Paper Folding Activity
Number of Sections
Number Number
of Folds of
(x)
Sections
(y)
0
1
2
3
4
5
6
7
8
Number of Sections
Number of Sections: How many times do you think you can fold a piece of paper
in half?
1. Fold an 8.5” x 11” sheet of paper in half and determine the number of sections the
paper has after each fold.
2. Record your data in the table below and continue folding in half until it becomes too
hard to fold the paper.
3. Then make a scatter plot of your data.
Number of Folds
4. Look at your data. Can you come up with a pattern that is like 𝑎 𝑥 , if x is the number
of folds? determine the mathematical model that represents this data:
y = ____________
This is an example of exponential growth. The thickness of the paper grows very
rapidly with each fold. To get an idea of this incredible growth, consider:
At 7 folds, it is as thick as a notebook.
At 17 folds, it would be taller than the average house.
At 20 folds, the sheet of paper is thick enough to extend a quarter of the way up
the Sears Tower in Chicago.
At 30 folds, it has crossed the outer limits of the atmosphere.
Virginia Department of Education 2007, revised 12/2011
1
Area of Smallest Section
5. Again, fold a piece of paper in half and determine the area of the smallest section
after you have made a fold. What is the original area of the sheet of paper?
6. Record your data in the table below.
7. Then make a scatter plot of your data.
0
1
2
3
4
5
6
7
8
Area Smallest Section
Number of Sections
Number of Area of Smallest
Folds
Section
Number of Folds
10. Look at your data. Can you come up with a pattern that is like 64 𝑎 𝑥 , if x is the
number of folds (note: 64 is the original area)? determine the mathematical
model that represents this data:
y = ______________.
This is an example of exponential decay.
12. What would be the area of the smallest section of the piece of paper, if you were able
to fold it 10 times?
Virginia Department of Education 2007, revised 12/2011
2