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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]
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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]
 
[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 =
<mm>[[Graphs And Polyhedrons.mm|Flash]]</mm>
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[[File:Graphs And Polyhedrons.mm|Flash]]
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__FORCETOC__
 
__FORCETOC__
    
= Textbook =
 
= Textbook =
[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]
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#[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]
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#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]
    
=Additional Information=
 
=Additional Information=
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[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==
[http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]
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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]
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[http://www.tess-india.edu.in/sites/default/files/imported/57360/SM15_AIE_Final.pdf Developing stories: Understanding graphs]
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Other useful websites
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# [http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]
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# [http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]
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# [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]<br>
 
[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]
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[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 =
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===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.''
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Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE
#Defining a Graph, node arc and Region
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#Framing Euler's Formula for graphs
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#Verifying Euler's Formula N + R = A + 2 for given Plane graphs
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#Drawing graphs for given N,R and A
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#Identifying the Traversible graphs
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#Explaining and using the condition for Traversible graphs
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#defining a Polyhedra
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#Framing Euler's formula for Polyhedra
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# verifying Euler's formula for the given Polyhedra
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''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 #1
 
Activity #1
[[Graphs_And_Polyhedra_activities#Activity_.231| Introduction to Graphs]]
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[[Graphs_And_Polyhedra_activities_Activity1| Introduction to Graphs]]
    
Activity #2
 
Activity #2
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===Activities===
 
===Activities===
#Activity No #1
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Activity No #1<br>
#Activity No #2
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[[Graphs_And_Polyhedra_regular_polyhedrons_activity_1#Activity_-_Construction_of_Regular_Polyhedrons | Construction of regular polyhedrons]] <br>
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Activity No #2
    
==Concept #3 Eulers formula for graph==
 
==Concept #3 Eulers formula for graph==
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Activity No #1  
 
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>
 
[[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
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Activity No #2 [[Graphs_And_Polyhedra_Concept_traversibility#Multimedia_resources| Activity on verification of eulers formula]]
    
==Concept # 4 Traversibility of a graph==
 
==Concept # 4 Traversibility of a graph==
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===Activities===
 
===Activities===
#Activity No #1
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Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br>
#Activity No #2
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Activity No #2 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]]
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==Concept # 5 Shapes of Polyhedrons==
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===Learning objectives===
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#Recognize regular and irregular polyhedron
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#Can write differences between regular and irregular polyhedron
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===Notes for teachers===
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''there can only be 5 platonic polyhedrons.''
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=Poly Hydrens=
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==Definition==
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===Activities===
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Activity No #1  
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[[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>
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Activity No #2
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[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]
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[https://www.mathsisfun.com/]
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==Concept # 6 Elements of Polyhedrons==
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===Learning objectives===
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#Recognizes vertexes faces and edges of a polyhedron
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#Can count number of vertexes faces and edges of a polyhedron
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===Notes for teachers===
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''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.''
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===Activities===
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Activity No #1
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[[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>
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Activity No #2
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[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]
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==Concept # 7 Euler's Formula for Polyhedrons==
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===Learning objectives===
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#Can count number of vertexes faces and edges of a polyhedron
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#Verifies Euler's formula for a given polyhedron
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 +
===Notes for teachers===
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''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.''
 +
 
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===Activities===
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Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br>
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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]
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[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 =
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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
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[[Category:Networks and Polyhedra]]

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