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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:
Line 84: − + − *Question Corner: − After drawing a chord,what are the two segregated parts of the circle called ? − − <!-- This portal was created using subst:box portal skeleton --> − <!-- BANNER ACROSS TOP OF PAGE --> − {| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;" − |- − |style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| − [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics] − |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics] − |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| − [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics] − |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| − [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] − |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| − [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics] − |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| − [http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks] − |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| − [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank] − |} − While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. − − = Concept Map = − <mm>[[circle.mm|flash]]</mm> − − = Textbook = − ==ncert books== − [http://ncert.nic.in/NCERTS/textbook/textbook.htm?iemh1=10-15 Class 9 Mathematics] contain simple description and theorems on circles. − [http://ncert.nic.in/NCERTS/textbook/textbook.htm?jemh1=10-14Class 9 Mathematics] contain higher level description and theorems on circles. − − =Additional Information= − ==Useful websites== − #[http://www.mathsisfun.com/geometry/circle.html maths is fun] A GOOD WEBSITE ON DEFINITIONS FOR CIRCLES − #[http://www.coolmath.com/reference/circles-geometry.html COOL MATH] GIVES CLEAR AND EASY DEFINITIONS − #[http://www.mathopenref.com/circle.html OPEN REFERENCE] CONTAINS FEW SIMULATIONS − #[http://en.wikipedia.org/wiki/Math_circle#History WIKIPEDIA] CONTAINS EXPLANATIONS FOR CIRCLES − #[http://www.khanacademy.org KHAN ACADEMY] CONTAIN GOOD VIDEOS − #[http://www.arvindguptatoys.com ARVIND GUPTA TOYS] CONTAIN VERY GOOD BOOKS ON MATHEMATICS AND SCIENCE − #[http://nrich.maths.org/2490 nrich.maths.org] Contain very good description of Pie − − ==Reference Books== − #[http://archive.org/stream/schoolgeometry00hall#page/n11/mode/2up School Geometry] By Hall and Stevens. Part3 pageno 143. Contains basic definitions and proofs given by Euclid. − − = Teaching Outlines = − Introduction − − ==Concept #1 CIRCLE== − =Notes for teachers = − Introduction: − The circle is the most primitive and rudimentary of all human inventions, and at the same time, the most dynamic. It is the cornerstone in the foundation of science and technology. It is the basic tool of all engineers and designers. It is used by the greatest artists and architects in the history of mankind. Without a circular shape the wheel, pulleys, gears, ball bearings and a thousand other items we take for granted wouldn’t exist. And of course we would never have the pleasure of driving a car, riding a giant wheel, or watching the moon landing on our television set.<br> − If you look through any old patent claim, you will most likely find the repeated use of circles, spheres, curves, arches, etc. circles are everything and they are nothing. They don’t exist in reality and yet they are the basis of all that mankind has brought into existence. That is why a circle is so fantastic. − − ===Learning objectives=== − # Appreciation of circle as an important shape as it is an intrical component in the invention of almost everything that we see around us. − # To make students know that circle is a 2-dimensional plane circular figure. − # All points on its edge are equidistant from the center. − # The method of drawing a circle − # The size of the circle is defined by its radius. − # To elicit the difference between a bangle or a circular ring and circle as such. − − − [[File:circle.gif]] − − − ===Activity No # 1. A discussion on “Life without wheels / circular shaped figures.”=== − {| 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;"> − ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − *Estimated Time: 45 minutes − *Materials/ Resources needed: Paper, pen − *Prerequisites/Instructions, if any: − Previous day homework : − # Ask the children to make a list of all circular objects that they can think of : − # List as many devices as you can think of that depend on the wheel.(Consider objects in your home, at school, games and toys, machines, vehicles and engines as you make your list.) − # Now imagine living in a world without any kind of wheels or rolling devices. How would life be different? Would it be harder? How and why? Describe what it would be like to live without any wheels. − *Multimedia resources − *Website interactives/ links/ / Geogebra Applets − − *Process:(How to do the activity) − Have an open discussion with children. Initially let the children share their ideas and do most of the talking. Ensure that the intended discussion remains within the context. Make a mind map on blackboard of all relavant points discussed . Let them appreciate the significance of circular shape thus setting the stage for further study of this fantastic shape called “circles”. − *Developmental Questions :(What discussion questions) − # What all shapes do we see around us ? − # Can you imagine bicycles and your other vehicles without circular wheels ? − # How different life would have been if wheel was not disovered ? − # How could we explain centrifugal force ? − # What about potter's wheel and stone mill? − # Do you think that it is necessary for us to study and understand the parameters of circle