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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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− | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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− | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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− | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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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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− |
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− | = Concept Map =
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| __FORCETOC__ | | __FORCETOC__ |
− | <mm>[[trapezium.mm|flash]]</mm>
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− |
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− | = Textbook =
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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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− |
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− | =Additional Information=
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− | ==Useful websites==
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− | ==Reference Books==
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| | | |
− | = Teaching Outlines =
| + | === Learning objectives === |
− | | |
− | ==Concept # A Trapezium and its properties==
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− | ===Learning objectives=== | |
| # A quadrangle with only two opposite sides parallel is called a trapezium, or trapezoid. | | # A quadrangle with only two opposite sides parallel is called a trapezium, or trapezoid. |
| # The parallel sides are called the bases of the trapezium and the other two sides are called the legs or the lateral sides. | | # The parallel sides are called the bases of the trapezium and the other two sides are called the legs or the lateral sides. |
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| # The distance between the bases is called height of trapezium. | | # The distance between the bases is called height of trapezium. |
| ===Notes for teachers=== | | ===Notes for teachers=== |
− | ===Activity No # === | + | ===Activity No # 1. Properties of a trapezium. === |
| {| 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 :40 minutes. |
− | *Materials/ Resources needed | + | *Materials/ Resources needed: |
| + | Laptop, geogebra file, projector and a pointer. |
| *Prerequisites/Instructions, if any | | *Prerequisites/Instructions, if any |
− | *Multimedia resources | + | # Knowledge about parallel lines, angles and diagnols. |
− | *Website interactives/ links/ / Geogebra Applets | + | *Multimedia resources: Laptop. |
− | *Process/ Developmental Questions
| + | *Website interactives/ links/ / Geogebra Applets: This file has been taken from www.geogebratube.org |
− | *Evaluation
| + | <span> </span> |
− | *Question Corner
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| | | |
− | ===Activity No # ===
| + | <span></span><div id="ggbContainer597bb1446b162898fe083f13cfdcd040"></div><span></span> |
− | {| 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. Measurements in Trapezium ==
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− | ===Learning objectives===
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− | # The trapeium contains two parallel sides and two non-parallel sides.
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− | # The area of trapezium is found by viewing it as a parallelogram.
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− | # The area of trapezium is 1/2(a+b)h where a and b are its parallel sides and h is the perpendicular distance between them.
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− | # The perimeter of a trapezium is obtained by sum of its 4 sides.
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− | ===Notes for teachers===
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− | # The area of most figures can be expressed in terms of its dimensions.
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− | # The area of most composite figures can be calculated using the area of primary figures.
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− | ===Activity No # 1.Area of a trapezium===
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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 : Laptop, geogebra file, projector and a pointer.
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− | *Prerequisites/Instructions, if any
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− | # The students should know a parallelogram and formula to find its area.
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− | # They should know the trapezium and its properties.
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− | *Multimedia resources: Laptop
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− | *Website interactives/ links/ / Geogebra Applets
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− | <ggb_applet width="1296" height="848" version="4.2" 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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 initially discuss about a trapezium. | + | # Show the geogebra file and explain its properties by asking the questions listed below. |
− | # She can then reiterate that formula for area of certain composite figures can be found by converting them into known simple figures.
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− | # Here the trapezium is converted into a parallelogram.
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− | # Area of parallelogram is then deduced.
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| *Developmental Questions: | | *Developmental Questions: |
| # What is a trapezium ? | | # What is a trapezium ? |
− | # Name its two parallel sides. | + | # How many sides does it have ? |
− | # What is meant by the height of the trapezium ? | + | # What can be said about the pair of sides ? |
− | # After cutting the trapezium exactly in the centre what would be the new height ? | + | # Identify the diagnols. Are they equal ? |
− | # What is the length of the new parallelogram formed ? | + | # What would be the sum of 4 angles of the trapezium ? Why so ? |
− | # What is the formula to find the area of a parallelogram ? | + | # What would be the sum of its two allied angles ? |
− | # What is the area of this parallelogram formed from a trapezium ? | + | # Are the two pairs of sides of a trapezium equal ? |
| *Evaluation: | | *Evaluation: |
− | # Explain the sequence of steps involved in deriving the formula for the area of a trapeium. | + | Are the students able to apply the theorems of parallel lines - transversal to prove the properties. |
| + | # Why are allied angles of the trapezium supplementary ? |
| + | # Are the diagnols equal ? |
| + | # Is trapezium a parallelogram ? |
| *Question Corner: | | *Question Corner: |
− | # Recall the steps involved in deriving the formula for area of a parallelogram. | + | # List the properties of a trapezium. |
− | | + | # What properties of other quadrilaterals does it share. Compare with other quadrilaterals. |
− | ==Concept # 3.Construction of Trapezium==
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− | ===Learning objectives===
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− | ===Notes for teachers===
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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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− | | |
− | ===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;">
| |
− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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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 # 4. Isosceles trapezium==
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− | ===Learning objectives===
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− | ===Notes for teachers===
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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;">
| |
− | ''[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
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− | *Evaluation
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− | *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
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− | | |
− | = Hints for difficult problems =
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− | | |
− | = Project Ideas =
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− | | |
− | = Math Fun =
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− | | |
− | '''Usage'''
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| | | |
− | Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
| + | [[Category:Quadrilaterals]] |