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Line 23: − <mm>[[Graphs And Polyhedrons.mm|Flash]]</mm>+ + − + + + + − [http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]+ − + + + + + + − + + Line 45:
Line 58: − ''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''+ − #Defining a Graph, node arc and Region − #Framing Euler's Formula for graphs − #Verifying Euler's Formula N + R = A + 2 for given Plane graphs − #Drawing graphs for given N,R and A − #Identifying the Traversible graphs − #Explaining and using the condition for Traversible graphs − #defining a Polyhedra − #Framing Euler's formula for Polyhedra − # verifying Euler's formula for the given Polyhedra − − − ''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.'' − + Line 74:
Line 75: − #Activity No #1+ − + + + + Line 86:
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added Category:Networks and Polyhedra using HotCat
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''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ನಕ್ಷೆ_ಮತ್ತು_ಬಹುಮುಖಘನಾಕೃತಿ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
[http://www.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://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]
[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]
[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]
[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]
[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]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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= Concept Map =
= Concept Map =
[[File:Graphs And Polyhedrons.mm|Flash]]
__FORCETOC__
__FORCETOC__
= Textbook =
= Textbook =
[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]
#[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter17.pdf Karnataka text book for Class 10, Chapter 17 - Graphs And Polyhedra]
#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]
=Additional Information=
=Additional Information=
[http://www.mhhe.com/math/ltbmath/bennett_nelson/conceptual/netgraphs/graphs.htm| More on Networks]<br>[http://resources.esri.com/help/9.3/arcgisengine/dotnet/e084da94-d4f7-4da7-86ed-7df684ff2144.htm| Extending Graph Theory]
==Useful websites==
==Useful websites==
The document linked below gives few ideas in using story telling as a tool for understanding, interpreting and constructing graphs. Suggestions on how to assist students in making connections between graphs and the real world have also been given here.
[http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]
[http://www.tess-india.edu.in/sites/default/files/imported/57360/SM15_AIE_Final.pdf Developing stories: Understanding graphs]
Other useful websites
# [http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]
# [http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]
# [http://www.mathsisfun.com/platonic_solids.html/ For interactive Platonic Solids]
==Reference Books==
==Reference Books==
[http://dsert.kar.nic.in/textbooksonline/Text%20book/Kannada/class%20x/maths/Kannada-class%20x-maths-contents.pdf| Click here for DSERT 10 th Text book chapter Graph Theory]
[http://dsert.kar.nic.in/textbooksonline/Text%20book/Kannada/class%20x/maths/Kannada-class%20x-maths-contents.pdf| Click here for DSERT 10 th Text book chapter Graph Theory]<br>
[http://toihoctap.wordpress.com/2013/02/13/introduction-to-graph-theory-and-solution-manual-by-douglas-b-west| Introduction to Graph Theory, By Douglas B.West/]
= Teaching Outlines =
= Teaching Outlines =
===Notes for teachers===
===Notes for teachers===
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE
===Activities===
===Activities===
Activity #1
Activity #1
[[Graphs_And_Polyhedra_activities#Activity_.231| Introduction to Graphs]]
[[Graphs_And_Polyhedra_activities_Activity1| Introduction to Graphs]]
Activity #2
Activity #2
===Activities===
===Activities===
Activity No #1<br>
#Activity No #2
[[Graphs_And_Polyhedra_regular_polyhedrons_activity_1#Activity_-_Construction_of_Regular_Polyhedrons | Construction of regular polyhedrons]] <br>
Activity No #2
==Concept #3 Eulers formula for graph==
==Concept #3 Eulers formula for graph==
===Activities===
===Activities===
Activity No #1 Verification of Euler's Formula for Graphs {{#widget:YouTube|id=5M-m62qTR-s}}
Activity No #1
[[Graphs_And_Polyhedra_Concept_3_Eulers_formula_for_graph_activity_1#Activity_-_Verification_of_Euler.27s_Formula_for_Graphs|Verification of Euler's Formula for Graphs]]<br>
Activity No #2 [[Graphs_And_Polyhedra_Concept_traversibility#Multimedia_resources| Activity on verification of eulers formula]]
==Concept # 4 Traversibility of a graph==
===Learning objectives===
#To Identify even order node
#To Identify Odd order node
#Condition for Traversibility
#Condition for Non- Traversibility of Graph
===Notes for teachers===
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
===Activities===
Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br>
Activity No #2 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]]
==Concept # 5 Shapes of Polyhedrons==
===Learning objectives===
#Recognize regular and irregular polyhedron
#Can write differences between regular and irregular polyhedron
===Notes for teachers===
''there can only be 5 platonic polyhedrons.''
=Poly Hydrens=
==Definition==
===Activities===
Activity No #1
[[Graphs_And_Polyhedra_Activities_6_Octahedron#Activity_-_Recognising_the_elements_through_the_construction_of_octahedron_in_origami|Construction of regular octahedron and recognising th elements of Polyhedrons]]<br>
Activity No #2
Activity No #2
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]
[https://www.mathsisfun.com/]
==Concept 1Representation of a graph==
==Concept # 6 Elements of Polyhedrons==
===Learning objectives===
===Learning objectives===
#Recognizes vertexes faces and edges of a polyhedron
#Can count number of vertexes faces and edges of a polyhedron
===Notes for teachers===
===Notes for teachers===
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
===Activities===
===Activities===
#Activity No #1
Activity No #1
[[Graphs_And_Polyhedra_Activities_6_Octahedron#Activity_-_Recognising_the_elements_through_the_construction_of_octahedron_in_origami|Construction of regular octahedron and recognising th elements of Polyhedrons]]<br>
Activity No #2
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]
==Concept # 7 Euler's Formula for Polyhedrons==
===Learning objectives===
#Can count number of vertexes faces and edges of a polyhedron
#Verifies Euler's formula for a given polyhedron
===Notes for teachers===
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
===Activities===
Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br>
Activity No #2 [[:File:G1-eulerworksheet.pdf| Work sheet on Verification of Eulers Formula for Ployhedrons]]
=Assessment activities for CCE=
=Assessment activities for CCE=
[http://wps.pearsoned.com.au/mfwa1-2/62/16069/4113811.cw/-/4113819/index.html| Check your basic knowledge on Polyhedrons]
[http://wps.pearsoned.com.au/mfwa1-2/62/16069/4113811.cw/-/4113819/index.html| Check your basic knowledge on Polyhedrons]<br>[http://www.mathsisfun.com/geometry/platonic-solids-why-five.html | Why there are only 5 platonic solids?]
= Hints for difficult problems =
= Hints for difficult problems =
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:Networks and Polyhedra]]