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Subject:   Integer Arithmetic with Signed Numbers
Author: Craig
Date: Jun 16 2005
I learned of this from a colleague, who learned it from Bob Davis of the Madison
Project (60's-70's era "new math")... the idea of "Postman Stories."

Imagine living in a crazy apartment building where the postman delivers either
bills (negative) or checks, but not very carefully.  Imagine a resident who
immediately adds received mail to her ledger, without regard to whether it
belonged to her.

So, one day the postman delivers a check for $4, a check for $19, and a bill for
$7.  The resident's ledger showed a balance of $10.  Upon receipt of her mail,
she immediately enters +4 +19 and +(-7) to get a balance of $26 (I hope).
Everyone's happy.

Except the next day, the postman delivers a check for $3 and a bill for $10, but
informs the resident that he needs to take back the bill he gave her yesterday,
because it was supposed to go to another resident.  No problem... add a check
and a bill and take away a bill goes into the ledger as +3 + (-10) - (-7).
Is the resident happy or sad that the postman is taking a bill away?

Multiplication comes into play when the postman delivers several checks for $3
[pos*pos], or several bills for $9 [pos*neg], or takes away several checks
[neg*pos] or takes away several bills [neg*neg].  Which of these situations make
the resident happy?

We usually give students a string of signed number arithmetic and have them
write down the corresponding postman story:

3(2) + -1(4) + (-6) + (-1)(-8) translates to receiving 3 checks for $2
each, giving back one check for $4, receiving a bill for $6, and giving back a
bill for $8.

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