Working through two problems with my kids today reminded me of the “attending to precision” idea in math education.
The first problem was #10 from 1994 American Junior High math exam:
You can find the problem (and the whole test here)
The 1994 AJHME on Art of Problem Solving’s website
This problem gave my younger son a bit of difficulty today. There are a couple of ideas in this problem that require you to be careful with your counting.
The next problem was Problem #19 from the 2015 AMC 10a which my old son had a little difficulty with today.
This problem required you to keep track of a few different geometric ideas and a few algebra / arithmetic ideas in order to get to the solution. No one of those ideas alone is super tough, but all of them together really require you to work carefully.
I really liked how these two problems required the kids to work carefully. That careful work makes getting to the solution really satisfying!
Mike's Math Page 