Difference between revisions of "Sector of a circle"

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Slice of a circle enclosed between any two radii is called a sector.Semicircle and quadrant are special types of sectors.
  
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=== Objectives ===
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* To understand area enclosed by two radii is sector.
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===Estimated Time===
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*15 minutes
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===Prerequisites/Instructions, prior preparations, if any===
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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* The students should know a circle, centre, radius,circumference and a sector.
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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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* They should know that circle is a planar figure.
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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:_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; "|
 
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[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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|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:_Question_Papers Question Bank]
 
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|}
 
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
  
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= Concept Map =
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===Materials/ Resources needed===
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<mm>[[CIRCLES BASIC TERMS..mm|Flash]]</mm>>
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Non digital: Laptop, geogebra file, projector and a pointer.
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__FORCETOC__
 
  
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= Textbook =
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Geogebra file: [https://ggbm.at/fqssprue Arcs and Sector of a circle]
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To add textbook links, please follow these instructions to:  
 
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([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 
  
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=Additional Information=
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{{Geogebra|fqssprue}}
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==Useful websites==
 
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==Reference Books==
 
  
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= Teaching Outlines =
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===Process (How to do the activity)===
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<span></span><span></span>
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# Move the endpoints of the sector and help them understand the types of sector.
  
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==Concept #1 CIRCLE CENTRE==
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# Name all the points on the circumference.
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===Learning objectives===
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# Name the endpoints of the sector.  
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#Define circle
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# Name the major and minor sectors.
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#give examples for circles
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# What can you say about the two straight lines of the sector?
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#Locate centre for the given circle.
 
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===Notes for teachers===
 
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Define circle and centre with the help of a diagram
 
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===Activity No # 1 To locate centres for circles ===
 
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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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20 minutes
 
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*Materials/ Resources needed
 
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For the teacher: chalk piece, geometry set.<br>
 
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for the student: paper
 
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*Prerequisites/Instructions, if any
 
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''Instructions for the teacher:'' Draw few circles of different radii and name the centres <br>
 
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''Instructions for the student'' : name the centres of different circles
 
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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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Identify the centre.
 
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*Evaluation
 
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#How many centres does a circle has?<br>
 
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#Where does the centre of the circle lie? (inside/outside)
 
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*Question Corner
 
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Is there a circle with 3/4/5 centres?
 
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===Activity No # 2 ===
 
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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 #2 diameter==
 
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===Learning objectives===
 
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to draw circle<br>
 
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to draw a diamter
 
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use of  geometrical instruments
 
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===Notes for teachers===
 
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explain the  concepts using requisite diagrams. Conduct this activity.
 
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===Activity No #1 ===
 
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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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20 minutes
 
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*Materials/ Resources needed
 
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different coloured circular cutouts
 
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*Prerequisites/Instructions, if any <br>
 
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#The student should have knowledge of circles.
 
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#The student should have skill of paper folding
 
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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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''instructions to the teacher:''<br>
 
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The teacher distributes the papeAre the students standing on the circumference of the circle considered to be in the interior or in the exterior ? Justify.r cut outs to all the students.<br>
 
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Ask every student to make 2 equal parts by folding.<br>
 
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What happens if it is folded again to get equal parts?<br>
 
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Ask the students to identify the folded lines/marks<br>
 
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''instructions to the student:''<br>
 
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fold the paper cut out as per instructions<br>
 
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observe and mark the folded line.<br>
 
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Identity the diameter and radius.<br>
 
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*Evaluation
 
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#Was the student successful in marking radius and diamter?<br>
 
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#Was the student successful in folding and marking?<br>
 
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#Was the student able to relate radius and diameter.<br>
 
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*Question Corner
 
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how many such radii and diameters can be drawn to a given circle?
 
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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
 
−
*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 CIRCUMFERENCE==
 
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===Learning objectives===
 
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The student needs to understand that the circumference is the outer boundary of a circle.
 
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===Notes for teachers===
 
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Explain that every point on the circumference is at equidistant from the centre.
 
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===Activity No #1 ===
 
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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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10 minutes.
 
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*Materials/ Resources needed
 
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white paper , compass and colour pencils.
 
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*Prerequisites/Instructions, if any
 
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The student should know to use the compass.<br>
 
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The student should understand the circumference as outer boundary.
 
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*Multimedia resources
 
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Geogebra
 
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*Website interactives/ links/ / Geogebra Applets
 
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*Process/ Developmental Questions
 
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'''Instructions to the teachers'''<br>
 
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Ask the children to draw circles.<br>
 
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'''Instructions for the students'''<br>
 
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Colour circumference by fitting small colour pencil in compass itself.
 
