Difference between revisions of "Graphs And Polyhedra"
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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== | ||
| − | [http:// | + | 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.tess-india.edu.in/sites/default/files/imported/57360/SM15_AIE_Final.pdf Developing stories: Understanding graphs] | ||
| − | [http://www.enchantedlearning.com/math/geometry/solids/ For More Informations on Platonic Solids] | + | 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]<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/ ] | + | [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=== | ||
| − | + | 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_Activity1| Introduction to Graphs]] |
Activity #2 | Activity #2 | ||
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===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== | ||
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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 [[ | + | 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 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br> | Activity No #1 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Transversable_Networks]]<br> | ||
| − | Activity No #2 | + | Activity No #2 [[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| Eulers formula verification]] |
| − | =Concept # 5 Shapes of Polyhedrons= | + | ==Concept # 5 Shapes of Polyhedrons== |
===Learning objectives=== | ===Learning objectives=== | ||
#Recognize regular and irregular polyhedron | #Recognize regular and irregular polyhedron | ||
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| − | ===Notes | + | ===Notes for teachers=== |
| − | '' | + | ''there can only be 5 platonic polyhedrons.'' |
| + | =Poly Hydrens= | ||
| + | ==Definition== | ||
===Activities=== | ===Activities=== | ||
| − | Activity No #1 <br> | + | 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 # 6 Elements of Polyhedrons= | + | ==Concept # 6 Elements of Polyhedrons== |
===Learning objectives=== | ===Learning objectives=== | ||
#Recognizes vertexes faces and edges of a polyhedron | #Recognizes vertexes faces and edges of a polyhedron | ||
| Line 111: | Line 131: | ||
| − | ===Notes | + | ===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 <br> | + | 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]] | ||
| − | =Concept # 7 Euler's Formula for Polyhedrons= | + | ==Concept # 7 Euler's Formula for Polyhedrons== |
===Learning objectives=== | ===Learning objectives=== | ||
#Can count number of vertexes faces and edges of a polyhedron | #Can count number of vertexes faces and edges of a polyhedron | ||
| Line 127: | Line 149: | ||
===Activities=== | ===Activities=== | ||
| − | Activity No #1 <br> | + | Activity No #1 [http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra/concept7/activity1| Activity on Eulers Theorem] <br> |
| − | Activity No #2 | + | 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 = | ||
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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:Networks and Polyhedra]] | ||
Latest revision as of 10:04, 5 November 2019
| Philosophy of Mathematics |
While creating a resource page, please click here for a resource creation checklist.
Concept Map
Textbook
Additional Information
More on Networks
Extending Graph Theory
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.
Developing stories: Understanding graphs
Other useful websites
- Wikipedia page for Graph Theory
- For More Informations on Platonic Solids
- For interactive Platonic Solids
Reference Books
Click here for DSERT 10 th Text book chapter Graph Theory
Introduction to Graph Theory, By Douglas B.West/
Teaching Outlines
Concept #1 Representation of a Graph
Learning objectives
- To define what is node.
- to define what is arc
- To define what is Region
- To represent a Graph with node, Arc and Regions
Notes for teachers
Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE
Activities
Activity #1 Introduction to Graphs
Activity #2 Graph Theory
Concept #2 Types of Graphs
Learning objectives
- To identify Plane Graph
- To identify Non-Plane 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
Construction of regular polyhedrons
Activity No #2
Concept #3 Eulers formula for graph
Learning objectives
- Generalization of Euler's formula
- Verification of Euler's formula for Networks
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
Verification of Euler's Formula for Graphs
Activity No #2 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 Transversable_Networks
Activity No #2 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
Construction of regular octahedron and recognising th elements of Polyhedrons
Activity No #2
Polyhedra_Elements
[1]
Concept # 6 Elements of Polyhedrons
Learning objectives
- Recognizes vertexes faces and edges of a polyhedron
- Can count number of vertexes faces and edges of a 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
Construction of regular octahedron and recognising th elements of Polyhedrons
Activity No #2
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 Activity on Eulers Theorem
Activity No #2 Work sheet on Verification of Eulers Formula for Ployhedrons
Assessment activities for CCE
Check your basic knowledge on Polyhedrons
| Why there are only 5 platonic solids?
Hints for difficult problems
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.
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html
For solution click here
Project Ideas
Math Fun
Usage
Create a new page and type {{subst:Math-Content}} to use this template