This is a game I got from my sister. It is called Catch The Frogs. There are cute little froggies with numbers 1-12 on their bellies.
For example, if you rolled a 4 and a 1, you could take frog #4 and frog #1, or you could add 4+1 and take frog #5. Or, if your children really know their stuff, they could come up with a different equation that would equal 5 (ie 3+2) and take those frogs.
This game was good for me to do with my boy, since he is very comfortable with number recognition on one die, but to add the numbers on the first die with the second die was a new and more challenging task. When he couldn't do it in his head, it was no big deal, we just counted the dots on the dice and found the answer that way.
If you wanted to have a winner for the game, you could add up the numbers on the frogs you 'catch' and whoever has the highest total could be the champ, but we didn't keep score.
Of course, you don't have to do this game with frogs. If you wanted to create a version that more closely fit your child's interests, it would be easy enough. You could play, "Pick the flowers" and make paper daisies with numbers in their centers, or "Catch the Fish" etc.