Lesson: Negative and Positive Numbers (Introduction)

boss-iPhysical 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 planefirst 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 coordinateor 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.