https://karnatakaeducation.org.in/KOER/en/api.php?action=feedcontributions&user=Sangameshkote&feedformat=atomKarnataka Open Educational Resources - User contributions [en]2024-03-28T14:45:54ZUser contributionsMediaWiki 1.35.6https://karnatakaeducation.org.in/KOER/en/index.php?title=Graphs_And_Polyhedra&diff=17956Graphs And Polyhedra2015-02-17T06:43:18Z<p>Sangameshkote: /* Additional Information */</p>
<hr />
<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ನಕ್ಷೆ_ಮತ್ತು_ಬಹುಮುಖಘನಾಕೃತಿ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
<br />
<!-- This portal was created using subst:box portal skeleton --><br />
<!-- BANNER ACROSS TOP OF PAGE --><br />
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"<br />
|-<br />
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]<br />
|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]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]<br />
|}<br />
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
= Concept Map =<br />
<mm>[[Graphs And Polyhedrons.mm|Flash]]</mm><br />
__FORCETOC__<br />
<br />
= Textbook =<br />
#[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]<br />
<br />
#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]<br />
<br />
=Additional Information=<br />
[http://www.mhhe.com/math/ltbmath/bennett_nelson/conceptual/netgraphs/graphs.htm| More on Networks]<br />
==Useful websites==<br />
[http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]<br />
<br />
[http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]<br>[http://www.mathsisfun.com/platonic_solids.html/ For interactive Platonic Solids]<br />
<br />
==Reference Books==<br />
<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><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/]<br />
<br />
= Teaching Outlines =<br />
==Concept #1 Representation of a Graph==<br />
===Learning objectives===<br />
#To define what is node.<br />
#to define what is arc<br />
#To define what is Region<br />
#To represent a Graph with node, Arc and Regions<br />
<br />
===Notes for teachers===<br />
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE<br />
<br />
===Activities===<br />
Activity #1<br />
[[Graphs_And_Polyhedra_activities_Activity1| Introduction to Graphs]]<br />
<br />
Activity #2<br />
[[Graphs_And_Polyhedra_Representation_of_a_Graph_activity_2| Graph Theory]]<br />
<br />
==Concept #2 Types of Graphs==<br />
===Learning objectives===<br />
#To identify Plane Graph<br />
#To identify Non-Plane Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1<br><br />
<br />
[[Graphs_And_Polyhedra_regular_polyhedrons_activity_1#Activity_-_Construction_of_Regular_Polyhedrons | Construction of regular polyhedrons]] <br><br />
<br />
Activity No #2<br />
<br />
==Concept #3 Eulers formula for graph==<br />
===Learning objectives===<br />
#Generalization of Euler's formula<br />
#Verification of Euler's formula for Networks<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <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><br />
Activity No #2 [[Graphs_And_Polyhedra_Concept_traversibility#Multimedia_resources| Activity on verification of eulers formula]]<br />
<br />
==Concept # 4 Traversibility of a graph==<br />
===Learning objectives===<br />
#To Identify even order node<br />
#To Identify Odd order node<br />
#Condition for Traversibility<br />
#Condition for Non- Traversibility of Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br><br />
Activity No #2 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]]<br />
<br />
==Concept # 5 Shapes of Polyhedrons==<br />
===Learning objectives===<br />
#Recognize regular and irregular polyhedron <br />
#Can write differences between regular and irregular polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''there can only be 5 platonic polyhedrons.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 6 Elements of Polyhedrons==<br />
===Learning objectives===<br />
#Recognizes vertexes faces and edges of a polyhedron <br />
#Can count number of vertexes faces and edges of a polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 7 Euler's Formula for Polyhedrons==<br />
===Learning objectives===<br />
#Can count number of vertexes faces and edges of a polyhedron<br />
#Verifies Euler's formula for a given polyhedron <br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br><br />
