Here's a game I've created that you can easily make at home with just index cards and 2 dice. My son and I play all the time and he LOVES it, but what he doesn't realize is that it's also a game that is great for practicing number decomposition.
Set out cards labeled 1-9. Roll 2 dice. Add the numbers of the dice together. Whatever the total of the die are, you must flip over cards in the same total in whatever variation works. For example, in this picture, I rolled 12 so I flipped over the 8 and 4. The goal of the game is to flip over as many cards as possible. Your turn ends when you roll a total in which you can not flip over any combination of cards that will amount to your rolled total. The numbers on your cards are then added up as points and then the next player begins their turn. The player with the least number of points wins.
My son and I will honestly play this over and over and play "winner of 5 rounds" or "first to 100 loses". It's a fantastic way to reinforce both addition as well as number decomposition in a fun and positive atmosphere.
Give it a try and let me know how it goes!