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*'''Evaluation'''
 
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Observe for the skill in using compass and drawing the circle.
 
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*'''Question Corner'''
 
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Is the distance between centre of the circle and its circumference constant ?<br>
 
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What is the distance between the center of a circle and its circumference called?
 
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==Concept #4 SEMICIRCLE==
 
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==='''Learning objectives'''===
 
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* The student should be able to understand that a diameter  divides the circle into two equal halves and each such half is a semicircle or hemicircle.<br>
 
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* The student learns how to form  a semicircle by joining any two points on the circumference through its centre .
 
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==='''Notes for teachers'''===
 
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Show children the forming of semicircle by drawing diameter.
 
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==='''Activity No # 1'''===
 
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Bring cut circles of different sizes, fold them into exact halves and help them recognise semicircles.  Let them colour each half with different colour.<br>
 
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'''Sub units of activities:'''<br>
 
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This is a classroom individual activity.<br>
 
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'''Materials:'''
 
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White paper, crayons.
 
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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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15 minutes.
 
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*'''Materials/ Resources needed'''
 
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White paper, crayons.
 
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*'''Prerequisites/Instructions, if any'''
 
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The students should have prior knowledge of circle and diameter.
 
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*'''Multimedia resources'''
 
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Geogebra
 
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*Website interactives/ links/ / Geogebra Applets
 
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*'''Process/ Developmental Questions'''
 
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'''Instructions to the teacher:'''
 
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Ask children the previous day to cut circles of given radius and bring.
 
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'''Instructions to the students:'''
 
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Instruct them to fold circle into exact half. Draw diameter on folded line and colour each half with different colour.
 
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*'''Evaluation'''
 
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Were the students able to draw and cut perfect circles?<br>
 
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Was the folded line (diameter) passing through the center of circle?<br>
 
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*'''Question Corner'''
 
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In how many different ways can you draw semicircles for a given circle?
 
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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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|}
 
−
*Estimated Time
 
−
*Materials/ Resources needed
 
−
*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 #5 Interior and Exterior of circle==
 
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==='''Learning objectives'''===
 
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The student needs to understand that any points on the planar surface of the circle are said to be  interior points and points on the outside of circumference are said to be its exterior points.
 
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==='''Notes for teachers'''===
 
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This knowledge is important to understand secant and tangent to the circle.
 
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==='''Activity No #1''' ===
 
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''''''A game of tiger and goat.''''''<br>
 
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Draw a circle on the playground. Make children stand on its circumference. Call one student inside the circle to be a goat and other student on the exterior would be the tiger. The tiger tries to get into the circle interior to catch the goat. All other students on the circumference defend the entry of tiger . If tiger forces itself inside, the goat is let out . If the tiger succeeds in catching the goat , the student enacting goat becomes out. Next two more students come forward to be the  next goat and tiger and hence the game continues.<br>
 
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'''Sub units of activity:'''
 
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This is an outdoor group activity<br>
 
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'''Instructions to the students:'''<br>
 
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Let this be a fun filled activity and during the game use the terms circle, circumference, interior and exterior .
 
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'''Instructions to the students:'''<br>
 
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Identify who is in the interior of circle and who is in the exterior.
 
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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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30mins
 
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*'''Materials/ Resources needed'''
 
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A meter length wool nailed to ground (to be centre of circle) and tied to stick on the other side to help draw a perfect circle.
 
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*'''Prerequisites/Instructions, if any'''
 
−
The students need to know that the circumference of the circle is its boundary and understand the terms interior and exterior of the circle.
 
−
 
 
−
*Multimedia resources
 
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−
*Website interactives/ links/ / Geogebra Applets
 
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*'''Process/ Developmental Questions'''
 
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*'''Evaluation'''
 
−
Guage if the students have understood the meaning of the terms interior and exterior.
 
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*'''Question Corner'''
 
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Are the students standing on the circumference of the circle considered to be in the interior or in the exterior ? Justify.
 
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===Activity No # ===
 
−
{| 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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*'''Estimated Time'''
 
−
30 minutes
 
−
*'''Materials/ Resources needed'''
 
−
A meter length wool nailed to ground (to be centre of circle) and tied to stick on the other side to help draw a perfect circle.
 
−
*'''Prerequisites/Instructions, if any'''
 
−
The students need to know that the circumference of the circle is its boundary and understand the terms interior and exterior of the circle.
 
