Someone hands me 3 $5 bills - I am up $15 = 3 * 5

The city sends me three $5 parking tickets in the mail - I'm down $15 = 3 * -5.

Someone takes three $5 bills from me, I'm down $15: -3 * 5.

The city takes away the three $5 parking tickets from me: I'm up $15, -3 * -5.

I adapted this example from a book by W. W. Sawyer I read years, ago, probably Vision in Elementary Mathematics.