It's always interesting to hear how people go about solving math problems. You mention a pie chart visualization and then the much more labor intensive (but maybe "correct"?) method. I used a third way, which was thinking that 13/13 would be one, so 12/13 is pretty close, so that's ~1. And 8/8 would be 1, so 7/8 is pretty close and also ~1. 1 + 1 = 2 :)
I imagine there are myriad other ways people approach estimation problems like this. In response to the rest of your post, I was never taught how to "think" about math. I was educated in a decent school system, but it was all rote memorization of multiplication tables. I think most people who are interested in learning will come up with their own tricks regardless of curriculum. Of course, imagine how much better I'd be at this stuff if I had math teacher's who were competent :)
I imagine there are myriad other ways people approach estimation problems like this. In response to the rest of your post, I was never taught how to "think" about math. I was educated in a decent school system, but it was all rote memorization of multiplication tables. I think most people who are interested in learning will come up with their own tricks regardless of curriculum. Of course, imagine how much better I'd be at this stuff if I had math teacher's who were competent :)