Last week I looked at converting temperatures in your head from Celsius to Fahrenheit. That made me thing about negative temperatures. That made me think about negatives in general.
When encountering negative numbers for the first time, many students reject the notion that numbers can be less than zero. But of course they can. While you can't have a negative number of apples, you can have a negative amount of money, degrees, elevations, etc.
Specifically, let's look at subtraction in finding a difference of elevation. The Dead Sea is at 1,414 feet below sea level. Jerusalem is at 2,582 feet above sea level. What is the difference in elevation? 2,582 - (-1,414) = 3,996 feet.
What if we subtract in the other order? -1,414 - 2,582 = -3,996 feet. What are we to make of the negative answer? That is what the absolute value is for. If a and b are elevations, the difference in elevation is |a-b|. This is easier than writing something cumbersome like: a-b if a > b and b-a if a < b.
This shows students a practical example of integer subtraction and the absolute value concept.
One more example of this: The Sea of Galilee flows into the Dead Sea by way of the Jordan River. All of these are below sea level. The Sea of Galilee is 696 feet below sea level. Here we are subtracting two negatives. |-696 - (-1,414)| = |-696 + 1,414)| = 712 feet.
