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# Algebra I

## Strengthen your algebra skills by exploring factorials, exponents, and the unknown.

Explore graphs of equations, exponents, counting problems, and more, emphasizing intuition and understanding over just finding an answer.

This course will deepen your knowledge of basic algebra and introduce you to some surprisingly useful applications of this powerful mathematical tool.

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1. 1

### Introduction

Strengthen your algebra skills by exploring factorials, exponents, and the unknown.

1. #### Exponent Shortcuts

Learn to solve exponent problems quickly and efficiently.

2. #### Line Exploration

Play with lines and build an understanding of the equations that define them.

3. #### When 1 = 2

What kind of algebraic errors lead to obviously wrong conclusions?

2. 2

### Equations and Unknowns

Sometimes x is unknown, and sometimes it's unknowable.

1. Included with

#### Combination Locks

How much information is needed to pin down the exact combination?

2. Included with

#### Equations and Variables

How does the number of variables affect what can be known about the equations?

3. Included with

Practice solving multi-equation problems.

4. Included with

#### Graphing Equations

Explore the connections between lines and the equations that generate them.

3. 3

### Manipulating Exponents

A powerful language for the very large and the very small.

1. Included with

#### Orders of Magnitude

Learn how to use scientific notation to more skillfully talk about very large and very small measures.

2. Included with

#### Same Bases 1

Derive the rules for combining exponential terms by thinking about exponents as repeated multiplication.

3. Included with

#### Same Bases 2

Learn to spot patterns that will help you simplify an exponential expression.

4. Included with

#### Negative Exponents

Learn how to interpret exponents that have a negative value.

4. 4

### Algebra in Motion

Mostly, we just want to see the collisions!

1. Included with

#### Distance, Rate, and Time

Explore the algebra that describes motion and change.

2. Included with

#### Stunt Driving and Collisions

Use these dangerous motion problems to practice and strengthen your skills!

3. Included with

#### The Harmonic Average

Learn how to calculate the average of two speeds.

4. Included with

#### Boats

Speed becomes more complicated when what you're travelling in (a river) is also moving.

5. 5

### Factorials

Bang! Now it's huge!

1. Included with

#### Counting and Factorials

Learn how to efficiently count cases when there are several sequential choices.

2. Included with

#### Factorials

Explore and practice techniques for efficiently manipulating factorials.

3. Included with

#### Operations and Simplification

The large values produced by factorials become easier to work with when simplified or reduced.

4. Included with

#### Permutations

Permutations count the number of ways things can be put in order.

6. 6

### Common Misconceptions

You'd be surprised how many contest these algebraic facts.

1. Included with

#### The Basics

Identify and repair the mistakes in thinking that lead to these common errors.

2. Included with

#### Ordering and Reordering

The order in which you evaluate the parts of a calculation can have a huge impact on the outcome.

3. Included with