I used this as a warm-up activity for 8th grade today. I got this off of 101qs.com from someone named Adam Bevan. (Whoever you are, thanks!)
Here's what I loved about it:
A. Some kids noticed right away that you could use the 9 as a 6.
B. Some noticed that 1's and 2's had to be on both cubes to make 11 and 22.
And that's as far as many got. Many were paralyzed by the fact that there was no certain way to know where the rest of the numbers went. They thought that there had to be one right answer, and could not decide on how to fill the rest of the blanks.
I had to keep pushing kids. Guess. Take a guess. Do you need a 3? Of course you need a 3. You don't know where to put it? Try putting it here. Will that work? I don't know either. Keep guessing and see what happens.
So my kids learned two valuable lessons today. 1. Sometimes you solve things by guessing. 2. Sometimes there's more than one right answer.
Looking back: It would have been better for me to have a physical representation of this. Some students never saw these blocks before and couldn't really grasp the concept.