This document is a lesson on writing and evaluating expressions with exponents. It contains examples of folding a piece of paper in half multiple times and tracking the exponential growth in the number of layers. It shows how this exponential relationship can be represented by the expression 2^f, where f is the number of folds. Another example shows the exponential growth of bacteria reproducing through binary fission, tracking the number of bacteria over generations and representing the relationship as 2^g, where g is the number of generations. A third example calculates the volume of a rectangular solid given the width and relationships between the width, height and length.

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MODULE 4 Expressions and Equations
Topic F: Writing & Evaluating
Expressions & Formulas
Lesson 22: Writing and Evaluating Expressions ‐
Exponents
Student Outcomes
§ Students evaluate and write formulas involving exponents for given values in real‐world problems.

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Let’s try an experiment: How many times do you think you
would be able to fold a piece of paper in half? The folds
must be as close to a half as possible. You must fold the
paper the same way each time.
1. Predict how many times you can fold a piece of paper in half.
My Prediction:
1. Before any folding (zero folds), there is only one layer of paper.
This is recorded in the first row of the table.
Fold your paper in half. Record the number of layers of paper that
result. Continue as long as possible. Record your results on the chart.

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a. Are you able to continue folding the paper indefinitely? Why or why not?
b. How could you use a calculator to find the next number in the series?
c. What is the relationship between the number of folds and the number of
layers?
d. How is this relationship represented in the exponential form of the numerical
expression?
e. If you fold a paper f times, write an expression to show the number of paper
layers.

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3. If the paper were to be cut instead of folded, the height of the stack would
double at each successive stage, and it would be possible to continue.
a. Write an expression that describes how many layers of paper result from
16 cuts.
b. Evaluate this expression by writing it in standard form.

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The Basics
"On"
Clear (to erase)
Enter Button (=)

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Exponents
Squared
(to the power of )
Exponents
OR
2
Always hit enter or equal
sign for your answer.
1. Press 4, x2
.
What appears on your calculator? _______________
Press ENTER.
Your calculator should read 16.
2. If you wanted to do 45
you could
press 4 × 4 × 4 × 4 × 4 on the calculator. Try it.
What is 45
?
Press the following buttons. Find the ^ button.
Press 4, ^, 5, ENTER.
Your calculator should read 1024.

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3. If the paper were to be cut instead of folded, the height of the stack would
double at each successive stage, and it would be possible to continue.
a. Write an expression that describes how many layers of paper result from
16 cuts.
b. Evaluate this expression by writing it in standard form.
216

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Bacteria are microscopic one‐celled organisms that reproduce in a couple of different ways, one of which is
called binary fission. In binary fission, a bacterium increases its size until it is large enough to split into two
parts that are identical. These two grow until they are both large enough to split into two individual
bacteria. This continues as long as growing conditions are favorable.
Example 2: Bacterial Infection
a. Record the number of bacteria that result from each generation.

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b. How many generations would it take until there were over one million bacteria
present?
c. Under the right growing conditions, many bacteria can reproduce every 15
minutes. Under these conditions, how long would it take for one bacterium to
reproduce itself into more than one million bacteria?
d. Write an expression for how many bacteria would be present after g
generations.

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Example 3: Volume of a Rectangular Solid
This box has a width,w. The height of the box, h , is twice
the width. The length of the box, l , is three times the
width. That is, the width, height, and length of a
rectangular prism are in the ratio of 1:2:3
For rectangular solids like this, the volume is calculated by
multiplying length times width times height.

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Follow the example to calculate the volume of these rectangular solids, given the width, w.

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Closing
Please take out your exit ticket for Lesson 22, close your
binder, and complete the exit ticket. This will be collected.

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