We've known numbers forever. We learn to count when we're about two and we never stop. It's kind of like they're our school friend we grew up with, sharing graham crackers and juice boxes. But this unit is kind of like what happens when that friend goes to camp over the summer and comes back sort of different, with a whole new vocabulary. We know they're the same, basically, but they don't really look like it.

Numbers can take all kinds of forms, and we have to be ready for any of them. Since we're used to talking mostly about positive integers, we have to adjust our thinking a little. Numbers can be negative. They don't have to be whole. They can be a composite of a couple of pieces, even. And if they are any of those things, the operations we can do with them have to change, too.

It's just like how you had to learn to play all the new games your friend brought back from camp, even if they were better suited to a campfire setting.

We're going to talk a lot about fractions. We know that they represent parts of a whole thing. But the real challenge is doing multiplication or subtraction when a fraction is involved. That's going to take learning some new rules. The same goes for numbers with decimals or numbers that are negative.

There is a lot to cover, and it may feel a little overwhelming. The important thing is to try and think about where the rules are coming from. It makes them easier to remember and makes this whole thing feel arbitrary.

But really, this is all a good thing. After all, math is about solving problems in the real world. And the real world is rarely so kind as to provide us with all whole, positive numbers. A lot of the time, there's decimals hanging around. And negative numbers can play an important role. By learning all these new rules, we make ourselves better equipped to answer all kinds of problems. And that's the goal, right?

It's kind of a bummer when a friend changes. But once you realize that they're still the same person with fun new features and capabilities added on, it makes it all better. Let's start expanding our number horizons.

- We'll start by defining rational numbers. We don't mean to put them in a box or anything, but we've got to start somewhere.
- Next, fractions. We'll talk about what they represent, their properties, and how to perform operations with them.
- After that we can talk about fraction's little brother, decimal. We will cover how place value works and how to complete operations when numbers have decimals.
- We'll spend some time talking about turning a fraction into a decimal and a decimal into a fraction. No magic wand necessary.
- Next, we get to the number line, a representation of all our math problems. We'll cover its basic anatomy and how we use it to help us figure out the tough stuff.
- Next we focus on the negative half of things. We'll also talk about how absolute value helps us get back to the positive.
- Finally, we'll review all of our operations with rational numbers and how they translate into real-world situations.

By the end of this unit, you should know and be able to

- identify rational numbers and perform operations with them.
- perform common operations on fractions and mixed numbers.
- find a common denominator between two fractions.
- convert between decimals and fractions.
- use the number line to model problems.
- understand and interpret absolute value signs.
- correctly apply the sign in arithmetic problems including negative numbers.
- interpret real-world situations into mathematical statements with appropriate operations and values.

#### Lesson 1: What is a Rational Number?

#### Reading 1.1: What is a Rational Number?

#### Lesson 2: Review of Fractions

#### Reading 1.2: Adding, Subtracting, and Multiplying Fractions

#### Lesson 3: Operations with Fractions

#### Reading 1.3: Dividing Fractions

#### Lesson 4: Real-World Problems with Fractions

#### Reading 1.4: Real-World Problems with Fractions

#### Lesson 5: Review of Decimals

#### Reading 1.5: Review of Decimals

#### Lesson 6: Operations with Decimals

#### Reading 1.6: Operations with Decimals

#### Lesson 7: Converting Rational Numbers to Decimals

#### Reading 1.7: Converting Rational Numbers into Decimals

#### Lesson 8: Converting Between Decimals and Fractions

#### Reading 1.8: Converting Between Decimals and Fractions

#### Lesson 9: On the Number Line

#### Reading 1.9: On the Number Line

#### Lesson 10: Real-World Problems on the Number Line

#### Reading 1.10: Real-World Problems on the Number Line

#### Lesson 11: Negative Numbers

#### Reading 1.11: Negative Numbers

#### Lesson 12: Absolute Value

#### Reading 1.12: Absolute Value

#### Lesson 13: Graphing Absolute Value

#### Reading 1.13: Graphing Absolute Value

#### Lesson 14: Negative Fractions

#### Reading 1.14: Negative Fractions

#### Lesson 15: Subtracting Rational Numbers

#### Reading 1.15: Subtracting Rational Numbers

#### Lesson 16: Multiplying and Dividing Rational Numbers

#### Reading 1.16: Multiplying and Dividing Rational Numbers

#### Lesson 17: Multiplying and Dividing Rational Numbers in the Real World

#### Reading 1.17: Multiplying and Dividing Rational Numbers in the Real World

#### Lesson 18: Operations with Rational Numbers

#### Reading 1.18: Operations with Rational Numbers

#### Lesson 19: Solving Problems with Rational Numbers

#### Reading 1.19: Solving Problems with Rational Numbers

#### Lesson 20: Study Days

#### Study Aid: Flashcards

#### Study Aid: Study Questions

#### Study Aid: Terms