FatNums: an alternative representation for school arithmetic | Hugonweb Annotated Link Bibliography
https://parentheticallyspeaking.org/articles/fat-nums/
The idea is, rather than performing carries, just write down the "fat" number in its place.
For example, adding 1234 + 5678:
1 2 3 4
5 6 7 8
----------
6 8 10 12
6 8 11 2
6 9 1 2
The result is 6912.
Instead of carrying at each digit, you "normalize" at the end. This could be useful for elementary students struggling with the concept of carrying.