Vertex-Edge Graphs 
 


  Grade 2
   
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Description of Lesson
Explanation of the fact that only four colors are needed to color a map or picture
with different sections
Definition of Edge and Vertex 
The use of odd and even vertices to determine whether only 2 colors are needed
or if 3 or 4 colors are required
Interactive practice coloring complex figures in a strategic manner



 
Grade 3 – Part 1


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Lesson
Homework Part 1
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Description of Lesson
Review and continuation of methods for coloring complex figures
Edge verses Perimeter     



  Grade 3 – Part 2

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Lesson
Homework Part 2
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Description of Lesson
Review and continuation of methods for coloring complex figures
The importance of Edges separating conflicting color areas in a picture or map
Creation of a Vertex-Edge Graph from a color picture.
Creation of a Vertex-Edge Graph from a map
Definition and examples of a Path on a Vertex-Edge Graph; interactive practice
Weights (time and distance) on the Edges of a Vertex-Edge graph;
interactive practice
Definition and examples of a Circuit on a Vertex-Edge graph




  Grade 4 – Part 1

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Lesson
Homework
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Description of Lesson
Review and continuation of methods for coloring complex figures
The importance of Edges separating conflicting color areas in a picture or map
Creation of a Vertex-Edge Graph from a color picture.
Creation of a Vertex-Edge Graph from a map
Definition and examples of a Path on a Vertex-Edge Graph; interactive practice
Weights (time and distance) on the Edges of a Vertex-Edge graph; interactive practice
Definition and examples of a Circuit on a Vertex-Edge graph
Definition of an Euler Path and Circuit; interactive practice



  Grade 4 – Part 2


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Lesson
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Note: Lesson file is very large and may take a few minutes to download depending on your connect speed.

Description of Lesson
Review of the derivation of a Vertex-Edge Graph from a picture, emphasizing the role of Edges.
Conflict Resolution using Vertex-Edge Graphs; interactive practice:
After School Activities – determining the minimum number of meeting times for all students to attend all their desired extracurricular activities
Habitat Problem – The minimum number of habitats needed to house 8 animals some of which cannot live in the same habitat.
Bat Project– The minimum number of days needed so that students can meet in two groups, each studying a particular type of bat.
Movies - The number of visits to the movie theater so all 5 students can each see their two favorite movie.



  Grade 5 Part 1

  
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Description of Lesson
Creation of a Vertex-Edge Graph from a color picture or map.
Definition and examples of Paths and Circuits on a Vertex-Edge Graph
Weights (time and distance) on the Edges of a Vertex-Edge graph
Definition of  Euler Paths and Euler Circuits
Interactive practice problems





Grade 5 Part 2


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Lesson 
Homework 
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Description of Lesson
Review of Euler Paths and Euler Circuits
The Degree of a Vertex
The rules for determining Euler Paths and Circuits
Interactive problem solving using Euler Paths and Circuits



  Grade 6

   
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Lesson
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Description of Lesson
The rules for determining Hamilton Paths and Circuits
Interactive problem solving using Hamilton Paths and Circuits
Solving shortest route problems





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