Folding Paper

Introduction

Exponential growth and decline are tricky subjects to comprehend. The numbers involved grow or shrink very rapidly, quickly transforming from numbers and sizes that we can understand to those that are extremely difficult to comprehend or work with. Folding a piece of paper in half represents the concept of exponential decline. The first fold gives you a piece of paper that is ½ the size of the original, the second fold gives you a piece that is ¼ the size of the original, the third fold gives you a piece that is 1/8 the size of the original. Then 1/16, 1/32, 1/64. As you can see, the fractions get very small very quickly and before long, the paper is too tiny to fold again. Understanding the concept of exponents is important to scientists because the principles of this type of growth or decline are used in a number of different fields.

Research Questions

• What types of fields use the principles of exponents?
• What types of things are measured in exponential growth?
• What types of things are measured in exponential decline?
• Does the size of a piece of paper affect your ability to fold it in half?
• Does the material of a piece of paper affect your ability to fold it in half?

Terms to Know

• Exponential growth
• Exponential decline
• Halving

Materials

• A piece of construction paper 9”x12”
• A piece of construction paper 4”x6”
• A piece of printer paper 9”x12”
• A piece of printer paper 4”x6”
• A piece of tissue paper 9”x12”
• A piece of tissue paper 4”x6”

Experimental Procedure

1. Begin by placing the 9”x12” piece of construction paper in front of you on a table.
2. Fold it in half, matching the short ends together.
3. On a piece of lined paper, make a tally mark to represent your first fold.
4. Fold the paper in half, again matching the shorter ends together.
5. Make another tally mark on the paper.
6. Continue folding and making tally marks until you cannot fold the paper again.
7. Record the results on a chart such as the one below.
8. Repeat steps 1-7, using the other types of paper.

References

• http://pomonahistorical.org/12times.htm
• http://www.abc.net.au/science/articles/2005/12/21/1523497.htm