−
*Multimedia resources
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
*'''Process/ Developmental Questions'''
 
−
'''Instructions to the teachers:'''
 
−
Let this be a fun filled activity and during the game use the terms circle, circumference, interior and exterior.<br>
 
−
'''Instructions to the students:'''
 
−
Identify who is in the interior of circle and who is in the exterior.
 
 
*'''Evaluation'''
 
*'''Evaluation'''
−
Guage if the students have understood the meaning of the terms interior and exterior.
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# Name the special types of sector?
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*'''Question Corner'''
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# Give some examples of sector.
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Are the students standing on the circumference of the circle considered to be in the interior or in the exterior ? Justify.
 
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==Concept #6 Chord==
 
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===Learning objectives===
 
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*The students should understand that the chord is a line segment joining any two distinct points on the circle
 
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*The students should understand that the longest chord in any circle is its diameter.
 
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===Notes for teachers===
 
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*Explain the concept by drawing chords of different sizes.
 
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*Make the students understand that the length of the chord increases as it moves closer to the centre and decreases as it moves away from the center.
 
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===Activity No # 1===
 
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Fold the cut-circular paper at different points. Draw folded lines with different coloured pencils and observe the length of chords.
 
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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 :'''20 minutes.
 
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*'''Materials/ Resources needed'''
 
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Circles cut from white paper, colour pencils, scale.
 
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*'''Prerequisites/Instructions, if any'''
 
−
The students should have the knowledge of circle, diameter, circumference and line segment.<br>
 
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'''Instructions to the teacher:'''
 
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Instruct the children to get cut circles ready:<br>
 
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'''Instructions to the children:'''
 
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Fold the circle at different points and try to form the smallest and biggest chords.
 
−
*'''Multimedia resources:'''Geogebra
 
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*Website interactives/ links/ / Geogebra Applets
 
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*'''Process/ Developmental Questions'''
 
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*'''Evaluation'''
 
−
Observe to see if the children are able to fold and mark the chord accurately.
 
−
*'''Question Corner'''
 
−
Name the chord that passes through the center of the circle.<br>
 
−
What happens to the length of the chord as it moves away from the centre?
 
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−
===Activity No # ===
 
−
{| 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>
 
−
|}
 
−
*Estimated Time
 
−
*Materials/ Resources needed
 
−
*Prerequisites/Instructions, if any
 
−
*Multimedia resources
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
*Process/ Developmental Questions
 
−
*Evaluation
 
−
*Question Corner
 
−
 
 
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==Concept #7==
 
−
===Learning objectives===
 
−
===Notes for teachers===
 
−
===Activity No # ===
 
−
{| 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>
 
−
|}
 
−
*Estimated Time
 
−
*Materials/ Resources needed
 
−
*Prerequisites/Instructions, if any
 
−
*Multimedia resources
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
*Process/ Developmental Questions
 
−
*Evaluation
 
−
*Question Corner
 
−
 
 
−
===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
 
−
 
 
−
==Concept #8==
 
−
===Learning objectives===
 
−
===Notes for teachers===
 
−
===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
 
−
 
 
−
===Activity No # ===
 
−
{| 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>
 
−
|}
 
−
*Estimated Time
 
−
*Materials/ Resources needed
 
−
*Prerequisites/Instructions, if any
 
−
*Multimedia resources
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
*Process/ Developmental Questions
 
−
*Evaluation
 
−
*Question Corner
 
−
 
 
−
==Concept #9==
 
−
===Learning objectives===
 
−
===Notes for teachers===
 
−
===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
 
−
 
 
−
===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
 
−
 
 
−
==Concept #10==
 
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===Learning objectives===
 
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===Notes for teachers===
 
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[[Category:Circles]]

Latest revision as of 05:54, 7 November 2019

Slice of a circle enclosed between any two radii is called a sector.Semicircle and quadrant are special types of sectors.

Objectives

  • To understand area enclosed by two radii is sector.

Estimated Time

  • 15 minutes

Prerequisites/Instructions, prior preparations, if any

  • The students should know a circle, centre, radius,circumference and a sector.
  • They should know that circle is a planar figure.

Materials/ Resources needed

Non digital: Laptop, geogebra file, projector and a pointer.

Geogebra file: Arcs and Sector of a circle


Download this geogebra file from this link.


Process (How to do the activity)

  1. Move the endpoints of the sector and help them understand the types of sector.
  1. Name all the points on the circumference.
  2. Name the endpoints of the sector.
  3. Name the major and minor sectors.
  4. What can you say about the two straight lines of the sector?
  • Evaluation
  1. Name the special types of sector?
  2. Give some examples of sector.
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