Paper Folding Activity
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 Sections
Number Number
of Folds of
Sections
0
1
2
3
4
5
6
7
8
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Number of Folds
4. Using your calculator, determine the mathematical model that represents this data:
y =
5. Explain in words what the mathematical model means.
6. What might be different if you tried this experiment with wax paper or tissue paper?
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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.
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Area of Smallest Section
7. 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?
8. Record your data in the table below.
9. Then make a scatter plot of your data.
Number of Sections
Number of Area of Smallest
Section
Folds
0
1
2
3
4
5
6
7
8
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N u m b e r of Folds
10. Using your calculator, determine the mathematical model that represents this data:
y =
•
This is an example of exponential decay.
11.
Explain what each part of the mathematical model means.
12. What would be the area of the smallest section of the piece of paper, if you were able
to fold it 10 times?
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