Learn about functions, graphs, lines, and polynomials. "Algebra" is the math for describing how different things are related.
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1. Addition and subtraction
Number line 
Locating integers and non-integers on the number line
Addition
Using the number line to add numbers
Subtraction
Moving left on the number line
Adding negatives
What happens when you add negative numbers?
Subtracting negatives
Turns out it's addition!
Absolute value
The "size" of a number, or how far it is from zero
Number line distance
Ways to find the distance between any two numbers
2. Multiplication and division
Multiplication
Multiplying positive numbers, in any order
Multiplying by 1 and 0
Discover what happens when you multiply by 1 and 0
Division
Dividing positive numbers, and ways to think about it
Dividing by 0
An operation you just can't perform...
Order of operations
Is there more than one way to evaluate an expression?
Distributive law
Getting rid of parentheses when you add and multiply
Multiplying negatives
What happens when you multiply negatives together?
Dividing negatives
What happens when you divide negative numbers?
Distributing negatives
Distributing a negative flips the signs
[Brackets] and {braces}
What to do when you have too many parentheses!
Finding the average
Discover how to find the "average" of numbers
3. Factoring
Factors
Dividing by a factor always gives you a whole number
Prime numbers
Their only factors are 1 and themselves
Factoring out
Pulling out common factors using the distributive law
Factoring out negatives
Flip the signs when you factor out negative numbers
Greatest common factor
The biggest factor that numbers have in common
Relatively prime
When two numbers have no common factors
Euclid's algorithm
A 2000-year-old way to calculate the GCF
Multiples
What you get when you multiply numbers by integers
Least common multiple
The smallest multiple numbers have in common
4. Fractions
Intro to fractions
Draw and compare fractions, and convert to decimals
Multiplying fractions
What's 1/2 times 3/5? Learn the trick in this lesson!
Comparing fractions
How to tell when fractions are equal or which is bigger
Cancellation
Simplifying fractions by removing common factors
Adding fractions
Add and subtract fractions using common denominators
Dividing fractions
Dividing by a fraction is really multiplying by its reciprocal!
Reciprocals
A number's multiplicative inverse is 1 over the number
Mixed fractions
Switching between mixed and improper fractions
Distributing division
The distributive law works for multiplying, but also dividing
When 'of' means multiply
Evaluating fractions of numbers (like 5/7 of 210)
5. Powers and roots
Squaring a number
Multiplying a number by itself
Raising to powers
Squaring, cubing, raising to the fourth, and so on...
Square roots
Work backwards to find the number that was squared
Roots of non-squares
How to find the roots of numbers that are NOT square
Square roots of negatives
Do negative numbers even have square roots?
Cube roots and beyond
Cube roots, fourth roots, fifth roots, and so on...
PEMDAS
Order of operations, now with exponents!
6. Rules for powers
Multiplying powers
A rule for multiplying one power by another
Dividing powers
A rule for dividing one power by another
Raising powers to powers
A rule for raising one power to another
Distributing powers
It works for multiplication and division, but that's it!
Raising to the zero
What happens when you raise a number to the zero?
Negative powers
What does it mean to raise to a NEGATIVE exponent?
Roots as powers
Taking a root is really the same as raising to a power
Fractional powers
What does it mean to raise to the 2/3 power?
Distributing roots
Roots are also exponents, so the same rules apply!
Simplifying roots
Getting smaller numbers under the root
7. Solving equations
Solving for unknowns
Solve for unknown values using the number line
Algebraic expressions
Learn how to evaluate expressions with variables
Solving by adding
Adding or subtracting on both sides of equations
Solving by multiplying
Multiplying or dividing on both sides of equations
Cross multiplication
A quick way to solve equations with fractions
Coefficients
Numbers in front of variables
Combining like terms
Adding/subtracting terms with matching variables
Multi-step equations
Sometimes it takes more than one step to solve!
Multivariable equations
Solving equations when they have more than one variable
Unsolvable equations
Some equations have no solutions, others have plenty!
8. Inequalities and simultaneous equations
Inequalities
Plotting inequalities on the number line
Solving inequalities
Solving and plotting multi-step inequalities
Negative inequalities
What happens when you multiply by a negative
2 equations, 2 unknowns
Solve for both variables when you have two equations
2 equations, no solution
Sometimes two equations have no solutions, or many!
9. Coordinates
The coordinate plane
Plotting points and finding their coordinates
Quadrants
The four quadrants, and the coordinates they contain
Finding a midpoint
Given two points, which point is exactly halfway between?
10. Slope
Slope (an introduction)
A number that tells you the steepness of a line
Slope formula
How to calculate the slope between any two points
Negative slopes
Discover what it means when slope is negative
Zero slope
What are the slopes of horizontal and vertical lines?
Find the slope of any line
Two steps that will always give you the correct slope
Parallel slopes
Explore why parallel lines have the same slope
Perpendicular slopes
Discover how slopes of perpendicular lines relate
11. Lines
Graphing an equation
Turn an equation into your very first graph!
Slope-intercept form
Turning an equation into a line, and vice versa
Point-slope form
A formula for when you know the slope and coordinates
Reading graphs
Forget equations, let's just look at the graphs!
Intercepts
Figuring out where lines cross the x- and y-axes
Solving for intersections
Given two lines, can you determine where they cross?
Graphing absolute value
Exploring a graph that's not a line
Inequalities (2 variables)
Simplify inequalities with two variables and test solutions
Graphing inequalities
Graph inequalities on the coordinate plane
12. Polynomials
What are polynomials?
Learn about a common type of algebraic expression
Adding polynomials
Computing sums and differences of polynomials
Multiplying monomials
Multiply and divide polynomials with one term
Multiplying binomials
Multiply binomials together using FOIL
Multiplying polynomials
How to multiply polynomials with many terms
Difference of squares
A neat trick for simplifying certain binomials
13. Quadratics
Quadratic equations
Sometimes, equations can have two solutions
Graphing a parabola
Plot points to draw your very first parabola
Graphing quadratics
Every quadratic graph boils down to these 3 numbers
Factoring quadratics
An extremely useful trick for solving some equations
The quadratic formula
A method for solving ANY quadratic equation!
Discriminants and roots
A quick way to tell how many solutions a quadratic has
14. Functions
15. Polynomials
