> WYV@ !bjbjצצ !P000D,,,,<h|D"(333a"c"c"c"c"c"c"$j$R&"0/3""Z0a"a"V'@F0ض~,r@g L"0"sJ'LJ'DD&J'0p3dae333""DDdDDDiscovering Pi Using Tape Measures, Cabri Jr., and the TI-Navigator
Teacher Instructions
In this activity, students will measure the circumference and diameter of several round objects. They will send in their measurements using the TI-Navigator Activity Center and discover the relationship between the circumference and diameter. Students will note why all points do not lie exactly on the line y=(x. Then students will use Cabri Jr. to measure the circumference and diameter of a constructed circle. After they send in their measurements through the Activity Center, students will note why all of the points created from Cabri Jr. do lie exactly on the line y=(x.
I. Have students complete the handout (see page 3 below). I have used this part of the activity in my classroom for several years. We call it Round-Up Day. Students bring round food to measure (and eat) such as round crackers, cookies, bagels, snack cakes, hard candy, etc. Students who dress western-style get a few bonus points. Alternately, one could have students measure a variety of round lids or other round objects. Once students have found the average of their ten measured objects, they should realize that their answer should be close to (. When I check their list, I look for items for which the ratio is obviously off (this usually happens on small objects) and have students measure those items again, if there is time.
II. Once students have measured their objects, have them login to Navnet and select 1 for Activity Center. As the teacher, you should go into Activity Center and setup the activity so that students can contribute lists. Clear any previous activity data under Edit/Clear Activity Data. Configure the lists so that students start with empty lists. Allow them to enter data for 2 lists (L1 should be the diameter, and L2 should be the circumference). Also allow students to resubmit lists in case they discover that they entered the data backwards during the course of the activity. Go into the List-Graph tab of Activity Center and configure plots so that the computer will plot the students data as they enter it. Start the activity. Have students divide the objects that they measured so that the measurements from each objects gets entered by someone in the group, enter the diameter in L1 and the circumference in L2 for all objects for which they are responsible and send. If the window in Activity Center is not appropriate, then View/Zoom Stat for an appropriate window. The data that students submit should be mostly linear. Connect the average of ratios that students found in their groups to the constant that relates the circumference and diameter. Once all data has been submitted and students have realized that ( is the relating constant, click on the Graph-Equation tab and add y=pi x to the equation list. Students should note that while most of the data lies very close to the line, not all data lies exactly on the line. Discuss error in measurement as the major reason that the data does not lie exactly on the line.
III. In the next section of the activity, students will measure the circumference and diameter of a circle constructed in Cabri Jr. Depending on the time you have, you could have students construct the diameter of a circle themselves (see Activity: Constructing a Diameter of a Circle). If you do not have time for students to construct the circle and diameter, then use the Navigator to force send the Application Variable Pi.8xv to students (Tasks/Send to Class/select file/select students/force send). Students should quit the TI-Navigator Home Screen so they can go into Cabri Jr and F1/Open PI. If there is time, you could F1/Undo/Explore and press the right arrow through each step of the construction so that students can review how to construct the diameter of the circle.
Now that students have opened the circle on their calculator, they need to make the circle a different size from other students in their group. Have every student make the solitary point on the circle dance. They should press INCLUDEPICTURE "C:\\DOCUME~1\\jwilson\\LOCALS~1\\Temp\\Alpha.png" \* MERGEFORMATINET to grab the point and make their circle smaller or larger with the arrow keys. Once each students circle is a different size from the others in the group, they should press INCLUDEPICTURE "C:\\DOCUME~1\\jwilson\\LOCALS~1\\Temp\\Enter.png" \* MERGEFORMATINET to drop the circle and record the circumference and diameter.
IV. Have student exit Cabri Jr., execute Navnet and select 1 for Activity Center. As the teacher, you should go into Activity Center and select the List-Graph. You might want to hide the data from the first part of the activity. Select the first row of data, hold the shift key down and select the last row of data. Then click on hide at the bottom of the list window. The activity should still be setup so that students can contribute lists. Start the activity. Have students enter the diameter in L1 and the circumference in L2 from their own measured circle from Cabri Jr. and send. If the window in Activity Center is not appropriate, then View/Zoom Stat for an appropriate window. The data that students submit should all lie on the line y=(x. Discuss why these data points differ from the ones that students measured previously. You can show the student-measured data along with the calculator-measured data by selecting the hidden data and clicking show.
Round-Up Day Group _____________________
Score__________ _____________________
Dress-up Bonus____ _____________________
_____________________
Supplies: Measuring Tapes, Yarn, Round Items, Ruler
For each of 10 different round items, measure and record the circumference (distance around the circle) and the diameter (distance across the circle at its center). If the object is too small for the measuring tape, use a piece of yarn to measure the circumference; then measure the amount of yarn needed to go around the object with the measuring tape or ruler. Important note: For each object, the circumference and diameter should be measured using the same units (both cm. , both in., etc.).
After you record the measurements, find and record the ratio c/d to two decimal places for each item.
After you have found all of the ratios, find the average of all ten of the ratios.
Upon teacher approval, you are ready to login to Navnet.
Item #DescriptionCircumferenceDiameterRatio of c:d rounded to 2 decimal places1.2.3.4.5.6.7.8.9.10.
AVERAGE (also rounded to 2 decimal places)
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