The typical explanation for modular arithmetic is calling it by another name, "clock-arithmetic", and comparing it to the way the hour value of clocks "resets" every time it has passed midnight.
This is great illustration in Europe. However, in America, notation for time presents the following problems:
- The numerical hour resets after 12 hours, rather than after a full day
- You have to deal with AM/PM
- Time goes from 1 to 12, rather than 0 to 23
For these reasons, I fear using the same illustration with American students would cause more confusion than clarity.
Is there a simple illustration that would show modular arithmetic, that would be more familiar to American students?