Part of my responsibilities at the after school tutoring center I work for has been to create fun, educational math activities. We use these activities for community "math fairs" where we play educational math games at nearby schools. Recently, we held a fair for 5th and 6th grade students, so I designed an activity that would help them practice operations with fractions.
The graphic organizer is made of posterboard and has spaces for six playing cards that form different number sentences using fractions. The long strip allows you to switch between the four operators (addition, subtraction, multiplication and division) by sliding it up and down. Students are given about half a deck of cards and can create any number sentences they want, provided that they are correct (this particular deck had the numbers 0-12 in place of face cards). Here's an example of each operation made with the same stack of cards:
The organizer is made of three pieces. The main piece is about 8.5" by 11", with a small square inch window cut out for the operators to show through. The operator strip is about 1.25" by 9", longer than the width of the main piece so it can be slid back and forth. Behind the strip is a slightly wider 1.5" by 8.5" piece taped to the main one, which forms a pocket for the operator strip to move. It's less complicated than it sounds.
It's not so much of a game as an activity that changes each time you do it, depending on the cards you get. The goal would be to create at least one correct number sentence with each operation. If you're using a standard deck, you can count all face cards as 10 and aces as 1 or 11. The alternative is to have jacks, queens and kings as 11, 12 and 13 and aces as 1 or 0. If you really want to raise the stakes, make red cards negative and black ones positive.
You can of course do this without the organizer, and the idea's still the same. You can also use cards in a similar way to do basic integer operations, or incorporate a number line for practice with positive and negative integers.