NCTM Standards: Represent and analyze mathematical situations and structures using algebraic symbols; Understand patterns, relations and functions

Activity 32: Pi Time!

Added on 5/7/2008

 Downloads:
TI-73 PDF file
ACTIVITY OVERVIEW

In this activity we will:

  • Use the GEOBOARD app on the TI-73 to draw circles and understand where PI comes from
  • Utilize Lists in the calculator to find ratios
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Using the Geoboard application, we will draw circles and measure the circumference and diameter of each circle and then compare the relationship of each pair.  
First, clear lists 1 and 2 in your calculator. Press  ,  to OPS and select 3:ClrList and press. Press , press  and then press   . then press .


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Press the  key on your TI-73 and arrow to GEOBOARD. Press . Press the right arrow to go to the circle menu. Arrow down to select 1/2 radius and select 12 pegs.  Your screen should look like the one on the right. Press the key below the GOTO softkey. no alt text supplied
In order to draw the circle press the key below the draw softkey,then press the add key and press the  key until you reach the last peg before your stating place. Press arc.  Press add again and go one more place to the right to complete the circle.  Press arc again and then done. Then press quit.
 
Press meas, select Perimeter and press  and press again. Your screen should look like the one on the right. Press the key below L1 to record the measurement in List 1. Press quit.
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Now draw a diameter in the circle. Press draw and then add. Press the right arrow key until your chord forms a diameter.  Press add again and then press done. Press quit.
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To measure the diameter, press the key under the meas softkey.  Select Length and then select the two endpoints of the diameter by pressing on each one.  Then press the key below L2 to store the length in L2.
  
Repeat the process for radius lengths of 1,2,3 and 4.  To draw a new circle, press option, select 1:main menu, select Yes for Exit board and select NO on save board. You can now arrow down and change the radius to. See the screen on the right.
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Once you have collected all of the data, go to the main menu and select quit to exit the application.
  
To use the data collected in the Lists, press the  key. Arrow to the top of L3 and type  L1  L2.  We will divide the lists to see if there is a constant relationship between the diameter and circumference.
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What number results from the divisions? ________
This number is the ratio of the circumference compared to the diameter.  It is also the relationship for all circles.  It is the number you call PI!
  
EXTENSION

        If you measured the radius for each circle instead of the diameter, how could you test the same relationship? Do you see a relationship between PI and the new ratio you get from the radius and the circumference?
  

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