6.1 Paper Folding Activity
Page 347-349
Step 1: Fold a piece of paper in half and determine the number of layers of paper. Then fold the sheet
of paper in half again and determine the number of layers of paper. Continue folding the paper in
half and counting the number of layers of paper. Fill in the table below.
Number of Folds
Process
Number of Layers of Paper
0
1
2
3
4
5
6
Recall: Repeated multiplication can be written with a base and an exponent.
For example, 5 x 5 x 5, can be rewritten as 53. The factor 5 is the base.
The number that tells how many times the base is multiplied is the exponent.
Step 2: Use the grid below to make a scatterplot of your data.



Layers of Paper

















Numbers of Folds
Step 3: Write a function for the number of layers of paper if you fold the paper n times.
Step 4: Is this function continuous or discrete?
Justify your answer.
Step 5: What are the domain and range of this
function?
Step 6: Use a graphing calculator to make a scatterplot of the data. Then sketch the graph of the
function on the scatterplot and record your window.
Step 7: A ream of paper is almost 2 inches thick. If a ream is 500 sheets of paper, about how thick is a
piece of paper?
Step 8: Complete the table below.
Number of Folds
0
1
2
3
4
5
6
Process
Thickness in inches
Step 9: Write a function rule for the thickness of the stack in inches if you fold the paper n times.
Step 10: How are the function that models the thickness of the stack and the function you found for
the number of layers after n folds related?
Step 11: Sketch a graph for the thickness of the stack, and label the axes.
Step 12: How is this graph transformed from the graph that you drew in Step 6?
Step 13: Complete the table below using the data from Questions 1 through 12.
Number of Folds
Number of Layers
0
1
2
3
4
5
6
Number of Folds
Thickness (inches)
0
1
2
3
4
5
6
Step 14: Recall that linear functions can be written from patterns that show repeated addition. The
two functions in this section are exponential functions. Exponential functions can be written from
patterns that show repeated multiplication or division. Show how the tables display a pattern of
repeated multiplication.
Recall: Functions can be written using either “y=” or “f(x) =” notation.
Step 15: A general form of an exponential equation is f(x)= a  bx . From the tables, what determines
the value of a? How is a related to the graph of the function?
Step 16: What determines the value of b?
6.1 Assignment
Page 350 #1-4
1. If you cut the paper 22 times, how many layers do you have? Write an equation to help you
solve this problem.
2. If you cut the paper 22 times and stack it up, how tall is the stack? Write an equation to help
you solve this problem.
3. A box of paper is 5 reams deep. A ream has 500 sheets of paper. About how many cuts would
you need to make stack at least as thick as a box of paper?
4. The Eiffel Tower is approximately 1050 feet tall. If you had a big enough piece of paper, how
many cuts would you need to have a stack that equals or exceed this height?