Ingrid...have you thawed out yet this year? I know of that area and it is quite cold!
You are right to use the Bull's Eye game with this student, but there are some things we want to help you with so that you get him on the right track. Your overall premise is good; each of you rate the day from a 1-5, 1 being bad and then you show each other the score. If you match he gets two stickers (or whatever you are using), if your one off he gets one sticker, and if your more than one, he gets nothing.
Frequency: First of all, set the game up for a limited time...10 school days is a good amount of time. You can always go back to it again later. If you do it for too long, it looses it's "funness". You are going to only check scores at the end of the day. As you probably felt already, it's going to be tricky to manage all of this especially if you have more than one student involved. (I had 6 at a time once) You want him to concentrate for the whole day so that is why maybe you choose only one thing for him to work on. For instance, he needs to work on following directions quickly. So for that day, he is only grading himself on the one aspect that you want him working on. Everything else is not being evaluated at this time. Later you can add more things to focus on.
Rewards: Whatever you decide to use, now and in the future, he is only going to get 1 reward at the end of the day or 2 if he matches right on the mark. There are not different levels of rewards...you mentioned a 10 point sticker and 5 point sticker and so on. Now maybe if this is the third or forth time in a year, then maybe the matching of the score gives him a point, which needs to be put with other points for a higher reward. That would work, but initially, let's just keep it simple.
With these simple adjustments, I think it will be easier on him and you. Remember, the point of the game is for him to make a conscious effort to change his own behavior.
Best of luck, keep us posted.
Chris R.
Power to the Teacher!