Problem: Take a piece of paper and cut it in half. Stack pieces on top of each other and cut in half again. After each cut record the information in the table. The column for thickness is blanked out for the first four rows because it is hard to measure. If you want, use calipers to measure even the smallest thicknesses. Repeat until you see a pattern and can generalize for the bottom line of the table.

# of cuts	# of pieces of paper	thickness (in inches to the nearest 1/16 inch)
0		--
1		--
2		--
3		--
4
5
6
7
8
9
10
c

Now, the Sears Tower, the tallest building in the U.S., is 1454 feet tall. (Information Please Almanac, 1996) Can you, do you think, make enough cuts to make a paper tower that tall? How many cuts would it take? How many pieces of paper would that number of cuts produce? Explain your solution and show your work. (HINT: Find the relationship between the number of cuts and the height of the stack.)

Extension: Define an algebraic expression that represents the number of pieces of paper if, instead of cutting the pieces in half, we cut the pieces in thirds. Be sure to define your variable.