I knew long ago that Aleks understood some basic math. He always used his own language to explain it, however. He'd say "creates" instead of "equals." He also had never really written math in problem form. He'd written numbers aplenty and has recently begun to write these backwards for some reason, which we note, but do not criticize.
Then, abruptly, one night while I was cleaning up the kitchen after dinner, he started drawing on a box he pulled out of the recycling. When I looked, they were math problems. He would ask me if his answer was correct, but I didn't realize at first that he was actually writing it down. Still, his numbers are backwards, but all the math is right and he worked it all out by himself.
It says 100 + 100 = 200 and 4 + 3 = 7. He also discovered that different numbers can have the same answer: 5 + 2 = 7.
11 + 1 = 12, 7 + 4 = 11 (which he later scratched out for some reason, even after verifying the answer and discussing it), 11 + 12 (not sure what happened there), and 8 + 4 = 12.
On Sunday, the box went to the curb for recycling, so perhaps someone sorting it will get to see it. I wonder if there are many drawn upon boxes that people in recycling facilities see - boxes that were once castles or ships, that once housed half-clothed fairies with marker upon faces and scarves dangling from their backs. We'll definitely to do more with boxes this spring...ideas are coming to me.