Activity No #2 [[:File:G1-eulerworksheet.pdf| Work sheet on Verification of Eulers Formula for Ployhedrons]]<br />
<br />
=Assessment activities for CCE=<br />
<br />
[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?]<br />
<br />
= Hints for difficult problems =<br />
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.<br />
<br />
<br />
http://photonics.cusat.edu/images/koning4.jpg<br />
<br />
<br />
<br />
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html<br />
<br />
For solution click [[Graphs_and_polyhedra_problems|'''here''']]<br />
<br />
= Project Ideas =<br />
<br />
= Math Fun =<br />
<br />
'''Usage''' <br />
<br />
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template</div>Sangameshkotehttps://karnatakaeducation.org.in/KOER/en/index.php?title=Graphs_And_Polyhedra&diff=17955Graphs And Polyhedra2015-02-17T06:41:03Z<p>Sangameshkote: /* Activities */</p>
<hr />
<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ನಕ್ಷೆ_ಮತ್ತು_ಬಹುಮುಖಘನಾಕೃತಿ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
<br />
<!-- This portal was created using subst:box portal skeleton --><br />
<!-- BANNER ACROSS TOP OF PAGE --><br />
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"<br />
|-<br />
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]<br />
|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]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]<br />
|}<br />
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
= Concept Map =<br />
<mm>[[Graphs And Polyhedrons.mm|Flash]]</mm><br />
__FORCETOC__<br />
<br />
= Textbook =<br />
#[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]<br />
<br />
#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]<br />
<br />
=Additional Information=<br />
==Useful websites==<br />
[http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]<br />
<br />
[http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]<br>[http://www.mathsisfun.com/platonic_solids.html/ For interactive Platonic Solids]<br />
<br />
==Reference Books==<br />
<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><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/]<br />
<br />
= Teaching Outlines =<br />
==Concept #1 Representation of a Graph==<br />
===Learning objectives===<br />
#To define what is node.<br />
#to define what is arc<br />
#To define what is Region<br />
#To represent a Graph with node, Arc and Regions<br />
<br />
===Notes for teachers===<br />
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE<br />
<br />
===Activities===<br />
Activity #1<br />
[[Graphs_And_Polyhedra_activities_Activity1| Introduction to Graphs]]<br />
<br />
Activity #2<br />
[[Graphs_And_Polyhedra_Representation_of_a_Graph_activity_2| Graph Theory]]<br />
<br />
==Concept #2 Types of Graphs==<br />
===Learning objectives===<br />
#To identify Plane Graph<br />
#To identify Non-Plane Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1<br><br />
<br />
[[Graphs_And_Polyhedra_regular_polyhedrons_activity_1#Activity_-_Construction_of_Regular_Polyhedrons | Construction of regular polyhedrons]] <br><br />
<br />
Activity No #2<br />
<br />
==Concept #3 Eulers formula for graph==<br />
===Learning objectives===<br />
#Generalization of Euler's formula<br />
#Verification of Euler's formula for Networks<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <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><br />
Activity No #2 [[Graphs_And_Polyhedra_Concept_traversibility#Multimedia_resources| Activity on verification of eulers formula]]<br />
<br />
==Concept # 4 Traversibility of a graph==<br />
===Learning objectives===<br />
#To Identify even order node<br />
#To Identify Odd order node<br />
#Condition for Traversibility<br />
#Condition for Non- Traversibility of Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br><br />
Activity No #2 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]]<br />
<br />
==Concept # 5 Shapes of Polyhedrons==<br />
===Learning objectives===<br />
#Recognize regular and irregular polyhedron <br />
#Can write differences between regular and irregular polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''there can only be 5 platonic polyhedrons.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 6 Elements of Polyhedrons==<br />
===Learning objectives===<br />
#Recognizes vertexes faces and edges of a polyhedron <br />
