“Add up all of the numbers between 1 and 100.”
Easy, once you realize that (1, 100) make a pair whose sum is 101, (2, 99) make another such pair, etc.
“Add up all of the numbers between 1 and 101.”
Harder to make sense of, because there’s an odd number of integers that you’re summing, so they can’t be paired off evenly.
I’ve got (at least) pieces of student work that show (at least) 3 different ways of handling an odd number of integers, as in the problem above.
In the comments below, try to catch ’em all. I’ll update this post with the actual student work tomorrow.
Update: For pictures of student work on this, see the next day’s post.