# Level 6: Unit 1 - Rational Numbers, Integers, and Number Lines

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## Instructor ## Reviews (2) Jonathan diaz Jonathan diaz

## Overview Wait, do we know the 10% above or below the water?

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If you thought that positive whole numbers are all that math class has to offer, think again. We're here to tell you that the no-fuss numbers you've multiplied, divided, added, and fawned over so far are only the tip of the iceberg. Or at least only half of the iceberg.

Grab an insulated scuba suit and an oxygen tank and get ready for an arctic dive. Actually, make that two oxygen tanks—we could be down here a while. We've dropped a (number) line and anchored the boat, and we're ready to do some exploring. On our list: arctic shipwrecks, whale sightings, maybe befriending a polar bear or two. Wait, scratch that. We'll stick to penguins.

But most importantly, we're diving below sea level to look at the negative end of the number line. Integers, fractions, and repeating decimals will now all fair game, no matter their sign. It's like diving for buried treasure, where "buried treasures" include all the rational numbers below zero. And they hopefully double as the right answers to your homework, too.

We've got a hot chocolate stash that could last us to negative infinity (or positive, for that matter) and beyond. We've got an "absolute value" medical team to bring us back above zero degrees when it gets too bitterly cold out there in the icy waters. And hey, that reminds us: we'll probably need you to sign a release form before we start.

### Summary

• We'll start things off by defining rational numbers and learning how to write them as fractions and decimals. It's amazing how many numbers are hiding in plain sight, in between the numbers we already know and love.
• Next we'll get to know the dark side of the number line. That is, negative numbers, which all lie to the left of zero.
• The number line stretches out to infinity in both directions (to negative infinity, and beyond!). We'll learn to plot any rational number in its correct place on the number line, relative to its neighbors. Home sweet home.
• We'll learn to add negative numbers and subtract positive numbers. Not to mention subtract negative numbers and add positive numbers. What we mean is, subtracting negatives is really like adding, while adding negatives is really like subtracting.
• We'll find the opposite of a number, which reflects it about zero on the number line. And you thought it was not opposite day.
• Sometimes rational numbers model real world situations. Fancy that.
• We'll draw swords—er, we mean comparisons—between numbers of different values using the inequality signs ">" and "<".
• Finally, we'll go over how to find the absolute value of a number and interpret it as a distance or other type of measurement in the real world.

### Objectives

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

• identify and define rational numbers. Politely, using your p's and q's.
• represent any rational number as a fraction or a decimal. That includes positives, negatives, and zero too.
• plot any rational number on a number line. (Where our negatives at? To the left of zero.)
• add and subtract negative and positive numbers together. Opposites attract…or, in the case of zero pairs, cancel.
• find the opposite of a negative or positive rational number by reflecting it about zero on the number line.
• apply rational numbers (including negatives and fractions) to real world, life-and-death scenarios, such as what to do when there's one piece of cake and four hungry students.
• use the pointy ends of the inequality signs ">" and "<" to relate numbers of different magnitudes. And not just to poke your neighbor.
• find the absolute value of any number, and interpret absolute value as a measurement, magnitude or distance in the real world.