Have you ever played golf? Ever gotten a "hole in one"? Ever tried to figure out a golf score? What does "par" have to do with anything? Well, if you understand how positive and negative numbers apply to golf, then you'd be on your way to figuring out "par," along with a winning or losing score.
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The golf course is one place where integers show up in the real world. To understand the role of integers in golf, you have to first understand the sport's scoring system. In golf, there are a number of strokes that are predetermined for every hole on the course. This predetermined number, called par, is calculated based on the difficulty of the hole.
If you go "over par," your score would be reported as a positive number of strokes above the predetermined number, and that isn't good. For example, if par were 5 and you took 8 strokes to get the ball in the hole, your score for that round would be an unfortunate +3. If you go "under par," then your score would be reported as a negative number of strokes below the predetermined number, and that is good! For instance, if you had actually taken 3 strokes to complete the hole in the previous example, then your score would be a terrific -2. It's a bit like thinking backwards. Your goal is to get the ball in the hole "under par" or "on par," but not "over par." Of course, everyone always loves a "hole in one"!
See for yourself: http://www.youtube.com/watch?v=qktGvobBfDc
Check out the following links to see a slide show presentation on integers in the real world, watch a video on integers describing elevations across the globe, and read an article on many more applications of integers in our day-to-day lives.