Teaching Algebra with Manipulatives

NAME ______________________________________________ DATE ____________ PERIOD ____
Algebra Activity Recording Sheet
(Use with the Lesson 10-1 Preview Activity on page 522 in the Student Edition.)
Investigating Exponential Functions
Materials:
notebook paper, scissors, grid paper, calculator
Analyze the Data
1. Write a list of ordered pairs (x, y), where x is the number of cuts and y
is the number of sheets in the stack. Notice that the list starts with the
ordered pair (0, 1), which represents the single sheet of paper before
any cuts were made.
2. Continue the list, beyond the point where you stopped cutting, until you
reach the ordered pair for 7 cuts. Explain how you calculated the last y
values for your list, after you had stopped cutting.
3. Plot the ordered pairs in your list on a coordinate grid. Be sure to
choose a scale for the y-axis so that you can plot all of the points.
4. Describe the pattern of the points you have plotted. Do they lie on a
straight line?
Algebra 2—Chapter 10
Make a Conjecture
5. Write a function that expresses y as a function of x.
6. Use a calculator to evaluate the function you wrote in Exercise 5 for
x 8 and x 9. Does it give the correct number of sheets in the stack
after 8 and 9 cuts?
7. Notebook paper usually stacks about 500 sheets to the inch. How thick
would your stack of paper be if you had been able to make 9 cuts?
8. Suppose each cut takes about 5 seconds. If you had been able to keep
cutting, you would have made 36 cuts in three minutes. At 500 sheets
to the inch, make a conjecture as to how thick you think the stack
would be after 36 cuts.
9. Use your function from Exercise 5 to calculate the thickness of your
stack after 36 cuts. Write your answer in miles.
© Glencoe/McGraw-Hill 275 Teaching Algebra with Manipulatives