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Circles (view source)

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*Question Corner
 
*Question Corner
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==Concept # ==
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==Concept # Measurements in circles==
 
===Learning objectives===
 
===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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# 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.
 
===Notes for teachers===
 
===Notes for teachers===
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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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*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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*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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===Activity No #  ===
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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
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*Materials/ Resources needed
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*Prerequisites/Instructions, if any
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*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
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==Concept #  Measuring a chord in a circle==
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===Learning objectives===
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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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# Length of chord is its linear measurement.
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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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===Notes for teachers===
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===Activity No # 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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*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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===Activity No # ===
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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
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*Materials/ Resources needed
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*Prerequisites/Instructions, if any
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*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
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==Concept #  3 Finding the Circumference of a circle==
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===Learning objectives===
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# The children understand that the distance around the edge of a circle is known as circumference.
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# The children learn to measure the circumference of the circle.
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# Derivation of formula for circumference.
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# They understand what is pi.
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===Notes for teachers===
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The circumference of a circle  relates to one of the most important mathematical constants in all of mathematics. This constant pi, is represented by the Greek letter П.  The numerical value of π is 3.14159 26535 89793 , and is defined by the ratio of a circle's circumference to its diameter.
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  C = п. D  or  C = 2пr.
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===Activity No # 1 Derivation of formula for circumference and the value for pi.===
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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;">
 +
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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*Estimated Time : 45 mins
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*Materials/ Resources needed:
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Note books, compass, pencil, mender, scale.
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*Prerequisites/Instructions, if any:
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# The children should have prior knowledge of circle, radius, diameter and circumference.
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# They should have measuring and computational skills.
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*Multimedia resources:
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*Website interactives/ links/ / Geogebra Applets
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*Process:
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#Ask the children to draw  five circles with different radii.
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# Let them carefully measure their circumferences using wool.
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# Mark the distance around the circle on the wool with a sketch pen.
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# Measure the length of the measured wool using a scale.
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# Make a table with columns radius, diameter and circumference
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# For every circle find Circumference / diameter.
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# Round C/d to two decimal places.
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# Observe the answers in each case. It would be aprroximately 3.14 .
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# The  value 3.14  is the value of pi which is constant.
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C/d = п    or    C = п d    or  C = 2п r.
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*Developmental Questions:
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# Have you noted down radius, diameter and their respective circumferences.
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# Check if your calculations are correct.
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# What do you infer from the observed results ?
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*Evaluation:
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# Are the children taking correct measurements.
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# Are they comparing the results of C/d with all circles.
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# Are they noticing that it is constant .
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# Are they questioning why it is constant?
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*Question Corner:
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# How do you derive the formula for circumference of a circle ?
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# What is the name of that constant ?
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# Try to collect more information on Pi.
    
= Hints for difficult problems =
 
= Hints for difficult problems =
sudha
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