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Circumference of a Circle: Difference between revisions
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I. Overview | '''I. Overview''' | ||
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This applet can be used for introducing circumference of a circle. The students can create circles with different diameters by dragging the blue point D vertically. The circle can be rolled along the x-axis by dragging the green point - the center of the circle. This will “peel off” the red outer layer and transfer it to the x-axis. When the circle is rolled to the end and the entire red line is transferred to the x axis, a slider appears. Dragging the slider the students will see that the diameter fits a little more than three times in the circumference. They can record the diameter and the corresponding circumference in the spreadsheet and calculate the ratio circumference/diameter. | This applet can be used for introducing circumference of a circle. The students can create circles with different diameters by dragging the blue point D vertically. The circle can be rolled along the x-axis by dragging the green point - the center of the circle. This will “peel off” the red outer layer and transfer it to the x-axis. When the circle is rolled to the end and the entire red line is transferred to the x axis, a slider appears. Dragging the slider the students will see that the diameter fits a little more than three times in the circumference. They can record the diameter and the corresponding circumference in the spreadsheet and calculate the ratio circumference/diameter. | ||
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* Learning some basics about the circle and disk. | '''ll. Suggested activities and learning outcomes''' | ||
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* Learning some basics about the circle and disk. | |||
Drag the blue point D up and down to create circles with different diameters. | **Drag the blue point D up and down to create circles with different diameters. | ||
Click the Radius checkbox. See the relationship between the radius and the diameter. | **Click the Radius checkbox. See the relationship between the radius and the diameter. | ||
*Define circumference. | *Define circumference. | ||
Drag point D to select a diameter. | **Drag point D to select a diameter. | ||
Drag the circle by the green point to transfer the red line onto the x-axis. (If the students have seen The Perimeter of the Rectangle applet http://www.geogebratube.org/student/m30142, they can be directed to discuss the similarities between the two). | **Drag the circle by the green point to transfer the red line onto the x-axis. (If the students have seen The Perimeter of the Rectangle applet http://www.geogebratube.org/student/m30142, they can be directed to discuss the similarities between the two). | ||
* Find the relationship between the diameter and the circumference. | * Find the relationship between the diameter and the circumference. | ||
Drag point D to select a diameter. | **Drag point D to select a diameter. | ||
Drag the circle by the green point as far as it can go. | **Drag the circle by the green point as far as it can go. | ||
Drag the slider to fit the diameter into the circumference. | **Drag the slider to fit the diameter into the circumference. | ||
How many times the diameter fits? What is a rough approximation for the circumference of the circle? | **How many times the diameter fits? | ||
Record in the spreadsheet below the diameter and the corresponding circumference for several circles from the activity above. | **What is a rough approximation for the circumference of the circle? | ||
Calculate the ratio circumference/diameter. Introduce Pi. | **Record in the spreadsheet below the diameter and the corresponding circumference for several circles from the activity above. | ||
Write a formula for the circumference using the diameter. | **Calculate the ratio circumference/diameter. | ||
**Introduce Pi. | |||
**Write a formula for the circumference using the diameter. | |||
* Experimental approximation of Pi. | * Experimental approximation of Pi. | ||
By | By finding the relationship between the diameter and the circumference, students discover that the circumference is proportional to the diameter (C=kd). Drag point D to make the diameter equal to 1 in order to approximate the value of k. | ||
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III. Learning | '''III. Learning Objectives''' | ||
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* To introduce the circle and some basic terminology by actively manipulating the object. | * To introduce the circle and some basic terminology by actively manipulating the object. | ||
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* To introduce the constant Pi and approximate its value. | * To introduce the constant Pi and approximate its value. | ||
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'''lV. Underlying pedagogical/teaching approach or rationale''' | |||
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The applet gives the opportunity to involve the students in the process of teaching. Each student can create and manipulate the circle, learn terminology by manipulating the objects. Students discover a relationship based on experimental data and mathematical calculation. The explorations can be done fast and accurate. | The applet gives the opportunity to involve the students in the process of teaching. Each student can create and manipulate the circle, learn terminology by manipulating the objects. Students discover a relationship based on experimental data and mathematical calculation. The explorations can be done fast and accurate. | ||