in depth and detail ? − *Evaluation: − # Do you all now agree that wheel is one of the greatest inventions of mankind? Justify − *Question Corner: − # Are shapes important ? How? − # Is bangle a circle ? − # Would it be possible to understand pi without understanding circles ? − − − ===Activity No #2. Circle of varying radius using Geogebra === − {| 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;"> − ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − *Estimated Time: 20 mins − − *Materials/ Resources needed: Laptop, geogebra,projector and a pointer − − *Prerequisites/Instructions, if any: − #The students should know a circle − #They should know the meaning of radius . − #They should know to measure radius using compass − #They should know to draw a circle of given radius using compass. − − *Multimedia resources: Laptop − − *Website interactives/ links/ / Geogebra Applets: − <ggb_applet width="1280" height="600" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" /> − − *Process: − #Review the terms plane closed figures, circle and radius. − #Show them how to measure radius on the compass − #Show them to draw a circle. − #Project the geogebra and let them view the changing size of the circle with changing radius. − *Developmental Questions: − # What is a circle ? − # Which point is the centre of the circle ? − # What is the radius of this circle ? − # How do you name the radius ? − − *Evaluation: − #By what parameter is the size of a circle defined ? − #Bigger the radius, _____________ is the size of the circle. − − # How do you name a circle ?+ − # Can you draw a circle without knowing the radius ? − − ===Activity No # 3.Is circle a Polygon ? - A debate.=== − {| 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;"> − ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − *Estimated Time: 40 minutes<br> − '''*Materials/ Resources needed''' − Laptop, geogebra file, projector and a pointer.<br> − *Prerequisites/Instructions, if any − #The students should know that the plane figures with 3 or more than 3 sides are called polygons. − #They should know that as the number of sides increases, the figure and hence its name also changes. − #They should know the basics of a circle. − '''*Multimedia resources''' − Laptop − *Website interactives/ links/ / Geogebra Applets − <ggb_applet width="1280" height="600" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" /> − *Process − #Ask the students what polygons are ? − #As you increase the number of sides ask them to count the number of sides. − #Ask them the name of the shape formed. − #As the number of sides increase,let them speak about the length of the sides ? − '''*Developmental Questions''' − #How many sides does this figure have ? − #Name the figure formed. − #What is hapenning to the length of the sides as the number of sides is increased ? − #What shape is this ? − #So, can circle be considered a polygon ? Justify − *Evaluation: − #Are the students able to comprehend that the number of sides is getting infinite as the shape resembles a circle ? − #Are the students able to appreciate the application of polygon anology to circles. − *Question Corner − Debate between two groups with these two perspectives.<br> − #Circle seems to have derived from polygons . Circle can be considered a polygon. − Vs − #A polygon is defined by a certain number of sides having non zero length. Then how can circle be a polygon ? (hint: all radii in a circle should be equal ???) − − ===Activity No # === − {| 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;"> − ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − *Estimated Time − *Materials/ Resources needed − *Prerequisites/Instructions, if any − *Multimedia resources − *Website interactives/ links/ / Geogebra Applets − − − *Process/ Developmental Questions − − *Evaluation − *Question Corner − + − ===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. − # The students should understand that radius, diameter and chord lengths are linear measurements. − # They should learn to relate the size of the circle with radius. − # They realise that to draw a circle knowing the measure of radius or diameter is essential. − # There can be infinite radii in a circle. − # Diameter is twice the radius. − # The students should understand what a chord is. − # Chords of different lengths can be drawn in a circle. − # 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 longest chord in the circle is its diameter. − # Distance of chord from the centre is its perpendicular distance from the centre. − # A chord divides the circle into two segments. − # Angle at the centre of the circle is 360º. − # Angles in circles are measured using protractor. − # Circumference and area are calculated using formula. − ===Notes for teachers=== − − ===Activity No # 1. Measuring radius and diameter. === − {| 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;"> − ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − *Estimated Time: 15 mins − *Materials/ Resources needed: − #Laptop, goegebra tool, projector and a pointer. − #students' geometry box − *Prerequisites/Instructions, if any: − # Children should have the knowledge of circle, centre, radius, diameter and circumference. − # The teacher should have the necessary skill of using geogebra tool. − *Multimedia resources: Laptop − *Website interactives/ links/ / Geogebra Applets − <ggb_applet width="1280" height="572" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" /> − *Process: − # Initially the teacher can explain the terms: circle, its centre, radius, diameter and circumference. − # Ask the children “What parameter is needed to draw a circle of required size ?” − # Show them how to measure radius on the scale accurately using