#Can count number of vertexes faces and edges of a polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 7 Euler's Formula for Polyhedrons==<br />
===Learning objectives===<br />
#Can count number of vertexes faces and edges of a polyhedron<br />
#Verifies Euler's formula for a given polyhedron <br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br><br />
Activity No #2 [[:File:G1-eulerworksheet.pdf| Work sheet on Verification of Eulers Formula for Ployhedrons]]<br />
<br />
=Assessment activities for CCE=<br />
<br />
[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?]<br />
<br />
= Hints for difficult problems =<br />
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.<br />
<br />
<br />
http://photonics.cusat.edu/images/koning4.jpg<br />
<br />
<br />
<br />
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html<br />
<br />
For solution click [[Graphs_and_polyhedra_problems|'''here''']]<br />
<br />
= Project Ideas =<br />
<br />
= Math Fun =<br />
<br />
'''Usage''' <br />
<br />
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template</div>Sangameshkotehttps://karnatakaeducation.org.in/KOER/en/index.php?title=Graphs_And_Polyhedra&diff=17954Graphs And Polyhedra2015-02-17T06:28:01Z<p>Sangameshkote: /* Activities */</p>
<hr />
<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ನಕ್ಷೆ_ಮತ್ತು_ಬಹುಮುಖಘನಾಕೃತಿ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
<br />
<!-- This portal was created using subst:box portal skeleton --><br />
<!-- BANNER ACROSS TOP OF PAGE --><br />
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"<br />
|-<br />
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]<br />
|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]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]<br />
|}<br />
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
= Concept Map =<br />
<mm>[[Graphs And Polyhedrons.mm|Flash]]</mm><br />
__FORCETOC__<br />
<br />
= Textbook =<br />
#[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]<br />
<br />
#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]<br />
<br />
=Additional Information=<br />
==Useful websites==<br />
[http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]<br />
<br />
[http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]<br>[http://www.mathsisfun.com/platonic_solids.html/ For interactive Platonic Solids]<br />
<br />
==Reference Books==<br />
<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><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/]<br />
<br />
= Teaching Outlines =<br />
==Concept #1 Representation of a Graph==<br />
===Learning objectives===<br />
#To define what is node.<br />
#to define what is arc<br />
#To define what is Region<br />
#To represent a Graph with node, Arc and Regions<br />
<br />
===Notes for teachers===<br />
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE<br />
<br />
===Activities===<br />
Activity #1<br />
[[Graphs_And_Polyhedra_activities_Activity1| Introduction to Graphs]]<br />
<br />
Activity #2<br />
[[Graphs_And_Polyhedra_Representation_of_a_Graph_activity_2| Graph Theory]]<br />
<br />
==Concept #2 Types of Graphs==<br />
===Learning objectives===<br />
#To identify Plane Graph<br />
#To identify Non-Plane Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1<br><br />
<br />
[[Graphs_And_Polyhedra_regular_polyhedrons_activity_1#Activity_-_Construction_of_Regular_Polyhedrons | Construction of regular polyhedrons]] <br><br />
<br />
Activity No #2<br />
<br />
==Concept #3 Eulers formula for graph==<br />
===Learning objectives===<br />
#Generalization of Euler's formula<br />
#Verification of Euler's formula for Networks<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <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><br />
Activity No #2 [[Graphs_And_Polyhedra_Concept_traversibility#Multimedia_resources| Activity on verification of eulers formula]]<br />
<br />
==Concept # 4 Traversibility of a graph==<br />
===Learning objectives===<br />
#To Identify even order node<br />
#To Identify Odd order node<br />
#Condition for Traversibility<br />
#Condition for Non- Traversibility of Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br><br />
Activity No #2=[[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]<br />
<br />
==Concept # 5 Shapes of Polyhedrons==<br />
===Learning objectives===<br />
#Recognize regular and irregular polyhedron <br />
