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| | <mm>[[Measurements in circles.mm|flash]]</mm> | | <mm>[[Measurements in circles.mm|flash]]</mm> |
| − | ==Concept # 1. Measurements in circles ==
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| − | ===Learning objectives===
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| − | # The students should learn to measure radius, diameter, circumference, chord length and angles subtended at the centre and on the circumference of the circle.
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| − | # The students should understand that radius, diameter and chord lengths are linear measurements.
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| − | # They should learn to relate the size of the circle with radius.
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| − | # They realise that to draw a circle knowing the measure of radius or diameter is essential.
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| − | # There can be infinite radii in a circle.
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| − | # Diameter is twice the radius.
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| − | # The students should understand what a chord is.
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| − | # Chords of different lengths can be drawn in a circle.
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| − | # Chord length can be measured using a scale and its units is cm.
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| − | # They should know that the length of the chord increases as it moves closer to the diameter.
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| − | # The longest chord in the circle is its diameter.
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| − | # Distance of chord from the centre is its perpendicular distance from the centre.
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| − | # A chord divides the circle into two segments.
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| − | # Angle at the centre of the circle is 360º.
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| − | # Angles in circles are measured using protractor.
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| − | # Circumference and area are calculated using formula.
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| − | ===Notes for teachers===
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| − |
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| − | ===Activity No # 1. Measuring radius and diameter. ===
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| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | |}
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| − | *Estimated Time: 15 mins
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| − | *Materials/ Resources needed:
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| − | #Laptop, goegebra tool, projector and a pointer.
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| − | #students' geometry box
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| − | *Prerequisites/Instructions, if any:
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| − | # Children should have the knowledge of circle, centre, radius, diameter and circumference.
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| − | # The teacher should have the necessary skill of using geogebra tool.
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| − | *Multimedia resources: Laptop
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | <ggb_applet width="1280" height="572" version="4.0" 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| − | *Process:
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| − | # Initially the teacher can explain the terms: circle, its centre, radius, diameter and circumference.
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| − | # Ask the children “What parameter is needed to draw a circle of required size ?”
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| − | # Show them how to measure radius on the scale accurately using compass.
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| − | # Show them to draw a circle.
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| − | # Given diameter, radius = D/2.
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| − | # 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.
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| − | #To measur diameter, measure the length of that chord which passes through the centre of the circle.
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| − | Then she can project the digital tool 'geogebra.' and further clarify concepts.
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| − |
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| − | *Developmental Questions:
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| − | # Name the centre of the circle.
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| − | # Name the point on the circumference of the circle.
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| − | # What is the linesegment AB called ?
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| − | # Name the line passing through the centre of the circle.
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| − | # Using what can you measure the radius and diameter.
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| − | # Name the units of radius/diameter.
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| − | *Evaluation:
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| − | # How do you measure exact radius on the compass?
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| − | # Are the children able to corelate the radius/diameter of a circle with its size ?
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| − | *Question Corner:
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| − | # If the centre of the circle is not marked , then how do you get the radius for a given circle.
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| − | # How many radii/diameter can be drawn in a circle?
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| − | # Are all radii for a given circle equal ?
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| − | # Is a circle unique for a given radius/diameter ?
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| − | # In how many parts does a diameter divide the circle ? What is each part called ?
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| − |
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| − | ===Activity No # 2 Measuring a chord in a circle.===
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| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | |}
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| − | *Estimated Time : 10 minutes
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| − | *Materials/ Resources needed:
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| − | Laptop, geogebra file, projector and a pointer.
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| − | *Prerequisites/Instructions, if any:
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| − | # The students should have prior knowledge of circle, radius , diameter and circumference..
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| − | # The teacher should have knowledge of using geogebra.
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| − | *Multimedia resources:
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| − | Laptop, geogebra file, projector and a pointer.
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | <ggb_applet width="1278" height="571" version="4.0" 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| − | *Process:
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| − | # The teacher can review the concept of a circle , radius , diameter and circumference .
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| − | # Any two points on the circumference can be joined.
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| − | # The joining line segment is called the chord.
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| − | # Let the students name the chord .
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| − | # Move the chord on the geogebra and let them observe its changing size.
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| − | # Let them observe the chord becoming a diameter while passing through the centre of the circle.
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| − | # The length of the chord is measued using a scale with its unit being cm.
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| − | *Developmental Questions:
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| − | # The teacher can point to centre of circle and ask the students as to what it is.
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| − | # She can point to radius and ask the students to name it.
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| − | # Then ask them if any two points on the circumference are joined by a line segment what is it called ?
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| − | # How many chords can be drawn in a circle ?
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| − | # Are lengths of all chords the same ?
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| − | # Name the biggest chord in a circle.
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| − | # How do you measure a chord and in what units ?
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| − | *Evaluation:
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| − | Were the students able to distinguish between radius, diameter and chord ?
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| − | *Question Corner:
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| − | After drawing a chord,what are the two segregated parts of the circle called ?
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| − |
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| − | |style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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| − | |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]
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| − | |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]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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| − | |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]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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| |
| − | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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| | = Textbook = | | = Textbook = |
| | ==ncert books== | | ==ncert books== |
