Circumference of a Circle - Revision history

JanetBlair: added Rinfo

2013-04-01T22:21:28Z

added Rinfo

← Older revision		Revision as of 22:21, 1 April 2013
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			[[Category:Maths]][[Category:Secondary]][[Category:ORBIT]]
			{{Rinfo

			\|type= Lesson idea
			\|attribution= Irina Boyadzhiev
			\|title= Circumference of a Circle.
			\|tagline= Interactive GeoGebra investigation that allows students to explore an element of mathematics for themselves.
			\|image= Circumference of a Circle.png
			\|topic= Visualisation
			\|subject= Maths
			\|resourcenumber= M00XX
			\|age= Secondary
			\|content= Geogebra has been used to create a simple interactive applet. The applet and guidance notes on how to use it with students are included with the resource.
			\|related resources= [[Perimeter of a rectangle]]
			\|other=
			\|final=yes
			\|licence=
			\|format= Embedded GeoGebra applet and guidance notes.
			\|resources=
			* GeoGebra file:
			[[file:Circumference of a Circle.ggb]]

			* Guidance notes:
			[[file:Circumference of a Circle.doc]]


			}}



	<ggb_applet width="1063" height="628" version="4.2" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" />

JanetBlair: added link to perimeter of a rectangle applet

2013-04-01T22:16:57Z

added link to perimeter of a rectangle applet

← Older revision		Revision as of 22:16, 1 April 2013
Line 24:		Line 24:
	* 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 a rectangle]] applet, they can be directed to discuss the similarities between the two).

JanetBlair: formatted guidance notes

2013-04-01T22:14:14Z

formatted guidance notes

← Older revision		Revision as of 22:14, 1 April 2013
Line 6:		Line 6:
	'''I. Overview'''		'''I. Overview'''
	<br />		<br />

	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.

Line 11:		Line 12:
	'''ll. Suggested activities and learning outcomes'''		'''ll. Suggested activities and learning outcomes'''
	<br />		<br />
	* Learning some basics about the circle and disk.

	**Drag the blue point D up and down to create circles with different diameters.		1) Learning some basics about the circle and disk.
	**Click the Radius checkbox. See the relationship between the radius and the diameter.
			* 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.


	*Define circumference.		2) 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.		3) 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?		* How many times the diameter fits?
	**What is a rough approximation for the circumference of the circle?		* 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.		* Record in the spreadsheet below the diameter and the corresponding circumference for several circles from the activity above.
	**Calculate the ratio circumference/diameter.		* Calculate the ratio circumference/diameter.
	**Introduce Pi.		* Introduce Pi.
	**Write a formula for the circumference using the diameter.		* Write a formula for the circumference using the diameter.

	* Experimental approximation of Pi.		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'''
	<br />		<br />

	* 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'''
	<br />		<br />

	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.

JanetBlair: formatted guidance notes

2013-04-01T22:09:27Z

formatted guidance notes

← Older revision		Revision as of 22:09, 1 April 2013
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	<br />		<br />
	I. Overview		'''I. Overview'''
	<br />		<br />
	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.

	~~I<br />~~
	~~I. Suggested activities and learning outcomes~~
	<br />		<br />
	* Learning some basics about the circle and disk.~~<br />~~		'''ll. Suggested activities and learning outcomes'''
			<br />
			* 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.~~<br />~~		*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.~~<br />~~		* 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.~~<br />~~		* Experimental approximation of Pi.

	By ~~doing activity 3~~ the 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.

	<br />		<br />
	III. Learning ~~objectives~~		'''III. Learning Objectives'''
	<br />		<br />
	* 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.

	I<br />		<br />
	V. Underlying pedagogical/teaching approach or rationale		'''lV. Underlying pedagogical/teaching approach or rationale'''
	<br />		<br />
	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.

JanetBlair: added guidance notes

2013-04-01T21:43:48Z

added guidance notes

← Older revision		Revision as of 21:43, 1 April 2013
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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" />

			== Guidance Notes ==

			<br />
			I. Overview
			<br />
			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.

			I<br />
			I. Suggested activities and learning outcomes
			<br />
			* Learning some basics about the circle and disk.<br />

			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.

			*Define circumference.<br />

			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).

			* Find the relationship between the diameter and the circumference.<br />

			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.

			* Experimental approximation of Pi.<br />

			By doing activity 3 the 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.

			<br />
			III. Learning objectives
			<br />
			* 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 constant Pi and approximate its value.

			I<br />
			V. Underlying pedagogical/teaching approach or rationale
			<br />
			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.

JanetBlair: added applet

2013-04-01T19:24:36Z

added applet

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