#Can write differences between regular and irregular polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''there can only be 5 platonic polyhedrons.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 6 Elements of Polyhedrons==<br />
===Learning objectives===<br />
#Recognizes vertexes faces and edges of a polyhedron <br />
#Can count number of vertexes faces and edges of a polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 7 Euler's Formula for Polyhedrons==<br />
===Learning objectives===<br />
#Can count number of vertexes faces and edges of a polyhedron<br />
#Verifies Euler's formula for a given polyhedron <br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br><br />
Activity No #2 [[:File:G1-eulerworksheet.pdf| Work sheet on Verification of Eulers Formula for Ployhedrons]]<br />
<br />
=Assessment activities for CCE=<br />
<br />
[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?]<br />
<br />
= Hints for difficult problems =<br />
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.<br />
<br />
<br />
http://photonics.cusat.edu/images/koning4.jpg<br />
<br />
<br />
<br />
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html<br />
<br />
For solution click [[Graphs_and_polyhedra_problems|'''here''']]<br />
<br />
= Project Ideas =<br />
<br />
= Math Fun =<br />
<br />
'''Usage''' <br />
<br />
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template</div>Sangameshkotehttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:G1-eulerworksheet.pdf&diff=17953File:G1-eulerworksheet.pdf2015-02-17T06:26:47Z<p>Sangameshkote: MsUpload</p>
<hr />
<div>MsUpload</div>Sangameshkotehttps://karnatakaeducation.org.in/KOER/en/index.php?title=Graphs_And_Polyhedra&diff=17952Graphs And Polyhedra2015-02-17T06:18:31Z<p>Sangameshkote: /* Activities */</p>
<hr />
<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ನಕ್ಷೆ_ಮತ್ತು_ಬಹುಮುಖಘನಾಕೃತಿ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
<br />
<!-- This portal was created using subst:box portal skeleton --><br />
<!-- BANNER ACROSS TOP OF PAGE --><br />
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"<br />
|-<br />
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]<br />
|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]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]<br />
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|<br />
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]<br />
|}<br />
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
= Concept Map =<br />
<mm>[[Graphs And Polyhedrons.mm|Flash]]</mm><br />
__FORCETOC__<br />
<br />
= Textbook =<br />
#[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]<br />
<br />
#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=15-16 NCERT book on Graphs]<br />
<br />
=Additional Information=<br />
==Useful websites==<br />
[http://en.wikipedia.org/wiki/Graph_theory Wikipedia page for Graph Theory]<br />
<br />
[http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids]<br>[http://www.mathsisfun.com/platonic_solids.html/ For interactive Platonic Solids]<br />
<br />
==Reference Books==<br />
<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><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/]<br />
<br />
= Teaching Outlines =<br />
==Concept #1 Representation of a Graph==<br />
===Learning objectives===<br />
#To define what is node.<br />
#to define what is arc<br />
#To define what is Region<br />
#To represent a Graph with node, Arc and Regions<br />
<br />
===Notes for teachers===<br />
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE<br />
<br />
===Activities===<br />
Activity #1<br />
[[Graphs_And_Polyhedra_activities_Activity1| Introduction to Graphs]]<br />
<br />
Activity #2<br />
[[Graphs_And_Polyhedra_Representation_of_a_Graph_activity_2| Graph Theory]]<br />
<br />
==Concept #2 Types of Graphs==<br />
===Learning objectives===<br />
#To identify Plane Graph<br />
#To identify Non-Plane Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1<br><br />
<br />
[[Graphs_And_Polyhedra_regular_polyhedrons_activity_1#Activity_-_Construction_of_Regular_Polyhedrons | Construction of regular polyhedrons]] <br><br />
<br />
Activity No #2<br />
<br />
==Concept #3 Eulers formula for graph==<br />
===Learning objectives===<br />
#Generalization of Euler's formula<br />
#Verification of Euler's formula for Networks<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <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><br />
