Here's a game my students have been playing for years called The Greatest Sum! I've put it together with lots of variations!
The basic game is played with two 2-digit numbers. The children choose one number square at a time, and decide where to place it on their boards. It takes them only a short time to figure out they should put the greater numbers in the tens column, and the lower numbers in the ones column. You can use the numbers included in this package, or you can use tiles, cubes, or other interesting manipulatives and write the numerals 0-9 on them, as I have done in these pictures.
Here's how to play:
1. Place the tiles (or number squares) face down between 2 "Greatest Sum" boards.
2. The first player takes a tile and places it in one of the squares on his board. That player should think about which square might bring them the greatest sum, since he isn't allowed to move it once he lets go!
3. Play continues between the two players until all squares on both boards are filled.
4. Which player has the greatest sum? Players may use paper & pencil, whiteboards, number grids, a calculator, or mental math to determine each round's winner. (Teacher's choice!)
Explore the image or explore this link: The Greatest Sum