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 33 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 X4 is the same as 4(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:
2nd (yellow button) then MODE (really QUIT) until you get to a blank screen. (You many need to press CLEAR to get a completely blank screen.

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 X (multiply), and then the X,T, ,n key. Press ENTER.


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 ENTER.


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 ENTER.


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 ENTER.


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 (located under the CLEAR button, and above the ÷), next push the 4, and then ENTER.


Y1= X^4
Y2=
Y3=
Y4=


Your screen should look like this

Special note:

X^4 is the calculator's way of writing X4.

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 X4.

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


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 X4 ? 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 X4. 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 X4. 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 X4? 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 X4 * X2? Circle the correct answer.

multiplying

dividing

adding

subtracting