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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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'''ll. Suggested activities and learning outcomes''' | '''ll. Suggested activities and learning outcomes''' | ||
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* | 1) Learning some basics about the circle and disk. | ||
* | |||
* 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. | |||
2) Define circumference. | |||
* 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). | ||
3) Find the relationship between the diameter and the circumference. | |||
* | * Drag point D to select a diameter. | ||
* | * Drag the circle by the green point as far as it can go. | ||
* | * 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? | ||
* | * Record in the spreadsheet below the diameter and the corresponding circumference for several circles from the activity above. | ||
* | * Calculate the ratio circumference/diameter. | ||
* | * Introduce Pi. | ||
* | * Write a formula for the circumference using the diameter. | ||
4) Experimental approximation of Pi. | |||
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. | 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 Objectives''' | '''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. | ||
* To introduce the circumference of the circle through a dynamic process, connecting the new concept to a familiar one (the perimeter of a rectangle). | * To introduce the circumference of the circle through a dynamic process, connecting the new concept to a familiar one (the perimeter of a rectangle). | ||
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'''lV. Underlying pedagogical/teaching approach or rationale''' | '''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. | ||
