**Graphing
Calculator (TI-83) Activity - Exponents**

**For the teacher****:**

This lesson was created for **6-8th grade pre-algebra** classes. The
lesson **emphasizes variables with exponents**. 9)The materials that
will be needed are paper, pencil, graphing calculator (preferably TI-83),
and copy of the worksheet. The following lesson is a generative activity,
meaning that there is more than one solution to a given problem. 10)By using
the generative activity format, the students are allowed to build on prior
knowledge, expand their understanding, and with the use of a graphing calculator,
the students are able to test their solutions and can normally self correct
with little guidance from the instructor. Finally, this lesson starts out
with a simple problem moving to concepts that tend to be more difficult
for beginning algebra students. 6)The following worksheet may be used as
is, or may be easily modified to ask for any particular problems, or any
number of solutions based on the student's level of performance. Depending
upon the modifications made, it may be of some benefit to re-scale the standard
window. For example by making the x-axis smaller, a more detailed graph
can be viewed with more accuracy. 12)Also, the worksheet was created in
order for students to complete the assignment in a traditional 45 minute
class period.

2)"Before algebra, students should have ample opportunity to explore
working with exponents on whole numbers rather than with letters or variables.
By doing so, they are able to deal directly with the concept and actually
generate the rules themselves." *Van de Walle* (p.40). 8)Certain
ideas should merge from this activity. For example, the students will be
able to identify the concept of exponent as a short hand for repeated multiplication.
7)Many students have the tendency to solve 3^{3} as they would 3(3).
However, this undeniably wrong, and will result in the student making many
mistakes, and receiving poor scores. Therefore, this exercise will allow
students to ** see** that at no time X

13)An activity that could easily follow this lesson is one in which you
have the students construct their own function, and then find other functions
that are the same as the one they created themselves. Another activity might
be having the students construct their own function, and then challenge
other students to find other functions that are the same as the ones prepared
by their classmates. The ideas seem limitless, modify your own lesson!

**Graphing Calculator (TI-83) Activity - Exponents**

__ Special note before you get started__If (when?) you get lost in using the calculator, DON'T worry!

Just push the following sequence:

As you will see, the arrow keys (4 blue directional keys in the upper right hand area) allow you to move around the screen.

Let's get started 11)

Step 1: Turn **ON** the calculator (lowest and left-most button).

[when you are done, press **2nd** (yellow button) then **ON** (really
OFF).]

Step 2: Press **2nd** (yellow button) and then **MODE** (it is
located to the right of the yellow 2nd button)

Step 3: Press **CLEAR** (under the arrows).

Step 4: Press **Y=** (top row, left-most blue button.)

Y1=

Y2= ignore anything

Y3= written here.

Y4=

*Your screen should look like this*

Step 5: Press **CLEAR** and there should be nothing next to Y1=

Step 6: Next to "ALPHA"(the green button) there is the "X,T,
,*n*" key. Press the **X,T, , n** key and then press
the

Y1=X*X

Y2=

Y3=

Y4=

*Your screen should look like this*

Step 7: Press **CLEAR**. Now type the number** 2**, then the **X,T,
, n** key. Press

Y1=X*X

Y2=2X

Y3=

Y4=

*Your screen should look like this*

Step 8: Now press **GRAPH** (top row, right-most blue button).

Step 9: Sketch what you see in the box provided below. You have entered
and graphed two separate functions!

Step 10: After you have sketched your functions, press the** Y=**
button. Now press **CLEAR**. Notice how the line is erased. Drive (using
the down arrow) to the next line and press **CLEAR** again.

Step 11: After all of the functions have been erased Press **GRAPH**.

Step 12: Draw what you see on your calculator screen now.

*Note:* All of the functions have been erased. The two lines you
see are not functions, but just part of the background. These lines are
called the* x and y axes*.

Now you will enter a simple function.

Y1=

Y2=

Y3=

Y4=

Step 13: Press **Y=**

*Your screen should look like this*

The calculator is waiting for you to give it a function.

Let's start by graphing a function that gives out exactly what you put
in.

Step 14: Press the **X,T, , n** key then

Y1=X

Y2=

Y3=

Y4=

*Your screen should look like this*

Step 15: Press **GRAPH**. In the box provided below, draw what you
see on your screen.

Step 16: Press **Y=** again. Press **ENTER**.

You are on a new line. You can enter a second function for the calculator
to graph. We are going to enter the SAME function to see what it looks like.

Step 17: Press the **X,T, , n** key then

Y1=X

Y2=X These are the same.

Y3=

Y4=

*Your screen should look like this*

Step 18: Press **GRAPH**. What do you see? Draw it below.

In Step 18 there are TWO functions on the screen. Why don't you see two
lines? In other words, what does it mean on a GRAPH for TWO FUNCTIONS to
be the SAME? Write your answer in the space provided.

**Exercise 1
**

Step 19: Press **Y=**, then press **CLEAR**. Press the **down
arrow**, and press **CLEAR**. Now press the **up arrow** until you
are at the Y1= location (this should only be once).

Step 20: Type in X 4. To do this Press the **X,T, , n** key,
then the

Y1= X^4

Y2=

Y3=

Y4=

*Your screen should look like this*

__Special note__:

X^4 is the calculator's way of writing X^{4}.

Step 21: Press **GRAPH**. Sketch what you get.

Step 22: After you have sketched your screen above, press **Y=** again.
You will want to leave the value for Y1= on the screen, so use the **down
arrow** once so that your cursor (blinking shaded box) is waiting for
input for Y2=

1)Find **FOUR** functions that are the **SAME** as **X ^{4}**.

Example: At Y2= enter X*X*X*X. [Press the **X,T, , n** key,
then the

Y1= X^4

Y2=X*X*X*X

Y3=

Y4=

*Your screen should look like this*

How will you know if the functions are the SAME as X^{4} ? Write
your answer on the line below.

Press **GRAPH**. So far you have TWO functions that are the same.
Now try to find *at least* 2 more functions that are the same as X^{4}.
15)Also, make sure you include at least **one** in which the exponent
is not a whole number.

4)Write down all four of the functions that are the same as X^{4}.
You should write them down as you find them.

3)**Thinking It Over**

From what you know about exponents, will these functions (4X __or__
4*X) be the same as X^{4}? Why, or why not? How could you find out
if they were the same, or not?

5)What are you doing to the exponents when you are solving a problem
like X^{4} * X^{2}? Circle the correct answer.

multiplying

dividing

adding

subtracting