# 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] | ||

− | + | ||

[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]<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 | + | 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== |

===Learning objectives=== | ===Learning objectives=== | ||

#To Identify even order node | #To Identify even order node | ||

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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=== | ||

+ | 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]] | ||

+ | [https://www.mathsisfun.com/] | ||

+ | |||

+ | ==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.'' | ''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 # | + | ==Concept # 7 Euler's Formula for Polyhedrons== |

===Learning objectives=== | ===Learning objectives=== | ||

− | # | + | #Can count number of vertexes faces and edges of a polyhedron |

− | # | + | #Verifies Euler's formula for a given polyhedron |

− | + | ===Notes for teachers=== | |

− | ===Notes | ||

''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 [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 04:34, 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

### 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

### 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