Before you take the kids outside for this lesson, you need to teach them about the Pythagorean theorem. Here's how it works: In a right triangle, the square of the side opposite the right angle is equal to the sum of the squares of the other two sides. This is normally written as a^2 + b^2 = c^2, where "c" is the side opposite the right angle.
You can create the side opposite the right angle by placing a string on the ground and staking one end on a slope. Move down the slope and stake the other end into the ground after pulling tight. Then, stake another string to the same spot as the higher end of the first string.
Now, you'll need to attach a string level to the second string, and pull it out from the first stake so that it is horizontal. Attach a plumb to the other end. When the plumb hangs down directly above the second stake on the first string and the string is level, measure the horizontal string's length ("a"). Then measure the string on the ground ("c").
The final step in this project involves plugging your values for "a" and "c" into the formula a^2 + b^2 = c^2. Once you've found "b," you know how far the string rises. The a-value tells you the horizontal distance traveled. The b-value is called the rise, and the a-value is called the run. Divide the b-value by the a-value to find the slope of the hill.