Today in 4th grade, we played a game called Remainders Wanted. I found it for FREE at this Teachers-Pay-Teachers shop, and it was a gem.
The students played in pairs and followed the directions for the game. The student whose turn it was solved the problem on his/her whiteboard. The other student was responsible for coaching her/his partner. So, they had to watch each part of the process carefully and look for mistakes. Since they were using the partial quotients ("Big 7") method, the coach could suggest something like, "I think you can make a bigger guess." Or, "I think your answer is going to be too big." Or, "You need to check your subtraction. You should regroup."
If I were to use this game again, I would also provide some sentence stems/examples with more specific math vocabulary. The sentences would include things like, "I think your product will be too big." Or, "Your remainder is bigger than your divisor. You can divide again." Or, "Your partial quotient can be bigger/smaller." These could also be student generated during a whole group discussion before they played the game.
How do you see this game being used in your classroom?