Flagpoles

Dear Mr. C,

The other day, I was trying to explain to someone how to add a positive integer with a negative one. That's when I realized I had no idea what I was talking about! Can you shed some light on this subject, because I'm thinking I may just have a conniption if I can't figure it out soon.

Love,

Florence Jean Castleberry

Dear Flo,

I feel your pain. It can be hard to think about positive and negative numbers without going crazy. Let's see if I can help you out, though.

First off, it may help to think of positive numbers, such as five, as a five foot hill. And also, think of a negative number, like four, as a four foot hole in the ground.

This is a four-foot hole. The bottom of it can be thought of as -4.

Now, let's say we have a ten-foot long flagpole. I know this isn't exactly normal, but let's say we dug that four-foot hold to plant the ten-foot flagpole. 

If you sink the flagpole down to the bottom of that hole, you know the entire ten feet are not going to be sticking up into the air. We know that only six feet of it will be sticking out of the ground. 

We can think of this like the mathematical expression -4 + 10. And then we know that if you make it into an equation, you can say that -4 + 10 = x, where x = 6. 

Similarly, let's set up another flagpole. This time, we don't want the high winds to take down the flag and flagpole. So we are going to dig a nine-foot hole this time! Crazy! 

So we already know that we are starting this math problem out with a -9.

Sadly, the first time we went shopping for a flagpole, the one we picked out was only seven feet tall. Needless to say, it sunk all the way into the ground, and the top of it still doesn't reach the top.

We can think of this as the mathematical problem -9 + 7 = x. If we solved this problem, we would find that the answer comes to -2. It's still two feet underground!

So we head back to the flagpole store. This time, we're smart enough to get one that is long enough. Let's see, the hole we dug is nine feet deep, so we are going to need a nine foot flagpole!

Uh-oh. We didn't take it into consideration this time that we have a math problem that looks like -9 + 9 = x. A negative nine plus a positive nine will just level out to zero! -9 + 9 = 0! You're flat on the ground!

So on our third trip to the flagpole store, we get an 18-footer. Here, we can discover that -9 + 18 = 9! Positive nine!

I'll post some more examples of this tomorrow without the visual aids, plus a helpful tip when it comes to adding a negative with a positive.

I hope this helped out out, Flo. Don't forget to know your negatives, but to always remain positive.