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Line 30: − + − # The teacher should have the necessary skill of using geogebra tool. − + Line 42:
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Line 69: − # The students should have prior knowledge of circle, radius , diameter and circumference.. − # The teacher should have knowledge of using geogebra. Line 78:
Line 74: − + − # Any two points on the circumference can be joined. − # The joining line segment is called the chord. − # Let the students name the chord . − # Move the chord on the geogebra and let them observe its changing size. − # Let them observe the chord becoming a diameter while passing through the centre of the circle. − # The length of the chord is measued using a scale with its unit being cm. Line 94:
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Line 95: − + − + − # They should know that an arc is a curved line along the circumference of a circle. − # If the end points of an arc are joined to a third point on the circumference of a circle, then an angle on the circumference is formed. − # If the end points of an arc are joined to the centre of a circle, then an angle at the centre of the circle is formed. − # They should know to measure the angles. − + − # Projecting geogebra file she can show the major and the minor arcs. − # Name the arc in discussion. − # Let students find out and name the angle subtended by the arc at the centre and angle subtended by the same arc on the circumference. − # Observe that the end points of the arc lie on the angle. − # Each side of the angle contains at least one end -point of the arc. − # Project different angles subtended by the same arc on the circumference. What is the inference ? − # Compare angle formed at the centre and angle formed on the circumference by the same arc. − # Change the angles/arc using slider. Note down the two angles in each case. − # Ask students what they observed ? Let them infer. Line 153:
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Line 199: − + − # They should have measuring and computational skills. Line 265:
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Text replacement - "</mm>" to ""
[[File:Measurements in circles.mm|flash]]
==Concept # Measurements in circles: 1. Radius and Diameter ==
==Concept # Measurements in circles: 1. Radius and Diameter ==
===Learning objectives===
===Learning objectives===
# The students should learn to measure radius, diameter, circumference, chord length and angles subtended at the centre and on the circumference of the circle.
# Ability to measure radius, diameter, circumference, chord length and angles subtended at the centre and on the circumference of the circle.
# The students should understand that radius, diameter and chord lengths are linear measurements.
# Radius, diameter and chord lengths are linear measurements.
# They should learn to relate the size of the circle with radius.
# Relate the size of the circle with radius.
# They realise that to draw a circle knowing the measure of radius or diameter is essential.
# They realise that to draw a circle knowing the measure of radius or diameter is essential.
# There can be infinite radii in a circle.
# There can be infinite radii in a circle.
# Chords of different lengths can be drawn in a circle.
# Chords of different lengths can be drawn in a circle.
# Chord length can be measured using a scale and its units is cm.
# Chord length can be measured using a scale and its units is cm.
# They should know that the length of the chord increases as it moves closer to the diameter.
# The length of the chord increases as it moves closer to the diameter.
# The longest chord in the circle is its diameter.
# The longest chord in the circle is its diameter.
# Distance of chord from the centre is its perpendicular distance from the centre.
# Distance of chord from the centre is its perpendicular distance from the centre.
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time: 15 mins
*Estimated Time: 15 mins
#students' geometry box
#students' geometry box
*Prerequisites/Instructions, if any:
*Prerequisites/Instructions, if any:
# Children should have the knowledge of circle, centre, radius, diameter and circumference.
# Circle and its basic parts should have been done.
*Multimedia resources: Laptop
*Multimedia resources: Laptop
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets : This file was done by ITfC-Edu-Team.
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />
*Process:
*Process:
# Given diameter, radius = D/2.
# Given diameter, radius = D/2.
# Also the other way i.e. If a circle is given, then its radius can be measured by using scale which is the linear distance between centre of the circle and any point on the circumference.
# Also the other way i.e. If a circle is given, then its radius can be measured by using scale which is the linear distance between centre of the circle and any point on the circumference.
#To measur diameter, measure the length of that chord which passes through the centre of the circle.
# To measure diameter, measure the length of that chord which passes through the centre of the circle.
Then she can project the digital tool 'geogebra.' and further clarify concepts.
Then she can project the digital tool 'geogebra.' and further clarify concepts.
*Developmental Questions:
*Developmental Questions:
# Name the centre of the circle.
# Name the centre of the circle.
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time : 10 minutes
*Estimated Time : 10 minutes
Laptop, geogebra file, projector and a pointer.
Laptop, geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any:
*Prerequisites/Instructions, if any:
*Multimedia resources:
*Multimedia resources:
Laptop, geogebra file, projector and a pointer.
Laptop, geogebra file, projector and a pointer.
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
*Process:
*Process:
# The teacher can review the concept of a circle , radius , diameter and circumference .
# Show the geogebra file and ask the following questions.
*Developmental Questions:
*Developmental Questions:
# The teacher can point to centre of circle and ask the students as to what it is.
# The teacher can point to centre of circle and ask the students as to what it is.
# How do you measure a chord and in what units ?
# How do you measure a chord and in what units ?
*Evaluation:
*Evaluation:
Were the students able to distinguish between radius, diameter and chord ?
# Were the students able to distinguish between radius, diameter and chord ?
*Question Corner:
*Question Corner:
After drawing a chord,what are the two segregated parts of the circle called ?
3 After drawing a chord,what are the two segregated parts of the circle called ?
==Concept # 2. Angles in circles==
==Concept # 2. Angles in circles==
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time : 40 minutes
*Estimated Time : 40 minutes
*Materials/ Resources needed : Laptop, geogebra file, projector and a pointer.
*Materials/ Resources needed : Laptop, geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
# The students should have prior knowledge of a circle and circumference.
# Circles and its parts should have been done.
*Multimedia resources: Laptop and a projector.
*Multimedia resources: Laptop and a projector.
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
*Process:
*Process:
# The teacher should initially discuss about the circle , radius, centre and circumference.
# Project the geogebra file and ask the questions listed below.
*Developmental Questions:
*Developmental Questions:
# Name the centre of the circle?
# Name the centre of the circle?
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time: 40 minutes
*Estimated Time: 40 minutes
*Materials/ Resources needed:Laptop, projector, geogebra file and a pointer.
*Materials/ Resources needed:Laptop, projector, geogebra file and a pointer.
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
#The students should have prior knowledge of a circle, angles, arcs and segments.
# Knowledge of a circle, angles, arcs and segments.
#The students should have a thorough knowledge about the types of angles.
# About the types of angles.
#They should have the skill of drawing a circle , angles and measuring them.
# Skill of drawing a circle , angles and measuring them.
*Multimedia resources : Laptop, Projector.
*Multimedia resources : Laptop, Projector.
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets: This file has been done by Mallikarjun Sudi of Yadgir.
<ggb_applet width="1280" height="600" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
*Process:
*Process:
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time : 45 mins
*Estimated Time : 45 mins
Note books, compass, pencil, mender, scale.
Note books, compass, pencil, mender, scale.
*Prerequisites/Instructions, if any:
*Prerequisites/Instructions, if any:
# The children should have prior knowledge of circle, radius, diameter and circumference.
# Circles basics should have been done.
*Multimedia resources:
*Multimedia resources:
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time:90 mins
*Estimated Time:90 mins
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time: 45mins
*Estimated Time: 45mins
Prior knowledge of circle, radius, square and area of square.
Prior knowledge of circle, radius, square and area of square.
*Multimedia resources: Laptop.
*Multimedia resources: Laptop.
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets: This file was done by Bindu.
<ggb_applet width="1280" height="600" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
*Process:
*Process: