#### Physical Oceanographer Emmanuel Boss enjoys spending time at sea level (elevation 0) and his work takes him into the ocean.

#### To understand how he does that, we need to understand:

## Integers in Real-World Contexts

— 5 and + 5 look similar, but they are very different numbers. **They are opposites and the difference between them is 10!**

+5 is the number 5 you have worked with since learning to count. It’s 5 units above zero (0). *Negative five (- 5) is five units below zero.*

**Positive and negative numbers can tell you how much money you have or you owe. **

If you save five dollars ($5), you might note that as +5. If you have no money at all, you have zero dollars: $0.

On the other hand, if you owe someone five dollars, you really have less than zero dollars and you might note what you have as -5. Debt (owing money) can be recorded with negative numbers.

**You can also describe locations with integers** (whole numbers and their negative opposites). + 8 might mean eight units north of a certain spot (or 8 units east of that spot). -8 might mean eight units south of a spot (or eight units west of it).

**And you can describe an object’s elevation (how high up it is) with positive and negative numbers.** We call sea level (the average height of the ocean in a given area) an elevation of zero. There is a place in California and Nevada that is 86 meters (282 feet) below sea level. That place, the Badwater Basin in Death Valley National Park, has an elevation of about – 86 m (- 282 ft). It is the spot in North America that is closest to the center of Planet Earth.

**
Temperature can also be described with positive and negative numbers.** Water freezes at zero degrees Celsius (0℃) and 32 degrees Fahrenheit (+ 32℉: 32 degrees above zero). Mercury, on the other hand, freezes at about – 39℃: 39 degrees below zero! (What temperature is that in degrees Fahrenheit?)

*Hint: When you compare integers (positive and negative numbers), be sure to remember that the further a negative number is from zero, the SMALLER it is. -7 > -15 and -3 < -2.*

*To use a number line, start by finding zero. Then put negative numbers to the left of zero and positive numbers to the right of zero. **Note: the further **left** you move on a number line, the **smaller **the numbers get.*

To **graph** a point **in the coordinate plane**, first decide whether it’s negative (if it is, there should be a subtraction sign (–) in front of it, because it’s the number you get when you subtract that amount from zero). Then move LEFT (**for the X coordinate**) or DOWN (**for the Y coordinate**), below zero.

If the number is positive, there will be a **+ **sign in front of it or it will have no symbol for its sign. Move to the RIGHT (for the X coordinate) or UP (for the Y coordinate), above zero.