Show a transparency of the current month's calendar and then distribute copies of the
calendar to each student. Ask them to select and circle any two-by-two box of four
dates, find the sum of these dates, and tell you their answer.
You can then instantly locate the block of dates any student selected.
Mentally divide the number the student gave you by 4.
Subtract 4 from that result to get the upper left hand date
in the two-by-two box of dates.
Why does this work? Use some algebra to prove it.
Let n = the number in the upper left corner of the 2 x 2 square.
Then the other three numbers in the square are represented as follows:
|n||n + 1|
|n + 7||n + 8|
The sum of the nine numbers is 4n + 16 = 4(n + 4).
So, when you divide by 4, you get n + 4,
and when you subtract 4, you get n (the upper left number).