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− | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics] | + | [http://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://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; "| | | |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] | + | [http://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; "| | | |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] | + | [http://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; "| | | |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] | + | [http://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; "| | | |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] | + | [http://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; "| | | |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] | + | [http://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''']. | | 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 = | | = Concept Map = |
| __FORCETOC__ | | __FORCETOC__ |
− | <mm>[[Circles_Constructions.mm|flash]]</mm>
| + | [[File:Circles_Constructions.mm|flash]] |
| | | |
| = Textbook = | | = Textbook = |
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| {| 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 | | *Estimated Time |
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| {| 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 | | *Estimated Time |
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| *Question Corner | | *Question Corner |
| | | |
− | ==Concept #== | + | ==Concept #2. Construction of Tangent.== |
| ===Learning objectives=== | | ===Learning objectives=== |
| ===Notes for teachers=== | | ===Notes for teachers=== |
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| {| 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 | | *Estimated Time |
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| {| 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 | | *Estimated Time |
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| *Question Corner | | *Question Corner |
| | | |
− | ==Concept #== | + | ===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://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://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 #3. Construction of direct common tangent.== |
| ===Learning objectives=== | | ===Learning objectives=== |
| ===Notes for teachers=== | | ===Notes for teachers=== |
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| {| 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 | | *Estimated Time |
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| {| 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 | | *Estimated Time |
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| *Evaluation | | *Evaluation |
| *Question Corner | | *Question Corner |
| + | ===Activity No # Construct a direct common tangent to two circles with given radii and given distance between the centre of two circles.=== |
| + | {| 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://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
| + | |} |
| + | *Estimated Time: 90 minutes |
| + | *Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer. |
| + | # Students' individual construction materials. |
| + | *Prerequisites/Instructions, if any: |
| + | # The students should have prior knowledge of a circle , tangent and the limiting case of a |
| + | secant as a tangent. |
| + | # They should understand that a tangent is always perpendicular to the radius of the circle. |
| + | # They should know construction of a tangent to a given point. |
| + | # If the same straight line is a tangent to two or more circles, then it is called a common tangent. |
| + | # If the centres of the circles lie on the same side of the common tangent, then the tangent is called a direct common tangent. |
| + | # Note: In general, |
| + | *The two circles are named as C1 and C2 |
| + | * The distance between the centre of two circles is 'd' |
| + | * Radius of one circle is taken as 'R' and other as 'r' |
| + | * The length of tangent is 't' |
| + | *Multimedia resources: Laptop |
| + | *Website interactives/ links/ / Geogebra Applets |
| + | *Process: |
| + | [Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]<br> |
| + | The teacher can explain the step by step construction of Direct common tangent and with an example |
| + | *Developmental Questions: |
| + | # What is a tangent |
| + | # What is a common tangent ? |
| + | # What is a direct common tangent ? |
| + | # What is R and r ? |
| + | # What does the length OA represent here ? |
| + | # Why was a third circle constructed ? |
| + | # Let us try to construct direct common tangent without the third circle and see. |
| + | # What should be the radius of the third circle ? |
| + | # Why was OA bisected and semi circle constructed ? |
| + | # What were OB and OC extended ? |
| + | # What can you say about lines AB and AC ? |
| + | # Name the direct common tangents . |
| + | # At what points is the tangent touching the circles ? |
| + | # Identify the two right angled triangles formed from the figure ? What do you understand ? |
| + | *Evaluation: |
| + | # Is the student able to comprehend the sequence of steps in constructing the tangent. |
| + | # Is the student able to identify error areas while constructing ? |
| + | # Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ? |
| + | # Is the student able to appreciate that the direct common tangents from the same external point are equal and subtend equal angles at the center. |
| + | *Question Corner: |
| + | # What do you think are the applications of tangent constructions ? |
| + | # What is the formula to find the length of direct common tangent ? |
| + | # Can a direct common tangent be drawn to two circles one inside the other ? |
| + | # Observe the point of intersection of extended tangents in relation with the centres of two circles. Infer. |
| + | # What are properties of direct common tangents ? |
| + | |
| + | ===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://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 # === | | ===Activity No # === |
| {| 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 | | *Estimated Time |
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| *Question Corner | | *Question Corner |
| | | |
| + | ==Concept #4. Construction of transverse common tangent.== |
| + | ===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://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://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://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://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://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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| | | |
| Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template | | Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template |
| + | |
| + | [[Category:Circles]] |