Wild Camping 
Sleeping Bags 
Hiking Adventures 
Survival Kits 
(And why does it matter?) 
You may have seen the scene in the movie "The Edge," where Anthony Hopkin's character rubs a needle on silk to magnetize it, and makes a compass out of it. Well, it not only works, but I have done it without floating the needle on a leaf. Cradled in a couple pieces of thread, a magnetized needle can be slowly lowered onto the surface of a cup of water, and will actually float there due to the surfacetension. Drop the ends of the thread and the needle will turn to align northsouth. Hiking high in the mountains can make you very hot. There are often snow banks that persist through summer above 12,000 feet, so why not use them to cool off. Rub that snow on your arms and put some on your head. The real point here is to lessen your need to sweat, so you can make your drinking water last longer. If you really must carry a bowl (I eat from the pan), use a plastic margarine tub. They are lighter than anything you can buy from a backpacking gear supplier. 
Forget how many feet are in a mile. Put the calculator away (actually I do all the math in my head  it makes the miles fly by). Just learn approximately how fast you hike in various terrains. This really is a useful for planning, and for locating yourself on the map.
The next time you hike a knowndistance, see how long it took you and do that little bit of math to figure your walking speed. If you know that on level ground you are walking 2.5 miles per hour, you can safely figure it will take you 4 hours (not counting breaks) to hike to that lake which is 10 miles away. If you have hiked for two and a half hours, you can figure roughly where you are on the map: 6.25 miles towards the lake from where you started.
Other little backpacking math facts:
 Hiking up mountain trails, you are unlikely to gain more than 1,500 feet in elevation per hour. 1,000 feet per hour is closer to the average for most people.
 The temperature will normally be about 3 degrees cooler for each 1,000 feet higher that you go. In other words, if the forecast for the nearest town calls for nighttime low of 45 degrees, but you'll be 5,000 feet higher than that town, expect a low of 30 degrees.
 For each 1,000 feet of elevation above sea level, the boiling point of water is about 1.8 degrees less. It is only 194 degrees Fahrenheit at 10,000 feet, for example, so you may want to boil that water a bit longer to kill any bacteria.
 Army studies found that a pound of weight on your feet is the equivalent of five pounds on your back, in terms of energy output. Get those lighter boots or hiking shoes!
1. Knowing how many feet are in a mile and doing a bit of math can help you plan and navigate.
2. There are easier ways to use a bit of math than my mental gymnastics.
