Introduction to algebra

Origins of algebra

Where did the word "Algebra" and its underlying ideas come from?

Abstract-ness

The general idea behind the word 'abstract'

The beauty of algebra

Why the abstraction of mathematics is so fundamental

Descartes and Cartesian coordinates

Bridging algebra and geometry. What makes linear equations so linear.

Why all the letters in algebra?

Jesse Roe and Sal Khan talk about why we use letters in algebra

What is a variable?

Our focus here is understanding that a variable is just a symbol that can represent different values in an expression. We got this. Just watch.

Why aren't we using the multiplication sign?

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Evaluating an expression example

Evaluate the given expression where the variable could have 3 possible values. Understanding how expressions are interpreted according to different variable values is a huge new skill. Pat on the back!

Evaluating an expression using substitution

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

Evaluating exponential expressions 2

Evaluating exponential expressions 2

Expressions with two variables

Basics of expression with two variables

Example: Evaluating expressions with 2 variables

Evaluating Expressions with Two Variables

Evaluating an expression in a word problem

In this example of evaluating expressions, we're dusting off some geometry. On top of that, it's a word problem. We're seeing how different concepts in math are layered on top of each to create more interesting and complex problems to solve.

Combining like terms

In simple addition we learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add the numbers.

Adding expressions

So what if we add not just numbers or variables..but expressions? Here's a simple example to get you thinking about this.

Combining like terms explained

Another good explanation (minus Chuck Norris) on the how we combine like terms in algebra. This will totally make sense.

Combining like terms example 2

We're going to simplify this expression together putting to use our new knowledge of how to combine like terms. Ok? Let's do it!

Combining like terms, but more complicated

This example of combining like terms in an expression get a little hairy. Listen closely.

Combining like terms and the distributive property

We've learned about order of operations and combining like terms. Let's layer the distributive property on top of this.

Applying the distributive property

In this example we are asked to expand an expression using the distributive property. Practice this one with us.

Equivalent forms of expressions

We're looking to find the expressions that are equivalent to a given expression that can be simplified. Give it a try with us.

Writing simple algebraic expressions

Can you write the algebraic expressions that represent what these statements are saying? Sure you can! We'll help you.

Writing algebraic expressions

These sentences describe or represent algebraic expressions. See if you can translate them for solving. We'll do it together.

Writing algebraic expressions example 2

Like other exercises in this tutorial, we're rewriting statements into algebraic expression. This time we have to choose which is the correct one among those given.

Interpreting linear expressions, 1

We match the expressions to their meaning in this example. We're reinforcing our knowledge of linear expressions.

Interpreting linear expressions, 2

Let's practice matching expressions to their meaning in this example of interpreting linear expressions.

Writing algebraic expressions word problem

Here we interpret data in a table and solve a word problem by writing an algebraic expression.

Writing algebraic expressions word problem example 2

We're writing an expression to answer a word problem about butter. Could there be a better reason to do this?

Writing algebraic expressions example 3

The more you practice, the better you get at writing algebraic expressions. So don't hesitate. Let's go!

Why we do the same thing to both sides: Simple equations

The example of a scale where we try to achieve balance helps to explain why we do the same thing to both sides of an equation.

Representing a relationship with a simple equation

Equations are about relationships (no, not girlfriends and boyfriends!) between the two sides of the equation. Let's again use a scale example to help us understand.

One-step equation intuition

This equation can be simplified through a single step to solve for the variable. Can you help?

One step equation intuition introduction

To find the value of a variable, you sometimes have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation. Watch. We'll explain why we do this.

Adding and subtracting from both sides of an equation

Let's watch as we demonstrate how we add and subtract to both sides of an equation in order to isolate the variable on one side.

Dividing from both sides of an equation

Let's get a conceptual understanding of why one needs to divide both sides of an equation to solve for a variable.

Solving two-step equations

Here's how we solve a two step equation. It begins with the concept of equality: what we do to one side of the equation must be done to the other.

Why all the letters in algebra?

Jesse Roe and Sal Khan talk about why we use letters in algebra

Variables and equations word problem: Putting them to work for Super Yoga

Using information from the Super Yoga word problem, explore all the possible combinations and create equations which express the possibilities. Let's figure out which plan is best!

Variables and equations word problem: Which Super Yoga plan is best?

If you're coming to this video before seeing the previous one, back up! Otherwise, we're solving one-step equations to learn which Super Plan is the best value for our budget.

Super Yoga plans: Plotting points

Visualizing the relationship between sessions attended and total cost

Super Yoga plans: Solving systems by substitution

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

Variables, expressions, and equations

This video will give you a great understanding of variables, expressions, and equations. If you've struggled with them before, this one may just do the trick!

Substituting variables and judging inequalities

In this word problem we're looking to see if various possible answers can be substituted for variables in the expressions, and if the resulting equality holds up. That may actually sound harder than it is, so just jump in with us!

Substituting variables and simple equation

This basic equation asks us to substitute for a variable with given values in order to find correct one.

Substituting variables and solving for an equality

The great thing about understanding expressions and equalities is that they can be used to solve real life problems, like how many dogs you can eat in a minute!

Substituting variables and solving for an inequality

Here's a slightly more complicated expression that seeks not equality, but a greater than relationship. Help us try out different values until we succeed.

Dependent and independent variables exercise: the basics

Here we have a problem that asks us to identify which variables are dependent and independent. Hint: independent variables are not influenced and remain unchanged by the other variable.

Dependent and independent variables exercise: graphing the equation

It's helpful to express an equation on a graph where we plot at least 2 points. Watch and we'll show you.

Dependent and independent variables exercise: express the graph as an equation

We're flipping the last video on its head and doing the opposite. This time we give you the graph and ask you to express it as an equation.