variables
Example: Evaluating expressions with 2 variables
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Evaluating Expressions with Two Variables
Examples of evaluating variable expressions
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Example evaluating expressions in word problems

Variables and expressions

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.

Combining like terms
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Leveraging the power of Chuck Norris to understand combining like terms in expressions
Adding like rational terms
Combining Like Terms 1
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Combining Like Terms 2
Simplifying expression with like terms
Combining Like Terms 3
Hairier example of combining like terms in an expression
Combining like terms and the distributive property
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Doing a few more involved examples of simplifying expressions
Factoring a linear expression with rational terms
Distributive property with rational terms
Equivalent forms of expressions 1

Manipulating 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. Great tutorial if you want to understand that expressions are just a way to express things!

Writing and interpreting 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 get experience writing algebraic expressions to elegantly represent real-life ideas.

Why we do the same thing to both sides: simple equations
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Thinking about how to solve for an unknown mystery mass
Representing a relationship with a simple equation
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Why we can represent the unknown mass problem as a simple equation
One-Step Equation Intuition
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Why we solve one-step equations the way we do.
Adding and subtracting the same thing from both sides
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Two worked examples of solving simple equations
Intuition why we divide both sides
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Conceptual understanding of why one needs to divide both sides of an equation to solve for a variable
Why we do the same thing to both sides: two-step equations
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Why we do the same thing to both sides: multi-step equations
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Why we do the same thing to both sides basic systems
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Why all the letters in Algebra?
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Jesse Roe and Sal Khan talk about why we use letters in algebra

The why of algebra

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.

Super Yoga Plans- Basic Variables and Equations
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Beginning to evaluate which yoga plan is better for me
Super Yoga Plans- Solving One-Step Equations
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Solving one-step equations to see how many sessions can be attended
Super Yoga Plans- Plotting Points
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Visualizing the relationship between sessions attended and total cost
Super Yoga Plans- Solving Systems by Substitution
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Continuing our Yoga plan debate by determining where the lines representing the two plans intersect
Super Yoga Plans- Solving Systems by Elimination
Another way to solve for the number of sessions at which both plans cost the same

Yoga plans

This tutorial is a survey of all the core ideas in a traditional first-year algebra course. It is by no means comprehensive (that's what the other 600+ videos are for), but it will hopefully whet your appetite for more algebra!

Variables Expressions and Equations
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Introduction and examples of variables, expressions and equations

Getting a feel for equations and inequalities

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.