Kass..pretty much correct. The 125/f16 image is basically 1 full stop over exposed at iso 200. The old sunny 16 rule was based on iso 100 and was a general starting point for sunny outdoor images. 1/250/f16 would have had you really close to start a base exposure.
When you guys take the images, you need to be in manual mode if possible. That way the shutter speed is set (by you) and the changes will be visable when you make the aperature adjustments. You can also use Aperature mode where you set the aperature and change the shutter for the changes to be seen, but manual in all honesty is where you want to be, that way you start developing how to set the exposure without input from the camera(except for the meter)
Here is a quick example of all this in action
Walking through the pits, I saw one of the companies that pays me to shoot for them. A quick shot in Shutter Priority netted me the first image
A quick look at the histogram showed it was underexposed (dark) so a quick +.07 adjustment using exposure compensation was added and the second image was taken.
Better, and I could have stood there and fiddled some more but the image is more for record then quality so it will suffice. Post process could easily clean it right up. Total time was literally a few seconds to make the change. Even though I shoot in RAW, I refer to still get as close as possible.