Activity No #2 [[Graphs_And_Polyhedra_Concept_traversibility#Multimedia_resources| Activity on verification of eulers formula]]<br />
<br />
==Concept # 4 Traversibility of a graph==<br />
===Learning objectives===<br />
#To Identify even order node<br />
#To Identify Odd order node<br />
#Condition for Traversibility<br />
#Condition for Non- Traversibility of Graph<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br><br />
Activity No #2=[[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]<br />
<br />
==Concept # 5 Shapes of Polyhedrons==<br />
===Learning objectives===<br />
#Recognize regular and irregular polyhedron <br />
#Can write differences between regular and irregular polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''there can only be 5 platonic polyhedrons.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 6 Elements of Polyhedrons==<br />
===Learning objectives===<br />
#Recognizes vertexes faces and edges of a polyhedron <br />
#Can count number of vertexes faces and edges of a polyhedron<br />
<br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 <br />
[[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><br />
Activity No #2<br />
[[Graphs_And_Polyhedra_Concept_7_polyhedra_elements#Activity_-_Polyhedra_Elements| Polyhedra_Elements]]<br />
<br />
==Concept # 7 Euler's Formula for Polyhedrons==<br />
===Learning objectives===<br />
#Can count number of vertexes faces and edges of a polyhedron<br />
#Verifies Euler's formula for a given polyhedron <br />
<br />
===Notes for teachers===<br />
''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.''<br />
<br />
===Activities===<br />
Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br><br />
Activity No #2<br />
<br />
=Assessment activities for CCE=<br />
<br />
[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?]<br />
<br />
= Hints for difficult problems =<br />
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.<br />
<br />
<br />
http://photonics.cusat.edu/images/koning4.jpg<br />
<br />
<br />
<br />
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html<br />
<br />
For solution click [[Graphs_and_polyhedra_problems|'''here''']]<br />
<br />
= Project Ideas =<br />
<br />
= Math Fun =<br />
<br />
'''Usage''' <br />
<br />
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template</div>Sangameshkotehttps://karnatakaeducation.org.in/KOER/en/index.php?title=Graphs_And_Polyhedra/concept7/activity1&diff=17951Graphs And Polyhedra/concept7/activity12015-02-17T06:16:39Z<p>Sangameshkote: /* Multimedia resources */</p>
<hr />
<div>_FORCETOC__<br />
=Activity - Recognising the elements through the construction of octahedron in origami=<br />
<br />
==Estimated Time==<br />
45 minutes<br />
<br />
==Materials/ Resources needed== <br />
==Prerequisites/Instructions, if any==<br />
==Multimedia resources==<br />
{{#widget:YouTube|id=VRcX9Fzu1Jo}}<br />
<br />
==Website interactives/ links/ simulations/ Geogebra Applets==<br />
==Process (How to do the activity)==<br />
==Developmental Questions (What discussion questions)==<br />
==Evaluation (Questions for assessment of the child)==<br />
==Question Corner==<br />
==Activity Keywords==<br />
<br />
'''To link back to the concept page'''<br />
[[Topic Page Link]]</div>Sangameshkotehttps://karnatakaeducation.org.in/KOER/en/index.php?title=Graphs_And_Polyhedra/concept7/activity1&diff=17950Graphs And Polyhedra/concept7/activity12015-02-17T06:16:02Z<p>Sangameshkote: Created page with "_FORCETOC__ =Activity - Recognising the elements through the construction of octahedron in origami= ==Estimated Time== 45 minutes ==Materials/ Resources needed== ==Prerequi..."</p>
<hr />
<div>_FORCETOC__<br />
=Activity - Recognising the elements through the construction of octahedron in origami=<br />
<br />
==Estimated Time==<br />
45 minutes<br />
<br />
==Materials/ Resources needed== <br />
==Prerequisites/Instructions, if any==<br />
==Multimedia resources==<br />
{{#widget:YouTube|id=mHv8pe5bKh4}}<br />
==Website interactives/ links/ simulations/ Geogebra Applets==<br />
==Process (How to do the activity)==<br />
==Developmental Questions (What discussion questions)==<br />
==Evaluation (Questions for assessment of the child)==<br />
==Question Corner==<br />
==Activity Keywords==<br />
<br />
'''To link back to the concept page'''<br />
[[Topic Page Link]]</div>Sangameshkote