That is not the mistake I expected. When I clicked over here from Twitter, I thought it was going to be along the lines of “the average of 13 and 9 is 11, so 13×9 should equal 11×11.” But in this one, they had the idea right, they just forgot that they did 10 thirteens and want to take away one thirteen, not one nine. Tricky! And very hard to catch in one’s own work.
mpershan
I actually made this mistake in my own calculation of this. I think that subtracting 9 is somehow tempting, probably because I have the habit of rounding to 10 for so many of my calculations involving 9’s.
Michael Paul Goldenberg
Too bad the student didn’t think 9 x 13 = 9 x (10 + 3) = 90 + 27, but can’t really blame her for the approach she did take, which was at least as good.
One math habit of mind I try to promote that could help her (or you, Michael) catch the mistake: always figure out the digit in the one’s place for addition, subtraction and multiplication problems. If you know 3 x 9 equals __ 7, and thus must have a 7 in the units place, you avoid can catch the mistake and perhaps reason your way into understanding your error AND getting the problem in question correct.
This is a great mistake, and there’s clearly an almost-there strategy at work. I started to wonder about what that strategy might be. Could it be, for example, that the student has taken examples of the form 12*9, 23*9… and constructed a rule that sounds something like: “round the 9 up to 10, multiply, and then subtract one of the _first factor given in the problem_”?