compass. − # Show them to draw a circle. − # 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. − #To measur 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. − − *Developmental Questions: − # Name the centre of the circle. − # Name the point on the circumference of the circle. − # What is the linesegment AB called ? − # Name the line passing through the centre of the circle. − # Using what can you measure the radius and diameter. − # Name the units of radius/diameter. − *Evaluation: − # How do you measure exact radius on the compass? − # Are the children able to corelate the radius/diameter of a circle with its size ? − *Question Corner: − # If the centre of the circle is not marked , then how do you get the radius for a given circle. − # How many radii/diameter can be drawn in a circle? − # Are all radii for a given circle equal ? − # Is a circle unique for a given radius/diameter ? − # In how many parts does a diameter divide the circle ? What is each part called ? − − ===Activity No # 2 Measuring a chord in a circle.=== − {| 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;"> − ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − *Estimated Time : 10 minutes − *Materials/ Resources needed: − Laptop, geogebra file, projector and a pointer. − *Prerequisites/Instructions, if any: − # The students should have prior knowledge of circle, radius , diameter and circumference.. − # The teacher should have knowledge of using geogebra. − *Multimedia resources: − Laptop, geogebra file, projector and a pointer. − *Website interactives/ links/ / Geogebra Applets − <ggb_applet width="1278" height="571" version="4.0" 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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" /> − *Process: − # The teacher can review the concept of a circle , radius , diameter and circumference . − # 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. − *Developmental Questions: − # The teacher can point to centre of circle and ask the students as to what it is. − # She can point to radius and ask the students to name it. − # Then ask them if any two points on the circumference are joined by a line segment what is it called ? − # How many chords can be drawn in a circle ? − # Are lengths of all chords the same ? − # Name the biggest chord in a circle. − # How do you measure a chord and in what units ? − *Evaluation: − Were the students able to distinguish between radius, diameter and chord ? − *Question Corner: − After drawing a chord,what are the two segregated parts of the circle called ? − − − ==Concept # 3 Angles in circles== Line 390:
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 438:
Line 130: − + − + − + − + − + + + + + + + + + + + + + + + + + + + + Line 469:
Line 180: − + Line 482:
Line 193: − + Line 488:
Line 199: − + − # They should have measuring and computational skills. Line 517:
Line 227: − + Line 531:
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Line 275: − +
Text replacement - "</mm>" to ""
[[File:Measurements in circles.mm|flash]]
==Concept # 1. Measurements in circles ==
==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.
<ggb_applet width="1280" height="572" version="4.0" 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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:
3 After drawing a chord,what are the two segregated parts of the circle called ?
==Concept # 2. Measurements in circles ==
==Concept # 2. Angles in circles==
===Learning objectives===
===Learning objectives===
# students should understand that the angle at the centre of the circle is 360 degrees.
# students should understand that the angle at the centre of the circle is 360 degrees.
{| 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" />
*Process:
# The teacher can recall the concept of circle, arc segment.
# She can then project the geogebra file , change slider and make clear the theorems about angles in a circle.
Developmental Questions:
# Name the minor and major segments.
# Name the angles formed by them.
# Where are the two angles subtended ?
# What is the relation between the two angles.
# Name the major and minor arcs.
# What is an acute angle?
# What is an obtuse angle?
# What type of angles are formed by minor arc ?
# What type of angles are formed by major arc ?
# What are your conclusions ?
*Evaluation:
# How many angles can a segment subtend on the circumference ?
# What can you say about these angles ?
*Question Corner:
# Recall the theorems related to angles in a circle.
*Process:
*Process:
# The teacher can recall the concept of circle, arc segment.
# The teacher can recall the concept of circle, arc segment.
# Recall the theorems related to angles in a circle.
# Recall the theorems related to angles in a circle.
==Concept # 4. Finding the Circumference of a circle==
==Concept # 3. Finding the Circumference of a circle==
===Learning objectives===
===Learning objectives===
# The children understand that the distance around the edge of a circle is known as circumference.
# The children understand that the distance around the edge of a circle is known as circumference.
{| 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
# Try to collect more information on Pi.
# Try to collect more information on Pi.
==Concept # 5 Finding the area of a circle.==
==Concept # 4. Finding the area of a circle.==
===Learning objectives===
===Learning objectives===
# The child should understand that the area of a circle is the entire planar surface.
# The child should understand that the area of a circle is the entire planar surface.
{| 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.
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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
*Process:
*Process: